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Morgarella [4.7K]
3 years ago
10

The sum of three consecutive even numbers is 48. what are the smallest of these numbers?

Mathematics
2 answers:
Mekhanik [1.2K]3 years ago
7 0
14 + 16 + 18= 48 so the answer would be 14
Kay [80]3 years ago
6 0
Consecutive numbers = 14, 16, 18. The smallest out of all three numbers are 14 so the answer is 14.
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Suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A samp
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Answer:

0.9910 = 99.10% probability that a sample of 170 steady smokers spend between $19 and $21

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 20, standard deviation of 5:

This means that \mu = 20, \sigma = 5

Sample of 170:

This means that n = 170, s = \frac{5}{\sqrt{170}}

What is the probability that a sample of 170 steady smokers spend between $19 and $21?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.

X = 21

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

By the Central Limit Theorem

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

Z = \frac{21 - 20}{\frac{5}{\sqrt{170}}}

Z = 2.61

Z = 2.61 has a p-value of 0.9955

X = 19

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

Z = \frac{19 - 20}{\frac{5}{\sqrt{170}}}

Z = -2.61

Z = -2.61 has a p-value of 0.0045

0.9955 - 0.0045 = 0.9910

0.9910 = 99.10% probability that a sample of 170 steady smokers spend between $19 and $21

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3 years ago
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Y=2x+1 is the right answer to this
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(x,y) –> (x+9, y+8)
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Find the area of a square<br> with side length 12 inch.
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A square has all of the same sides, so just do 12x12 which is 144
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Answer:

Step-by-step explanation:

Correlation measures the strength of the linear relationship between two variables.

A linear relationship exists between two variables if one variable increases as the other increases or decreases.

Use the formula for correlation coefficient to determine the strength of the relationship.

Correlation coefficient, r is equal to the sum of squares of xy divided by the product of the square root of the sum of squares of xx and xy.

The sample correlation coefficient r measures the strength of the linear relationship and has the following properties:  

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