which of the following could be the first step in solving the equation below?5^x=21a. 1/5×5^x=1/5×21b. log5^x=log21c. log5^x=21d. sqrt[5]{ {5}^{x} } = sqrt[5]{21}

Answer: There are 2 strokes below par that the team has scored in the first round.

Step-by-step explanation:

Since we have given that

Scores of a team

69, 73, 70 and 74

on the first round on a part 72 course.

Now, we need to find the number of strokes above or below the par.

So, we will compare all the scores with 72.

So,

69-72 = -3(below par)

73-72 = 1 (above par)

70-72= - 2 (below par)

74-72 = 2 ( above par)

So, Number of strokes above or below par is given by

Hence, there are 2 strokes below par that the team has scored in the first round.

Answer:

$175

Step-by-step explanation:

Cost to store: $140

Markup: 25%

• The selling price= $140 + 25% = $140*1.25= $175

Answer:

Case I

Null hypothesis:  

Alternative hypothesis:  

Since is a two sided  test the p value would given by:  

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis.  

We can say that at 5% of significance the true mean is different from 64.

Case II

Null hypothesis:  

Alternative hypothesis:

The statistic not changes but the p value does and we have:

And we reject the null hypothesis on this case.

So we can conclude that the true mean is significantly higher than 64 at 5% of singnificance

Step-by-step explanation:

Data given and notation  

represent the sample mean  

represent the sample standard deviation  

sample size  

represent the value that we want to test  

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the population mean is different from 64 the system of hypothesis are :  

Null hypothesis:  

Alternative hypothesis:  

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

(1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

P-value  

We need to calculate the degrees of freedom first given by:  

Since is a two sided  test the p value would given by:  

Conclusion  

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis.  

We can say that at 5% of significance the true mean is different from 64.

Now let's assume that we want to see if the mean is significantly higher than 64

Null hypothesis:  

Alternative hypothesis:

The statistic not changes but the p value does and we have:

And we reject the null hypothesis on this case.

So we can conclude that the true mean is significantly higher than 64 at 5% of singnificance

Answer:

A.2 B.4 C.3 D.4 E.6

Step-by-step explanation:

1/2 ÷ 3/4 = 1/2 x 4/3 (flip 3/4 and keep 1/2)

If you multiply 1/2 x 4/3 you will get 4/6.

The solution consists of all of the true intervals is −4 < x < −1   x > 1.

−4<x<−1  or  x>1

Inequality Form: −4<x<−1  or  x>1

Interval Notation: (−4,−1)  ∪  (1,∞)

x^3 + 4x^2 > x + 4

Subtract x from both sides of the inequality.

x^3 + 4x^2 − x > 4

Convert the inequality to an equation.

x^3 + 4x^2 − x = 4

Move 4 to the left side of the equation by subtracting it from both sides.

x^3 + 4x^2>x+4

2 − x − 4 = 0

Factor the left side of the equation

(x + 4)(x + 1)(x − 1) = 0

If any individual factor on the left side of the equation is equal to, the entire expression will be equal to 0

x + 4 = 0

x + 1 = 0

x − 1 = 0

Set x + 4 equal to 0 and solve for x

x = −4

Set x + 1 equal to 0 and solve for x

What is inequality?

Inequality is the difference in social status, wealth, or opportunity between people or groups. People are concerned about social inequality.

x = −1

Set x + -1 equal to 0 and solve for x

x = 1

The final solution is all the values that make (x + 4)(x + 1)(x − 1) = 0  true

x = −4, −1, 1

Use each root to create test intervals.

x < −4

−4 < x < −1

−1 < x < 1

x > 1

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the

inequality.

x < −4  ←False

−4 < x < −1  ←True

−1 < x < 1  ←False

x > 1  ←True

The solution consists of all of the true intervals.

−4 < x < −1 x > 1

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The  simplified expression is -8a² - 24ab.

Given expression: (2a + 6b)(6b - 2a) - (2a + 6b)^2

First, let's expand the squared term (2a + 6b)^2:

(2a + 6b)(6b - 2a) - (2a + 6b)(2a + 6b)

Now, we have a common factor of (2a + 6b) in both terms, so let's factor it out:

(2a + 6b)[(6b - 2a) - (2a + 6b)]

Now, simplify the expression inside the brackets:

(2a + 6b)[6b - 2a - 2a - 6b]

Combining like terms within the brackets:

(2a + 6b)[-4a]

Now, multiply the remaining terms:

-4a(2a + 6b)

-8a² - 24ab

Therefore, the simplified expression is -8a² - 24ab.

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Answer:

-8a(a+3b)

Step-by-step explanation:

(2a+6b)(6b−2a)−(2a+6b)^2

(2a+6b) {(6b−2a)−(2a+6b)(2a+6b)}

2(a+3b) (6b-2a-2a-6b)

2(a+3b) (-4a)

-2(a+3b) x 4a

-2 x 4a (a+3b)

-8a(a+3b)