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Sindrei [870]
3 years ago
7

What is the 87th term of the arithmetic sequence?

Mathematics
1 answer:
Norma-Jean [14]3 years ago
4 0

Step-by-step explanation:

1) The first term is -1352, and the common difference is 18.  So the 87th term is:

a = -1352 + 18 (87 − 1)

a = 196

2) 1/64 + 1/16 + 1/4 + 1 + 4

This is a geometric series, where the first term is 1/64 and the common ratio is 4.

∑⁵ᵢ₌₁ 1/64 (4)ⁱ⁻¹

Since 1/64 = 4⁻³:

∑⁵ᵢ₌₁ 4⁻³ (4)ⁱ⁻¹

∑⁵ᵢ₌₁ (4)ⁱ⁻⁴

3) The first term is -2100, and the common ratio is -0.1, so the 7th term is:

a = -2100 (-0.1)⁷⁻¹

a = -0.0021

4) The first term is 48, and the fifth term is 243/16, so the common ratio is:

243/16 = 48 r⁵⁻¹

81/256 = r⁴

r = 3/4

So the sequence is:

48, 36, 27, 81/4, 243/16

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spayn [35]

Answer:

0.98 = 98% probability that the average midterm score of these students is at most 75 points.

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.

The average midterm score of students in a certain course is 70 points.

This means that \mu = 70

29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points.

This means that \sigma = 13.15, n = 29, s = \frac{13.15}{\sqrt{29}} = 2.44

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This is the pvalue of Z when X = 75. So

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

By the Central Limit Theorem

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

Z = \frac{75 - 70}{2.44}

Z = 2.05

Z = 2.05 has a pvalue of 0.98.

0.98 = 98% probability that the average midterm score of these students is at most 75 points.

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Ne4ueva [31]

Answer:

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Step-by-step explanation:

Obviously the first step is to find the missing measurement. To do this, you use the Pythagorean theorem; <em>a² + b² = c².</em>

In this case, let's label the the missing side A, the height B, and the hypotenuse C.

<em>X² + 15² = 25²</em>

Then you must figure out what 15² and 25².

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<em>25² = 625</em>

The next step is to subtract 15² (225) from 25² (625), which will give you the result of X².

<em>625 - 225 = 400. </em>

Now you know X² = 400, you can find the square root of 400 to give you the length of the triangle.

<em>√400 = 20.</em>

<u>The missing length of the triangle is 20 yards. </u>

Now it's just a matter of finding the area by using the formula;

<em>A = </em>\frac{bh}{2}

Or,

<em>(20 × 15) ÷ 2 = 150.</em>

<u>And there's your answer. Don't forget to add the units.</u>

<u />

<h2>Hope this helped.</h2>
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