Basic Math Questions and Answers

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines.
y = x, y = 0, X = 6
(a) the x-axis
(b) the y-axis
(c) the line x = 6
(d) the line x = = 9
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Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = x, y = 0, X = 6 (a) the x-axis (b) the y-axis (c) the line x = 6 (d) the line x = = 9
A city's population in the year x = 1959 was y = 1,775,650. In 1953 the population was 1,774,750.
Compute the slope of the population growth (or decline) and choose the most accurate statement from the following:
The population is increasing at a rate of 150 people per year.
The population is increasing at a rate of 50 people per year.
The population is decreasing at a rate of 250 people per year.
The population is decreasing at a rate of 150 people per year.
The population is decreasing at a rate of 50 people per year.
The population is increasing at a rate of 250 people per year.
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A city's population in the year x = 1959 was y = 1,775,650. In 1953 the population was 1,774,750. Compute the slope of the population growth (or decline) and choose the most accurate statement from the following: The population is increasing at a rate of 150 people per year. The population is increasing at a rate of 50 people per year. The population is decreasing at a rate of 250 people per year. The population is decreasing at a rate of 150 people per year. The population is decreasing at a rate of 50 people per year. The population is increasing at a rate of 250 people per year.
Convert the measurement
2710 g=
kg
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Convert the measurement 2710 g= kg
Suppose the number of prisoners held in a certain type of prison, measured in thousands, can be described by the quadratic equation P = -1.94x²+76.35x+737. The variable x represents the number of years since 1990. According to the equation, how many prisoners were there in the year 2001 (x = 11) and 2006 (x = 16)?
There were approximately     thousand prisoners in 2001.
(Simplify your answer. Round to two decimal places as needed.)
There were approximately thousand prisoners in 2006.
(Simplify your answer. Round to two decimal places as needed.)
*****
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Suppose the number of prisoners held in a certain type of prison, measured in thousands, can be described by the quadratic equation P = -1.94x²+76.35x+737. The variable x represents the number of years since 1990. According to the equation, how many prisoners were there in the year 2001 (x = 11) and 2006 (x = 16)? There were approximately thousand prisoners in 2001. (Simplify your answer. Round to two decimal places as needed.) There were approximately thousand prisoners in 2006. (Simplify your answer. Round to two decimal places as needed.) *****
Convert the measurement.
3 yd =
inches
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Convert the measurement. 3 yd = inches
The projected worldwide spending for a certain type of service, in millions of dollars, for the years 2006-2011 can be estimated by the polynomial s= -35.4x² +924.6x +493, where x is the number of years after 2006. Find the projected worldwide spending for x=0, x=2, and x = 5. 
Use the polynomial to estimate the projected worldwide spending for this service, in millions of dollars, for the year 2006 (x = 0). 
$million (Type an integer or a decimal.)
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The projected worldwide spending for a certain type of service, in millions of dollars, for the years 2006-2011 can be estimated by the polynomial s= -35.4x² +924.6x +493, where x is the number of years after 2006. Find the projected worldwide spending for x=0, x=2, and x = 5. Use the polynomial to estimate the projected worldwide spending for this service, in millions of dollars, for the year 2006 (x = 0). $million (Type an integer or a decimal.)
Graph the following quadratic function.
f(x) = 2x² + 4x + 5
Find the vertex of the function.
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Graph the following quadratic function. f(x) = 2x² + 4x + 5 Find the vertex of the function.
Leo invested $1900 in an account with annually compounded interest. After 3 years, he had $2275 in the account. What was the interest rate of the account? Round your answer to one decimal place. Do not write the percent sign. Provide your answer below:
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Leo invested $1900 in an account with annually compounded interest. After 3 years, he had $2275 in the account. What was the interest rate of the account? Round your answer to one decimal place. Do not write the percent sign. Provide your answer below:
Determine whether the ordered pair is a solution to the inequality.
y≥(x-1)²
(a) (-4, 31)
(b) (3, 0)
(c) (-3,-15)
(a) Is the ordered pair (-4, 31) a solution to the inequality?
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Determine whether the ordered pair is a solution to the inequality. y≥(x-1)² (a) (-4, 31) (b) (3, 0) (c) (-3,-15) (a) Is the ordered pair (-4, 31) a solution to the inequality?
Darryl made a deposit into an account that earns 7% annual compound interest. After 36 months, the value of his account was $1,041.29. What was the approximate amount of Darryl's initial deposit?
