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storchak [24]
3 years ago
6

A survey was conducted to determine the amount of time, on average, during a given week SCAD students spend outside of class on

class work (projects, homework, and studying). The data shows: 5, 7, 11, 14, 18, 22 (in hours). Calculate the standard deviation by using the appropriate formula. Round your answer to three decimal places.
Mathematics
1 answer:
fiasKO [112]3 years ago
5 0

Answer:

Standard Deviation = 5.928

Step-by-step explanation:

a) Data:

Days  Hours spent  (Mean - Hour)²

1              5                61.356

2             7                34.024

3            11                  3.360

4           14                   1.362

5           18               26.698

6          22               84.034

6 days 77 hours,    210.834

mean

77/6 = 12.833    and 210.83/6 =  35.139

Therefore, the square root of 35.139 = 5.928

b) The standard deviation of 5.928 shows how the hours students spend outside of class on class work varies from the mean of the total hours they spend outside of class on class work.

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Given:

The last year sales = $288,000,000

Company increased its sales from last year to this year by 34%.

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The this year's sales to the nearest million dollars.

Solution:

We have,

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The company increased its sales from last year to this year by 34%. So,

This year's sales =288+288\times \dfrac{34}{100}

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Therefore, this year's sales were 386 million dollars or $386,000,000.

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7. Identify a horizontal or vertical stretch or compression of the function f(x)=√x by observing the equation of the function g(
Effectus [21]

It is a vertical stretch.

<h3>What is functions?</h3>

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Given

To solve this problem you must apply the procedure shown below:

1. You have the following parent function given in the problem above:

f(x) = √x

2. And you have the function g(x) = √3x

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4. Therefore, you have that:

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6 0
2 years ago
A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen
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Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}

The restriction is that the perimeter have to be 12 ft at most:

P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12

We can express b in function of a as:

2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a

Then, the area become:

A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2

To maximize the area, we derive and equal to zero:

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