MATHS QUESTIONS
Various types of Math Problem Answers are solved here.
1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Solution:Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
2. The value of x + x(xx) when x = 2 is:
(a) 10, (b) 16, (c) 18, (d) 36, (e) 64
Solution:
x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer: (a)
3. Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
(a) broke even, (b) lost 4 cents, (c) gained 4 cents, (d) lost 10 cents, (e) gained 10 cents
Solution:
20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
Answer: (a)
4. The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
(a) 587 × 108 miles, (b) 587 × 1010 miles, (c) 587 × 10-10 miles, (d) 587 × 1012 miles, (e) 587 × 10-12 miles
Solution:
The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 1012 miles.
Answer: (d)
5. A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:
(a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 %
Solution:
Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.
Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.
= $ 160.
Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer: (e)
6. Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
(a) three times as much, (b) twice as much, (c) the same, (d) half as much, (e) a third as much
Solution:
Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
Answer: (b)
7. If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
(a) -10.0, (b) -0.5, (c) -0.4, (d) -0.2, (e) 10.0
Solution:
(0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
Answer: (c)
8. If 102y = 25, then 10-y equals:
(a) -1/5, (b) 1/625, (c) 1/50, (d) 1/25, (e) 1/5
Solution:
102y = 25
(10y)2 = 52
10y = 5
1/10y = 1/5
10-y = 1/5
Answer: (e)
9. The fraction (5x-11)/(2x2 + x - 6) was obtained by adding the two fractions A/(x + 2) and B/(2x - 3). The values of A and B must be, respectively:
(a) 5x, -11, (b) -11, 5x, (c) -1, 3, (d) 3, -1, (e) 5, -11
Solution:
Answer: (d)
10. The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is:
(a) 15, (b) 20, (c) 30, (d) 32, (e) 33
Solution:
Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2/3.
x/y = 2/3.
x = 2/3 × y.
x = 2y/3.
The ratio of the second to the third is 5/8.
y/z = 5/8.
z/y = 8/5.
z = 8/5 × y.
z = 8y/5.
Put the value of x = 2y/3 and z = 8y/5 in (i).
2y/3 + y + 8y/5 = 98
49y/15 = 98.
49y = 98 × 15.
49y = 1470.
y = 1470/49.
y = 30 .
Therefore, the second number is 30.
Answer: (c)
Unsolved Questions:
1. Fahrenheit temperature F is a linear function of Celsius temperature C. The ordered pair (0, 32) is an ordered pair of this function because 0°C is equivalent to 32°F, the freezing point of water. The ordered pair (100, 212) is also an ordered pair of this function because 100°C is equivalent to 212° F, the boiling point of water.
2. A sports field is 300 feet long. Write a formula that gives the length of x sports fields in feet. Then use this formula to determine the number of sports fields in 720 feet.
3. A recipe calls for 2 1/2 cups and I want to make 1 1/2 recipes. How many cups do I need?
4. Mario answered 30% of the questions correctly. The test contained a total of 80 questions. How many questions did Mario answer correctly?
Some more unsolved questions
Math Unsolved Questions :
1. If you add the two digits of the mystery number and then multiply the sum by 7, the answer is the mystery number. Find three or more numbers that fit this pattern.
2. You are taking a course that has 4 exams. the first three tests are 100 points each, and the final exam is 200 points. to get an A you need to score at least 90%. If your first three scores were 87, 92, and 84, what score do you need to get on the final exam to get an A?
3.Your manager asks you to set up a display of 10 wrenches that are on sale this week. The wrenches will be 1/3 off of the regular price, $57.00 ($19.00). After the sale is over, your manager asks for the sales figures. If 150 sets were sold this week, what amount of revenue will you report?
4. To reach a destination, a pilot is plotting a course that will result in a velocity of 450 miles per hour at an angle of 30 degrees north of west. The wind is blowing 50 miles per hour to the north. Find the direction and speed the pilot should set to achieve the desired resultant.
5. Between 15000yd cubed and 16000 yd cubed of earth must be trucked away from a construction site . The trucks can remove 1000 yard cubed per day and 10500 yd cubed has already been removed. How many days are needed?
6. An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6900 dollars. If she earns a total of 95700 dollars per year, what is her monthly salary in dollars?
7. The sum of three numbers is -2. The sum of three times the first number, twice the second and third numbers is 9. The difference between the second number and half the third number is 10. Find the numbers and equations.
8. Anita and Nick are playing tug-of-war near a mud puddle. They are each holding on to an end of a taut rope that has a knot exactly in the middle. Anita's position is 5.6 meters east of the center of the puddle and Nick's position is 3.0 meters west of the center of the puddle. What is the location of the knot relative to the center of the puddle? Treat east as positive and west as negative.
9. Clara has a bag of 60 coins with a value of $2.00. The coins are all pennies and nickels. How many of each coin are in the bag?
10. Two cars on a highway passed one another going in opposite directions at 10:30 am. The southbound car was traveling 10mi/hr faster than the northbound car, At 1:00pm, they were 225 miles apart. At what speed was each car traveling?
11. The width of a rectangle is 13 centimeters. Find all possible values for the length of the the rectangle if the perimeter is at least 228 cm.
12. Susan bought a 6 month $1,400 certificate of deposit. At the end of 6 months, she received $126 simple interest. What annual rate of interest did the certificate pay?
13. A Chemist needs 120 milliliters of a 21% solution but only has 3% and 27% solutions available. Find how many milliliters of 27% solution should be used to the desired solution.
14. A window in an apartment is 32m above the ground. From this window, the angle of elevation of the top of the taller building across the street is 36degress and the angle of depression of the bottom of the taller bulding is 47degrees. Calculate the height of the taller building to one decimal place.
15. A steel bar is 96 inches long. It is sawn up into 2 1/4 inches long. Assuming each saw cut wastes 1/8th of an inch, how much scrap is left at the end of the bar?
16. You sell electronics online. Last month, your business had 22 credit card transactions that totaled $47,456. The credit card company charged you $0.25 per transaction and 2 percent of the total transactions. How much did it cost you last month to provide this service to your customers?
17. Mr. de long travels to state a to purchase coming equipment she must pay the prevailing sales tax of 8 percent on what she buy the store will ship her purchase to her home in state b without charging at but with a fixed shipping fee of 3.20 what is the least number of dollar she can spend so that having the purchase shipped will not be more expensive than paying the sales tax.
18. At the cable car museum you can see the four cables lines that are used to pull cable cars up and down the hills of San Francisco. Each cable travels at a speed of 9.55 miles per hour , caused by a rotating wheel whose diameter is 8.5 feet. How fast is the wheel rotating? Express your answer in revolutions per minute.
19. How fast would you have to travel on the surface of earth at the equator to keep up with the sun that is so that the sun would appear to remain in the same position in the sky.
20. Helene is building a garage on her farm near stavley. She knows that the angle of elevation on the roof must be 23 degrees for the peak of the roof to be 3.2 metres above the end of the rafters. how long is each rafter?
21. Jospeh can eat 15 hotdog in 36 second. how long will take him to eat 66 hotdog?
22. A five foot man can cast a 6 foot shadow. if a certain tree castsa a 27 foot shadow,. hoe tall is the tree?
23. A boat can travel 114 miles upstream in the same time it can travel 186 miles downstream. If the speed of the current is 6 miles per hour, find the speed of the boat without a current.
24. A research department of a company that manufactures children’s fruit drinks is experimenting with a new flavor. A 17.5% fructose solution is needed, but only 10% and 20% solutions are available. How many gallons of each solution should be mixed in order to obtain 20 gallons of the 17.5% fructose solution?
25. A bag has 15 different cards. What is the probability of pulling a red, blue, green in any order?
26. Find the annual percentage yield for an account earning 6.7% annual interest compounded quarterly. Round your percentage to two places after the decimal point(so an answer of 12.9763% would be entered as 12.98).
27. Solve with elimination: A plan traveled 416 miles to Des Moines and back. The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip back took 8 hours. Find the speed of the plane in still air and the speed of the wind.
28. 3 singers are each looking for a piano player to accompany them. There are 4 piano players available. How many different pairs of singer and piano player are possible?
29. A string quartet has members that play these instruments: cello, bass, violin and viola. In how many different ways can these 4 musicians arrange themselves in a row onstage?
30. After the first term 2, ea. term of the sequence, 2, 6, 18, .. is obtained by multiplying the preceding term by 3. Which of the terms in the sequence is divisible by 3^4?
31. Simplify: (2x + 5)(3x - 7)
32. The following graph shows data for a particular SUV driven on city streets. Suppose a compact car can travel twice as far as the SUV on the same amount of gas. Answer the following questions. Please show all of your work. At what rate does the SUV consume gas? At what rate does the compact car consume gas? What is the amount of gasoline used by the compact car after 120 miles?
33. In the year 2000, Texas' population was about 20.85 million. In 2006, the population had increased by 12.7%.
a. Assuming this growth continued what should Texas population today be?
b. In what year will the population reach about 30 million?
34. Triangle ABC has sides measuring 10cm. If ABC undergoes a size transformation of magnitude 4...what would the new lengths of the sides be?
35. On a map, Elmwood Drive passes through R (4, -11) and S(0, -9), and Taylor Road passes through J(6, -2) and K(4, -5). If they are straight lines, are the two streets perpendicular? Explain.