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Darryl made a deposit into an account that earns 7% annual compound interest. After 36 months, the value of his account was $1,041.29. What was the approximate amount of Darryl's initial deposit?
Hunter makes shoelaces for the cleats to earn money for the football team. Each shoelace needs to measure 50 3/4 inches long. He needs to make 4 shoelaces. How many inches does he need to make the 4 shoelaces?
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Hunter makes shoelaces for the cleats to earn money for the football team. Each shoelace needs to measure 50 3/4 inches long. He needs to make 4 shoelaces. How many inches does he need to make the 4 shoelaces?
The position function of a particle is given by
s = 2t³ - 15t²-81t, t> 0.
where s is measured in meters and t in seconds.
Find all values of t> 0 for which the particle is moving at a velocity of 3 m/s
t=
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The position function of a particle is given by s = 2t³ - 15t²-81t, t> 0. where s is measured in meters and t in seconds. Find all values of t> 0 for which the particle is moving at a velocity of 3 m/s t=
A pumpkin is launched 19.6 meters per second from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is s (t)=-4.92t2 +19.6t+58.8, where s is in meters. When does the pumpkin strike the ground?
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A pumpkin is launched 19.6 meters per second from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is s (t)=-4.92t2 +19.6t+58.8, where s is in meters. When does the pumpkin strike the ground?
The ages of 10 grooms at their first marriage are listed below. Find the midquartile.
35.1 24.3 46.6 41.6 32.9 26.8 39.8 21.5 45.7 33.9
34.2
43.7
34.1
34.5
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The ages of 10 grooms at their first marriage are listed below. Find the midquartile. 35.1 24.3 46.6 41.6 32.9 26.8 39.8 21.5 45.7 33.9 34.2 43.7 34.1 34.5
x+2y-2z = 10
-3x+4y+z=-5
-5x+y+3z=-21
Find the unique solution to this system of equations. Give your answer as a point.
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x+2y-2z = 10 -3x+4y+z=-5 -5x+y+3z=-21 Find the unique solution to this system of equations. Give your answer as a point.
Josie and Red are two dogs standing next to each other at the dog park. Josie starts running straight west and Red starts running straight east. After 22 seconds, the two dogs are 1,100 feet apart. Suppose Red runs 4 feet per second faster than Josie. How fast were each of the dogs running?
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Josie and Red are two dogs standing next to each other at the dog park. Josie starts running straight west and Red starts running straight east. After 22 seconds, the two dogs are 1,100 feet apart. Suppose Red runs 4 feet per second faster than Josie. How fast were each of the dogs running?
A gardener has 880 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. shorter side: 
 What dimensions would guarantee that the garden has the greatest possible area? ft (feet) longer side:
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A gardener has 880 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. shorter side: What dimensions would guarantee that the garden has the greatest possible area? ft (feet) longer side:
Find the x-intercept(s) algebraically.
f(x)=2x²-9x+9
X=
(Type an exact answer, using radicals needed. Use integers or fractions for any numbers in the expression. Type each solution only once. Use a comma to separate
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Find the x-intercept(s) algebraically. f(x)=2x²-9x+9 X= (Type an exact answer, using radicals needed. Use integers or fractions for any numbers in the expression. Type each solution only once. Use a comma to separate
Solve the system by elimination or by any convenient method. (If the system is dependent, enter DEPENDENT. If there is no solution, enter NO SOLUTION.)
x + 2y = 3
3x+6y= 12
(x, y) =
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Solve the system by elimination or by any convenient method. (If the system is dependent, enter DEPENDENT. If there is no solution, enter NO SOLUTION.) x + 2y = 3 3x+6y= 12 (x, y) =
If a car travels 37 miles per gallon of fuel (in other words, the car does 37 mpg), how many kilometers does it travel per liter of fuel? Use the conversion factors on page 55 (that is, use 1 mile 8/5 km and 1 gallon = 8 pints and 1 liter ≈ 2 pints). The car trav's about km on one liter of fuel
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If a car travels 37 miles per gallon of fuel (in other words, the car does 37 mpg), how many kilometers does it travel per liter of fuel? Use the conversion factors on page 55 (that is, use 1 mile 8/5 km and 1 gallon = 8 pints and 1 liter ≈ 2 pints). The car trav's about km on one liter of fuel
Suppose you wish to take out a loan for $15,000 at an annual interest rate of 5.25%, compounded monthly. If you want each payment to be as close as possible to $200.00, how long should the period of the loan be?
Choose the correct answer below.
