1. For each event, write the sample space and tell how many outcomes there are.

Nuetrik [128]

$\textbf{Given that,}\\\\~~~\dfrac{5^4}{5^7}\\\\\\=5^{4-7}~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Apply exponent rule:}~\dfrac{a^m}{a^n} = a^{m-n}\\\\\\=5^{-3}\\\\\\=\dfrac 1{5^3}~~~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Apply exponent rule:}~ a^{-n} = \dfrac 1 {a^n},~~~a \neq 0 \\\\\\=\dfrac 1{125}\\\\\\=0.008$

5 0

2 years ago

Read 2 more answers

A retail clothing store offers customers an opportunity to open up a credit card during checkout. One location of the retail clo

svetoff [14.1K]

A function assigns the value of each element of one set to the other specific element of another set. The total amount of credit cards opened at the two locations is given as 45+3t.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

Given that the number of credit cards, A, that is opened t months since January can be modeled by the function A(t) = 20 + 4t, while the number of credit cards opened at another location, B, is defined by the function B(t)=25−t.

Now, the total number of credit cards that are opened at both the location together will be,

Total number of credit cards = A(t) + B(t)

= 20 + 4t + 25 - t

= 20 + 25 + 4t - t

= 45 + 3t

Hence, the total amount of credit cards opened at the two locations is given as 45+3t.

Learn more about Function here:

brainly.com/question/5245372

#SPJ1

3 0

2 years ago

Help.this question ha sbeen egttin on my nerves for days

pogonyaev

Answer: 8y4+25y3+60y2+10y+7

Step-by-step explanation:

(y2+3y+7)(8y2+y+1)

=(y2+3y+7)(8y2+y+1)

=(y2)(8y2)+(y2)(y)+(y2)(1)+(3y)(8y2)+(3y)(y)+(3y)(1)+(7)(8y2)+(7)(y)+(7)(1)

=8y4+y3+y2+24y3+3y2+3y+56y2+7y+7

=8y4+25y3+60y2+10y+7

hope this helps!:)

8 0

3 years ago

A rectangle that has an area of 357 square inches is 17 inches wide. Using the formula for area (A=lw), how long is the rectangl

Lynna [10]

----------------------------------------------------------------------------------------
Formula
----------------------------------------------------------------------------------------
Area of rectangle = Length x Width

----------------------------------------------------------------------------------------
Find Length
----------------------------------------------------------------------------------------
357 = Length x 17

----------------------------------------------------------------------------------------
Divide by 17 through
----------------------------------------------------------------------------------------
Length = 357 ÷ 7
Length = 51 inches

----------------------------------------------------------------------------------------
Answer: The length of the rectangle is 51 inches
----------------------------------------------------------------------------------------

7 0

3 years ago

Several years ago, 50% of parents who had children in grades K-12 were satisfied with the quality of education the students r

galina1969 [7]

Answer:

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

We have to see if 50% = 0.5 is part of the confidence interval.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 1095, \pi = \frac{478}{1095} = 0.4365$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 - 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4118$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4365 + 1.96\sqrt{\frac{0.4365*0.5635}{1095}} = 0.4612$

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.

5 0

3 years ago