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3 years ago

Suppose the length and width of the box in exercise 12 double. Does the surface area S double? Explain

1 answer:

4 0

No, it does not.

In general, surface area is the sum of the areas of each face of a prism. In a rectangular prism, we have length, width, and height.

The area of the bottom of the prism and the top of the prism is the same, and can be represented as l*w. This means that together, it is 2lw.

The area of the left and right faces of the prism is the same, and can be represented as l*h. This means that together, it is 2lh.

The area of the front and back faces of the prism is the same, and can be represented as w*h. This means that together, it is 2wh.

This gives us the equation

SA = 2lw+2lh+2wh

If we double the length and width, making them each 2l, we then have:

SA = 2(2l*2w) + 2(2l*h) + 2(2w*h)
= 2(4lw) + 4lh + 4wh
= 8lw + 4lh + 4wh

If the surface area had been doubled, we would expect
4lw + 4lh + 4wh

No, it is not doubled.

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40. In a statistics class of 30 students, there were 13 men and 17 women. Two of the men and three of the women received an A in

Harrizon [31]

Answer:

a) 56.67% probability that the student is a woman

b) 16.67% probability that the student received an A

c) 63.33% probability that the student is a woman or received an A.

d) 83.33% probability that the student did not receive an A.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We have that:

30 students

13 men

17 women

2 men that got an A and 11 men that did not get an A.

3 women that got an A and 14 women that did not get an A.

a. Find the probability that the student is a woman.

30 students, of which 17 are women.

$P = \frac{17}{30} = 0.5667$

56.67% probability that the student is a woman

b. Find the probability that the student received an A.

30 students, of which 5 received an A

$P = \frac{5}{30} = 0.1667$

16.67% probability that the student received an A

c. Find the probability that the student is a woman or received an A.

30 students, of which 17 are women and 2 are men who received an A. So

$P = \frac{19}{30} = 0.6333$

63.33% probability that the student is a woman or received an A.

d. Find the probability that the student did not receive an A.

30 students, of which 25 did not receive an A.

$P = \frac{25}{30} = 0.8333$

83.33% probability that the student did not receive an A.

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3 years ago

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean outpu

Zarrin [17]

Answer: brother

Step-by-step explanation:

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2 years ago

Compare and contrast the following two equations. Determine if they are linear equations and explain why or why not.

igor_vitrenko [27]

Answer:

xy = -1 and y = -1/x are the same.

They are not linear equations because they are not written in the form

Ax + By = C.

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2 years ago

A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of

harkovskaia [24]

Let A(4,12) and B(6,18)

RATE OF CHANGE = m = (y₂ - y₁) / (x₂ - x₁) = (18-12)/ (6-4)

m= 6/2 or m = 3

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3 years ago

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The designer also programs a bird with a path that can be modeled by a quadratic function. The bird starts at the vertex of the

Nady [450]

Answer:

-1.2

Step-by-step explanation:

Given that the designer also programs a bird with a path that can be modeled by a quadratic function.

The bird starts at the vertex of the path at (0, 20) and passes through the point (10, 8).

If we treat this curve as line joining these two points then we can find the slope by the formula

Slope = change in y coordinate/change in x coordinate

Here the points given are

(0,20) and (10,8)

$Change in y coordinate = 8-20 = -12\\Change in x coordinate = 10-0 = 10\\Slope = -1.2$

Slope of the line that represents the turtle's path

=-1.2

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3 years ago