10 years
9 years
8 years
7 years
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Suppose you wish to take out a loan for $15,000 at an annual interest rate of 5.25%, compounded monthly. If you want each payment to be as close as possible to $200.00, how long should the period of the loan be? Choose the correct answer below. 10 years 9 years 8 years 7 years
Tomas needs exactly 6 potatoes to make 12 potato pancakes.
Which of the following statements are true?
Tomas needs exactly 12 potatoes to make 24 potato pancakes.
Tomas needs exactly 18 potatoes to make 36 potato pancakes.
Tomas needs exactly 24 potatoes to make 44 potato pancakes.
Tomas needs exactly 30 potatoes to make 60 potato pancakes.
Tomas needs exactly 36 potatoes to make 78 potato pancakes.
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Tomas needs exactly 6 potatoes to make 12 potato pancakes. Which of the following statements are true? Tomas needs exactly 12 potatoes to make 24 potato pancakes. Tomas needs exactly 18 potatoes to make 36 potato pancakes. Tomas needs exactly 24 potatoes to make 44 potato pancakes. Tomas needs exactly 30 potatoes to make 60 potato pancakes. Tomas needs exactly 36 potatoes to make 78 potato pancakes.
Fourteen of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item is defective?
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Fourteen of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item is defective?
In ΔCDE, M∠C = (x − 4)°, m∠D = (11x – 11)°, and m∠E = (x + 13)°.
Find m∠C.
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In ΔCDE, M∠C = (x − 4)°, m∠D = (11x – 11)°, and m∠E = (x + 13)°. Find m∠C.
Find the LCM of the set of algebraic expressions.
20y², 12yz, 15z
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Find the LCM of the set of algebraic expressions. 20y², 12yz, 15z
The owner of Kensington Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 15 small arrangements and 15 large arrangements, which took her a total of 195 minutes. After lunch, she arranged 12 small arrangements and 7 large arrangements, which took 121 minutes. How long does it take to assemble each type?
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The owner of Kensington Florist is assembling flower arrangements for Valentine's Day. This morning, she assembled 15 small arrangements and 15 large arrangements, which took her a total of 195 minutes. After lunch, she arranged 12 small arrangements and 7 large arrangements, which took 121 minutes. How long does it take to assemble each type?
The function g is defined as follows.
g(x)=4x²+3
If the graph of g is translated vertically downward by 8 units, it becomes the graph of a function f.
Find the expression for f(x).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
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The function g is defined as follows. g(x)=4x²+3 If the graph of g is translated vertically downward by 8 units, it becomes the graph of a function f. Find the expression for f(x). Note that the ALEKS graphing calculator may be helpful in checking your answer.
Four joules of work is required to stretch a spring 0.5 meter from its natural length. Find the work required to stretch the spring an additional 0.40 meter.
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Four joules of work is required to stretch a spring 0.5 meter from its natural length. Find the work required to stretch the spring an additional 0.40 meter.
Standard form:
Expanded form: 9 * 1,000,000 + 8 * 1,000 + 7 * 100 + 6 * 10
Word form:
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Standard form: Expanded form: 9 * 1,000,000 + 8 * 1,000 + 7 * 100 + 6 * 10 Word form:
Robert can complete 10 inspections in 8 hours. Which represents the unit rate for the number of inspections he completes per hour?
 0.8 of an inspection in 1 hour
4 inspections in 5 hours
 1.25 inspections in 1 hour
 5 inspections in 4 hours
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Robert can complete 10 inspections in 8 hours. Which represents the unit rate for the number of inspections he completes per hour? 0.8 of an inspection in 1 hour 4 inspections in 5 hours 1.25 inspections in 1 hour 5 inspections in 4 hours
Greg deposited $4000 into an account with 4.3% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 3 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
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Greg deposited $4000 into an account with 4.3% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 3 years? Do not round any intermediate computations, and round your answer to the nearest cent.
Write the equation of the line passing through (-2,-4) that is parallel to 3x + 5y = 11.
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Write the equation of the line passing through (-2,-4) that is parallel to 3x + 5y = 11.
A projection made in January of 2005 determined that x years later, the average property tax on a three-bedroom home in a certain community will be 
T(x) = 48x 3/2 + 40x + 1300 
dollars. Estimate the percentage change by which the property tax will increase during the first half of the year 2012.
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A projection made in January of 2005 determined that x years later, the average property tax on a three-bedroom home in a certain community will be T(x) = 48x 3/2 + 40x + 1300 dollars. Estimate the percentage change by which the property tax will increase during the first half of the year 2012.
