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mestny [16]
2 years ago
15

A portrait without its frame has a height 2.5 times its width, w, in inches. Its frame is 3 in. wide all

Mathematics
1 answer:
Greeley [361]2 years ago
4 0

Answer:

2 inches

Step-by-step explanation:

it is ,2inches because they are joining

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you are riding a train. your carry-on bag can weigh no more than 50 pounds. Your bag weighs 38 pounds. How much more can you add
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Let the additional weight that can be added be = x

Current weight of the bag = 38 pounds

Total weight can be = 50 pounds

The equation becomes:

38+x\leq50

x\leq50-38=12

Hence, a weight of 12 pounds cab be added to the current wight.

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3 years ago
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Yuliya22 [10]
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The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 104 inches, and a standard
dsp73

Answer:

91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

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 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, the sample means with size n of at least 30 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 = 104, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2

What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

This is the pvalue of Z when X = 106.8. So

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

By the Central Limit Theorem

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

Z = \frac{106.8 - 104}{2}

Z = 1.4

Z = 1.4 has a pvalue of 0.9192

0.9192 = 91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

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3 years ago
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