36. Fcator completely: 3x4 - 3w4x4
37. You are standing (at sea level) a certain distance from a hill, and measure the angle to the top of the hill as 3°. You walk directly away from the top of the hill 500 feet, and now measure the angle to the top of the hill to be 2°. How high is hill?
38. You have invested 34,000 in bonds and stocks. Bonds account paid you interest according the interest rate of 12%, stocks account does it with interest rate of 5%. What are the portions invested in each account if the total interest received in one year from both accounts was 2,950?
39. Jenna ordered 28 t shirts for her soccer team. Seventy five percent of those shirts were size large. How many large shirts did Jenna ordered?
40. Samuel has run for 45 minutes. If he has completed 60% of his run, how many minutes will Samuel run in all? 3. Sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?
41. Douglas sold 125 sandwiches to raise money for his boy scout troop eighty percent of those sandwiches were sold in his neighborhood how many sandwiches did Douglas sell in his neighborhood
42. Line 1_ y = 1/3 - 1 line 2_ - x + 3y = - 3, if the line is inconsistent, consistent independent, consistent dependent.
43. A rock band has 3 members: a guitarist, a drummer and a bass guitarist. They are taking publicity photos. In how many different ways can these 3 musician’s stands together in a row? Describe the order.
44. The musicians are choosing a costume to wear on stage. How many different outfits can be made with a white shirt, a striped, a blue shirt, black pants and gray pants?
45. Ria is making a poster to advertise a concert. She can use any 2 of these colors; red, blue, yellow or green. List all the possible color combinations she could use.
46. Find the x and y values for the item below;
ax ∙ ay = a173; x and y differ by 85
47. Find the x and y values for the item below;
ax ∙ ay= a82; x and y differ by 62
48. Find the x and y values for the item below;
ax ∙ ay = a162; x and y differ by 84
49. Find the x and y values for the item below;
ax ∙ ay = a178; x and y differ by 60.
50. The Sugar Sweet Company is going to transport its sugar to market. It will cost $ 5800 to rent trucks, and it will cost an additional $ 200 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating to C ,to S.
51. The first term of geometric sequence is 1 and the common ratio is 10.What is the 10th term of the sequence?
52. What is the 11th term of the geometric sequence 3,6,,12,24?
53. Write an equation of the line with slope 5 that passes through the point (-1,-8).
54. Write an equation of the line with the slope -4/3 that passes through the point (6,2).
55. Write an equation of the line that passes through the origin and has a slope of 5.
56. Create your own polynomial with a degree of 3 that when divided by x + 2 has a remainder of -4.
57. A cylindrical container must be constructed to contain 250 cubic inches of liquid.
A. Express the entire surface area of the container as a function of its radius r and height h. Don’t forget the top and bottom.
B. Express the volume as a function of r and h, and set this expression equal to 250.
C. Use your work from part b to solve for h in terms of r. Then substitute this expression for h into your area expression from part a.
D. Using a graphing technique, find the value of r that makes the surface area a minimum.
E. What dimensions of the container should the manufacturer use if his goal is to minimize the amount of material used in its manufacture?
58. A rectangular box with a square base of length s and height y is to have a volume of 16 cubic feet. The cost of top and bottom material for the box is 25 cents per square foot, and the cost for the sides is 10 cents per square foot.
A. Find an expression for the volume of the box in terms of s and y, and set this equal to 16.
B. Find an expression for the cost of the material used to make the box in terms of s and y.
C. Use your work from part a to express the cost of the box in terms of s only.
D. Find the dimensions of the box that will minimize the cost of materials used to make it.
59. A box without a lid is formed by taking a piece of cardboard that is 40 inches by 20 inches, cutting out square pieces from the four corners, and then bending up the sides to form a box.
A. Find an expression for the volume of the box in terms of the side length x of the cut-out squares.
B. Find the value of x that yields maximum volume.
60. Jeff has been saving his change. If he puts his coins in jars of 50 each there is one coin left over. If instead he puts them in boxes of 37 each there is one coin left over. If he puts them in containers of 11 each then there are none left over. What is the smallest number of coins that Jeff has?
61. The temp of a six pack of pop is 90 degrees it is put in a cooler at 2:00 pm at a constant temp of 40 degrees. It cools to 60 degrees in one hour. When will it reach 45 degrees?
62. Julie Burgmeire receives twice the profit in a business venture than Peter Ancona does. If the profit for the year was $120,000, how much will each receive?
63. One number is 12 less than 5 times the other. Find the two numbers if their sum is 42.
64. The sum of two integers is 158. Find the two integers if the larger is 10 less than twice the smaller.
65. William Echols is going to hire a snow plowing service. Elizabeth Suco charges an annual fees of $80, plus $5 each time she plows. Jon Wilkins charges an annual fee of $50, plus $10 each time he plows. How many times would the snow need to be plowed for the cost of both plans to be the same?
66. Alice and Bonnie start running at the same time from the same point and run in the same direction. Alice runs at 8mph while Bonnie runs at slower pace. After 2 hours they are 4 miles apart. determine the speed at which Bonnie is running?
67. A Hair Salon rents booths for $200 per month plus a 5% commission on receipts. How much rent does Qiana owe for one month when her receipts total $4500?
68. The smith family decided to go on a road trip last summer. Their family car can hold up to 16 gallon of gas. over the course of their trip they had to fill up the car 3 times each way. If their trip was 2568 miles in total. At what rate did their car consume gas?
69.Write the equation of the line that passes through(1,1) and throught the center of the circle (x - 2)2 + (y - 4)2 = 20. Write in Ax + By = C form.
70. Lisa is looking up to the top of a giant elephant. The angle of elevation to the giant elephant is 38 degrees and the height of the giant elephant is 21 feet. What is the distance from Lisa to the giant elephant?
a) 0.04 feet b) 16.65 feet c) 16.41 feet d) 26.88 feet
Answer: d) 26.88 feet
71. A 37.54 meter line is used to tether a hot air balloon. Because of a breeze the makes an angle of 50 degrees with the ground. What is the height of the hot air balloon.
a) 49 meters b) 24.13 meters c) 0.02 meters d) 28.76 meters
Answer: d) 28.76 meters
72. A 13 Feet tall lamppost casts a shadow. If the angle of depression looking down from the top of the lamppost to the tip of the shadow is 7 degrees what is the length of the shadow.
a) 105.88 feet b) 0.01 feet C) 12.9 Feet D) 1.6 feet
Answer: a) 105.88 feet
If students have any queries regarding the questions given in the math unsolved questions, please fill-up the below comment box to convey your message, so that we can help you.
Solved Questions
1. Which is greater than 4?
(a) 5,
(b) -5,
(c) -1/2,
(d) -25.
Solution:
5 greater than 4.
Answer: (a)
2. Which is the smallest?
(a) -1,
(b) -1/2,
(c) 0,
(d) 3.
Solution:
The smallest number is -1.
Answer: (a)
3. Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
Solution:
12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22b.
Answer: (c)
4. Simplify: (4 – 5) – (13 – 18 + 2).
(a) -1,
(b) –2,
(c) 1,
(d) 2.
Solution:
(4 – 5) – (13 – 18 + 2).
= -1-(13+2-18).
= -1-(15-18).
= -1-(-3).
= -1+3.
= 2.
Answer: (d)
5. What is |-26|?
(a) -26,
(b) 26,
(c) 0,
(d) 1
Solution:
|-26|
= 26.
Answer: (b)
6. Multiply: (x – 4)(x + 5)
(a) x2 + 5x - 20,
(b) x2 - 4x - 20,
(c) x2 - x - 20,
(d) x2 + x - 20.
Solution:
(x – 4)(x + 5).
= x(x + 5) -4(x + 5).
= x2 + 5x – 4x – 20.
= x2 + x - 20.
Answer: (d)
7. Factor: 5x2 – 15x – 20.
(a) 5(x-4)(x+1),
(b) -2(x-4)(x+5),
(c) -5(x+4)(x-1),
(d) 5(x+4)(x+1).
Solution:
5x2 – 15x – 20.
= 5(x2 – 3x – 4).
= 5(x2 – 4x + x – 4).
= 5{x(x - 4) +1(x - 4)}.
= 5(x-4)(x+1).
Answer: (a).
8. Factor: 3y(x – 3) -2(x – 3).
(a) (x – 3)(x – 3),
(b) (x – 3)2,
(c) (x – 3)(3y – 2),
(d) 3y(x – 3). Solution:
3y(x – 3) -2(x – 3).
= (x – 3)(3y – 2).
Answer: (c).
9. Solve for x: 2x – y = (3/4)x + 6.
(a) (y + 6)/5,
(b) 4(y + 6)/5,
(c) (y + 6),
(d) 4(y - 6)/5.
Solution:
2x – y = (3/4)x + 6.
or, 2x - (3/4)x = y + 6.
or, (8x -3x)/4 = y + 6.
or, 5x/4 = y + 6.
or, 5x = 4(y + 6).
or, 5x = 4y + 24.
or, x = (4y + 24)/5.
Therefore, x = 4(y + 6)/5.
Answer: (b).
10. Simplify:(4x2 - 2x) - (-5x2 - 8x).
Solution:
(4x2 - 2x) - (-5x2 - 8x)
= 4x2 - 2x + 5x2 + 8x.
= 4x2 + 5x2 - 2x + 8x.
= 9x2 + 6x.
= 3x(3x + 2).