Find the zeros of the following polynomial.
f(x) = x³ + 12x4 +36x³
List the zeros separated by commas. For example, if you found that the zeros were x = 1, x = 2,
enter 1, 2, 3.
Provide your answer below:
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Find the zeros of the following polynomial. f(x) = x³ + 12x4 +36x³ List the zeros separated by commas. For example, if you found that the zeros were x = 1, x = 2, enter 1, 2, 3. Provide your answer below:
A fence is to have 3 1/2 wide boards between two posts that are 94 1/4 apart so that the space between each board is the same. Calculate the number of boards and the spacing so that the spacing between the boards is as small as possible. Round your answer for the spacing to the nearest 16th of an inch.
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A fence is to have 3 1/2 wide boards between two posts that are 94 1/4 apart so that the space between each board is the same. Calculate the number of boards and the spacing so that the spacing between the boards is as small as possible. Round your answer for the spacing to the nearest 16th of an inch.
A particle moves according to the law of motion
s = t³ - 8t2 + 3t, t ≥ 0,
where t is measured in seconds and s in feet.
(a) Find the average velocity over the interval [1,2]
(b) Find the velocity at time t.
(c) What is the velocity after 3 seconds?
(d) What is the acceleration after 7 seconds?
(e) Fort > 0, when is the particle moving in the positive direction?
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A particle moves according to the law of motion s = t³ - 8t2 + 3t, t ≥ 0, where t is measured in seconds and s in feet. (a) Find the average velocity over the interval [1,2] (b) Find the velocity at time t. (c) What is the velocity after 3 seconds? (d) What is the acceleration after 7 seconds? (e) Fort > 0, when is the particle moving in the positive direction?
After a baby was born, he began to gain weight at a rate of 1.5 pounds per month. The weight of the baby at birth was 10 pounds. Write an equation for W, in terms of t, representing weight, in pounds, of the newborn baby t months after birth.
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After a baby was born, he began to gain weight at a rate of 1.5 pounds per month. The weight of the baby at birth was 10 pounds. Write an equation for W, in terms of t, representing weight, in pounds, of the newborn baby t months after birth.
If a single pane of glass obliterates 2% of the light passing through it, the percent p of light that passes through n successive panes is given approximately by the function below.
p(n)= 100(0.98)n
(a) What percent of light will pass through 20 panes?
(b) What percent of light will pass through 30 panes?
(c) Explain the meaning of the base 0.98 in this problem.
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If a single pane of glass obliterates 2% of the light passing through it, the percent p of light that passes through n successive panes is given approximately by the function below. p(n)= 100(0.98)n (a) What percent of light will pass through 20 panes? (b) What percent of light will pass through 30 panes? (c) Explain the meaning of the base 0.98 in this problem.
A gray crayon is made with 5 mL of black wax for every 6 mL of white wax.
Which of the following wax mixtures will create the same shade of gray?
Choose 2 answers:
10 mL of black wax mixed with 24 mL of white wax
15 mL of black wax mixed with 18 mL of white wax
35 mL of black wax mixed with 42 mL of white wax
20 mL of black wax mixed with 26 mL of white wax
45 mL of black wax mixed with 48 mL of white wax
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A gray crayon is made with 5 mL of black wax for every 6 mL of white wax. Which of the following wax mixtures will create the same shade of gray? Choose 2 answers: 10 mL of black wax mixed with 24 mL of white wax 15 mL of black wax mixed with 18 mL of white wax 35 mL of black wax mixed with 42 mL of white wax 20 mL of black wax mixed with 26 mL of white wax 45 mL of black wax mixed with 48 mL of white wax
Sketch the graph of a function f that satisfies all of the following properties. Indicate all asymptotes.
(a) f(x) is defined for all real numbers except x = 1.
(b) f(x) is discontinuous at x = -2 and x = 1, but is continuous for all other z.
(c) f(x) is not differentiable at x = -2, x = 1, and x = 4 but it is differentiable for all other .
(d) lim f(x) = 3,
(e) lim f(x) = -2,
(f) lim f(x) = -0.
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Sketch the graph of a function f that satisfies all of the following properties. Indicate all asymptotes. (a) f(x) is defined for all real numbers except x = 1. (b) f(x) is discontinuous at x = -2 and x = 1, but is continuous for all other z. (c) f(x) is not differentiable at x = -2, x = 1, and x = 4 but it is differentiable for all other . (d) lim f(x) = 3, (e) lim f(x) = -2, (f) lim f(x) = -0.
