Hey Siri the sum of two numbers is 50 and the larger number is six less than 3 times the smaller number find the smaller number

Sales increased by only 12% last month. If the sales from the previous month were $152,850, what were last months sales

Tamiku [17]

Answer:

$\$171,192$

Step-by-step explanation:

Remember that

$100\%+12\%=112\%=112/100=1.12$

we know that

The sales from the previous month were $152,850

This amount represent the 100%

so

Find out what were last months sales, multiply the sales from the previous month by the factor 1.12

$\$152,850(1.12)=\$171,192$

3 0

3 years ago

Which pair is made up of prime numbers 11 & 33 , 42 & 56 , 37 & 67, 57 & 97

Cerrena [4.2K]

Answer:

37 & 67

Step-by-step explanation:

11 & 33

11 - 1, 11

11 is prime

33 - 1, 3, 11, 33

33 is composite number

11 & 33 is incorrect

42 & 56

42 - 1, 2, 3, 6, 7, 14, 21, 42
56 - 1, 2, 4, 7, 8, 14, 28, 56
Both 42 and 56 are composite numbers
42 & 56 is incorrect

37 & 67

37 - 1, 37
67 - 1, 67
Both 37 and 67 are prime numbers
37 & 56 is correct

57 & 97

57 - 1, 3, 19, 57
97 - 1, 97
57 is a composite number, 97 is a prime number
57 & 97 is incorrect

3 0

3 years ago

In a random sample of 75 American women age 18 to 30, 26 agreed with the statement that a woman should have the right to a legal

ddd [48]

Answer:

a) $z=\frac{0.347-0.328}{\sqrt{0.338(1-0.338)(\frac{1}{75}+\frac{1}{64})}}=0.236$

$p_v =2*P(Z>0.236)=0.813$

If we compare the p value and using any significance level for example $\alpha=0.01$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant differences between the two proportions.

b) We are confident at 99% that the difference between the two proportions is between $-0.188 \leq p_B -p_A \leq 0.226$

Step-by-step explanation:

Previous concepts and data given

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion of women age 18 to 30 agreed with the statement that a woman should have the right to a legal abortion for any reason

$\hat p_A =\frac{26}{75}=0.347$ represent the estimated proportion of women age 18 to 30 agreed with the statement that a woman should have the right to a legal abortion for any reason

$n_A=75$ is the sample size for A

$p_B$ represent the real population proportion for women age 58 to 70 agreed with the statement that a woman should have the right to a legal abortion for any reason

$\hat p_B =\frac{21}{64}=0.328$ represent the estimated proportion of women age 58 to 70 agreed with the statement that a woman should have the right to a legal abortion for any reason

$n_B=64$ is the sample size required for B

$z$ represent the critical value for the margin of error and for the statisitc

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part a

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

Null hypothesis: $p_{A} = p_{B}$

Alternative hypothesis: $p_{A} \neq p_{B}$

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

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

Where $\hat p=\frac{X_{A}+X_{B}}{n_{A}+n_{B}}=\frac{26+21}{75+64}=0.338$

Calculate the statistic

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

$z=\frac{0.347-0.328}{\sqrt{0.338(1-0.338)(\frac{1}{75}+\frac{1}{64})}}=0.236$

Statistical decision

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

$p_v =2*P(Z>0.236)=0.813$

If we compare the p value and using any significance level for example $\alpha=0.01$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant differences between the two proportions.

Part b

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$(0.347-0.328) - 2.58 \sqrt{\frac{0.347(1-0.347)}{75} +\frac{0.328(1-0.328)}{64}}=-0.188$

$(0.347-0.328) + 2.58 \sqrt{\frac{0.347(1-0.347)}{75} +\frac{0.328(1-0.328)}{64}}=0.226$

And the 99% confidence interval for the difference of proportions would be given (-0.188;0.226).

We are confident at 99% that the difference between the two proportions is between $-0.188 \leq p_B -p_A \leq 0.226$

5 0

3 years ago

Which term refers to a statistical value that is a measure of the spread or variation in the scores in a given data set?

IRINA_888 [86]

Answer:

A

Step-by-step explanation:

The dispersion refers to the overall spread of the data — how "disperse" it is across values.

The independent variable is what you manipulate in a study, whereas the dependent variable is what you measure.

Central tendency is another word for average.

6 0

2 years ago

<3 and what is a linear pair

mylen [45]

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. hope it helps

7 0

3 years ago