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3 years ago

Twelve more than seven times a number is the number plus 18. What is the number?

Mathematics

1 answer:

dangina [55]3 years ago

3 0

Answer:

Step-by-step explanation:

Let the number be X

condition

12 more than seven times the number

it can be represented numerically by using process given belwo

seven times the number will be 7 * X = 7X

12 more than 7X will be equal to 7X + 12

______________________________

This number (7X + 12) is equal to number plus 19

number plus 18 will be X + 18

therefore according to the question

7X + 12 = X + 18

=> 7X - X = 18 - 12

=> 6X = 6

=> X = 6/6 = 1 (Answer)

The number is 1.

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The box plots represent the distributions of typing speeds of students before and after a computer-programming course.

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Answer: the range of two distributions are the same

Step-by-step explanation:

So the last one

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3 years ago

Social Sciences Alcohol Abstinence The Harvard School of Public Health completed a study on alcohol consumption on college campu

Scilla [17]

Answer:

a) There is a 6.69% probability that a randomly selected female student abstains from alcohol.

b) If a randomly selected female student abstains from alcohol, there is a 82.87% probability that she attends a coeducational college.

Step-by-step explanation:

This is a probability problem:

We have these following probabilities:

-20.7% of a woman attending an all-women college abstaining from alcohol.

-6% of a woman attending a coeducational college abstaining from alcohol.

-4.7% of a woman attending an all-women college

- 100%-4.7% = 95.3% of a woman attending a coeducational college.

(a) What is the probability that a randomly selected female student abstains from alcohol?

$P = P_{1} + P_{2}$

$P_{1}$ is the probability of a woman attending an all-women college being chosen and abstaining from alcohol. There is a 0.047 probability of a woman attending an all-women college being chosen and a 0.207 probability that she abstain from alcohol. So:

$P_{1} = 0.047*0.207 = 0.009729$

$P_{2}$ is the probability of a woman attending a coeducational college being chosen and abstaining from alcohol. There is a 0.953 probability of a woman attending a coeducational college being chosen and a 0.06 probability that she abstain from alcohol. So:

$P_{2} = 0.953*0.06 = 0.05718$

So, the probability of a randomly selected female student abstaining from alcohol is:

$P = P_{1} + P_{2} = 0.009729 + 0.05718 = 0.0669$

There is a 6.69% probability that a randomly selected female student abstains from alcohol.

(b) If a randomly selected female student abstains from alcohol, what is the probability she attends a coedücational colege?

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

Here:

What is the probability of a woman attending a coeducational college, knowing that she abstains from alcohol.

It can be calculated by the following formula:

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

We have the following probabilities:

$P(B)$ is the probability of a woman from a coeducational college being chosen. So $P(B) = 0.953$

$P(A/B)$ is the probability of a woman abstaining from alcohol, given that she attends a coeducational college. So $P(A/B) = 0.06$

$P(A)$ is the probability of a woman abstaining from alcohol. From a), $P(A) = 0.0669$

So, the probability that a randomly selected female student attends a coeducational college, given that she abstains from alcohol is:

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{(0.953)*(0.06)}{(0.0669)} = 0.8287$

If a randomly selected female student abstains from alcohol, there is a 82.87% probability that she attends a coeducational college.

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3 years ago

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2 years ago

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3 years ago

The amounts of electricity bills for all households in a city have a skewed probability distribution with a mean of $139 and a

ZanzabumX [31]

Answer:

P (within $6 of 4) = 0.9164

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 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 $s = \frac{\sigma}{\sqrt{n}}$ .

Mean of $139 and a standard deviation of $30.

This means that $\mu = 139, \sigma = 30$

Random sample of 75 households

This means that $n = 75, s = \frac{30}{\sqrt{75}} = 3.464$

75 > 30, which means that the sampling distribution is approximately normal.

Find the probability that the mean amount of electric bills for a random sample of 75 households selected from this city will be within $6 of the population mean.

This is the pvalue of Z when X = 139 + 6 = 145 subtracted by the pvalue of Z when X = 139 - 6 = 133.

X = 145

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

By the Central Limit Theorem

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