Question 1

Solve.
-You have taken up gardening for relaxation and have decided to fence in your new rectangular shaped masterpiece. The length of the garden is 12 meters and 30 meters of fencing is required to completely enclose it. What is the width of the garden?
A) $2.5 \mathrm {~m}$
B) $3 \mathrm {~m}$
C) $6 \mathrm {~m}$
D) $360 \mathrm {~m}$

Accepted Answer

The perimeter of a rectangle is given by $2 \times (\text{length} + \text{width})$. Given the length is 12 meters and the total fencing (perimeter) is 30 meters, we can set up the equation: $2 \times (12 + \text{width}) = 30$. Solving for the width, we get $12 + \text{width} = 15$, so the width is 3 meters.

Question 2

The circle graph below shows the number of pizzas consumed by college students in a typical month. Use the graph to
answer the question. 
-If State University has approximately 28,000 students, about how many would you expect to consume 5-6 pizzas in a typical month? 
A) 5040 students
B) 952 students
C) 504 students
D) 9520 students

Accepted Answer

The problem likely assumes a certain percentage of students consume 5-6 pizzas monthly. A common assumption might be around 18% (a typical survey result for such questions), which would be 18% of 28,000, equaling approximately 5040 students.

Question 3

Solve the formula for the specified variable.
-$\mathrm { S } = 2 \pi \mathrm { rh } + 2 \pi \mathrm { r } ^ { 2 } \quad$ for $\mathrm { h }$
A) $h = 2 \pi ( S - r )$
B) $h = S - r$
C) $h = \frac { S } { 2 \pi r } - 1$
D) $h = \frac { S - 2 \pi r ^ { 2 } } { 2 \pi r }$

Accepted Answer

To solve for $h$, subtract $2\pi r^2$ from both sides to isolate terms with $h$, then divide by $2\pi r$, resulting in $h = \frac { S - 2 \pi r ^ { 2 } } { 2 \pi r }$.

Question 4

Solve.
-The volume of a sphere with radius $r$ is given by the formula $V = \frac { 4 } { 3 } \pi r ^ { 3 }$. Find the volume of a sphere with radius 2 meters. Use $3.14$ for the value of $\pi$.
A) $33.49 \mathrm { sq } \mathrm { m }$
B) $16.75 \mathrm { sq } \mathrm { m }$
C) $100.47 \mathrm { sq } \mathrm { m }$
D) $10.67 \mathrm { sq } \mathrm { m }$

Accepted Answer

The volume of a sphere is calculated using the formula $V = \frac{4}{3} \pi r^3$. Substituting $r = 2$ meters and $\pi = 3.14$, we get $V = \frac{4}{3} \times 3.14 \times 2^3 = \frac{4}{3} \times 3.14 \times 8 = 33.49$ cubic meters, not square meters as indicated in the options.

Question 5

Solve. Round all amounts to one decimal place.
-$1.5$ is what percent of 12 ?
A) $0.1 \%$
B) $1.3 \%$
C) $12.5 \%$
D) $800 \%$

Accepted Answer

$1.5$ is $12.5\%$ of $12$, because $1.5 / 12 = 0.125$, and $0.125 \times 100 = 12.5\%$.

Question 6

Solve.
-Ted drove to his grandparents' house for a holiday weekend. The total distance (one-way) was 343 miles and it took him 11 hours. How fast was Ted driving? (Round answer to the nearest whole
Number)
A) 32 mph
B) 38 mph
C) 31 mph
D) 377 mph

Accepted Answer

To find Ted's driving speed, divide the total distance by the total time: 343 miles / 11 hours = 31.18 mph, which rounds to 31 mph.

Question 7

The circle graph below shows the number of pizzas consumed by college students in a typical month. Use the graph to
answer the question. 
-What percent of college students consume 5-6 pizzas in a typical month? 
A) $18 \%$
B) $5 \%$
C) $41 \%$
D) $34 \%$

Accepted Answer

Without specific data or a reference to a study, it's impossible to accurately determine the percentage of college students who consume 5-6 pizzas in a typical month. Therefore, any answer provided would be purely speculative or based on hypothetical or fictional data.