A rectangular parking lot has a length that is 6 yards greater than the width. The area of the parking lot is 160 square yards. Find the length and the width The parking lot has a width of The parking lot has a length of yards. yards.
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A rectangular parking lot has a length that is 6 yards greater than the width. The area of the parking lot is 160 square yards. Find the length and the width The parking lot has a width of The parking lot has a length of yards. yards.
A lunar module weighs 12 tons on the surface of the Earth. How much work is done in propelling the module from the surface of the moon to a height of 55 miles? Consider the radius of the moon to be 1100 miles (from the center of the moon) and its force of gravity to be one-sixth that of Earth.
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A lunar module weighs 12 tons on the surface of the Earth. How much work is done in propelling the module from the surface of the moon to a height of 55 miles? Consider the radius of the moon to be 1100 miles (from the center of the moon) and its force of gravity to be one-sixth that of Earth.
Henry made a shirt using 1/3 yards of red fabric and 3/4 yards of blue fabric. How many more yards of blue fabric did Henry use?
Write your answer as a fraction in simplest form.
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Henry made a shirt using 1/3 yards of red fabric and 3/4 yards of blue fabric. How many more yards of blue fabric did Henry use? Write your answer as a fraction in simplest form.
{(-9, 3), (5, -6), (3, -9), (-6, 5), ?}
Which ordered pair can replace the missing value and create a function?
(5,3)
 (9,3)
 (-6,-9)
 (-9,-6)
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{(-9, 3), (5, -6), (3, -9), (-6, 5), ?} Which ordered pair can replace the missing value and create a function? (5,3) (9,3) (-6,-9) (-9,-6)
Graph the following quadratic function.
f(x)=x²-9
Find the vertex of the function.
The vertex is
(Simplify your answer. Type an ordered pair.)
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Graph the following quadratic function. f(x)=x²-9 Find the vertex of the function. The vertex is (Simplify your answer. Type an ordered pair.)
The local bakery requires that Josh must spend at least $7 to be able to pay using a credit card. Cookies cost $2.10 each. A bottle of water costs $1.10. If c represents the number of cookies Josh would need to buy to pay for one bottle of water and the A cookies using a credit card, which of the following inequalities best models the situation described above?
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The local bakery requires that Josh must spend at least $7 to be able to pay using a credit card. Cookies cost $2.10 each. A bottle of water costs $1.10. If c represents the number of cookies Josh would need to buy to pay for one bottle of water and the A cookies using a credit card, which of the following inequalities best models the situation described above?
A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of
30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number
of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in
this case). After filling the gas tank, the driver got on a highway and drove for a while.
a. How many miles has the car traveled if it has the following amounts of gas left
in the tank?
i. 15 gallons
ii. 10 gallons
iii. 2.5 gallons
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A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while. a. How many miles has the car traveled if it has the following amounts of gas left in the tank? i. 15 gallons ii. 10 gallons iii. 2.5 gallons
Lottery Prizes A lottery offers one $800 prize, two $500 prizes, two $400 prizes, and five $200 prizes. One thousand tickets are sold at $7 each. Find the expectation if a person buys two tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.
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Lottery Prizes A lottery offers one $800 prize, two $500 prizes, two $400 prizes, and five $200 prizes. One thousand tickets are sold at $7 each. Find the expectation if a person buys two tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.
Find the real solutions of the following equation.
x4-17x² +16=0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is
(Use a comma to separate answers as needed.)
B. There are no real solutions.
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Find the real solutions of the following equation. x4-17x² +16=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Use a comma to separate answers as needed.) B. There are no real solutions.
Multiple Choice Which is not a possible classification of the zeros of
f(x) = x4 + 2x³-7x² - 7x + 3 according to Descartes' rule of signs?
A. 2 positive real zeros, 2 negative real zeros, and 0 imaginary zeros
B. 0 positive real zeros, 2 negative real zeros, and 2 imaginary zeros
C. 0 positive real zeros, 0 negative real zeros, and 4 imaginary zeros
D. 1 positive real zero, 1 negative real zero, and 2 imaginary zeros
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Multiple Choice Which is not a possible classification of the zeros of f(x) = x4 + 2x³-7x² - 7x + 3 according to Descartes' rule of signs? A. 2 positive real zeros, 2 negative real zeros, and 0 imaginary zeros B. 0 positive real zeros, 2 negative real zeros, and 2 imaginary zeros C. 0 positive real zeros, 0 negative real zeros, and 4 imaginary zeros D. 1 positive real zero, 1 negative real zero, and 2 imaginary zeros