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4 years ago

Find the area of the shaded region. Round to the nearest tenth.

Mathematics

1 answer:

AURORKA [14]4 years ago

7 0

Answer:

3.5 square cm

Step-by-step explanation:

$Area \: of \: both \: squares \\ = {2}^{2} + {3}^{2} \\ = 4 + 9 \\ = 13 \: {cm}^{2} \\ \\ Area \: of \: both \: right \: \triangle s \\ = \frac{1}{2} \times (2 + 3) \times 2 + \frac{1}{2} \times3 \times 3 \\ = 5 \times 1+ 1.5 \times 3 \\ = 5 + 4.5 \\ = 9.5 \: {cm}^{2} \\ \\ Area \: of \:shaded \: region \\ = Area \: of \: both \: squares\\ - Area \: of \: both \: right \: \triangle s \\ = 13 - 9.5 \\ \purple { \boxed{ \bold{Area \: of \:shaded \: region = 3.5 \: {cm}^{2} }}}$

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What is the mean salary of a salesperson at the company

Whitepunk [10]

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3 years ago

A circular plate has circumference 32 inches. What is the area of this plate? Use 3.14 for pi. The area of this plate is about

Novosadov [1.4K]

Answer:

A = 82.53 in²

Step-by-step explanation:

We use the circumference equation C = 2πr and the area equation A = πr².

Using the first equation and the given circumference (32 in), we find the radius of the circle, and then use this result to find the area of the circle.

C 32 in

C = 2πr becomes r = ----------- and here r = ---------- = 5.10 in

2π 6.28

Then the area of the circle is A = πr², which here is A = 3.14(5.10 in)², which, when rounded off to two decimal places, is A = 82.53 in²

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3 years ago

Determine whether the pair of triangles below are similar. If they are similar, write the similarity criterion that can be used

Ugo [173]

Answer:

Cannot be determined

Step-by-step explanation:

The information given for the triangles are not enough to evaluate them for similarity. How ever they are both equilateral triangles given the angle measures.

8 0

3 years ago

The average production cost for major movies is 57 million dollars and the standard deviation is 22 million dollars. Assume the

Degger [83]

Using the normal distribution, we have that:

The distribution of X is $X \approx (57,22)$ .

The distribution of $\mathbf{\bar{X}}$ is $\bar{X} \approx (57, 5.3358)$ .

0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.

0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem, the parameters are given as follows:

$\mu = 57, \sigma = 22, n = 17, s = \frac{22}{\sqrt{17}} = 5.3358$

Hence:

The distribution of X is $X \approx (57,22)$ .

The distribution of $\mathbf{\bar{X}}$ is $\bar{X} \approx (57, 5.3358)$ .

The probabilities are the <u>p-value of Z when X = 58 subtracted by the p-value of Z when X = 55</u>, hence, for a single movie:

X = 58:

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

$Z = \frac{58 - 57}{22}$

Z = 0.05.

Z = 0.05 has a p-value of 0.5199.

X = 55:

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

$Z = \frac{55 - 57}{22}$

Z = -0.1.

Z = -0.1 has a p-value of 0.4602.

0.5199 - 0.4602 = 0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.

For the sample of 17 movies, we have that:

X = 58:

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

$Z = \frac{58 - 57}{5.3358}$

Z = 0.19.

Z = 0.19 has a p-value of 0.5753.

X = 55:

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

$Z = \frac{55 - 57}{5.3358}$

Z = -0.38.

Z = -0.38 has a p-value of 0.3520.

0.5753 - 0.3520 = 0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

8 0

2 years ago

Sung Lee invests $5,000 at age 18. He hopes the investment will be worth $20,000 when he turns 25. If the interest compounds con

Temka [501]

Answer:

19.8%

Step-by-step explanation:

We have the following formula for continuous compound interest:

A = P * e ^ (i * t)

Where:

A is the final value

P is the initial investment

i is the interest rate in decimal

t is time.

The time can be calculated as follows:

25 - 18 = 7

That is, the time corresponds to 7 years. In addition, A is 20,000 for A and P would be 5,000, we replace:

20000 = 5000 * e ^ (7 * i)

20000/5000 = e ^ (7 * i)

e ^ (7 * i) = 4

ln e ^ (7 * i) = ln 4

7 * i = ln 4

i = (ln 4) / 7

i = 0.198

Which means that the rounded percentage will be 19.8% per year

3 0

3 years ago