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3 years ago

Sonya wants to sew ribbon along each side of a square pillow.

Mathematics

1 answer:

Eduardwww [97]3 years ago

5 0

We are given area of the ribbon = 144 square inches.

We know formula for side of a square = $\sqrt{Area \ of \ a \ square }$ .

Plugging value of area in the formula, we get

Side of the square $= \sqrt{144}$

= 12 inches.

Sonya wants to sew ribbon along each side of a square pillow.

So, we need to find the perimeter of the square pillow.

<h3>Perimeter = 4 × side = 4 × 12 = 48 inches.</h3><h3>Therefore, she buy 48 inches of ribbon to have the exact amount that she needs.</h3>

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3 years ago

83 random samples were selected from a normally distributed population and were found to have a mean of 32.1 and a standard devi

arlik [135]

Answer:

$\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}$

$4.525 \leq \sigma^2 \leq 7.602$

Now we just take square root on both sides of the interval and we got:

$2.127 \leq \sigma \leq 2.757$

Step-by-step explanation:

Information given

$\bar X=32.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.4 represent the sample standard deviation

n=83 represent the sample size

Confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The degrees of freedom given by:

$df=n-1=8-1=7$

The confidence level is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.05,82)" "=CHISQ.INV(0.95,82)". so for this case the critical values are:

$\chi^2_{\alpha/2}=104.139$

$\chi^2_{1- \alpha/2}=62.132$

The confidence interval is given by:

$\frac{(82)(2.4)^2}{104.139} \leq \sigma^2 \leq \frac{(82)(2.4)^2}{62.132}$

$4.525 \leq \sigma^2 \leq 7.602$

Now we just take square root on both sides of the interval and we got:

$2.127 \leq \sigma \leq 2.757$

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3 years ago

What is the difference in surface areas, in square feet, of the two boxes?

Katarina [22]

The difference is 3ft since the surface area for the prism is 57, and the surface area for the cube is 54.

You can use the surface area formula
2(wl+hl+hw) = Area
2·(3·4.5+2·4.5+2·3)=57

And a cubes surface area formula
6a^2 = Area
6·32=54

3 0

3 years ago

Between which two integers does the square root of 17 fall between?

Mrrafil [7]

Two integers mean numbers that do not have decimals. Whole numbers

to figure out between what two integers get a calculator and do square root 17
which is 4.123 (to three decimal places)

thus it falls between 4 and 5. since it is above 4 and below 5 and there are no integers in between possible.

Hope this helps :P

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3 years ago