Given parallelogram ABCD with c(5,4), find the coordinates of A if the diagonals intersect at (2,7)

Which number is a solution of the inequality x <-4? Use the number line to help answer the question.

Fantom [35]

Answer:

0 is the answer

Step-by-step explanation:

4 0

3 years ago

Write a polynomial in factored form.

enyata [817]

Answer:

f(x)= x^3

Step-by-step explanation:

5 0

2 years ago

The College Boards, which are administered each year to many thousands of high school students, are scored so as to yield a mean

Marysya12 [62]

Answer:

a) 15.87% of the scores are expected to be greater than 600.

b) 2.28% of the scores are expected to be greater than 700.

c) 30.85% of the scores are expected to be less than 450.

d) 53.28% of the scores are expected to be between 450 and 600.

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 500, \sigma = 100$

a. Greater than 600

This is 1 subtracted by the pvalue of Z when X = 600. So

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

$Z = \frac{600 - 500}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

1 - 0.8413 = 0.1587

15.87% of the scores are expected to be greater than 600.

b. Greater than 700

This is 1 subtracted by the pvalue of Z when X = 700. So

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

$Z = \frac{700 - 500}{100}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% of the scores are expected to be greater than 700.

c. Less than 450

Pvalue of Z when X = 450. So

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

$Z = \frac{450 - 500}{100}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085.

30.85% of the scores are expected to be less than 450.

d. Between 450 and 600

pvalue of Z when X = 600 subtracted by the pvalue of Z when X = 450. So

X = 600

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

$Z = \frac{600 - 500}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413.

X = 450

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

$Z = \frac{450 - 500}{100}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.3085.

0.8413 - 0.3085 = 0.5328

53.28% of the scores are expected to be between 450 and 600.

6 0

2 years ago

Find the value of x in the isosceles triangle shown below.

joja [24]

Answer: C. 10

Explanation:

Take half right triangle from the isosceles triangle:

We get side lengths:

12/2 = 6, 8, and x

And use Pythagorean’s theorem to find x:

6^2 + 8^2 = x^2
36 + 64 = x^2
100 = x^2
10 = x

7 0

3 years ago

In preparation for an earnings report, a large retailer wants to estimate p= the proportion of annual sales

mr Goodwill [35]

Using the z-distribution, it is found that the 95% confidence interval for the proportion of sales that occured in December is (0.1648, 0.2948).

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

The sample size and the estimate are given by:

$n = 161, \pi = \frac{37}{161} = 0.2298$

Hence:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2298 - 1.96\sqrt{\frac{0.2298(0.7702)}{161}} = 0.1648$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2298 + 1.96\sqrt{\frac{0.2298(0.7702)}{161}} = 0.2948$

The 95% confidence interval for the proportion of sales that occured in December is (0.1648, 0.2948).

More can be learned about the z-distribution at brainly.com/question/25890103

5 0

2 years ago