Answer: 3x(3x + 2)
11. Find the value of 3 + 2 • (8 – 3)
(a) 25,
(b) 13,
(c) 17,
(d) 24,
(e) 15.
Solution:
3 + 2 • (8 – 3)
= 3 + 2 (5)
= 3 + 2 × 5
= 3 + 10
= 13
Answer: (d)
12. Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?
Solution:
33/4 ÷ 4 pounds.
= (4 × 3 + 3)/4 ÷ 4 pounds.
= 15/4 ÷ 4 pounds.
= 15/4 × 1/4 pounds.
= 15/16 pounds.
Now we know that, 1 pound = 16 ounces.
Therefore, 15/16 pounds = 15/16 × 16 ounces.
= 15 ounces.
Answer: 15 ounces.
13. Factor: 16w3 – u4w3
Solution:
16w3 – u4w3.
= w3(16 – u4).
= w3(42 - ((u2)2).
= w3(4 + u2)(4 - u2).
= w3(4 + u2)(22 - u2).
= w3(4 + u2)(2 + u)(2 - u).
Answer: w3(4 + u2)(2 + u)(2 - u).
14. Factor: 3x4y3 – 48y3.
Solution:
3x4y3– 48y3.
= 3y3(x4 – 16).
= 3y3[(x2)2 - 42].
= 3y3(x2 + 4)(x2 - 4).
= 3y3(x2 + 4)(x2 - 22).
= 3y3(x2 + 4)(x + 2)(x -2).
Answer: 3y3(x2 + 4)(x + 2)(x -2)
15. What is the radius of a circle that has a circumference of 3.14 meters?
Solution:
Circumference of a circle = 2πr.
Given, circumference = 3.14 meters.
Therefore,
2πr = Circumference of a circle
or, 2πr = 3.14.
or, 2 × 3.14r = 3.14,[Putting the value of pi (π) = 3.14].
or, 6.28r = 3.14.
or, r = 3.14/6.28.
or, r = 0.5.
Answer: 0.5 meter.
2. Give Deluded 100 milligrams IM from a vial that is labeled 50 milligrams per milliner every 4 hours. Give how much?
3. Ordered: Atropine sulfate 0.6 milligram IM every 4 hours Have Atropine sulfate 0.4 milligrams per milliliter. Give how much?
4. The physician has ordered calcitonin-salmon 500 units IM for the client. The calcitonin-salmon vial reads 200 International Units per milliliter. Give how much?
5. The physician has ordered adrenalin 0.9 milligrams sub-Q stat. The adrenalin label reads 1 : 1000 solutions. Give how much?
6. Ordered: cefotetan disodium 1.25 grams every 24 hours piggy-back IV Have: Cefotetan disodium 1 gram in 50 milliliters. Give how much?
7. The physician has ordered magnesium sulfate 4 grams stat. The magnesium sulfate vial is labeled 50% solution. Give how much?
8. Give butorphanol tart rate 1.5 milligrams IV for the client every 3-4 hours. The butorphanol drug label reads 2 milligrams per milliliter. Give how much?
9. The physician orders Imitrex 5 milligrams sub-Q as needed for headache for the client. The Imitrex drug label on the vial reads 12 milligrams per milliliter. Round to the nearest hundredth. Give how much?
10. Cala cut 2 1/2 inches off her hair three times last year how much longer would her hair have been at the end of the year if she had not cut it?
11. What is the perimeter of a rectangle with vertices at (-4,-4) and (-4,4) (4,4) (4,-4)?
12. What is the area of a quadrilateral with the vertices (0,0) (4,0) (6,3) and (2,3)?
13. 2 yd + 3 ft write the sum in yards.
14. The temperature rose from -18 to 19how many degrees did the temperature increase? 15. 2 meters + 100 centimeters write the answer in meters.
16. Suppose x and y vary inversely. Write a function that models each inverse variation. Graph the function and find y when x=10. What’s the domain and range of the function? Identify the asymptotes. x=3 and y=12.
17. David has a box with 5 green markers and 3 red markers. He chooses a marker at random and does not return it to the box he then chooses another marker at random. What is the probability that David chooses a green marker followed by a red marker?
18. If the average retail price of gas sold at the pump in Chicago increased from $4.50 per gallon on 1/1/2012 to $6.50 per gallon on 9/1/2012, what is the corresponding annual percentage increase in the price of gasoline?
19. There are 4 boys and 5 girls running for class president. Mr. Santos will choose 1 boy and 1 girl. How many different combinations of 1 boy and 1 girl can be chosen?
20. An 100 lb force acts of the end of the 24 inch lever as shown. (You may need to scroll down to see drawing.) Determine the moment of the force about the bottom end of the lever. F = 100 lb L = 24 in theta = 60 degrees alpha = 30 degrees Report your answer to the nearest whole number. Assume that the moment is positive if it rotates in the counter-clockwise direction.
21. Bobbi Jo and Chaz run a photography business that specializes in engagement photos and senior portraits. Bobbi Jo takes the photos and Chaz does the editing. Each engagement session takes 4 hours of work from Bobbi Jo and 4 hours of work from Chaz. Each senior portrait session takes Bobbi Jo 2 hours and Chaz 4 hours. Bobbi Jo goes to school full-time and is limited to working no more than 16 hours per week. Chaz’s girlfriend says he can’t work more than 24 hours per week. Bobbi Jo and Chaz know at least one couple will want engagement photos done each week. Bobbi Jo and Chaz charge $150 for engagement photos and $100 for senior portraits. How can Bobbi Jo and Chaz earn the most money?
22. If product of (1+2), (2+3), and (3+4) is equal to one-half the sum of 20 and X, what is the value of X?
23. An engine piston has a diameter of 9.2 cm, with a tolerance on 0.01 cm. what absolute value inequality represents the range of values for the diameter of the piston?
24. A survey is taken and finds that 5,000 people in town would vote for candidate A. the survey company says their results are accurate within 3%. Write an absolute value inequality with X as the possible survey results.
25. To ride you have to be 4 1/2 feet tall but no taller than 6 1/2 feet. How can you write this as an absolute value inequality?
26. The dimensions of a rectangle are multiplied by an unknown value, k. The area of the original rectangle is 525 cm squared. the area of the new rectangle is 21 cm squared. if the width of the original rectangle is 25 cm squared. what is the width of the new rectangle?
27. Aleah left Edmonton and drove toward Blue River BC at a speed of 110 km/hr. Michaela left Blue River at the same time and drove toward Edmonton at a speed of 100km/hr. If Blue River is 700km from Edmonton how far had they each driven when they passed each other on the highway?
28. If two similar cubes have an edge ratio of 3:2, what would be the ratio of their volumes?
29. Joe wants to have a 40% alcohol solution. He has an unknown amount of a 10% solution and 40 liters of a 50% solution. He has to mix the two solutions. What is the unknown amount? Round to two decimal places and also include the unit.
30. During the four periods of a baseball game you scored 15, 8, 27 and 25 points respectively. Find the average number of points scored per period. Answer in units of points.
31. Your favorite author has published a series of 5 science fiction books. Each book costs $4.50. The book store is offering the whole series for $21. What is the cost per book for the series? Answer in units of dollars.
32. You signed up for 18 dance lessons. The total cost for the lessons is $120. What is the cost per lesson? We had put $6.67 but it wasn't right when i went to put it in the computer for homework. Is there another way to do this problem?
33. You went to buy a TV there was a 25 discount. You can get an additional 10 discount for the floor model and another 5 for paying in cash. The discounts are applied successively and you paid 371.93 for the TV. What was the original price?
34. When Christopher Columbus was 41 years old he sailed across the Atlantic ocean for the first time. He went on his final expedition 10 years later, which took 2 years. He died 2 years after his final expedition ended, in 1506. What year was Columbus Born?
35. An equilateral triangle has perimeter 54 inches. What would be the perimeter of a square whose sides each measure the same length as the side of the triangle?
36. A personal identification number (PIN) consists of four digits. Digits are allowed to be used more than once. How many possible PINs are there?
37. A shark swims at a rate of 18 feet per second while chasing his prey and then slows down to a rate of 7 feet per second. The shark chases his prey for t seconds and then swims at the slower speed for s seconds, and covers a total distance of 1200 feet. If all traveling is done in the same direction, which equation best describes this information?
38. A fund raising charity sponsored a 15K boat race; the winner of the race will be award $50. 40 people entered the race; every entrant paid a $20 fee. Assuming they are all equally likely to win, what is a fair price for the competition?
39. A parking meter contains quarters and dimes worth $7.85. There are 41 coins in all. Find how many of each there are.
40. Ticket to a school play was $21 each. but performers and student volunteer can get a ticket for a half price. for the performance , there were 20 performers, 40 student, and 270 audiences attending it. what was the amount collected for the night?
41. NELLA DROVE FROM CITY A TO A GARDEN IN CITY B. IT TOOK HER 4 HOURS TO TRAVEL 220MILES IF=VER TEG MOUNTAIN ROAD. SHE CANE HOME ON THE HIGHWAY. ON THE HIGHWAY SHE TOOK 3 HOURS TO TRAVEL 195 MILES. HOW FAST DID SHE TRAVEL USING THE MOUNTAIN ROUTE? HOW MUCH FASTER (MPH) DUD SGE TRAVEL USING THE HIGHWAY ROUTE? 42. The length of a rectangular piece of steel in a bridge is 4 meters less than double the width. The perimeter of the piece of steel is 34 meters. Find the length and the width.
