How to determine the domain and range of a function?

Warren has a container which holds 22 books of the same shape and size. The exact breakdown of his books is shown below:

ohaa [14]

Given:

Total number of book = 22

Number of white books = 6

Number of Purple books = 9

Number of green books = 7

To find:

The probability that Warren takes out a green book in both draws (with replacement).

Solution:

We know that,

$\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$P(\text{White})=\dfrac{6}{22}$

$P(\text{Purple})=\dfrac{9}{22}$

$P(\text{green})=\dfrac{7}{22}$

After replacement, the probability of event remains the same and the independent.

The probability that Warren takes out a green book in both draws is:

$P=P(\text{green})\times P(\text{green})$

$P=\dfrac{7}{22}\times \dfrac{7}{22}$

$P=\dfrac{49}{484}$

Therefore, the correct option is (a).

7 0

2 years ago

Ten engineering schools in the United States were surveyed. The sample contained 250 electrical engineers, 80 being women; 175 c

steposvetlana [31]

Answer:

There is a significant difference between the two proportions.

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for difference between population proportions is:

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

Compute the sample proportions as follows:

$\hat p_{1}=\frac{80}{250}=0.32\\\\\hat p_{2}=\frac{40}{175}=0.23$

The critical value of <em>z</em> for 90% confidence interval is:

$z_{0.10/2}=z_{0.05}=1.645$

Compute a 90% confidence interval for the difference between the proportions of women in these two fields of engineering as follows:

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

$=(0.32-0.23)\pm 1.645\times\sqrt{\frac{0.32(1-0.32)}{250}+\frac{0.23(1-0.23)}{175}}\\\\=0.09\pm 0.0714\\\\=(0.0186, 0.1614)\\\\\approx (0.02, 0.16)$

There will be no difference between the two proportions if the 90% confidence interval consists of 0.

But the 90% confidence interval does not consists of 0.

Thus, there is a significant difference between the two proportions.

4 0

2 years ago

An item is regularly priced at $25. Kaitlin bought it on sale for 20% off the regular price. How much did Kaitlin pay?

horsena [70]

Answer:

$20

Step-by-step explanation:

25 x (20/100) = 5

25 - 5 = 20

8 0

2 years ago

Read 2 more answers

Select the correct answer. Simplify the expression below. 4x(3x − 7) − 19x2 A. -7x2 − 7 B. -35x2 C. -7x2 − 28x D. -31x2 − 28x

morpeh [17]

Answer:

$C. -7x^2-28x$

Step-by-step explanation:

The given expression is $4x(3x-7)-19x^2$

We apply the distributive property to expand the parenthesis

$12x^2-28x-19x^2$

Regroup similar terms to get:

$12x^2-19x^2-28x$

Combine the similar terms to obtain:

$-7x^2-28x$

The correct option is C.

5 0

2 years ago

Which number line plots the integers -2, 3 and 4

Leokris [45]

Answer:

* * *

|-4|___|-3|___|-2|___|-1|___|0|___|1|___|2|___|3|___|4|___|5|___|6|

Step-by-step explanation:

You are looking for a dot over -2 (that is 2 units to the left of 0).

You are looking for a dot over 3 (that is 3 units to the right of 0).

You are looking for a dot over 4 (that is 4 units to the right of 0).

If you find one of the graphs matches this, then you should select.

The graph would look like this:

* * *

|-4|___|-3|___|-2|___|-1|___|0|___|1|___|2|___|3|___|4|___|5|___|6|

3 0

2 years ago

Read 2 more answers