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3 years ago

The price of a TV rose from $350 to $371 in one month. By what percent did the TV price rise?

1 answer:

4 0

6% increase

To calculate the percentage increase:
First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number

Then: divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

If your answer is a negative number, then this is a percentage decrease.

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Solve x^2-6x+25 = 0 by completing the square.

Oksana_A [137]

First, subtract both sides by 25:

x^2 - 6x = -25

Because we're completing the square, we subtract both sides by 9:

x^2 - 6x - 9 = -34

(x - 3) = 5.831 (about)

x = 8.831

3 0

3 years ago

What is the length x of a side of the small inner square? Drawing is enclosed in OS link.

Rama09 [41]

So based on your question about the line A and B meet and the four lines are congruent to each other. The graph doesnt show any measurements so there is no exact value to the length of X. But you must consider that the lines are proportional to each other so it means that they are congruent.

5 0

3 years ago

Assume the average height for American women is 64 inches with a standard deviation of 2 inches. A sorority on campus wonders if

satela [25.4K]

Answer:

a) s = 0.4

b) Z = 2.5

c) 99th percentile.

d) The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

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 establishes 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.

Assume the average height for American women is 64 inches with a standard deviation of 2 inches

This means that $\mu = 64, \sigma = 2$

A) Calculate the standard error for the distribution of means.

Sample of 25 means that $n = 25$ , so $s = \frac{2}{\sqrt{25}} = 0.4$ .

B) Calculate the z statistic for the sorority group.

Sample mean of 65 means that $X = 65$ .

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{0.4}$

$Z = \frac{65 - 64}{0.4}$

$Z = 2.5$

C) What is the approximate percentile for this sample? Enter as a whole number.

Z = 2.5 has a p-value of 0.9938, so 0.99*100 = 99th percentile.

D) If the sorority actually had 36 members (still with an average of 65 inches), would you expect the percentile value to increase or decrease? why?

The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.

3 0

3 years ago

Solve (x +9)2 = 25.

alexandr1967 [171]

Answer:

$x = - 4 \: or \: x = - 14$