43. Each lab counts once and each test counts as two labs. At the end of the semester there is a final lab that counts as 3 regular lads. Danielle received scores 90, 94, 97 on her labs, and scores of 93 and 99 on her tests. What must she get on the final lab to receive an A is 95.
44. A designer plans the top of a rectangular workbench to be four times as long as it is wide and then determines if the width is 1500 mm greater and the length is 4500 mm less, it would be a square. What are its dimensions?
45. Each day the exchange rate between U. S. dollars and foreign currency changes. One day, 4 dollars were equivalent to approximately 3 euro. On the same day 3 euro were equivalent to approximately 168.37 Indian rupees. To the nearest rupee, how many Indian rupees are equivalent to 1 dollar?
A) 25 rupees B) 37 rupees C) 42 rupees D) rupees
Math Word Problems:
1. Two cities are 1580 miles apart. A plane leaves one of them traveling towards the other at an average speed o 400 mile per hour. At that time a plane leaves the other traveling towards the first at an average speed of 390 miles per hr. How long will it take them to meet?
Answer: 2 hours
2. How much pure acid is in 180 milliliters of a 15% solution?
Answer: 117 ml
3. A table is three times as long as it is wide. If it were 5ft shorter and 5 ft wider it would be square (with all sides equal). How long and how wide is the table?
Answer: Length 15, Width 5
4. Nico is saving money for his college education. He invests some money at 9% and 800 less than that amount @ 6%. The investments produced a total f $222 interest in 1 yr. How much did he invest at each rate?
Answer: $1800 at 9% and $1000 at 6%
5. I had $1.60 in dimes and nickels and had four more dines then nickels. How many of both would I have?
Answer: Nickels 8, Dimes 12
6. How many litters of a 60% acid solution must be mixed with a 25¬id solution to get a 315L of a 50% acid?
Answer:
7. A Dr. Wishes to mix a solution that is 7% monoxide. She has on hand 60 ml of a 6% solution ad wishes to add 9% solution to obtain the desired 7% solution she should add ___ ML
Answer:
8. When 1 is added to the difference between four time’s number and 9, the result is greater than 13 added to 3 times the number. Find all such numbers.
Answer:
9. Randy has $15,000 that he would like to invest. He has a choice of two interest paying bonds, one offering a 4% annual interest and the other paying 8% annual interest. He would like to earn $760 in interest in one year using both types of bonds that he can put towards his vacation. How much money should he invest in each bond?
Answer: $11000 at 4% and $4000 at 8%
10. An elementary school teacher wishes to use 17 feet of scalloped border to enclose a rectangular region on her bulletin board. What is the maximum area that she can enclose with the border?
Answer:
11. The expression 10,000 – 1,000t can be used to calculate the tax value in dollars of a farm tractor that is t years old. How old will the tractor be when its tax value reaches zero?
(a) 12 yr old, (b) 11 yr old, (c) 10 yr old, (d) 13 yr old
Answer: (c) 10 years
12. The total cost of a video game was $42.39. This included 6% sales tax. Find the price without sales tax.
Answer: $ 39.99 (Approx)
13. Clear-water High School expects a 41% increase in enrollment next year. There are 1850 students enrolled this year. How many students will the school gain? What is the expected enrollment next year?
Answer: School gain 1632 students and expected enrollment next year = 2109
14. A fair die is tossed once. Which event is more likely, "the number showing is divisible by three" or "the number showing is even"?
Answer: 6
15. An electric clock was stopped by a power failure. What is the probability that the minute hand stopped between the following two numerals on the face of the clock? a) 12 and 3 b) 1 and 5 c) 11 and 1
Answer: (a) P(12 and 3) = 1/4, (b) P(1 and 5) = 1/3, (c) P(11 and 1) = 1/6
16. Amy the chicken is tied to one corner of a rectangular barn with a 12 foot rope. If the width of the barn is 8 ft and the length is 2 yards, find the area outside the barn in which Amy can travel. Leave pi (Π) in the answer.
Answer:
17. A swimming pool has to be drained for maintenance. The pool is shaped like a cylinder with a diameter of 10m and a depth of 2.2 m . If the water is pumped out of the pool at the rate of 17 m^3 per hour, how many hours does it take to empty the pool? Use the value 3.14 for , and round your answer to the nearest hour.
Answer:
18. The height of a triangle is 4 feet more than 3 times the base. If the area is 32 ft2, find the base and height of the triangle.
Answer: Base = 4 feet, Height = 16 feet.
19. In general, the y-intercept of the function F(x) = a*b^x is the point _____.
Answer: (0, a)
20. The domain of F(x)=(2/3)^x is all negative numbers.
A. True B. False
Answer: B. False
21. For all values of a and b that make F(x) = a * b^x a valid exponential function, the graph always has a horizontal asymptote at y = 0.
A. True B. False
Answer: A. True
22. The range of F(x) = 5 * 2^x is all positive real numbers.
A. True B. False
Answer: A. True
23. The range of the function given below is the set of all positive real numbers greater than 6.
F(x) = 6 + 2^x
A. True B. False
Answer: A. True
24. Graduate students were asked to participate in an evaluation of beers. Each student was given three glasses in a random order. Glasses 1 and 2 both had the same inexpensive local beer, while Glass 3 contained a more expensive imported beer. Students were told that the beer in glass 1 was expensive, but that the beer in glass 2 was not. They were not told anything about glass 3. Students were asked to rate the beers from 1 to 20 with higher ratings indicating better taste. 8 students responses were randomly selected and are presented below. What is your question? Analyze the data to answer the question.
So, the rubric is:
(a) Provide support for a particular approach by exploring whether assumptions underlying parametric/nonparametric/et., assumptions are met.
(b) Surface ideas with techniques (e.g. scatter plot, outliers, etc.) used to analyze the data.3. Define the question and hypotheses ( which of course you will then test).
(c) Identify the key ideas, variables, or issues that frame the research problem
25. A rectangles perimeter is 16 units and its area is 11 square units. please find its exact dimensions.
Answer: Length = 4 + √5 units, Width = 4 - √5 units
26. Astronauts who waked on the moon felt as if they weighed about one sixth of their weight on earth. this is because the weight of an object is determined by the gravitational attraction between the object and the planet (or moon) its on. you can use the following formula to estimate the weight of an object on the surface of any of the planets: gravitational force=GmM/r^2, where G=universal gravitational constant,m=mass of the object, M=mass of the planet, and r=radius of the planet. For a given object, Grandma remain constant, so the force of gravity depends only on the variables named r.
Answer:
27. A store is having a sale on liquid soap and sponges the cost of 6 bottles of soap is 9.12 the coast of 4 sponges is 5.00 what is the total cost of buying 2 bottles of liquid soap and 3 sponges.
Answer:
28. A line contains the points(a, b) and ( a+3, b+3). Find the slope of the line.
Answer: Slope = 1
29. Put the following list of real numbers in order from LEAST to GREATEST. Make sure you show all the steps you took to get to your final answer. -√64 ,-7/2, 3.3, √10, 27/3
Answer: -√64, -3.5, √10, 3.3, 27/3
30. Johnathon and Talia simplified the following expression on their Algebra 1 midterm: 7 - 2(x - 5).
Answer: Johnathon's work --- Correct Process
31. What is the sales tax and total price of an item that is $45.69 if the sales tax is 7.5 %?
a. sales tax = $3.00; total price = $50.00
b. sales tax = $3.40; total price = $49.09
c. sales tax = $3.43; total price = $49.12
d. sales tax = $3.42; total price = $49.11
Answer: c. sales tax = $3.43; total price = $49.12
32. Kate earns a weekly allowance of $12. How much money will she earn in 8 weeks? Do not enter $.____ dollars
Answer: $ 96
33. A table is shaped like a square and has an area of 100 square feet. Find the length of one side of the table.____ feet
Answer: 10 feet.
34. Juan bought n video games. Write an expression to show the total cost of the games if each game cost $16. Do not enter $ in your answer.
Answer: Total cost f(n) = 16n
35. A sandpit in the shape of a pentagon ABCDE is to be built in such a way that each of its sides are of equal length, but its angles are not all equal. The pentagon is symmetrical about DX, where X is the midpoint of AB. The angle AXE and BXC are both 45 degrees and each side is 2m long.
(a) Find angle XEA.
(b) Find the length of EX.
(c) How much sand is required if the sandpit is 30 cm deep?
Give your answer to three decimal place.
36. An aircraft takes off from an airstrip and then flies for 16.2 km on a bearing of 066 degrees true. The pilot then makes a let turn of 88 degrees and flies for a further 39.51 km on this course before deciding to return to the airstrip. (a) Through what angle must the pilot turn to return to the airstrip? (b) How far will the pilot have to fly to return to the airstrip?
37. Gracie decided to rent a limo for her wedding. The Bedazzled Limo Com- pany charges a $50 gas fee, $56.48 per hour to rent the limo and requires a tip of 20% on the total price of the rental (so 20% of the total cost of the rental). The Wedding Bell Limo Company charges $68.36 per hour and requires a 25% tip to the driver. For how long of a rental will the hourly cost be the same? (Round to the nearest half hour).
Answers for the different types of math word problems are given below to check the exact answers of the above math questions.
Various types of Math Problem Answers are solved here.
