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2 years ago

Help I will be marking brainliest!!!

Mathematics

1 answer:

Keith_Richards [23]2 years ago

4 0

<h3>Answer: A. 18*sqrt(3)</h3>

=============================================

Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

tan(30) = TH/54

sqrt(3)/3 = TH/54 ... use the unit circle

54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

18*sqrt(3) = TH

TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer

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An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

a^2 + b^2 = c^2

(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

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Eduardwww [97]

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Answer: Letter Choice, (A), = 1/3

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1 ===> 8, 1 ===> 9

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Hope that helps!!!! : )

8 0

2 years ago

Read 2 more answers

Find the median, mean, and range.

RSB [31]

Hey there!

The median is 8.5

The mean is 7

The range is 11

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5 0

3 years ago

Parts being manufactured at a plant are supposed to weigh 65 grams. Suppose the distribution of weights has a Normal distributio

andrew-mc [135]

Answer:

0.64%.

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 estabilishes 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.

Mean of 75 grams and a standard deviation of 22 grams.

This means that $\mu = 75, \sigma = 22$

Sample of 144:

This means that $n = 144, s = \frac{22}{\sqrt{144}} = 1.8333$

More than 80 or less than 70:

Both are the same distance from the mean, so we find one probability and multiply by 2.

The probability that it is less than 70 is the pvalue of Z when X = 70. So

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

By the Central Limit Theorem

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

$Z = \frac{70 - 75}{1.8333}$

$Z = -2.73$

$Z = -2.73$ has a pvalue of 0.0032

2*0.0032 = 0.0064.

0.0064*100% = 0.64%

The probability is 0.64%.

3 0

3 years ago

Find the solution set of the inequality:<br><br> 82 + 2 > 34<br><br> SOMEONE PLS HELP

Romashka [77]

Answer:

82+2>34

84>34

True

I hope this helps :)

6 0

2 years ago

The "core" inflation rate is typically defined as the change in consumer prices for all goods included in the CPI basket except

Ganezh [65]

Answer:

Higher

Step-by-step explanation:

1) In Macroeconomics, The core inflation rate does not include food and energy since these categories are way more volatile, due to oil and season matters. And statistically this measure looks for more robust items, to compose the core inflation in a more accurate way. The Consumer Prices Index (CPI) is the metric used for the cost of living.

Another Index, used by the Fed is the PCE, for the goods and services consumed by the US residents.

So, the Core inflation is based on CPI and PCE, <em>Personal Consumption Expenditure</em> therefore the inflation rate for the past year was higher than 4%, for it is not solely based on CPI index.

6 0

3 years ago