Answer C): 1,018

The pool is in the shape of a cylinder, so we can use the formula for the volume of a cylinder:
V = πr2h

Given that the diameter is 18 feet, the radius (half of the diameter) is 18/2 = $9$ feet. The height of the pool is 4.5 feet.

First, convert 6 inches to feet: 6/12 $=0.5$ feet

Now, the effective height of the water in the pool is $=4$

Substitute these values into the volume formula:
V = π × (9)² × 4

Calculate the volume:

V = 81π × 4
V ≈ 324π

Now, use the approximate value of $\pi$ as 3.14 to get:

V ≈ 324 × 3.14
V ≈ 1,018.16

So, the volume of water in the pool is approximately 1,018 cubic feet.

Therefore the correct answer is: C. 1,018.

Answer D) y = −0.054(44) + 44.54

Explanation: The equation given is y = −0.054x + 44.54y where x represents the number of years after 1976 and y is the winning time in seconds. To predict the winning time in the year 2020, we substitute
x = 2020 − 1976 = 44 into the equation. So, the correct equation for predicting the winning time in 2020 is y = −0.054(44) + 44.54, which corresponds to option D.

Therefore the correct answer is D. y = −0.054(44) + 44.54

Answer C): It is the only point that satisfies both equations simultaneously

Answer C) The transformation cannot be done because figure L is not congruent to figure M.

Answer C) 16⁄7

To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is
V = πr²h where r is the radius and ℎ is the height. The diameter is twice the radius (d = 2r), so the radius is r = 14/2 = 7 centimeters.

The volume is given as $112\pi$, so we can set up the equation:

112π = π . 7² . h

Now, we can solve for ℎ:

h = 112π/π.7² = 112/49 = 16/7

Therefore correct answer is option C, 16⁄7.

Answer A) Function 1 has the greater rate of change and the greater y-intercept.

Answer C) prism

Answer B) B

Answer A):  It is the only solution to the system

To check if the ordered pair (−6,8) is a solution to the system of equations, we can substitute these values for $x$ and $y$ into both equations and see if the equations are true.

Given system:

5x + 3y = −6
2x + y = $-4$

Substitute (−6,8) into the first equation:
5(−6) + 3(8) = −30 + 24 = −6

So, the ordered pair satisfies the first equation.

Now, substitute (−6,8) into the second equation:

2(−6) + 8 = −12 + 8 = −4

So, the ordered pair also satisfies the second equation.

Since (−6,8) satisfies both equations, it is a solution to the system.

Therefore, the correct answer is A. It is the only solution to the system

This means that the ordered pair (−6,8) is the unique solution that satisfies both equations simultaneously.

Answer B) y = 3⁄4x − 1

To find the equation of a line given two points (x1,y1) and (x2,y2), you can use the slope-intercept form:

y = mx + b

where:

• $m$ is the slope,

• $b$ is the y-intercept.

The slope ($m$) is calculated using the formula:

m = y2 − y1/x2 −x1

Let's use the given points (4,2) and $(0,-1)$ to find the slope:

m = −1−2/0 − 4
m = −3/−4 = 3/4

Now that we have the slope, let's find the y-intercept ($b$) by substituting one of the points into the slope-intercept form:

2 = 3⁄4(4) + b

Solving for $b$:

2 = 3 + b

b = −1

Now, we can write the equation of the line:

y = 3/4x −1

So, the correct answer is B. 3⁄4x − 1

This equation represents the line passing through the points (4, 2) and (0, -1).

Answer B):  4.4

The volume (V) of a cone is given by the formula:

V = ⅓πr²h

where $r$ is the radius and ℎ is the height.

Plugging in the values for the cone in question:

V = ⅓π(1.2)² (2.9)

Calculating this expression:

V ≈ 4.4

So, the answer is B. 4.4 cubic inches (to the nearest tenth).

Answer A) A

Answer A) A series of translations will transform figure X to figure Y, and the figures will be congruent.

Answer C) 93° and 55°

Answer A) The average number of customers at 7 p.m

Answer A) 3.5x + 7

The correct equation is:

y = 3.5x + 7

Explanation: The initial fee of $7.00 is added to the product of $3.50 (the cost per hour) and the number of hours (x) Therefore, option A, = 3.5x + 7 correctly models the relationship between the total cost ($y$) and the number of hours rented ($x$).

Answer B) 24

Answer: C) 20

Let's set up equations for both companies to find out when the total cost will be the same:

Let $x$ be the number of miles.

For Laguna’s Truck Rentals:
Cost Laguna = 20 + 2x

For Salvatori’s Truck Rentals:
Cost Salvatori = 3x​​

Now, we want to find when the total cost is the same, so we set the two expressions equal to each other and solve for $x$:

20 + 2x = 3x

Subtract $2x$ from both sides:

$x$

So, after 20 miles, the total cost for both companies will be the same. Therefore, the answer is C. 20.

Answer B ) between −2 and 0

Answer D) D

Answer B) (−3, 2)

Answer D) D

Answer C) (0, 0), (8, 0), (0, 8)

Let's calculate the slopes:

A. (0, 1), (–1, 3):
Slope = (3 - 1) / (-1 - 0) = 2 / -1 = -2

B. (4, 2), (2, 1):
Slope = (1 - 2) / (2 - 4) = -1 / -2 = 1/2

C. (0, 0), (8, 0):
Slope = (0 - 0) / (8 - 0) = 0 / 8 = 0

D. (1, 2), (2, 4):
Slope = (4 - 2) / (2 - 1) = 2 / 1 = 2

From these calculations, we see that only option C has all three points lying on the same straight line because the slope between any two points is 0.

So, the correct answer is C. (0, 0), (8, 0), (0, 8).