1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Solution:Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
2. The value of x + x(xx) when x = 2 is:
(a) 10, (b) 16, (c) 18, (d) 36, (e) 64
Solution:
x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer: (a)
3. Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
(a) broke even, (b) lost 4 cents, (c) gained 4 cents, (d) lost 10 cents, (e) gained 10 cents
Solution:
20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
Answer: (a)
4. The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
(a) 587 × 108 miles, (b) 587 × 1010 miles, (c) 587 × 10-10 miles, (d) 587 × 1012 miles, (e) 587 × 10-12 miles
Solution:
The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 1012 miles.
Answer: (d)
5. A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:
(a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 %
Solution:
Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.
Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.
= $ 160.
Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer: (e)
6. Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
(a) three times as much, (b) twice as much, (c) the same, (d) half as much, (e) a third as much
Solution:
Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
Answer: (b)
7. If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
(a) -10.0, (b) -0.5, (c) -0.4, (d) -0.2, (e) 10.0
Solution:
(0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
Answer: (c)
8. If 102y = 25, then 10-y equals:
(a) -1/5, (b) 1/625, (c) 1/50, (d) 1/25, (e) 1/5
Solution:
102y = 25
(10y)2 = 52
10y = 5
1/10y = 1/5
10-y = 1/5
Answer: (e)
9. The fraction (5x-11)/(2x2 + x - 6) was obtained by adding the two fractions A/(x + 2) and B/(2x - 3). The values of A and B must be, respectively:
(a) 5x, -11, (b) -11, 5x, (c) -1, 3, (d) 3, -1, (e) 5, -11
Solution:
Answer: (d)
10. The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is:
(a) 15, (b) 20, (c) 30, (d) 32, (e) 33
Solution:
Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2/3.
x/y = 2/3.
x = 2/3 × y.
x = 2y/3.
The ratio of the second to the third is 5/8.
y/z = 5/8.
z/y = 8/5.
z = 8/5 × y.
z = 8y/5.
Put the value of x = 2y/3 and z = 8y/5 in (i).
2y/3 + y + 8y/5 = 98
49y/15 = 98.
49y = 98 × 15.
49y = 1470.
y = 1470/49.
y = 30 .
Therefore, the second number is 30.
Answer: (c)
Unsolved Questions:
1. Fahrenheit temperature F is a linear function of Celsius temperature C. The ordered pair (0, 32) is an ordered pair of this function because 0°C is equivalent to 32°F, the freezing point of water. The ordered pair (100, 212) is also an ordered pair of this function because 100°C is equivalent to 212° F, the boiling point of water.
2. A sports field is 300 feet long. Write a formula that gives the length of x sports fields in feet. Then use this formula to determine the number of sports fields in 720 feet.
3. A recipe calls for 2 1/2 cups and I want to make 1 1/2 recipes. How many cups do I need?
4. Mario answered 30% of the questions correctly. The test contained a total of 80 questions. How many questions did Mario answer correctly?
Some more unsolved questions
Math Unsolved Questions :
1. If you add the two digits of the mystery number and then multiply the sum by 7, the answer is the mystery number. Find three or more numbers that fit this pattern.
2. You are taking a course that has 4 exams. the first three tests are 100 points each, and the final exam is 200 points. to get an A you need to score at least 90%. If your first three scores were 87, 92, and 84, what score do you need to get on the final exam to get an A?
3.Your manager asks you to set up a display of 10 wrenches that are on sale this week. The wrenches will be 1/3 off of the regular price, $57.00 ($19.00). After the sale is over, your manager asks for the sales figures. If 150 sets were sold this week, what amount of revenue will you report?
4. To reach a destination, a pilot is plotting a course that will result in a velocity of 450 miles per hour at an angle of 30 degrees north of west. The wind is blowing 50 miles per hour to the north. Find the direction and speed the pilot should set to achieve the desired resultant.
5. Between 15000yd cubed and 16000 yd cubed of earth must be trucked away from a construction site . The trucks can remove 1000 yard cubed per day and 10500 yd cubed has already been removed. How many days are needed?
6. An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6900 dollars. If she earns a total of 95700 dollars per year, what is her monthly salary in dollars?
7. The sum of three numbers is -2. The sum of three times the first number, twice the second and third numbers is 9. The difference between the second number and half the third number is 10. Find the numbers and equations.
8. Anita and Nick are playing tug-of-war near a mud puddle. They are each holding on to an end of a taut rope that has a knot exactly in the middle. Anita's position is 5.6 meters east of the center of the puddle and Nick's position is 3.0 meters west of the center of the puddle. What is the location of the knot relative to the center of the puddle? Treat east as positive and west as negative.
9. Clara has a bag of 60 coins with a value of $2.00. The coins are all pennies and nickels. How many of each coin are in the bag?
10. Two cars on a highway passed one another going in opposite directions at 10:30 am. The southbound car was traveling 10mi/hr faster than the northbound car, At 1:00pm, they were 225 miles apart. At what speed was each car traveling?
11. The width of a rectangle is 13 centimeters. Find all possible values for the length of the the rectangle if the perimeter is at least 228 cm.
12. Susan bought a 6 month $1,400 certificate of deposit. At the end of 6 months, she received $126 simple interest. What annual rate of interest did the certificate pay?
13. A Chemist needs 120 milliliters of a 21% solution but only has 3% and 27% solutions available. Find how many milliliters of 27% solution should be used to the desired solution.
14. A window in an apartment is 32m above the ground. From this window, the angle of elevation of the top of the taller building across the street is 36degress and the angle of depression of the bottom of the taller bulding is 47degrees. Calculate the height of the taller building to one decimal place.
15. A steel bar is 96 inches long. It is sawn up into 2 1/4 inches long. Assuming each saw cut wastes 1/8th of an inch, how much scrap is left at the end of the bar?
16. You sell electronics online. Last month, your business had 22 credit card transactions that totaled $47,456. The credit card company charged you $0.25 per transaction and 2 percent of the total transactions. How much did it cost you last month to provide this service to your customers?
17. Mr. de long travels to state a to purchase coming equipment she must pay the prevailing sales tax of 8 percent on what she buy the store will ship her purchase to her home in state b without charging at but with a fixed shipping fee of 3.20 what is the least number of dollar she can spend so that having the purchase shipped will not be more expensive than paying the sales tax.
18. At the cable car museum you can see the four cables lines that are used to pull cable cars up and down the hills of San Francisco. Each cable travels at a speed of 9.55 miles per hour , caused by a rotating wheel whose diameter is 8.5 feet. How fast is the wheel rotating? Express your answer in revolutions per minute.
19. How fast would you have to travel on the surface of earth at the equator to keep up with the sun that is so that the sun would appear to remain in the same position in the sky.
20. Helene is building a garage on her farm near stavley. She knows that the angle of elevation on the roof must be 23 degrees for the peak of the roof to be 3.2 metres above the end of the rafters. how long is each rafter?
21. Jospeh can eat 15 hotdog in 36 second. how long will take him to eat 66 hotdog?
22. A five foot man can cast a 6 foot shadow. if a certain tree castsa a 27 foot shadow,. hoe tall is the tree?
23. A boat can travel 114 miles upstream in the same time it can travel 186 miles downstream. If the speed of the current is 6 miles per hour, find the speed of the boat without a current.
24. A research department of a company that manufactures children’s fruit drinks is experimenting with a new flavor. A 17.5% fructose solution is needed, but only 10% and 20% solutions are available. How many gallons of each solution should be mixed in order to obtain 20 gallons of the 17.5% fructose solution?
25. A bag has 15 different cards. What is the probability of pulling a red, blue, green in any order?
26. Find the annual percentage yield for an account earning 6.7% annual interest compounded quarterly. Round your percentage to two places after the decimal point(so an answer of 12.9763% would be entered as 12.98).
27. Solve with elimination: A plan traveled 416 miles to Des Moines and back. The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip back took 8 hours. Find the speed of the plane in still air and the speed of the wind.
28. 3 singers are each looking for a piano player to accompany them. There are 4 piano players available. How many different pairs of singer and piano player are possible?
29. A string quartet has members that play these instruments: cello, bass, violin and viola. In how many different ways can these 4 musicians arrange themselves in a row onstage?
30. After the first term 2, ea. term of the sequence, 2, 6, 18, .. is obtained by multiplying the preceding term by 3. Which of the terms in the sequence is divisible by 3^4?
31. Simplify: (2x + 5)(3x - 7)
32. The following graph shows data for a particular SUV driven on city streets. Suppose a compact car can travel twice as far as the SUV on the same amount of gas. Answer the following questions. Please show all of your work. At what rate does the SUV consume gas? At what rate does the compact car consume gas? What is the amount of gasoline used by the compact car after 120 miles?
33. In the year 2000, Texas' population was about 20.85 million. In 2006, the population had increased by 12.7%.
a. Assuming this growth continued what should Texas population today be?
b. In what year will the population reach about 30 million?
34. Triangle ABC has sides measuring 10cm. If ABC undergoes a size transformation of magnitude 4...what would the new lengths of the sides be?
35. On a map, Elmwood Drive passes through R (4, -11) and S(0, -9), and Taylor Road passes through J(6, -2) and K(4, -5). If they are straight lines, are the two streets perpendicular? Explain.
36. Fcator completely: 3x4 - 3w4x4
37. You are standing (at sea level) a certain distance from a hill, and measure the angle to the top of the hill as 3°. You walk directly away from the top of the hill 500 feet, and now measure the angle to the top of the hill to be 2°. How high is hill?
