What is the area of the shaded region?

At a concert, you purchase 3 T-shirts and a concert program for a total cost of $90. The program cost $15 and the T-shirts all c

Law Incorporation [45]

Answer:

the anwers is 105

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen

guajiro [1.7K]

Answer:

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

p1 -> 1993

20 out of 100, so:

$p_1 = \frac{20}{100} = 0.2$

$s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04$

p2 -> 1997

10 out of 100, so:

$p_2 = \frac{10}{100} = 0.1$

$s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03$

Distribution of p1 – p2:

$p = p_1 - p_2 = 0.2 - 0.1 = 0.1$

$s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05$

Confidence interval:

$p \pm zs$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower bound of the interval is:

$p - zs = 0.1 - 1.645*0.05 = 0.01775
$

The upper bound of the interval is:

$p + zs = 0.1 + 1.645*0.05 = 0.18225
$

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

6 0

3 years ago

Formulating and solving inverse variation functions

andreyandreev [35.5K]

Answer:

See below.

Step-by-step explanation:

A. k = 50 * 3.6 = 180.

B. The equation is y = 180/x.

C. When x = 75, y = 180/75

= 2.4.

D. Checking C: 2.4 = 180/75 = 2.4. Correct

7 0

2 years ago

At the candy store there are 420 gumdrops and 280 chocolate bars, for a total of 700 candies all together. What is the ratio of

Mekhanik [1.2K]

Answer:

5 : 2

Step-by-step explanation:

Given that:

Number of gumdrops = 420

Number of chocolate bars = 280

Total Number of candies = 700

To find:

The ratio of candies to chocolate bars = ?

Solution:

First of all, let us discuss the method to find the ratio of any two quantities.

Suppose, we need to find the ratio of two numbers $p$ and $q$ .

Then to find the ratio $p:q$ , we need to divide p by q and represent it in the simplest form $\frac{a}{b}$ such that a and b can not be divided further.