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ella [17]
3 years ago
8

What is the value of a in the equation −14a−5=−12?

Mathematics
1 answer:
-BARSIC- [3]3 years ago
7 0
-14a-5=-12
+5 +5
-14a=-7
Divide -7 by -14a
a=2
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The answer is c) y=2/3x
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Please give me the right answer if the algebraic expression is 11 decreased by k is thirty-two. How to write it.
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3 years ago
Let X represent the amount of gasoline (gallons) purchased by a randomly selected customer at a gas station. Suppose that the me
Alexus [3.1K]

Answer:

a) 18.94% probability that the sample mean amount purchased is at least 12 gallons

b) 81.06% probability that the total amount of gasoline purchased is at most 600 gallons.

c) The approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers is 621.5 gallons.

Step-by-step explanation:

To solve this question, we use 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 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.

For sums, we can apply the theorem, with mean \mu and standard deviation s = \sqrt{n}*\sigma

In this problem, we have that:

\mu = 11.5, \sigma = 4

a. In a sample of 50 randomly selected customers, what is the approximate probability that the sample mean amount purchased is at least 12 gallons?

Here we have n = 50, s = \frac{4}{\sqrt{50}} = 0.5657

This probability is 1 subtracted by the pvalue of Z when X = 12.

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

By the Central Limit theorem

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

Z = \frac{12 - 11.5}{0.5657}

Z = 0.88

Z = 0.88 has a pvalue of 0.8106.

1 - 0.8106 = 0.1894

18.94% probability that the sample mean amount purchased is at least 12 gallons

b. In a sample of 50 randomly selected customers, what is the approximate probability that the total amount of gasoline purchased is at most 600 gallons.

For sums, so mu = 50*11.5 = 575, s = \sqrt{50}*4 = 28.28

This probability is the pvalue of Z when X = 600. So

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

Z = \frac{600 - 575}{28.28}

Z = 0.88

Z = 0.88 has a pvalue of 0.8106.

81.06% probability that the total amount of gasoline purchased is at most 600 gallons.

c. What is the approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers.

This is X when Z has a pvalue of 0.95. So it is X when Z = 1.645.

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

1.645 = \frac{X- 575}{28.28}

X - 575 = 28.28*1.645

X = 621.5

The approximate value of the 95th percentile for the total amount purchased by 50 randomly selected customers is 621.5 gallons.

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3 years ago
Triangle ABC has vertices A(1,2), B(1,5), and C(4,2) and undergoes a transformation. Circle the set of vertices that does not be
allochka39001 [22]
The statement says, "Triangle ABC has vertices A(1,2), B(1,5), and C(4,2) and undergoes a transformation."

The question asked is to find the set of vertices that does not belong to the group. This means that an attachment is expected to be there. The absence of any attachment makes this question hard to answer. Maybe this helps answer you question.

8 0
3 years ago
Find the cos of angle y
Minchanka [31]

ANSWER

\cos(y)  =  \frac{4}{5}

EXPLANATION

From the mnemonics SOH-CAH-TOA.

We want to find the cosine of y

CAH means cosine ratio involves adjacent over the hypotenuse.

\cos(y)  =  \frac{adjacent}{hypotenuse}

From the right by triangle, the side ajacent to angle y is 64 units and the hypotenuse is 80 units.

\cos(y)  =  \frac{64}{80}

\cos(y)  =  \frac{4}{5}

3 0
3 years ago
Read 2 more answers
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