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DiKsa [7]
3 years ago
8

Each multiple-choice question on an exam has four choices. Suppose that there are 10 questions and the choice is selected random

ly and independently for each question. Let X denote the number of questions answered correctly. Does X have a discrete uniform distribution? Why or why not?
Mathematics
1 answer:
Anika [276]3 years ago
3 0

Answer:

It is discrete, but not uniform, since each outcome is not equally as likely.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is answered correctly, or it is not. The probability of answered a question is independent from the probability of answeing other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Each multiple-choice question on an exam has four choices.

This means that p = \frac{1}{4} = 0.25

10 questions

This means that n = 10

Let X denote the number of questions answered correctly. Does X have a discrete uniform distribution? Why or why not?

It is discrete, because the number of questions answered correctly is a discrete value.

However, it is not uniform. A distribution is uniform when each outcome is equally as likely. For example, the probability of answering 0 questions correctly is different of the probability of answering 1 question correctly, as we see below.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.25)^{0}.(0.75)^{10} = 0.0563

P(X = 1) = C_{10,1}.(0.25)^{1}.(0.75)^{9} = 0.1877

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Answer:

904.9 in^3

Step-by-step explanation:

Given data

We are told that the ball is 12 inches in diameter

R= diamter/2= 12/2= 6 in

The volume of a sphere is given as

V= 4/3πr^3

substitute

V= 4/3*3.142*6^3

V= 4/3*3.142*216

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4 0
2 years ago
One of the legs of a right triangle measures 9 cm and the other leg measures 11 cm.
ikadub [295]

Answer:

\boxed {\boxed {\sf 14.2 \ cm}}

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem to solve for the sides.

a^2+b^2=c^2

where <em>a</em> and<em> b</em> are the legs and <em>c</em> is the hypotenuse. In this triangle, we know the legs are 9 centimeters and 11 centimeters, or:

  • a= 9 cm
  • b= 11 cm

Substitute these values into the formula.

(9 \ cm)^{2}  +(11 \ cm)^{2} =c^{2}

Solve the exponents.

  • (9 cm)²= 9 cm*9 cm=81 cm²

81 \ cm^{2}  +(11 \ cm)^{2} =c^{2}

  • (11 cm)²= 11 cm*11 cm= 121 cm²

81 \ cm^{2}  +121 cm^{2} =c^{2}

Add the values on the left side.

202 \ cm^{2} =c^{2}

Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.

\sqrt {202 \ cm^{2} }=\sqrt{c^{2} }

\sqrt {202 \ cm^{2} }=c

14.2126704036 \ cm =c

We are told to round to the nearest tenth.

  • 14.2<u>1</u>26704036

The 1 in the hundredth place tells us to leave the 2 in the tenth place.

14.2 \ cm= c

The hypotenuse is equal to <u>14.2 centimeters.</u>

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3 years ago
the probability that your ticket will be chosen in a drawing is 6% there are 250 tickets in the drawing how many tickets are you
julsineya [31]
No the answer should be 15 tickets. 250x0.06=15. number of tickets multiplied by percentage (in decimal form) to find what 6% of 250.
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3 years ago
Please find out the answer and I will mark your answer as the brain test with a five-star rating and a thank you. But only if th
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Answer:

Below

Step-by-step explanation:

Let x be that missing number

One third of it is x/3

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Multiply x/3 and x/9

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Multiply both sides by 27

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So there are two possibilities 54 and -54.

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Help solving this acceleration problem.
Misha Larkins [42]

Answer:

168.4953 (m/s)

Step-by-step explanation:

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a(3.85)=11.412*3.85²-0.606*3.85+1.674=168.4953

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