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2 years ago

Cyruer.

Mathematics

1 answer:

Maslowich2 years ago

4 0

Answer:

Hello,

Step-by-step explanation:

Area of the sphere:

$S=4*\pi *r^2$

Volume of the sphere:

$V=\dfrac{4*\pi *r^3}{3}$

$\dfrac{S}{3} =\dfrac{V}{7} \\\\\dfrac{4*\pi *r^2}{3} =\dfrac{4*\pi *r^3}{3*7} \\\\1=\dfrac{r}{7} \\\\\\r=7\\\\great \ circle: 2*\pi* r=14*\pi\\$

$Volume=\dfrac{4*\pi *7^3}{3} =\dfrac{1372*\pi }{3} \approx{1436,7550...(cm^3)}$

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If a project will take 35 employees 2,940 hours to complete, how many hours will each employee have to work?

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2 years ago

A group of high school athletes has an average GPA of 2.7 with a standard deviation of 0.9. a)Find the percentage of athletes wh

mart [117]

Answer:

a) The percentage of athletes whose GPA more than 1.665 is 87.49%.

b) John's GPA is 3.645.

Step-by-step explanation:

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 2.7, \sigma = 0.9$

a)Find the percentage of athletes whose GPA more than 1.665.

This is 1 subtracted by the pvalue of Z when X = 1.665. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1.665 - 2.7}{0.9}$

$Z = -1.15$

$Z = -1.15$ has a pvalue of 0.1251

1 - 0.1251 = 0.8749

The percentage of athletes whose GPA more than 1.665 is 87.49%.

b) John's GPA is more than 85.31 percent of the athletes in the study. Compute his GPA.

His GPA is X when Z has a pvalue of 0.8531. So it is X when Z = 1.05.

$Z = \frac{X - \mu}{\sigma}$

$1.05 = \frac{X - 2.7}{0.9}$

$X - 2.7 = 1.05*0.9$

$X = 3.645$

John's GPA is 3.645.

8 0

3 years ago

The point A(0,3) and point B(4,19) lie on the line L.<br> Find the equation of line L

IRISSAK [1]

Answer: The equation is y = 4x+3

Slope = 4

y intercept = 3

========================================================

Explanation:

Let's start off by finding the slope.

$A = (x_1,y_1) = (0,3) \text{ and } B = (x_2,y_2) = (4,19)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{19 - 3}{4 - 0}\\\\m = \frac{16}{4}\\\\m = 4\\\\$

The slope is 4.

The y intercept is 3 because of the point (0,3)

We go from y = mx+b to y = 4x+3

m = slope

b = y intercept

---------------

Check:

Plug in x = 0 and we should get to y = 3

y = 4x+3

y = 4(0)+3

y = 0+3

y = 3

That works out. Now try x = 4. It should lead to y = 19

y = 4x+3

y = 4(4)+3

y = 16+3

y = 19

The answer is confirmed.

4 0

2 years ago