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3 years ago

Beth spins a fair spinner numbered 1 - 8 and flips a fair coin.

Mathematics

1 answer:

Basile [38]3 years ago

4 0

Answer:

1/8

Step-by-step explanation:

To find the probability of two events happening we need to find the probability of each event happening first:

For the spinner there are 8 possibilites (landing 1, 2, 3...8) and we are looking for factors of 3 which are 1 and 3 (3 is prime) therefore:

The chance of landing a factor of 3 on the spinner is 2/8=1/4

For the head there are two possibilities (heads and tails) and only one event we want happening (heads), therefore:

The chance of landing on heads on a fair coin is 1/2

Now to find the chances of both events happening we must multiply them to find that:

(1/2) ⋅ (1/4) = 1/8 the chances of the event happening

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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

Solve the inequality 2x – 5 > 7<br> a. x>6<br> b. x >12<br> c. x

julsineya [31]

You start with 2x -5>7 the you add five to both sides 2x-5+5>7 +5 2x.12 then divide both sides by 2 2x divided by 2 > and 12 divided by 2 and get x>6

3 0

3 years ago

The price of tiling a room varies directly as the size of the room. Sam is laying tile in his kitchen. If the tiling costs $4,22

stiv31 [10]

Answer:

<h3>The answer is option A</h3>

Step-by-step explanation:

Let the price of the room be p

Let the size of the room be s

To find the size of a kitchen that costs $3,824.00 we must first find the relationship between them

The statement

The price of tiling a room varies directly as the size of the room is written as

where k is the constant of proportionality

when

p = $4,224.00

s = 264 square feet

Substitute the values into the expression to find k

That's

4224 = 264k

Divide both sides by 264

k = 16

So the formula for the variation is

when

p = 3824

$s = \frac{p}{16}$

$s = \frac{3824}{16}$

s = 239

The final answer is

239 square feet

Hope this helps you

6 0

3 years ago

Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers.

Natasha2012 [34]

<span>The missing angle measure in triangle ABC is 55°.

The measure of angle BAC in triangle ABC is equal to the measure of angle
EDF in triangle DEF.

The measure of angle ABC in triangle ABC is equal to the measure of </span><span>angle EFD in triangle DEF.

Triangles ABC and DEF are similar by the angle-angle criterion.
True </span>

5 0

3 years ago

What conditions would be enough to prove that P is the circumcenter of HJK ? Select all that apply.

nadezda [96]

Answer:

B trust me

Step-by-step explanation:

6 0

2 years ago