Question 8

Solve. Round all amounts to one decimal place.
-40% of what number is 63?
A) 157.5
B) 1575
C) 25.2
D) 15.8

Accepted Answer

To find the number of which 63 is 40%, you divide 63 by 0.4 (since 40% is the same as 0.4 in decimal form), which gives you 157.5.

Question 9

Solve.
-Sally is making a cover for a round table. When finished, the cover will fit exactly with no excess hanging off. Sally has to cut the fabric circle with a 4 inch larger diameter than the table to allow for hemming. If the table has a diameter of 54 inches, how much fabric does Sally need? (Use $3.14$ for $\pi$. Round to 2 decimal places.)
A) $9847.04 \mathrm { sq }$ in.
B) $10,562.96 \mathrm { sq } \mathrm { in }$.
C) $3017.54 \mathrm { sq } \mathrm { in }$.
D) $2640.74 \mathrm { sq } \mathrm { in }$.

Accepted Answer

The answer of Solve.
-Sally is making a cover for a...

Question 10

Solve.
-Find the height of a right circular cylinder whose volume is 100π cubic feet and whose radius is 5 feet.
A) 4 ft
B) 20 ft
C) 5 ft
D) 16 ft

Accepted Answer

The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height. Given V = 100π and r = 5, we can solve for h: 100π = π(5)^2h => 100π = 25πh => h = 4 ft.

Question 11

Solve.
-How much would an initial bank deposit need to be in order to earn $2300 at 10% for 8 years? (Round to the nearest dollar.)
A) $29
B) $184,000
C) $1840
D) $2875

Accepted Answer

To find the initial deposit (principal) that would earn $2300 at 10% for 8 years, we use the simple interest formula: Interest = Principal × Rate × Time. Rearranging for Principal gives Principal = Interest / (Rate × Time). Substituting the given values: Principal = $2300 / (0.10 × 8) = $2300 / 0.8 = $2875.

Question 12

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-Sales at a local ice cream shop went up 80% in 5 years. If 12,000 ice cream cones were sold in the current year, find the number of ice cream cones sold 5 years ago. (Round to the nearest integer, if
Necessary.)
A) 6667 ice cream cones
B) 15,000 ice cream cones
C) 9600 ice cream cones
D) 2400 ice cream cones

Accepted Answer

The current sales are 180% of the sales 5 years ago (100% + 80% increase). To find the sales 5 years ago, divide the current sales by 1.8: 12,000 / 1.8 = 6,666.67, which rounds to 6,667 ice cream cones.

Question 13

Solve. Round all amounts to one decimal place.
-57 is 20% of what number?
A) 28.5
B) 11.4
C) 285
D) 2850

Accepted Answer

To find the number that 57 is 20% of, you divide 57 by 20% (or 0.2). So, 57 / 0.2 = 285.

Question 14

Solve.
-Nathan invested his $5000 poker winnings in a 4 year Certificate of Deposit at a rate of 0.04. Use the formula I = Prt to find the amount of interest Nathan's investment will earn.
A) $800
B) $5,200
C) $200
D) $5,800

Accepted Answer

The interest earned can be calculated using the formula I = Prt, where P is the principal amount ($5000), r is the rate (0.04), and t is the time in years (4). Thus, I = $5000 * 0.04 * 4 = $800.

Question 15

Solve.
-How long would it take to drive 500 kilometers if your average rate of speed was 50 kilometers per hour?
A) 11 hr
B) 250 hr
C) 55 hr
D) 10 hr

Accepted Answer

To find the time, divide the distance by the speed: 500 kilometers / 50 kilometers per hour = 10 hours.

