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3 years ago

What is CD?

Mathematics

2 answers:

Tema [17]3 years ago

4 0

Answer:

Step-by-step explanation:

Line segment CG is amount to 12 and line segment GD is 6. The length of the whole line segment, CD is 18 by adding 12 and 6.

✌

victus00 [196]3 years ago

3 0

Answer:

Step-by-step explanation:

Point G is the centroid of triangle ABC.
C is a vertex of the triangle

D is the midpoint of the side opposite the vertex.

From Centroid Theorems, we know that the distance from the centroid to the vertex is twice as long as the distance from the centroid to the midpoint of the side opposite the vertex.

Therefore:

CG=2DG

Let the length of segment DG =x

The length of segment CG is 6 units greater, therefore: CG=x+6

Substituting into CG=2DG:

x+6=2x

2x-x=6

x=6 Units

Therefore:

CD=CG+GD

=6+6+6

=18 Units

<u><em>The correct option is C.</em></u>

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A store pays $85 for a table. The markup is 90%. What is the selling price?

Harman [31]

Answer:

$161.5

Step-by-step explanation:

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3 years ago

A survey sampled men and women workers and asked if they expected to get a raise or promotion this year. Suppose the survey samp

Oksanka [162]

Answer:

The null hypothesis is: $H_0: p_M - p_W = 0$

The alternative hypothesis is: $H_1: p_M - p_W > 0$

b) For men is of 0.49 and for women is of 0.36.

c) The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Men:

98 out of 200, so:

$p_M = \frac{98}{200} = 0.49$

$s_M = \sqrt{\frac{0.49*0.51}{200}} = 0.0353$

Women:

72 out of 200, so:

$p_W = \frac{72}{200} = 0.36$

$s_W = \sqrt{\frac{0.36*0.64}{200}} = 0.0339$

a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.

At the null hypothesis, we test if the proportion are similar, that is, if the subtraction of the proportions is 0, so:

$H_0: p_M - p_W = 0$

At the alternative hypothesis, we test if the proportion of men is greater, that is, the subtraction is greater than 0, so:

$H_1: p_M - p_W > 0$

b. What is the sample proportion for men? For women?

For men is of 0.49 and for women is of 0.36.

c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?

From the sample, we have that:

$X = p_M - p_W = 0.49 - 0.36 = 0.13$

$s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0353^2 + 0.0339^2} = 0.0489$

The test statistic is:

$z = \frac{X - \mu}{s}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, and s is the standard error, so:

$z = \frac{0.13 - 0}{0.0489}$

$z = 2.66$

P-value of the test and decision:

The p-value of the test is the probability of finding a difference above 0.13, which is the p-value of z = 2.66.

Looking at the z-table, z = 2.66 has a p-value of 0.9961.

1 - 0.9961 = 0.0039.

The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.

4 0

3 years ago

According to a milk carton, 2% milk contains 70 % less fat than whole milk. The nutrition label on the other side of the carton

Ostrovityanka [42]

Answer:

8.33 grams of fat

Step-by-step explanation:

One serving of the milk contains 2.5 grams of fat.

2% milk has 70% less fat than whole milk.

This means 2% milk has 30% of the fat that whole milk has.

Let W = amount of fat in whole milk

30% of the fat that whole milk has