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Dahasolnce [82]

3 years ago

6

The radius of the bull’s-eye of the dartboard is 8 inches. The radius of each concentric circle is 8 inches more than the radius

of the circle inside it. If a dart lands at random on the dartboard, what is the probability that the dart will hit in area C?
A. 9/16
B. 5/16
C. 1/4
D. 3/4

1 answer:

UNO [17]3 years ago

5 0

Answer with Step-by-step explanation:

The radius of the bull’s-eye of the dartboard is 8 inches.

The radius of each concentric circle is 8 inches more than the radius of the circle inside it.

Radius of first circle=8 in.

Radius of second circle=16 in.

Radius of third circle=24 in.

Radius of fourth circle=32 in.

Area of C=Area of the third circle-Area of second circle

= π×24×24-π×16×16

= 320π sq. in.

Total area of dartboard=Area of fourth circle=π×32×32

=1024π sq. in.

P( the dart will hit in area C)= area of c/total area of dart board

=320π/1024π

= 5/16

Hence, correct option is:

B.5/16

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3 years ago

lilavasa [31]

Answer:

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2 years ago

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Answer:

The enrollment after 5 years is 10,724

Step-by-step explanation:

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4 0

3 years ago

A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

<em>So, the 95% confidence interval is (46.4, 53.6)</em>

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

<em>So, the 95% confidence interval is (47.9, 52.1)</em>

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

<em>Notice that the margin of error decreases when the sample size increases.</em>

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3 years ago