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3 years ago

Choose the correct description of the graph of the inequality x - 3 >= 5.

Mathematics

2 answers:

lions [1.4K]3 years ago

8 0

The correct answer is:

D) Closed circle on 8, shading to the right.

Explanation:

First we must solve the inequality:

x - 3 ≥ 5

Add 3 to each side:

x - 3 + 3 ≥ 5 + 3

x ≥ 8

To graph this, we want a circle on 8 Since it is "greater than or equal to," 8 is included in the solution set. This means the circle will be closed.

Since it is "greater than," we want the numbers to the right of 8 on the number line.

This means the inequality will be a closed circle and shaded to the right.

Jobisdone [24]3 years ago

6 0

X - 3 > = 5
x > = 5 + 3
x > = 8

closed circle on 8...because of the equal sign.....shaded to the right...because of the > sign.

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In a survey of 2957 adults, 1455 say hey have started paying bills online in the least year construct a 99% confidence interval

Vikki [24]

Answer: 0.49 ± 0.0237

Step-by-step explanation: A interval of a 99% confidence interval for the population proportion can be found by:

$p_{hat}$ ± z. $\sqrt{\frac{p_{hat}(1-p_{hat})}{n} }$

$p_{hat}$ is the proportion:

$p_{hat}$ = $\frac{1455}{2957}$

$p_{hat}$ = 0.49

For a 99% confidence interval, z = 2.576:

0.49 ± 2.576. $\sqrt{\frac{0.49(1-0.49)}{2957} }$

0.49 ± 2.576. $\sqrt{\frac{0.49*0.51}{2957} }$

0.49 ± 2.576.(0.0092)

0.49 ± 0.0237

For a 99% confidence interval, the proportion will be between 0.4663 and 0.5137 or 0.49 ± 0.0237

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3 years ago

An environmental scientist wants to use a 95% confidence interval to estimate the mean number of hours per day her solar panel r

MissTica

Answer:

a) The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

b) The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

Step-by-step explanation:

We have the standard deviation for the sample. So we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 48 - 1 = 47

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 47 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 2.0117

The margin of error is:

M = T*s = 2.0117*2.3 = 4.6

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 7.1 - 4.6 = 2.5 hours of sunlight per day

The upper end of the interval is the sample mean added to M. So it is 7.1 + 4.6 = 11.7 hours of sunlight per day

a) Compute the 95% confidence interval for the mean.

The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

b) Explain your confidence interval from part (a) in context.

The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.

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3 years ago

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antoniya [11.8K]

Answer:

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3 years ago