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3 years ago

Solve the following inequalities and give the solutions in both set and interval notations.

Mathematics

1 answer:

andrew11 [14]3 years ago

7 0

Given:

The inequality is

$-\dfrac{x}{8}+\dfrac{8}{3}\geq 3$

To find:

The solution for the given inequality in both set and interval notations.

Solution:

We have,

$-\dfrac{x}{8}+\dfrac{8}{3}\geq 3$

It can be written as

$-\dfrac{x}{8}\geq 3-\dfrac{8}{3}$

$-\dfrac{x}{8}\geq \dfrac{9-8}{3}$

$-\dfrac{x}{8}\geq \dfrac{1}{3}$

Multiply both sides by -8 and change the inequality sign.

$x\leq -\dfrac{8}{3}$

It means all the values of $x$ which are less than or equal to $-\dfrac{8}{3}$ are included in the solution set.

Set notation is $\{x|x\leq -\dfrac{8}{3}\}$ .

Interval notation is $\left(-\infty,-\dfrac{8}{3}\right ]$ .

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8 Leandra's fastest time for the 400 m is 70 seconds. In his next race he improves by

disa [49]

8) a) The new fastest time is 56.7 seconds, b) The <em>overall percentage</em> improvement is 19 %.

9) The height after the first increase is 1.375 meters and after the second increase is 1.54 meters.

<h3>How to apply percentages in real life applications</h3>

In this problem we have two examples from real life, in which percentages are used. The first is the distance traveled by a runner in a given time and the second is the growth of a person in time. Change in variables based on percentages are described by the following formula:

C' = C · (1 + r / 100) (1)

Where:

C - Initial value
C' - Final value
r - Percentage of change.

Now we proceed to resolve on each case. 8) a) Please notice that the runner must cover the trail in less time and percentage time must be negative. If we know that C = 70 and r = - 10, then his new fastest time is:

C' = 70 · (1 - 10 / 100)

C' = 70 · 0.90

C' = 63

And again: (C' = 63, r = - 10)

C'' = 63 · (1 - 10 / 100)

C'' = 63 · 0.90

C'' = 56.7

The new fastest time is 56.7 seconds.

b) And the overall percentage improvement is:

r = (|C'' - C| / C) × 100 %

r = (|56.7 - 70| / 70) × 100 %

r = 19 %

The <em>overall percentage</em> improvement is 19 %.

9) If we know that C = 1.25 and r = 10, then the height next year is:

C' = 1.25 · (1 + 10 / 100)

C' = 1.375

And again: (C' = 1.375, r = 12)

C'' = 1.375 · (1 + 12 / 100)

C'' = 1.54

The height after the first increase is 1.375 meters and after the second increase is 1.54 meters.

To learn more on percentages: brainly.com/question/13450942

#SPJ1

3 0

2 years ago

What causes changes of states in matter?

Reptile [31]

The answer is A I believe

5 0

3 years ago

Read 2 more answers

Please help! I don't understand how to solve this problem

Ilia_Sergeevich [38]

Using the z-distribution, a sample of 142,282 should be taken, which is not practical as it is too large of a sample.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

The margin of error is:

$M = z\frac{\sigma}{\sqrt{n}}$

In which:

$\overline{x}$ is the sample mean.

z is the critical value.

n is the sample size.

$\sigma$ is the standard deviation for the population.

Assuming an uniform distribution, the standard deviation is given by:

$S = \sqrt{\frac{(4 - 0)^2}{12}} = 1.1547$

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

The sample size is found solving for n when the margin of error is of M = 0.006, hence:

$M = z\frac{\sigma}{\sqrt{n}}$

$0.006 = 1.96\frac{1.1547}{\sqrt{n}}$

$0.006\sqrt{n} = 1.96 \times 1.1547$

$\sqrt{n} = \frac{1.96 \times 1.1547}{0.006}$

$(\sqrt{n})^2 = \left(\frac{1.96 \times 1.1547}{0.006}\right)^2$

n = 142,282.

A sample of 142,282 should be taken, which is not practical as it is too large of a sample.

More can be learned about the z-distribution at brainly.com/question/25890103

#SPJ1

8 0

1 year ago

The time you have before finance charges are assessed is called the a. credit limit. c. APR. b. incentive. d. grace period.

Tanya [424]

Answer:

The time you have before finance charges are assessed is called the Grace period

option-D

Step-by-step explanation:

we know that

Grace period is the extra time given to customer to pay amount before finance charges

But once grace period passes , customer will have to pay extra fee or penalty with interest with passing days

So,

The time you have before finance charges are assessed is called the Grace period

So,

option-D

6 0

4 years ago

Item 18

nasty-shy [4]

The first thing we have to do is to calculate the midpoint of the min and max speeds. We are given that the min and max is 74 and 95 respectively. The midpoint is then calculated as (max+min) / 2. Therefore:

midpoint = (74 + 95) / 2 = 84.5

Next, we calculate the distance from the midpoint to the endpoint by doing subtraction. Therefore:

min endpoint: 84.5 – 74 = 10.5

max endpoint: 95 – 84.5 = 10.5

Now we know that v minus the midpoint will equal the distance such that:

| v - midpoint | = distance.

To our problem,

| v – 84.5 | = 10.5

7 0

3 years ago