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andreyandreev [35.5K]
3 years ago
14

The sum of four consecutive integers is 342. What is the third term in the sequence

Mathematics
1 answer:
Fofino [41]3 years ago
4 0

Answer:

86

Step-by-step explanation:

let  four consecutive integers: n  , n+1  , n+2  , n+3

n  + n+1  + n+2 + n+3 = 342

4n + 6 = 342

4n + 6  - 6  = 342 - 6

4n = 336

divid by : 4

n = 84

but the third term is : n +2   so : 84+2 = 86

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Step-by-step explanation:

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15 MIN = 0.25 h

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<em>x</em> = 6.5 mi/0.25 h = 26 mi

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6. The dimensions of a rectangular garden are 380ft x 250ft. If you want to walk around this garden to make 3 miles for a mornin
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Step-by-step explanation:

L=3(5280)/(2(380+250))

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2 years ago
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Answer:

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Step-by-step explanation:

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if a staircase rises 52° from the ground and a vertical distance of 12 yards. How much horizontal distance does the staircase co
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The horizontal distance will be found using the formula:
tan θ= opposite/adjacent
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3 0
3 years ago
The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 30,393 miles, with a standard
Pie

Answer:

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, 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 random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 30393, \sigma = 2876, n = 37, s = \frac{2876}{\sqrt{37}} = 472.81

What is the probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

This probability is the pvalue of Z when X = 30393 + 339 = 30732 subtracted by the pvalue of Z when X = 30393 - 339 = 30054. So

X = 30732

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

By the Central Limit Theorem

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

Z = \frac{30732 - 30393}{472.81}

Z = 0.72

Z = 0.72 has a pvalue of 0.7642.

X = 30054

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

Z = \frac{30054 - 30393}{472.81}

Z = -0.72

Z = -0.72 has a pvalue of 0.2358

0.7642 - 0.2358 = 0.5284

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

4 0
3 years ago
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