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2 years ago

Solve the inequality -12 ≤ 2x -4 < 10

Mathematics

2 answers:

damaskus [11]2 years ago

8 0

Answer:

-4 ≤ x < 7

Step-by-step explanation:

Method 1: Split the inequality into two parts,

-12 ≤ 2x-4

and

2x -4 < 10

Solve.

-8 ≤ 2x

2x ≥ -8

x ≥ -4

and

2x < 14

x < 7

So, x is greater than (or equal to) -4, but less than 7.

-4 ≤ x < 7

Method 2:

-12 ≤ 2x - 4 < 10

Add 4 to both sides.

-8 ≤ 2x < 14

Divide both sides by 2.

-4 ≤ x < 7

Fofino [41]2 years ago

5 0

Answer:

-4 ≤ x <7

x is greater than or equal to -4, and x is less than 7

Step-by-step explanation:

Take each side and solve

-12 ≤ 2x -4

subtract 4 on both sides

-8 ≤ 2x

divide by 2 on both sides

-4 ≤ x

2x -4 < 10

add 4 on both sides

2x < 14

divide by two on both sides

x < 7

Final answer:

-4 ≤ x <7

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vladimir1956 [14]

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3 years ago

The proportion of left handed people in the population is about 0.10. Suppose a random sample of 300 people is observed. (a) Wha

pantera1 [17]

Answer: $(\hat{p})\sim N(0.10,\ 0.017)$

Step-by-step explanation:

Sampling distribution of the sample proportion $(\hat{p})$ :

$(\hat{p})\sim N(p,\ \sqrt{\dfrac{p(1-p)}{n}})$

The sampling distribution of the sample proportion $(\hat{p})$ has mean = $\mu_{\hat{p}}=p$ and standard deviation = $\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}$ .

Given : The proportion of left handed people in the population is about 0.10.

i.e. p=0.10

sample size : n= 300

Then , the sampling distribution of the sample proportion $(\hat{p})$ will be :-

$(\hat{p})\sim N(0.10,\ \sqrt{\dfrac{0.10(1-0.10)}{300}})$

$(\hat{p})\sim N(0.10,\ \sqrt{0.0003})$

$(\hat{p})\sim N(0.10,\ 0.017)$ (approx)

Hence, the sampling distribution of the sample proportion $(\hat{p})$ is $(\hat{p})\sim N(0.10,\ 0.017)$

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2 years ago

Can someone help please :)

andrew-mc [135]

Answer:

x = 5

Step-by-step explanation:

These triangles are similar, so they are in proportion to each other. Because of this we can say $\frac{2.5}{3.5}$ (the lengths of the vertical sides) = $\frac{x}{7}$ (the lengths of the hypotenuses). If we solve by cross-multiplying the numbers and then dividing we get x = 5.