Find the circumference of the circle. Rounded to the nearest tenth the circle is 40 in

Is 4.5 same as 4.50?

Softa [21]

Answer:

Yes

Step-by-step explanation:

0s after all the decimals do not count

4 0

3 years ago

Read 2 more answers

An individual needs a daily supplement of at least 420 units of vitamin C and 170 units of vitamin E and agrees to obtain this s

Ierofanga [76]

Answer:

To obtain equivalent amount from both foods we can eat 10 ounces of Food I and 5 Ounces of food II

To obtain minimum cholesterol, the individual should eat only 21 ounces of food II and zero ounce of food for the daily supplement of the individual

Step-by-step explanation:

Food I contains 32×C + 10×E per ounce

Food II contains 20×C + 14×E

Here we have X × (Food I) + Y × (Food II) = 420 C + 170 E

32·X + 20·Y = 420 C

10·X + 14·Y = 170 E

Therefore

X = 10 and Y = 5

To minimize the cholesterol, we can increase amount of Food II to get

21 ounces of food II gives

420 units of vitamin E and 294 units of vitamin E with 273 units of cholesterol.

3 0

3 years ago

What is the bases, height, perimeter, and the area from the trapezoid? please help me

Sergio039 [100]

Answer:

base : 30 cm

height : 20 cm

perimeter : 92 cm

Area : 400 cm

Step-by-step explanation:

base : 30 cm

height : 20 cm

perimeter : 27 + 30 + 25 + 10

: 92 cm

Area : (1/2 ( a + b) ) x h

: (1/2 ( 10 + 30) ) x 20

: (20) x 20

: 400 cm

3 0

3 years ago

What Is The Mass, Volume, Density

m_a_m_a [10]

Answer:

The volume is the amount of space an object takes up.

The mass is the measure of how much matter in a object.

The density is the mass divided by volume.

6 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