38. You have invested 34,000 in bonds and stocks. Bonds account paid you interest according the interest rate of 12%, stocks account does it with interest rate of 5%. What are the portions invested in each account if the total interest received in one year from both accounts was 2,950?
39. Jenna ordered 28 t shirts for her soccer team. Seventy five percent of those shirts were size large. How many large shirts did Jenna ordered?
40. Samuel has run for 45 minutes. If he has completed 60% of his run, how many minutes will Samuel run in all? 3. Sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?
41. Douglas sold 125 sandwiches to raise money for his boy scout troop eighty percent of those sandwiches were sold in his neighborhood how many sandwiches did Douglas sell in his neighborhood
42. Line 1_ y = 1/3 - 1 line 2_ - x + 3y = - 3, if the line is inconsistent, consistent independent, consistent dependent.
43. A rock band has 3 members: a guitarist, a drummer and a bass guitarist. They are taking publicity photos. In how many different ways can these 3 musician’s stands together in a row? Describe the order.
44. The musicians are choosing a costume to wear on stage. How many different outfits can be made with a white shirt, a striped, a blue shirt, black pants and gray pants?
45. Ria is making a poster to advertise a concert. She can use any 2 of these colors; red, blue, yellow or green. List all the possible color combinations she could use.
46. Find the x and y values for the item below;
ax ∙ ay = a173; x and y differ by 85
47. Find the x and y values for the item below;
ax ∙ ay= a82; x and y differ by 62
48. Find the x and y values for the item below;
ax ∙ ay = a162; x and y differ by 84
49. Find the x and y values for the item below;
ax ∙ ay = a178; x and y differ by 60.
50. The Sugar Sweet Company is going to transport its sugar to market. It will cost $ 5800 to rent trucks, and it will cost an additional $ 200 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating to C ,to S.
51. The first term of geometric sequence is 1 and the common ratio is 10.What is the 10th term of the sequence?
52. What is the 11th term of the geometric sequence 3,6,,12,24?
53. Write an equation of the line with slope 5 that passes through the point (-1,-8).
54. Write an equation of the line with the slope -4/3 that passes through the point (6,2).
55. Write an equation of the line that passes through the origin and has a slope of 5.
56. Create your own polynomial with a degree of 3 that when divided by x + 2 has a remainder of -4.
57. A cylindrical container must be constructed to contain 250 cubic inches of liquid.
A. Express the entire surface area of the container as a function of its radius r and height h. Don’t forget the top and bottom.
B. Express the volume as a function of r and h, and set this expression equal to 250.
C. Use your work from part b to solve for h in terms of r. Then substitute this expression for h into your area expression from part a.
D. Using a graphing technique, find the value of r that makes the surface area a minimum.
E. What dimensions of the container should the manufacturer use if his goal is to minimize the amount of material used in its manufacture?
58. A rectangular box with a square base of length s and height y is to have a volume of 16 cubic feet. The cost of top and bottom material for the box is 25 cents per square foot, and the cost for the sides is 10 cents per square foot.
A. Find an expression for the volume of the box in terms of s and y, and set this equal to 16.
B. Find an expression for the cost of the material used to make the box in terms of s and y.
C. Use your work from part a to express the cost of the box in terms of s only.
D. Find the dimensions of the box that will minimize the cost of materials used to make it.
59. A box without a lid is formed by taking a piece of cardboard that is 40 inches by 20 inches, cutting out square pieces from the four corners, and then bending up the sides to form a box.
A. Find an expression for the volume of the box in terms of the side length x of the cut-out squares.
B. Find the value of x that yields maximum volume.
60. Jeff has been saving his change. If he puts his coins in jars of 50 each there is one coin left over. If instead he puts them in boxes of 37 each there is one coin left over. If he puts them in containers of 11 each then there are none left over. What is the smallest number of coins that Jeff has?
61. The temp of a six pack of pop is 90 degrees it is put in a cooler at 2:00 pm at a constant temp of 40 degrees. It cools to 60 degrees in one hour. When will it reach 45 degrees?
62. Julie Burgmeire receives twice the profit in a business venture than Peter Ancona does. If the profit for the year was $120,000, how much will each receive?
63. One number is 12 less than 5 times the other. Find the two numbers if their sum is 42.
64. The sum of two integers is 158. Find the two integers if the larger is 10 less than twice the smaller.
65. William Echols is going to hire a snow plowing service. Elizabeth Suco charges an annual fees of $80, plus $5 each time she plows. Jon Wilkins charges an annual fee of $50, plus $10 each time he plows. How many times would the snow need to be plowed for the cost of both plans to be the same?
66. Alice and Bonnie start running at the same time from the same point and run in the same direction. Alice runs at 8mph while Bonnie runs at slower pace. After 2 hours they are 4 miles apart. determine the speed at which Bonnie is running?
67. A Hair Salon rents booths for $200 per month plus a 5% commission on receipts. How much rent does Qiana owe for one month when her receipts total $4500?
68. The smith family decided to go on a road trip last summer. Their family car can hold up to 16 gallon of gas. over the course of their trip they had to fill up the car 3 times each way. If their trip was 2568 miles in total. At what rate did their car consume gas?
69.Write the equation of the line that passes through(1,1) and throught the center of the circle (x - 2)2 + (y - 4)2 = 20. Write in Ax + By = C form.
70. Lisa is looking up to the top of a giant elephant. The angle of elevation to the giant elephant is 38 degrees and the height of the giant elephant is 21 feet. What is the distance from Lisa to the giant elephant?
a) 0.04 feet b) 16.65 feet c) 16.41 feet d) 26.88 feet
Answer: d) 26.88 feet
71. A 37.54 meter line is used to tether a hot air balloon. Because of a breeze the makes an angle of 50 degrees with the ground. What is the height of the hot air balloon.
a) 49 meters b) 24.13 meters c) 0.02 meters d) 28.76 meters
Answer: d) 28.76 meters
72. A 13 Feet tall lamppost casts a shadow. If the angle of depression looking down from the top of the lamppost to the tip of the shadow is 7 degrees what is the length of the shadow.
a) 105.88 feet b) 0.01 feet C) 12.9 Feet D) 1.6 feet
Answer: a) 105.88 feet
If students have any queries regarding the questions given in the math unsolved questions, please fill-up the below comment box to convey your message, so that we can help you.
Solved Questions
1. Which is greater than 4?
(a) 5,
(b) -5,
(c) -1/2,
(d) -25.
Solution:
5 greater than 4.
Answer: (a)
2. Which is the smallest?
(a) -1,
(b) -1/2,
(c) 0,
(d) 3.
Solution:
The smallest number is -1.
Answer: (a)
3. Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
Solution:
12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22b.
Answer: (c)
4. Simplify: (4 – 5) – (13 – 18 + 2).
(a) -1,
(b) –2,
(c) 1,
(d) 2.
Solution:
(4 – 5) – (13 – 18 + 2).
= -1-(13+2-18).
= -1-(15-18).
= -1-(-3).
= -1+3.
= 2.
Answer: (d)
5. What is |-26|?
(a) -26,
(b) 26,
(c) 0,
(d) 1
Solution:
|-26|
= 26.
Answer: (b)
6. Multiply: (x – 4)(x + 5)
(a) x2 + 5x - 20,
(b) x2 - 4x - 20,
(c) x2 - x - 20,
(d) x2 + x - 20.
Solution:
(x – 4)(x + 5).
= x(x + 5) -4(x + 5).
= x2 + 5x – 4x – 20.
= x2 + x - 20.
Answer: (d)
7. Factor: 5x2 – 15x – 20.
(a) 5(x-4)(x+1),
(b) -2(x-4)(x+5),
(c) -5(x+4)(x-1),
(d) 5(x+4)(x+1).
Solution:
5x2 – 15x – 20.
= 5(x2 – 3x – 4).
= 5(x2 – 4x + x – 4).
= 5{x(x - 4) +1(x - 4)}.
= 5(x-4)(x+1).
Answer: (a).
8. Factor: 3y(x – 3) -2(x – 3).
(a) (x – 3)(x – 3),
(b) (x – 3)2,
(c) (x – 3)(3y – 2),
(d) 3y(x – 3). Solution:
3y(x – 3) -2(x – 3).
= (x – 3)(3y – 2).
Answer: (c).
9. Solve for x: 2x – y = (3/4)x + 6.
(a) (y + 6)/5,
(b) 4(y + 6)/5,
(c) (y + 6),
(d) 4(y - 6)/5.
Solution:
2x – y = (3/4)x + 6.
or, 2x - (3/4)x = y + 6.
or, (8x -3x)/4 = y + 6.
or, 5x/4 = y + 6.
or, 5x = 4(y + 6).
or, 5x = 4y + 24.
or, x = (4y + 24)/5.
Therefore, x = 4(y + 6)/5.
Answer: (b).
10. Simplify:(4x2 - 2x) - (-5x2 - 8x).
Solution:
(4x2 - 2x) - (-5x2 - 8x)
= 4x2 - 2x + 5x2 + 8x.
= 4x2 + 5x2 - 2x + 8x.
= 9x2 + 6x.
= 3x(3x + 2).
Answer: 3x(3x + 2)
11. Find the value of 3 + 2 • (8 – 3)
(a) 25,
(b) 13,
(c) 17,
(d) 24,
(e) 15.
Solution:
3 + 2 • (8 – 3)
= 3 + 2 (5)
= 3 + 2 × 5
= 3 + 10
= 13
Answer: (d)
12. Rice weighing 33/4 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?
Solution:
33/4 ÷ 4 pounds.