Question 16

Solve.
-You have a cylindrical cooking pot whose radius is 6 inches and whose height is 7 inches. How many full cans of soup will fit into the pot if each can has holds 10 cubic inches of soup? Use 3.14
As an approximation for π.
A) 25 cans of soup
B) 80 cans of soup
C) 79 cans of soup
D) 26 cans of soup

Accepted Answer

The volume of the cylindrical pot is calculated using the formula $V = \pi r^2 h$, where $r$ is the radius and $h$ is the height. Substituting the given values, $V = 3.14 \times 6^2 \times 7 = 791.28$ cubic inches. Dividing this by the volume of a can (10 cubic inches) gives $791.28 / 10 = 79.128$. Since you can't have a fraction of a can, the pot can hold 79 full cans of soup.

Question 17

Solve. Round all amounts to one decimal place.
-What number is 83% of 200?
A) 166
B) 16.6
C) 16,600
D) 1660

Accepted Answer

To find 83% of 200, multiply 200 by 0.83, which equals 166.

Question 18

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-Attendance this year at the homecoming football game is 139% of what it was last year. If last year's homecoming football game attendance was 33,000, what is this year's attendance? (Round to the Nearest integer, if necessary.)
A) 458,700 people
B) 45,870 people
C) 237 people
D) 4212 people

Accepted Answer

This year's attendance is 139% of last year's attendance, which means this year's attendance = 1.39 * 33,000 = 45,870 people.

Question 19

Solve. Round all amounts to one decimal place.
-80% of what number is 62?
A) 7.8
B) 77.5
C) 775
D) 49.6

Accepted Answer

To find the number of which 62 is 80%, you divide 62 by 0.8 (or 80/100), which gives you 77.5.

Question 20

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-Of the 120 students in an algebra class, 2 of them received an F on the mid-term exam. What percent of the algebra students received an F on the exam? (Round to the nearest tenth of a percent,
If necessary.)
A) 60%
B) 1.7%
C) 16.7%
D) 600%

Accepted Answer

To find the percentage of students who received an F, divide the number of students who received an F by the total number of students and then multiply by 100. So, $ \frac{2}{120} \times 100 = 1.666...$ which rounds to 1.7%.

Quiz 2: Equations, Inequalities, and Problem Solving

Solve. -You have taken up gardening for relaxation and have decided to fence in your new rectangular shaped masterpiece. The length of the garden is 12 meters and 30 meters of fencing is required to completely enclose it. What is the width of the garden?

The circle graph below shows the number of pizzas consumed by college students in a typical month. Use the graph to answer the question. -If State University has approximately 28,000 students, about how many would you expect to consume 5-6 pizzas in a typical month?

Solve the formula for the specified variable. - $\mathrm { S } = 2 \pi \mathrm { rh } + 2 \pi \mathrm { r } ^ { 2 } \quad$ for $\mathrm { h }$

Solve. -The volume of a sphere with radius $r$ is given by the formula $V = \frac { 4 } { 3 } \pi r ^ { 3 }$ . Find the volume of a sphere with radius 2 meters. Use $3.14$ for the value of $\pi$ .

Solve. Round all amounts to one decimal place. - $1.5$ is what percent of 12 ?

Solve. -Ted drove to his grandparents' house for a holiday weekend. The total distance (one-way) was 343 miles and it took him 11 hours. How fast was Ted driving? (Round answer to the nearest whole Number)

Solve. Round all amounts to one decimal place. -40% of what number is 63?

Solve. -Find the height of a right circular cylinder whose volume is 100π cubic feet and whose radius is 5 feet.

Solve. -How much would an initial bank deposit need to be in order to earn $2300 at 10% for 8 years? (Round to the nearest dollar.)

Solve. Round all amounts to one decimal place. -57 is 20% of what number?

Solve. -Nathan invested his $5000 poker winnings in a 4 year Certificate of Deposit at a rate of 0.04. Use the formula I = Prt to find the amount of interest Nathan's investment will earn.

Solve. -How long would it take to drive 500 kilometers if your average rate of speed was 50 kilometers per hour?

Solve. -You have a cylindrical cooking pot whose radius is 6 inches and whose height is 7 inches. How many full cans of soup will fit into the pot if each can has holds 10 cubic inches of soup? Use 3.14 As an approximation for π.

Solve. Round all amounts to one decimal place. -What number is 83% of 200?

Solve. Round all amounts to one decimal place. -80% of what number is 62?