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1 year ago

Which of the following is the solution to 3I x-1 I≥ 12?

Mathematics

1 answer:

hichkok12 [17]1 year ago

5 0

The solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.

<h3>What are inequalities?</h3>

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

For the given inequality the solution can be found as,

When the value of x is negative,

3|x-1| ≥ 12

x-1 ≥ 4

x ≥ 5

When the value of x is positive,

3|x-1| ≥ 12

- x + 1 ≥ 4

-x ≥ 3

x ≤ -3

Hence, the solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.

Learn more about Inequality:

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A pew research Center project on the state of news media showed that the clearest pattern of news audience growth in 2012 came o

KengaRu [80]

Answer:

Step-by-step explanation:

Given that:

the sample proportion p = 0.39

sample size = 100

Then np = 39

Using normal approximation

The sampling distribution from the sample proportion is approximately normal.

Thus, mean $\mu _{\hat p} = p = 0.39$

The standard deviation;

$\sigma = \sqrt{\dfrac{p(1-p)}{n} }$

$\sigma = \sqrt{\dfrac{0.39(1-0.39)}{100} }$

$\sigma = 0.048$

The test statistics can be computed as:

$Z = \dfrac{{\hat _{p}} - \mu_{_ {\hat p}} }{\sigma_{\hat p}}$

$Z = \dfrac{0.3 - 0.39 }{0.0488}$

$Z = -1. 8 4$

From the z - tables;

$P (\hat p \le 0.3 ) = P(z \le -1.84)$

$\mathbf{P (\hat p \le 0.3 ) = 0.0329}$

(b)

Here;

the sample proportion = 0.39

the sample size n = 400

Since np = 400 * 0.39 = 156

Thus, using normal approximation.

From the sample proportion, the sampling distribution is approximate to the mean $\mu_{\hat p} = p = 0.39$

the standard deviation $\sigma_{\hat p} = \sqrt{\dfrac{p(1-p)}{n} }$

$\sigma_{\hat p} = \sqrt{\dfrac{0.39 (1-0.39)}{400} }$

$\sigma_{\hat p} =0.0244$

The test statistics can be computed as:

$Z = \dfrac{{\hat _{p}} - \mu_{_ {\hat p}} }{\sigma_{\hat p}}$

$Z = \dfrac{0.3 - 0.39 }{0.0244}$

$Z = -3.69$

From the z - tables;

$P (\hat p \le 0.3 ) = P(z \le -3.69)$

$\mathbf{P (\hat p \le 0.3 ) = 0.0001}$

As sample size builds up, the standard deviation of the sampling distribution decreases.

In addition to that, reduction in the standard deviation resulted in increases in the Z score, and the probability of having a sample proportion that is less than 30% also decreases.

6 0

2 years ago

Please answer the following:

serg [7]

The sum of all interior angles in a polygon is
180(n - 2), where n = the number of sides in the polygon.

now, notice this figure above, it has 5 sides, namely is a PENTAgon, so the sum of all its interior angles is 180( 5 - 2), or 540, therefore

$\bf (4x)~+~(3x+15)~~+~~(4x-25)~~+~~(3x+25)~~+~~(2x-3)=540
\\\\\\
16x+12=540\implies 16x=528\implies x=\cfrac{528}{16}\implies x=33$

3 0

2 years ago

Which sequence is geometric? 1, 5, 9, 13, ... 2, 6, 8, 10, ... 5, 7, 9, 11, ... 4, 8, 16, 32, ...

Sliva [168]

Answer:

4, 8, 16, 32

Step-by-step explanation:

4, 8, 16, 32 is a geometric sequence. The value multiplies by 2 every time.

6 0

2 years ago

Identify the solution of each equation from the list given.

sp2606 [1]

Answer:

1.) The answer is b = 6

2.) The answer is t = 10

Step-by-step explanation:

For the first equation in order to fin out the answer we do.....

b + 8 = 14

b + 8 - 8 = 14 - 8

b = 6

For the second question we do....

25 - t = 15

25 - t + t = 15 + t

25 = 15 + t

25 - 15 = 15 + t -15

10 = t

4 0

2 years ago

5/7 = x/11 round your answer to the nearest tenth.

Scilla [17]

Answer:

7.9

Step-by-step explanation:

Multiply both sides of the equation by 11. This cancels out the fraction so 11 * 5/7 = x

lmk if I misunderstood the question or need to elaborate

6 0

2 years ago

Read 2 more answers