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3 years ago

Example 2: Identify the reference angle. A) 135° B) 260° C) 310

Mathematics

1 answer:

jonny [76]3 years ago

4 0

Answer:

A) 45

B) 80

C) 50

Step-by-step explanation:

When the terminal side is in the first quadrant (angles from 0° to 90°), our reference angle is the same as our given angle. This makes sense, since all the angles in the first quadrant are less than 90°.

When the terminal side is in the second quadrant (angles from 90° to 180°), our reference angle is 180° minus our given angle.

When the terminal side is in the third quadrant (angles from 180° to 270°), our reference angle is our given angle minus 180°.

When the terminal side is in the fourth quadrant (angles from 270° to 360°), our reference angle is 360° minus our given angle.

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After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175 (U.S. Ne

Arte-miy333 [17]

Using the normal distribution and the central limit theorem, it is found that:

a) The standard deviation is of $955.34.

b) 0.5 = 50% probability that the sample mean will be more than $27,175.

c) There is a 0.2938 = 29.38% probability that the sample mean will be within $1,000 of population mean.

d) There is a 0.177 = 17.7% probability that the sample mean will be within $1,000 of population mean.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, 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 average is of $27,175, hence $\mu = 27175$ .

The population standard deviation is of $7,400, hence $\sigma = 7400$ .

A sample of 60 students is taken, hence $n = 60$ .

Item a:

$s = \frac{\sigma}{\sqrt{n}} = \frac{7400}{\sqrt{60}} = 955.34$

The standard deviation is of $955.34.

Item b:

This probability is 1 subtracted by the p-value of Z when X = 27175, hence:

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

By the Central Limit Theorem

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

$Z = \frac{27175 - 27175}{0}$

$Z = 0$

$Z = 0$ has a p-value of 0.5.

1 - 0.5 = 0.5

0.5 = 50% probability that the sample mean will be more than $27,175.

Item c:

$Z = \frac{1000}{s}$

$Z = \frac{1000}{955.34}$

$Z = 1.05$

The probability is P(|Z| > 1.05), which is 2 multiplied by the p-value of Z = -1.05.

Looking at the z-table, Z = -1.05 has a p-value of 0.1469.

2 x 0.1469 = 0.2938

There is a 0.2938 = 29.38% probability that the sample mean will be within $1,000 of population mean.

Item d:

Sample of 100, hence $n = 100, s = \frac{7400}{\sqrt{100}} = 740$

$Z = \frac{1000}{s}$

$Z = \frac{1000}{740}$

$Z = 1.35$

Z = -1.35 has a p-value of 0.0885.

2 x 0.0885 = 0.177

There is a 0.177 = 17.7% probability that the sample mean will be within $1,000 of population mean.

To learn more about the normal distribution and the central limit theorem, you can take a look at brainly.com/question/24663213

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Aiden has a job that pays $44,000 per year. How much will he pay in Medicare taxes? (Medicare taxes are 1.45% of earnings.)

Slav-nsk [51]

Answer: $638.00

Step-by-step explanation:

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A rectangular aquarium has length (x+ 10), width (x + 4), and height (t + 6). Determine a simplified function that represents th

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Answer:

V = x³ + 20x² + 124x + 240

Step-by-step explanation:

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V = wlh

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V = (x + 4)(x + 10)(x + 6)

V = (x + 4)(x² + 16x + 60)

V = x²(x + 4) + 16x(x + 4) + 60(x + 4)

V = x³ + 4x² + 16x² + 64x + 60x + 240

V = x³ + 20x² + 124x + 240

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Brendan and Marie are each assigned a paper for a class they share. Brendan decides to write 41 pages at a time while Marie deci

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Answer:

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3 years ago

Jerry and Carlos each have $1,000 and are trying to increase their savings. Jerry will keep his money at home and add $50 per mo

8_murik_8 [283]

Answer:

Jerry has a better saving plan for increasing his savings than Carlos

Step-by-step explanation:

Jerry's initial principal = $1000

Carlos initial principal = $1000

Jerry add $50 monthly this means that in 6 months he has

$50 x 6 = $300 as interest

This means that at the end of 6 months, Jerry would have $1,300 dollars at home

For Carlos the interest rate is 4% per year compounded monthly

If we calculate his interest per month we have:

Interest = 1000 x 4/(100 x 12) = $3.33

2nd month = 1003.33 x 4/(100 x 12) = $3.34

3rd month = 1006.68 x 4/(100 x 12) = $3.36

4th month = 1010.04 x 4/(100 x 12) = $3.37

5th month = 1013.41 x 4/(100 x 12) = $3.38

6th month = 1016.79 x 4/(100 x 12) = $3.40

At the end of 6 month, Carlos would have $1020.18 in the bank

Hence, Jerry has a better saving plan for increasing his savings than Carlos

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3 years ago