How would i solve these?

What is the difference between exponent form and expanded form (repeated multiplication)?

Inga [223]

Expanded FormExpanded form refers to a base and an exponent written as repeated multiplication. ExponentExponents are used to describe the number of times that a term is multiplied by itself. ExpressionAn expression is a mathematical phrase containing variables, operations and/or numbers.

5 0

3 years ago

For every 3 wrapped packages Mary uses 1/2 roll of wrapping paper how many packages can she wrap with 2 1/2 rolls of wrapping pa

8_murik_8 [283]

Answer:

15 packages

Step-by-step explanation:

Set up a proportion, where x is the number of packages she can wrap with 2.5 rolls of wrapping paper:

$\frac{3}{0.5}$ = $\frac{x}{2.5}$

Cross multiply and solve for x:

0.5x = 7.5

x = 15

So, with 2.5 rolls of wrapping paper, she can wrap 15 packages

8 0

2 years ago

Assume that they all agree on the sample size and the sample mean use the pairs below to select the team that has the smallest s

Archy [21]

Step-by-step explanation:

A.Confidence Level: 99.7%; Confidence Interval: 42 to 48

B.Confidence Level: 95%; Confidence Interval: 43 to 47

C.Confidence Level: 68%; Confidence Interval: 44 to 46

D.Confidence Level: 95%; Confidence Interval: 44 to 46

6 0

2 years ago

Which of the following is the solution to | x -12 | < 15

KiRa [710]

Hello,
Answer D -3<x<27
Indeed:
1)
if x-12≥0 then x≥12 and
|x-12|=x-12x-12<15 → x<27
so 12≤x<27
2) if x-12<0 then
x<12 and|x-12|=-(x-12)<15
-x+12<15-x<3 → x>-3
So -3<x<12
Thus -3<x<12 U 12≤x<27 ⇔ -3<x<27

7 0

2 years ago

2.06. In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nucle

DaniilM [7]

Answer:

$z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795$

$p_v =2*P(Z>2.795)= 0.005$

So if we compare the p value and using any significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=74$ represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

$X_{2}=70$ represent the number of people suburban residents are in favor

$n_{1}=100$ sample 1 selected

$n_{2}=125$ sample 2 selected

$p_{1}=\frac{74}{100}=0.74$ represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

$p_{2}=\frac{70}{125}=0.56$ represent the proportion of suburban residents are in favor

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportions are different, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{74+70}{100+125}=0.64$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795$

Statistical decision

The significance level provided is $\alpha=0.05$ ,and we can calculate the p value for this test.

Since is a two tailed test the p value would be:

$p_v =2*P(Z>2.795)= 0.005$

So if we compare the p value and using any significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.

5 0

3 years ago