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Gemiola [76]
3 years ago
14

Which expressions are equivalent to the one below? Check all that apply.

Mathematics
1 answer:
gladu [14]3 years ago
8 0
16^x / 4^x
= 4^2x / 4^x
= 4^x   so E is one choice.
also C and D
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Solve the compound inequality. Graph your solution. 2x – 2 < –12 or 2x + 3 > 7 x < –5 or x > 5 x < –5 or x > 2
Brilliant_brown [7]

Answer:

The solution region is x < –5 and x > 2

Step-by-step explanation:

We are given the inequalities, 2x–2 < –12 or 2x+3 > 7

Upon simplifying the inequalities, we get,

A. 2x-2 < -12

2x-2 < -12 i.e. 2x < -10 i.e. x < -5

B.  2x+3 > 7

2x+3 > 7 i.e. 2x > 4 i.e. x > 2

So, we get the solution is x or x>2 and the plotted region can be seen below.

4 0
3 years ago
A random sample of 150 men found that 88 of the men excercise regularly, while a random sample 200 women found that 130 of the w
melamori03 [73]

Answer:

The hypothesis is:

<em>H₀</em>: p_{X}-p_{Y}=0.

<em>Hₐ</em>: p_{X}-p_{Y}.

Step-by-step explanation:

Let <em>X</em> = number of men who exercise regularly and <em>Y</em> = number of women who exercise regularly.

The information provided is:

n_{X}=150\\X=88\\n_{Y}=200\\Y=130

Compute the sample proportion of men and women who exercise regularly as follows:

\hat p_{X}=\frac{X}{n_{X}}=\frac{88}{150}=0.587

\hat p_{Y}=\frac{Y}{n_{Y}}=\frac{130}{200}=0.65

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 150 and \hat p_{X}=0.587.

The random variable <em>Y</em> also follows a Binomial distribution with parameters <em>n</em> = 200 and \hat p_{Y}=0.65.

According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

\hat p=p

The standard deviation of this sampling distribution of sample proportion is:

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

So, the sampling distribution of the proportion of men and women who exercise regularly follows a Normal distribution.

A two proportion <em>z</em>-test cab be performed to determine whether the proportion of women is more than men who exercise regularly.

The hypothesis for this test cab be defined as:

<em>H₀</em>: The proportion of women is same as men who exercise regularly, i.e. p_{X}-p_{Y}=0.

<em>Hₐ</em>: The proportion of women is more than men who exercise regularly, i.e. p_{X}-p_{Y}.

6 0
3 years ago
Read 2 more answers
John has a coin and a spinner with 4 equal sections, one colored red, one blue, one colored green, and one colored, purple. Crea
dem82 [27]

Answer:

Heads/red

Heads/green

Heads/purple

Heads/blue

Tails/red

Tails/green

Tails/purple

Tails/blue

Possible outcomes: 8

3 0
3 years ago
Multi step equation that equal 27 when solved
Ksenya-84 [330]
Sample Equation:  3x - 3 = 27

Multiple step:

3x    -  3  =    27
 <u>       + 3       +3</u>  Step1. Remove the -3 by adding 3 to both sides
3x            =   30
<u>÷3                ÷ 3</u>  Step2. Remove the multiplicand 3 by dividing both sides by 3
x              =  10

To check: substitute x by its value

3x - 3 = 27
3(10) - 3 = 27
30 - 3 = 27
27 = 27

6 0
3 years ago
A. If you know the diameter of a sphere, you can find its radius.
USPshnik [31]

A. If you know the diameter, you can find the radius of a sphere by dividing the diameter in half. If you know the circumference, you can find the radius by dividing the circumference by 2 times pi

B. π × r2 × h

7 0
3 years ago
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