Multiply.

A school gives awards in five subjects to a class of 30 students but no one is allowed to win more than one award. how many outc

kupik [55]

6 cause u have to multiply 30 and 5

6 0

3 years ago

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 $\pi = 0.5$

So

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

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

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

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

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

$n = 4144.1$

Rounding up

We need a sample size of at least 4145.

8 0

3 years ago

A fair coin is tossed 3 times in a row. What is the probability that heads appears on only the last toss? A. `1/8` B. `3/8` C. `

expeople1 [14]

Answer:

P(heads appears on only the last toss) = $\frac{1}{8}$

Step-by-step explanation:

A fair coin is tossed 3 times in a row.

When a coin is tossed we get a tail or head T or H

The possible outcomes of 3 coins are

T T T , H H H , T H H, H T H, H H T, H T T , T H T, T T H

So total of 8 possible outcomes

heads appears on only the last toss , first and second toss should be tail

So its T T H. Only one possibility

Probability(any event) = number of outcomes / total outcomes

P(heads appears on only the last toss) = $\frac{1}{8}$

6 0

3 years ago

The hypotenuse and one of the legs of a right triangle form an angle that has a cosine of 2 2 . what is the measure of the angle

creativ13 [48]

The correct question is
The hypotenuse and one of the legs of a right triangle form an angle that has a cosine of √2/2 .
What is the measure of the angle?

Let
∅--------> the angle
cos ∅=√2/2
cos ∅=[distance of one of the leg/hypotenuse]
[distance of one of the leg/hypotenuse]=√2/2

I could say that
distance of one of the leg=√2
and
hypotenuse=2
so
applying the Pythagorean theorem
c=hypotenuse=2
a=√2
b=?
c²=a²+b²-------> b²=c²-a²------> b²=2²-(√2)²-----> b²=2-----> b=√2

therefore
if a=b
then
the angle ∅=45°

the answer is the option
b.45 degrees

7 0

3 years ago

Angle XYZ is rotated 270 degrees counterclockwise about the origin to form angle X’Y’Z’. Which statement shows the measure of an

Kruka [31]

Hi i a doing the same thing and i have the answer as a hope this helps

6 0

3 years ago