= (4 × 3 + 3)/4 ÷ 4 pounds.
= 15/4 ÷ 4 pounds.
= 15/4 × 1/4 pounds.
= 15/16 pounds.
Now we know that, 1 pound = 16 ounces.
Therefore, 15/16 pounds = 15/16 × 16 ounces.
= 15 ounces.
Answer: 15 ounces.
13. Factor: 16w3 – u4w3
Solution:
16w3 – u4w3.
= w3(16 – u4).
= w3(42 - ((u2)2).
= w3(4 + u2)(4 - u2).
= w3(4 + u2)(22 - u2).
= w3(4 + u2)(2 + u)(2 - u).
Answer: w3(4 + u2)(2 + u)(2 - u).
14. Factor: 3x4y3 – 48y3.
Solution:
3x4y3– 48y3.
= 3y3(x4 – 16).
= 3y3[(x2)2 - 42].
= 3y3(x2 + 4)(x2 - 4).
= 3y3(x2 + 4)(x2 - 22).
= 3y3(x2 + 4)(x + 2)(x -2).
Answer: 3y3(x2 + 4)(x + 2)(x -2)
15. What is the radius of a circle that has a circumference of 3.14 meters?
Solution:
Circumference of a circle = 2πr.
Given, circumference = 3.14 meters.
Therefore,
2πr = Circumference of a circle
or, 2πr = 3.14.
or, 2 × 3.14r = 3.14,[Putting the value of pi (π) = 3.14].
or, 6.28r = 3.14.
or, r = 3.14/6.28.
or, r = 0.5.
Answer: 0.5 meter.
Math Questions
1. The physician orders megestrol acetate 750 milligrams per day. The megestrol acetate label reads oral suspension 40 milligrams per milliliter. Give how much?2. Give Deluded 100 milligrams IM from a vial that is labeled 50 milligrams per milliner every 4 hours. Give how much?
3. Ordered: Atropine sulfate 0.6 milligram IM every 4 hours Have Atropine sulfate 0.4 milligrams per milliliter. Give how much?
4. The physician has ordered calcitonin-salmon 500 units IM for the client. The calcitonin-salmon vial reads 200 International Units per milliliter. Give how much?
5. The physician has ordered adrenalin 0.9 milligrams sub-Q stat. The adrenalin label reads 1 : 1000 solutions. Give how much?
6. Ordered: cefotetan disodium 1.25 grams every 24 hours piggy-back IV Have: Cefotetan disodium 1 gram in 50 milliliters. Give how much?
7. The physician has ordered magnesium sulfate 4 grams stat. The magnesium sulfate vial is labeled 50% solution. Give how much?
8. Give butorphanol tart rate 1.5 milligrams IV for the client every 3-4 hours. The butorphanol drug label reads 2 milligrams per milliliter. Give how much?
9. The physician orders Imitrex 5 milligrams sub-Q as needed for headache for the client. The Imitrex drug label on the vial reads 12 milligrams per milliliter. Round to the nearest hundredth. Give how much?
10. Cala cut 2 1/2 inches off her hair three times last year how much longer would her hair have been at the end of the year if she had not cut it?
11. What is the perimeter of a rectangle with vertices at (-4,-4) and (-4,4) (4,4) (4,-4)?
12. What is the area of a quadrilateral with the vertices (0,0) (4,0) (6,3) and (2,3)?
13. 2 yd + 3 ft write the sum in yards.
14. The temperature rose from -18 to 19how many degrees did the temperature increase? 15. 2 meters + 100 centimeters write the answer in meters.
16. Suppose x and y vary inversely. Write a function that models each inverse variation. Graph the function and find y when x=10. What’s the domain and range of the function? Identify the asymptotes. x=3 and y=12.
17. David has a box with 5 green markers and 3 red markers. He chooses a marker at random and does not return it to the box he then chooses another marker at random. What is the probability that David chooses a green marker followed by a red marker?
18. If the average retail price of gas sold at the pump in Chicago increased from $4.50 per gallon on 1/1/2012 to $6.50 per gallon on 9/1/2012, what is the corresponding annual percentage increase in the price of gasoline?
19. There are 4 boys and 5 girls running for class president. Mr. Santos will choose 1 boy and 1 girl. How many different combinations of 1 boy and 1 girl can be chosen?
20. An 100 lb force acts of the end of the 24 inch lever as shown. (You may need to scroll down to see drawing.) Determine the moment of the force about the bottom end of the lever. F = 100 lb L = 24 in theta = 60 degrees alpha = 30 degrees Report your answer to the nearest whole number. Assume that the moment is positive if it rotates in the counter-clockwise direction.
21. Bobbi Jo and Chaz run a photography business that specializes in engagement photos and senior portraits. Bobbi Jo takes the photos and Chaz does the editing. Each engagement session takes 4 hours of work from Bobbi Jo and 4 hours of work from Chaz. Each senior portrait session takes Bobbi Jo 2 hours and Chaz 4 hours. Bobbi Jo goes to school full-time and is limited to working no more than 16 hours per week. Chaz’s girlfriend says he can’t work more than 24 hours per week. Bobbi Jo and Chaz know at least one couple will want engagement photos done each week. Bobbi Jo and Chaz charge $150 for engagement photos and $100 for senior portraits. How can Bobbi Jo and Chaz earn the most money?
22. If product of (1+2), (2+3), and (3+4) is equal to one-half the sum of 20 and X, what is the value of X?
23. An engine piston has a diameter of 9.2 cm, with a tolerance on 0.01 cm. what absolute value inequality represents the range of values for the diameter of the piston?
24. A survey is taken and finds that 5,000 people in town would vote for candidate A. the survey company says their results are accurate within 3%. Write an absolute value inequality with X as the possible survey results.
25. To ride you have to be 4 1/2 feet tall but no taller than 6 1/2 feet. How can you write this as an absolute value inequality?
26. The dimensions of a rectangle are multiplied by an unknown value, k. The area of the original rectangle is 525 cm squared. the area of the new rectangle is 21 cm squared. if the width of the original rectangle is 25 cm squared. what is the width of the new rectangle?
27. Aleah left Edmonton and drove toward Blue River BC at a speed of 110 km/hr. Michaela left Blue River at the same time and drove toward Edmonton at a speed of 100km/hr. If Blue River is 700km from Edmonton how far had they each driven when they passed each other on the highway?
28. If two similar cubes have an edge ratio of 3:2, what would be the ratio of their volumes?
29. Joe wants to have a 40% alcohol solution. He has an unknown amount of a 10% solution and 40 liters of a 50% solution. He has to mix the two solutions. What is the unknown amount? Round to two decimal places and also include the unit.
30. During the four periods of a baseball game you scored 15, 8, 27 and 25 points respectively. Find the average number of points scored per period. Answer in units of points.
31. Your favorite author has published a series of 5 science fiction books. Each book costs $4.50. The book store is offering the whole series for $21. What is the cost per book for the series? Answer in units of dollars.
32. You signed up for 18 dance lessons. The total cost for the lessons is $120. What is the cost per lesson? We had put $6.67 but it wasn't right when i went to put it in the computer for homework. Is there another way to do this problem?
33. You went to buy a TV there was a 25 discount. You can get an additional 10 discount for the floor model and another 5 for paying in cash. The discounts are applied successively and you paid 371.93 for the TV. What was the original price?
34. When Christopher Columbus was 41 years old he sailed across the Atlantic ocean for the first time. He went on his final expedition 10 years later, which took 2 years. He died 2 years after his final expedition ended, in 1506. What year was Columbus Born?
35. An equilateral triangle has perimeter 54 inches. What would be the perimeter of a square whose sides each measure the same length as the side of the triangle?
36. A personal identification number (PIN) consists of four digits. Digits are allowed to be used more than once. How many possible PINs are there?
37. A shark swims at a rate of 18 feet per second while chasing his prey and then slows down to a rate of 7 feet per second. The shark chases his prey for t seconds and then swims at the slower speed for s seconds, and covers a total distance of 1200 feet. If all traveling is done in the same direction, which equation best describes this information?
38. A fund raising charity sponsored a 15K boat race; the winner of the race will be award $50. 40 people entered the race; every entrant paid a $20 fee. Assuming they are all equally likely to win, what is a fair price for the competition?
39. A parking meter contains quarters and dimes worth $7.85. There are 41 coins in all. Find how many of each there are.
40. Ticket to a school play was $21 each. but performers and student volunteer can get a ticket for a half price. for the performance , there were 20 performers, 40 student, and 270 audiences attending it. what was the amount collected for the night?
41. NELLA DROVE FROM CITY A TO A GARDEN IN CITY B. IT TOOK HER 4 HOURS TO TRAVEL 220MILES IF=VER TEG MOUNTAIN ROAD. SHE CANE HOME ON THE HIGHWAY. ON THE HIGHWAY SHE TOOK 3 HOURS TO TRAVEL 195 MILES. HOW FAST DID SHE TRAVEL USING THE MOUNTAIN ROUTE? HOW MUCH FASTER (MPH) DUD SGE TRAVEL USING THE HIGHWAY ROUTE? 42. The length of a rectangular piece of steel in a bridge is 4 meters less than double the width. The perimeter of the piece of steel is 34 meters. Find the length and the width.
