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sergij07 [2.7K]
2 years ago
11

Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?

Mathematics
1 answer:
Anon25 [30]2 years ago
6 0
The pythagoream theorem (not sure if I spelled that right...lol): a^2 + b^2 = c^2......where c is the hypotenuse and it is the longest side

5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169....(correct)...so it is a right triangle
You might be interested in
Solve for x.<br><br> 4−(2x+4)=5<br><br> A. x=32<br> B. x=−52<br> C. x=−10<br> D. x = 6
Dennis_Churaev [7]
  • <em>Answer:</em>

<em>x = - 2.5</em>

  • <em>Step-by-step explanation:</em>

<em>Hi there !</em>

<em>4 - (2x + 4) = 5</em>

<em>4 - 2x - 4 = 5</em>

<em>- 2x = 5</em>

<em>2x = - 5</em>

<em>x = - 5 : 2</em>

<em>x = - 2.5</em>

<em>Good luck !</em>

6 0
3 years ago
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t
skad [1K]

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that \mu = 273, \sigma = 100

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 30, s = \frac{100}{\sqrt{30}}

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

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

By the Central Limit Theorem

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

Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}

Z = 0.88

Z = 0.88 has a p-value of 0.8106

X = 257

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

Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}

Z = -0.88

Z = -0.88 has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 50, s = \frac{100}{\sqrt{50}}

X = 289

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

By the Central Limit Theorem

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

Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}

Z = 1.13

Z = 1.13 has a p-value of 0.8708

X = 257

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

Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}

Z = -1.13

Z = -1.13 has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that n = 100, s = \frac{100}{\sqrt{100}}

X = 289

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

By the Central Limit Theorem

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

Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}

Z = 1.6

Z = 1.6 has a p-value of 0.9452

X = 257

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

Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}

Z = -1.6

Z = -1.6 has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

6 0
2 years ago
A triangle has vertices A(1, 1), B(2, 4), and C(4, 2). Line p is parallel to side AB and contains point C.
kenny6666 [7]

Answer:

p:y = 3x-10

Step-by-step explanation:

We are given the following in the question:

A(1, 1), B(2, 4), C(4, 2)

i) Slope of AB

A(1, 1), B(2, 4)\\\\m = \dfrac{y_2-y_1}{x_2-x_1}\\\\m = \dfrac{4-1}{2-1}=3

Thus, slope of AB is 3.

ii) Point slope form

The point slope form of a line can be written as:

y - y_1 = m(x - x_1)

The point intercept form of line can be written as:

y = mx + c

The line is parallel to AB and contains point C(4, 2). Since line p is parallel to AB, line p will have the same slope as line AB

Putting values, we get,

y - 2 = 3(x-4)\\y = 3x-12+2\\y = 3x-10

which is the required slope intercept equation of line p.

4 0
3 years ago
What is the length of YZ?
Bogdan [553]

Answer: C

Hello,

Step-by-step explanation:

WZ=7-3=4

YW²=XW*WZ=3*4=12 ==> WY=2√3

In the right triangle YWZ, using the Pythagorean's theorem:

YZ²=WY²+WZ²=12+4²=28

YZ=2√7≅5.29150....

Answer C

3 0
2 years ago
PLEASEEEEE HELPPPP ASAPPP
Ivanshal [37]

Answer:

  40.5°

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

In this triangle, that means ...

  tan(x°) = 4.7/5.5

The angle is found using the inverse function:

  x° = arctan(4.7/5.5) ≈ 40.5°

8 0
2 years ago
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