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qwelly [4]
2 years ago
11

POSSIBLE POINTS: 28.57

Mathematics
1 answer:
malfutka [58]2 years ago
4 0
18.344 should be right. Have a good day!
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Joan's gross pay is $400, from which $24.80 is deducted for FICA, $5.20 for Medicare, and $45 for income tax. What is her net pa
WITCHER [35]
400 - 24.80 = 375.20
375.20 - 5.20 = 370
370 - 45 = $325
8 0
3 years ago
The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls
kumpel [21]

Answer:

standard error = 1.63

Step-by-step explanation:

To calculate the standard error we need to know the standard deviation (σ) and the sample size (n) (see the attached formula).

To obtain the standard deviation we use the given sample variance of 77.4 years:

σ²= variance

Therefore:

σ = √77.4 = 8.8

Now we can calcuate the estimated standard error:

standard error = σ /√n = 8.8/√29 = 1.63

The standard error gives us an estimation about how far the mean of the sample is from the mean of the entire population, and in this case is 1.63.

7 0
2 years ago
Which two movements will show a positive movement?
fiasKO [112]
Answer:
Right and up
3 0
2 years ago
A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si
Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

Area = 128

Let the dimension of the paper be x and y;

Such that:

Length = x

Width = y

So:

Area = x * y

Substitute 128 for Area

128 = x * y

Make x the subject

x = \frac{128}{y}

When 1 inch margin is at top and bottom

The length becomes:

Length = x + 1 + 1

Length = x + 2

When 2 inch margin is at both sides

The width becomes:

Width = y + 2 + 2

Width = y + 4

The New Area (A) is then calculated as:

A = (x + 2) * (y + 4)

Substitute \frac{128}{y} for x

A = (\frac{128}{y} + 2) * (y + 4)

Open Brackets

A = 128 + \frac{512}{y} + 2y + 8

Collect Like Terms

A = \frac{512}{y} + 2y + 8+128

A = \frac{512}{y} + 2y + 136

A= 512y^{-1} + 2y + 136

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

A' = -512y^{-2} + 2

Set

A' = 0

This gives:

0 = -512y^{-2} + 2

Collect Like Terms

512y^{-2} = 2

Multiply through by y^2

y^2 * 512y^{-2} = 2 * y^2

512 = 2y^2

Divide through by 2

256=y^2

Take square roots of both sides

\sqrt{256=y^2

16=y

y = 16

Recall that:

x = \frac{128}{y}

x = \frac{128}{16}

x = 8

Recall that the new dimensions are:

Length = x + 2

Width = y + 4

So:

Length = 8 + 2

Length = 10

Width = 16 + 4

Width = 20

To double-check;

Differentiate A'

A' = -512y^{-2} + 2

A" = -2 * -512y^{-3}

A" = 1024y^{-3}

A" = \frac{1024}{y^3}

The above value is:

A" = \frac{1024}{y^3} > 0

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0
2 years ago
Determine the intercepts of the line.
djverab [1.8K]

y = -3x +12\\\\\text{Plug x = 0 to find  y - intercept,}\\\\y = -3(0) +12 = 12\\\\\text{So, y-intercept is (0,12).}\\\\\text{Plug y=0 to find  x - intercept,}\\\\0 = -3x +12\\\\\implies -3x = -12\\\\\implies 3x = 12\\\\\implies x = \dfrac{12}{3} = 4 \\\\\\\text{So, x - intercept is (4,0).}

5 0
2 years ago
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