The area of a circle is A = πr^2. We let A1 And A2 the areas of the circles and r1 and r2 the radius of each, respectivley.

A1 + A2 = 80π
Substitute the formula for the area,
π(r1)^2 + π (r2)^2 = 80π

From the statement, we know that r2=2(r1).

<span>π(r1)^2 + π (2 x r1)^2 = 80π
</span>We can cancel π, we will have

5 x (r1)^2 = 80
Thus,

r1 = 4 and r2 = 8

5 0

3 years ago

The lengths of nails produced in a factory are normally distributed with a mean of 4.84 centimeters and a standard deviation of

Helga [31]

Answer:

Top 3%: 4.934 cm

Bottom 3%: 4.746 cm

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

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:

$\mu = 4.84, \sigma = 0.05$

Top 3%

Value of Z when Z has a pvalue of 1 - 0.03 = 0.97. So X when Z = 1.88.

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

$1.88 = \frac{X - 4.84}{0.05}$

$X - 4.84 = 0.05*1.88$

$X = 4.934$

Bottom 3%

Value of Z when Z has a pvalue of 0.03. So X when Z = -1.88.

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

$-1.88 = \frac{X - 4.84}{0.05}$

$X - 4.84 = 0.05*(-1.88)$

$X = 4.746$

8 0

2 years ago

Cards with the numbers 1 through 40 are placed in a box and throughly shuffled. What is the probability of randomly selecting a

Alecsey [184]

There are 9 numbers less than 10. 1,2,3,4,5,6,7,8,9
And there are 2 multiples of 15. 15,30
There are 11 of the 40 cards that are either less than 10 or multiples of 15, so the answer is B

5 0

3 years ago