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2 years ago

In a group of 42 students, 9 study both Art and Biology.

1 answer:

3 0

Answer:
The probability the student studies Art and
Biology is 0.2143.
Step-by-step explanation:
Denote the events as follows:
A = a students studies Art
B= a students studies Biology
The information provided is:
N = 42
n (An B) = 9
n (A' n B) = 10
n (A' n B') =7
Then the number of students who study Art
but not Biology is:
n(An B') = N -n (An B) -n (A' nB) - n (A'n B')
= 42 - 10 - 7 - 9
= 16
The number of students who study Art but
not Biology is 16.
Compute the probability the student studies
Art and Biology as follows:
P(ANB)
n(ANB)
= 0.2143
Thus, the probability the student studies Art
and Biology is 0.2143.

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A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained i

Scorpion4ik [409]

Answer:

a) We need a sample size of at least 3109.

b) We need a sample size of at least 4145.

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:

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

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

(a) he uses a previous estimate of 25%?

we need a sample of size at least n.

n is found when $M = 0.02, \pi = 0.25$ . So

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

$0.02 = 2.575\sqrt{\frac{0.25*0.75}{n}}$

$0.02\sqrt{n} = 2.575\sqrt{0.25*0.75}$

$\sqrt{n} = \frac{2.575\sqrt{0.25*0.75}}{0.02}$

$(\sqrt{n})^{2} = (\frac{2.575\sqrt{0.25*0.75}}{0.02})^{2}$

$n = 3108.1$

We need a sample size of at least 3109.

(b) he does not use any prior estimates?

When we do not use any prior estimate, we use $\pi = 0.5$

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

$0.02 = 2.575\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 2.575\sqrt{0.5*0.5}$

$\sqrt{n} = \frac{2.575\sqrt{0.5*0.5}}{0.02}$

$(\sqrt{n})^{2} = (\frac{2.575\sqrt{0.5*0.5}}{0.02})^{2}$

$n = 4144.1$

Rounding up

We need a sample size of at least 4145.

8 0

3 years ago

Please help! 2x + 6 (x=4)

Anna007 [38]

Answer:

2(4)+6

8+6

Step-by-step explanation:

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3 years ago

Layton made 117$ for 9 hours of work.at the same rate,how many hours would she have to work to make $65?

Bogdan [553]

Since she makes $13 per hour, she would have to work 5 hours to make $65.

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3 years ago

*50 POINTS -- FRESHMEN ~ ALGEBRA I *

aniked [119]

Step-by-step explanation:

so we know X= Numbers of Large boxes and Y= Numbers of Small boxes

And we know the large boxes weigh 75 pounds and the small boxes weigh 40 pounds

So I would have to say the the same except you have to flip the inequality sign like this:

75x + 40y

$\geqslant \\$

200

And if that doesnt somehow work and the question is wording it wrong then

My guess for why its wrong us because its not in slope intercept form Although you still can solve for either varible ( x or y) using standard form also.

So to get from standard form to Slope intercept form (y=mx+b) these are the steps:

Ax+by=C

75x + 40y ≤ 200

Turn it into a linear equation.

75x+ 40y =200

In order to go from one form to another, all you have to do is change the order of the given numbers. First you want to move the Ax to the opposite side of the equation, by either adding or subtracting it. At this point your equation will be set up By = -Ax + C. Then you want to divide the B from the By and the rest of the equation. Therefore you will have y = - Ax/B + C/B. This is the same thing as the slope-intercept form, just a few of the letters are different.

40y=-75x+200 first subtract 75x

y=−1.875×+5 then dived every varible (everything) by 40. and you have your Linear eqaution.

And your second question would be A. >The number of boxes must be a whole number. 

Because you cannot split boxes in half or in any quarter in a real life scenario.

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3 years ago

The formula for the volume of a cube is V = s³, where s represents the side length of the cube. If a cube has a side length of 4

Alla [95]

Answer:

91.125 or 729/8

Step-by-step explanation:

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3 years ago

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