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3 years ago

Which of the following is the complete factorization of 3x2-6x-240?

1 answer:

4 0

1. Reduce 3x2-6x-240 to x^2 - 2x - 80

2. Use " ^ " to indicate exponentiation

3. Factor x^2 - 2x - 80 using completing the square:

x^2 - 2x + 1^2 - 1^2 - 80

(x+1)^2 - 1 - 80
(x+1)^2 - 81
(x+1)^2 - 9^2 = (x+1-9)(x+1 +9), or (x-8)(x+10)

Final answer, with all factors shown: 3(x-8)(x+10)

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A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

4 0

3 years ago

Determine the probability of having 1 girl and 3 boys i a 4 child family assuming boys and girls are equally likely

Helga [31]

Answer:

$\frac{1}{4}$

Step-by-step explanation:

Im glad i could help out.

4 0

2 years ago

What is -18 + (-45) + 12

qaws [65]

The answer is -51, hope this helps

5 0

3 years ago

Read 2 more answers

What is the answr to -5(b + 1) = 8

julsineya [31]

$- 5(b + 1) = 8 \\ - 5b - 5 = 8 \\ - 5b = 8 + 5 \\ - 5b = 13 \\ b = \frac{ - 13}{5}$

PLEASE GIVE BRAINLIEST

8 0

2 years ago

Read 2 more answers

9. How many lines of symmetry does the figure have? (1 point) Amico OOOO 6

Dvinal [7]

Answer:

6 lines of symmetry

Step-by-step explanation:

This is a 6 sided polygon which is known as hexagon.

Now, line of symmetry of this hexagon is a line that passes through the centre of it and thereby divides it into equal parts.

Now, we can see the short lines on each side of the hexagon. When they are extended to join a similar line on the opposite face, they all pass through the centre.

Thus, there are

6 0

3 years ago