43. Each lab counts once and each test counts as two labs. At the end of the semester there is a final lab that counts as 3 regular lads. Danielle received scores 90, 94, 97 on her labs, and scores of 93 and 99 on her tests. What must she get on the final lab to receive an A is 95.
44. A designer plans the top of a rectangular workbench to be four times as long as it is wide and then determines if the width is 1500 mm greater and the length is 4500 mm less, it would be a square. What are its dimensions?
45. Each day the exchange rate between U. S. dollars and foreign currency changes. One day, 4 dollars were equivalent to approximately 3 euro. On the same day 3 euro were equivalent to approximately 168.37 Indian rupees. To the nearest rupee, how many Indian rupees are equivalent to 1 dollar?
A) 25 rupees B) 37 rupees C) 42 rupees D) rupees
Math Word Problems:
1. Two cities are 1580 miles apart. A plane leaves one of them traveling towards the other at an average speed o 400 mile per hour. At that time a plane leaves the other traveling towards the first at an average speed of 390 miles per hr. How long will it take them to meet?
Answer: 2 hours
2. How much pure acid is in 180 milliliters of a 15% solution?
Answer: 117 ml
3. A table is three times as long as it is wide. If it were 5ft shorter and 5 ft wider it would be square (with all sides equal). How long and how wide is the table?
Answer: Length 15, Width 5
4. Nico is saving money for his college education. He invests some money at 9% and 800 less than that amount @ 6%. The investments produced a total f $222 interest in 1 yr. How much did he invest at each rate?
Answer: $1800 at 9% and $1000 at 6%
5. I had $1.60 in dimes and nickels and had four more dines then nickels. How many of both would I have?
Answer: Nickels 8, Dimes 12
6. How many litters of a 60% acid solution must be mixed with a 25¬id solution to get a 315L of a 50% acid?
Answer:
7. A Dr. Wishes to mix a solution that is 7% monoxide. She has on hand 60 ml of a 6% solution ad wishes to add 9% solution to obtain the desired 7% solution she should add ___ ML
Answer:
8. When 1 is added to the difference between four time’s number and 9, the result is greater than 13 added to 3 times the number. Find all such numbers.
Answer:
9. Randy has $15,000 that he would like to invest. He has a choice of two interest paying bonds, one offering a 4% annual interest and the other paying 8% annual interest. He would like to earn $760 in interest in one year using both types of bonds that he can put towards his vacation. How much money should he invest in each bond?
Answer: $11000 at 4% and $4000 at 8%
10. An elementary school teacher wishes to use 17 feet of scalloped border to enclose a rectangular region on her bulletin board. What is the maximum area that she can enclose with the border?
Answer:
11. The expression 10,000 – 1,000t can be used to calculate the tax value in dollars of a farm tractor that is t years old. How old will the tractor be when its tax value reaches zero?
(a) 12 yr old, (b) 11 yr old, (c) 10 yr old, (d) 13 yr old
Answer: (c) 10 years
12. The total cost of a video game was $42.39. This included 6% sales tax. Find the price without sales tax.
Answer: $ 39.99 (Approx)
13. Clear-water High School expects a 41% increase in enrollment next year. There are 1850 students enrolled this year. How many students will the school gain? What is the expected enrollment next year?
Answer: School gain 1632 students and expected enrollment next year = 2109
14. A fair die is tossed once. Which event is more likely, "the number showing is divisible by three" or "the number showing is even"?
Answer: 6
15. An electric clock was stopped by a power failure. What is the probability that the minute hand stopped between the following two numerals on the face of the clock? a) 12 and 3 b) 1 and 5 c) 11 and 1
Answer: (a) P(12 and 3) = 1/4, (b) P(1 and 5) = 1/3, (c) P(11 and 1) = 1/6
16. Amy the chicken is tied to one corner of a rectangular barn with a 12 foot rope. If the width of the barn is 8 ft and the length is 2 yards, find the area outside the barn in which Amy can travel. Leave pi (Π) in the answer.
Answer:
17. A swimming pool has to be drained for maintenance. The pool is shaped like a cylinder with a diameter of 10m and a depth of 2.2 m . If the water is pumped out of the pool at the rate of 17 m^3 per hour, how many hours does it take to empty the pool? Use the value 3.14 for , and round your answer to the nearest hour.
Answer:
18. The height of a triangle is 4 feet more than 3 times the base. If the area is 32 ft2, find the base and height of the triangle.
Answer: Base = 4 feet, Height = 16 feet.
19. In general, the y-intercept of the function F(x) = a*b^x is the point _____.
Answer: (0, a)
20. The domain of F(x)=(2/3)^x is all negative numbers.
A. True B. False
Answer: B. False
21. For all values of a and b that make F(x) = a * b^x a valid exponential function, the graph always has a horizontal asymptote at y = 0.
A. True B. False
Answer: A. True
22. The range of F(x) = 5 * 2^x is all positive real numbers.
A. True B. False
Answer: A. True
23. The range of the function given below is the set of all positive real numbers greater than 6.
F(x) = 6 + 2^x
A. True B. False
Answer: A. True
24. Graduate students were asked to participate in an evaluation of beers. Each student was given three glasses in a random order. Glasses 1 and 2 both had the same inexpensive local beer, while Glass 3 contained a more expensive imported beer. Students were told that the beer in glass 1 was expensive, but that the beer in glass 2 was not. They were not told anything about glass 3. Students were asked to rate the beers from 1 to 20 with higher ratings indicating better taste. 8 students responses were randomly selected and are presented below. What is your question? Analyze the data to answer the question.
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(a) Provide support for a particular approach by exploring whether assumptions underlying parametric/nonparametric/et., assumptions are met.
(b) Surface ideas with techniques (e.g. scatter plot, outliers, etc.) used to analyze the data.3. Define the question and hypotheses ( which of course you will then test).
(c) Identify the key ideas, variables, or issues that frame the research problem
25. A rectangles perimeter is 16 units and its area is 11 square units. please find its exact dimensions.
Answer: Length = 4 + √5 units, Width = 4 - √5 units
26. Astronauts who waked on the moon felt as if they weighed about one sixth of their weight on earth. this is because the weight of an object is determined by the gravitational attraction between the object and the planet (or moon) its on. you can use the following formula to estimate the weight of an object on the surface of any of the planets: gravitational force=GmM/r^2, where G=universal gravitational constant,m=mass of the object, M=mass of the planet, and r=radius of the planet. For a given object, Grandma remain constant, so the force of gravity depends only on the variables named r.
Answer:
27. A store is having a sale on liquid soap and sponges the cost of 6 bottles of soap is 9.12 the coast of 4 sponges is 5.00 what is the total cost of buying 2 bottles of liquid soap and 3 sponges.
Answer:
28. A line contains the points(a, b) and ( a+3, b+3). Find the slope of the line.
Answer: Slope = 1
29. Put the following list of real numbers in order from LEAST to GREATEST. Make sure you show all the steps you took to get to your final answer. -√64 ,-7/2, 3.3, √10, 27/3
Answer: -√64, -3.5, √10, 3.3, 27/3
30. Johnathon and Talia simplified the following expression on their Algebra 1 midterm: 7 - 2(x - 5).
Johnathon's work
7 - 2(x - 5) = 7 - 2(x) - 2(-5) = 7 - 2x + 10 = - 2x + 17 |
Talia's work
7 - 2(x - 5) = 7 - 2(x) - 2(5) = 7 - 2x - 10 = - 2x - 3 |
31. What is the sales tax and total price of an item that is $45.69 if the sales tax is 7.5 %?
a. sales tax = $3.00; total price = $50.00
b. sales tax = $3.40; total price = $49.09
c. sales tax = $3.43; total price = $49.12
d. sales tax = $3.42; total price = $49.11
Answer: c. sales tax = $3.43; total price = $49.12
32. Kate earns a weekly allowance of $12. How much money will she earn in 8 weeks? Do not enter $.____ dollars
Answer: $ 96
33. A table is shaped like a square and has an area of 100 square feet. Find the length of one side of the table.____ feet
Answer: 10 feet.
34. Juan bought n video games. Write an expression to show the total cost of the games if each game cost $16. Do not enter $ in your answer.
Answer: Total cost f(n) = 16n
35. A sandpit in the shape of a pentagon ABCDE is to be built in such a way that each of its sides are of equal length, but its angles are not all equal. The pentagon is symmetrical about DX, where X is the midpoint of AB. The angle AXE and BXC are both 45 degrees and each side is 2m long.
(b) Find the length of EX.
(c) How much sand is required if the sandpit is 30 cm deep?
Give your answer to three decimal place.
36. An aircraft takes off from an airstrip and then flies for 16.2 km on a bearing of 066 degrees true. The pilot then makes a let turn of 88 degrees and flies for a further 39.51 km on this course before deciding to return to the airstrip. (a) Through what angle must the pilot turn to return to the airstrip? (b) How far will the pilot have to fly to return to the airstrip?
37. Gracie decided to rent a limo for her wedding. The Bedazzled Limo Com- pany charges a $50 gas fee, $56.48 per hour to rent the limo and requires a tip of 20% on the total price of the rental (so 20% of the total cost of the rental). The Wedding Bell Limo Company charges $68.36 per hour and requires a 25% tip to the driver. For how long of a rental will the hourly cost be the same? (Round to the nearest half hour).
Answers for the different types of math word problems are given below to check the exact answers of the above math questions.
| questions by www.maths-only-maths.com |
