50 11th graders were asked to choose which of 6 options the school’s color should be. The table below shows the number of studen

Answer:

Step-by-step explanation:

Denote the rectangular prism's volume as VR and the volume of the right triangular prism as VT. Given that the rectangular prism's volume exceeds that of the triangular prism by 32 cubic feet, we establish that VR = 32 + VT.

Calculating VR: VR = length * width * height = 6*x*3.

This simplifies to VR = 18x ft³.

For the triangular prism, VT can be calculated as Length * width * Height / 2, yielding VT = (7 * x * 4) / 2.

Thus, VT = 28x / 2, which simplifies to VT = 14x ft³.

Equating VR to 32 + VT allows the substitution: 18x = 32 + (14x).

Now, simplify the equation:

Combine like terms: 18x - 14x = 32.

This results in 4x = 32.

Dividing both sides by 4:

x = 8.

The volume for the rectangular prism comes to 18x, which equals 18*8.

The volume of the rectangular prism calculates to 144 ft³.

The volume for the right triangular prism calculates to 14x, which equals 14*8.

The volume of the right triangular prism calculates to 112 ft³.

Answer:

Choice C. $6,012

Step-by-step explanation:

We know that

The formula to find the depreciated value is given by

where

V stands for the depreciated value

P represents the original value

r corresponds to the depreciation rate in decimal

t refers to the Number of Time Periods

In this scenario, we have

t = 7 years

P = $8,000

r = 0.04

Plug these into the formula mentioned earlier

Hope this assists you:)

Answer:

m∠ABE = 27°

Step-by-step explanation:

* To analyze the figure to address the query

- AC represents a line

- Ray BF crosses line AC at point B

- Ray BF is perpendicular to line AC

Thus, both ∠ABF and ∠CBF are classified as right angles

Which gives us ∠ABF = ∠CBF = 90°

- Rays BE and BD meet line AC at point B

Since m∠ABE is equal to m∠DBE, as indicated by the same symbol in the figure

It implies that BE acts as the angle bisector of angle ABD

Given that m∠EBF = 117°

Then m∠EBF = m∠ABE + m∠ABF

Where m∠ABF = 90°

So, 117° = m∠ABE + 90°

- By subtracting 90 from both sides

It follows that m∠ABE = 27°

Answer:

E 240

Step-by-step explanation:

Mean of the geometric distribution = (1- p) / p

16 = (1 - p) / p

16p = 1 - p;  17p = 1; thus, p = 1/17 = 0.058  

Standard Deviation = (1 - p) / p^2

= (1 - 0.058) / (0.058)^2

0.942 / 0.003364

= 280, which is closest to 240