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2 years ago

What is true about the solution to the system of inequities shown?

Mathematics

1 answer:

SpyIntel [72]2 years ago

5 0

The true solution to the system of inequities shown is B; All values that satisfy $y \leq \dfrac{ 1}{3}x - 3$ are solutions.

<h3>What is a system of inequalities?</h3>

When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalities.

A collection of inequalities for which we consider a common solution for all inequalities is called a system of inequalities.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true.

A set of such values is called a solution set to the considered equation or inequality.

The true solution to the system of inequities shown is B;

All values that satisfy $y \leq \dfrac{ 1}{3}x - 3$ are solutions.

Learn more about solutions to the system of inequalities here:

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In a simple random sample of 14001400 young people, 9090% had earned a high school diploma. Complete parts a through d below.

ratelena [41]

Answer:

(a) The standard error is 0.0080.

(b) The margin of error is 1.6%.

(c) The 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).

(d) The percentage of young people who earn high school diplomas has increased.

Step-by-step explanation:

Let p = proportion of young people who had earned a high school diploma.

A sample of n = 1400 young people are selected.

The sample proportion of young people who had earned a high school diploma is:

$\hat p=0.90$

(a)

The standard error for the estimate of the percentage of all young people who earned a high school diploma is given by:

$SE_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Compute the standard error value as follows:

$SE_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=\sqrt{\frac{0.90(1-0.90)}{1400}}\\$

$=0.008$

Thus, the standard error for the estimate of the percentage of all young people who earned a high school diploma is 0.0080.

(b)

The margin of error for (1 - α)% confidence interval for population proportion is:

$MOE=z_{\alpha/2}\times SE_{\hat p}$

Compute the critical value of z for 95% confidence level as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the margin of error as follows:

$MOE=z_{\alpha/2}\times SE_{\hat p}$

$=1.96\times 0.0080\\=0.01568\\\approx1.6\%$

Thus, the margin of error is 1.6%.

(c)

Compute the 95% confidence interval for population proportion as follows:

$CI=\hat p\pm MOE\\=0.90\pm 0.016\\=(0.884, 0.916)\\\approx (88.4\%,\ 91.6\%)$

Thus, the 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).

(d)

To test whether the percentage of young people who earn high school diplomas has increased, the hypothesis is defined as:

H₀: The percentage of young people who earn high school diplomas has not increased, i.e. p = 0.80.

Hₐ: The percentage of young people who earn high school diplomas has not increased, i.e. p > 0.80.

Decision rule:

If the 95% confidence interval for proportions consists the null value, i.e. 0.80, then the null hypothesis will not be rejected and vice-versa.

The 95% confidence interval for the percentage of all young people who earned a high school diploma is (88.4%, 91.6%).

The confidence interval does not consist the null value of p, i.e. 0.80.

Thus, the null hypothesis is rejected.

Hence, it can be concluded that the percentage of young people who earn high school diplomas has increased.

8 0

3 years ago

A professor wants to award prizes for 1st, 2nd, 3rd, 4th and 5th in the class of 30. In how many ways can the prizes be awarded

aniked [119]

Answer:

$Selection = 17100720\ ways$

Step-by-step explanation:

Given

$Students = 30$

$Positions = 5$ i.e. first to fifth

Required

Determine number of selection

1st position = Any of the 30 students

2nd position = Any of the 29 students

3rd position = Any of the 28 students

4th position = Any of the 27 students

5th position = Any of the 26 students

Number of selection is then calculated as:

$Selection = 30 * 29 * 28 * 27 * 26$

$Selection = 17100720\ ways$

8 0

3 years ago

HELP me please! Please I really need it!

Crank

Answer:

The radius is 6.1 cm

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3

There is a typo in the problem.

We know the volume

950 = 4/3 (3.14) r^3

Multiply each side by 3/4

3/4 *950 = 3.14 r^3

712.5 = 3.14 r^3

Divide each side by 3.14

712.5/3.14 = r^3

226.910828 = r^3

Take the cube root of each side

226.910828 ^ (1/3) = r^3 ^ 1/3

6.099371323 = r

The radius is 6.1 cm

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3 years ago

Find the percent change from 50 to 22

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Answer:

Step-by-step explanation:

50 - 22 = 28

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3 years ago

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Reducing the solution to a problem in lowest terms

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