How many ways are there to choose the students?

Nostrana [21]

1. You have a small typo in your answer: cubic inches is a measure of volume not surface area. Since the a TV is basically a rectangular prism, we are going to use the formula for the volume of a rectangular prism to solve this.
$V=whl$
where
$V$ is the volume of the rectangular prism.
$w$ is the width of the base.
$l$ is the length of the base.
$h$ is the height of the prism.

We know from our problem that the television that has a total volume of 75 cubic inches, so $V=75in^3$ . We also know that the length of the base is 7.5 inches and the width is 4 inches, so $l=7.5in$ and $w=4in$ . Lets replace those values in our formula to find $h$ :
$V=whl$
$75in^3=(4in)(h)(7.5in)$
$75in^3=30hin^2$
$h= \frac{75in^3}{30in^2}$
$h=2.5in$

We can conclude that the height of the television is 2.5 inches; therefore, the correct answer is: A. 2.5 inches.

2. To solve this, we are going to use the formula for the surface area of a rectangular prism: $S=2(wl+hl+hw)$
where
$S$ is the surface area of the rectangular prism.
$w$ is the width.
$l$ is the length.
$h$ is the height.

We know form our problem that the dimensions of our prism are:length of 12 inches, a width of 9 inches, and a height of 2 inches, so $l=12in$ , $w=9in$ , and $h=2in$ . Lets replace those values in our formula to find $S$ :
$S=2(wl+hl+hw)$
$S=2[(9in)(12in)+(2in)(12in)+(2in)(9in)]$
$S=2(108in^2+24in^2+18in^2)$
$S=2(150in^2)$
$S=300in^2$

We can conclude that the surface area of the prism is 300 square inches; therefore, the correct answer is: D. 300

4 0

3 years ago

Find the slope of the line that passes through the points (4, 3) and (2,7).

victus00 [196]

Answer:

Slope is -2

Step-by-step explanation:

5 0

3 years ago

Mark had 312 books. He has 11 times more fiction than nonfiction. How many fiction does he have

andrew11 [14]

He has about 28 fiction books. Since 312 divided by 11 is equal to 28.3636363636, you can't have a decimal number for the amount of books, so you round down to 28.

8 0

3 years ago

Solve the quadratic equation: 3x2 + x - 5 = 0

Yuri [45]

Hey there!

$3x^2 + x -5 = 0$

This equation is in standard form, which is $ax^2+bx+c=0$ .

We are going to solve this with the quadratic equation, so we need to find the values for a, b, and c in the given equation. We can just look at it and identify the variables.

a = 3, b = 1, c = -5

Let's plug these values into the quadratic equation:

$x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$