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BlackZzzverrR [31]

4 years ago

10

Mr. Jansen listened to 8 songs in 28 minutes. He later listened to 5 songs in 21 minutes. Determine whether the ratios are equiv

alent.

1 answer:

sammy [17]4 years ago

3 0

Set up proportions

8/28=5/21
8*21=168
5*28=140
so no, they are not equivalent

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In a multiple choice quiz there are 5 questions and 4 choices for each question (a, b, c, d). Robin has not studied for the quiz

Ahat [919]

Answer:

a) There is a 18.75% probability that the first question that she gets right is the second question.

b) There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

c) There is a 10.35% probability that she gets the majority of the questions right.

Step-by-step explanation:

Each question can have two outcomes. Either it is right, or it is wrong. So, for b) and c), we use the binomial probability distribution to solve this problem.

Binomial probability distribution

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

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

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

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

And $\pi$ is the probability of X happening.

In this problem we have that:

Each question has 4 choices. So for each question, Robin has a $\frac{1}{4} = 0.25$ probability of getting ir right. So $\pi = 0.25$ . There are five questions, so $n = 5$ .

(a) What is the probability that the first question she gets right is the second question?

There is a 75% probability of getting the first question wrong and there is a 25% probability of getting the second question right. These probabilities are independent.

So

$P = 0.75(0.25) = 0.1875$

There is a 18.75% probability that the first question that she gets right is the second question.

(b) What is the probability that she gets exactly 1 or exactly 2 questions right?

This is: $P = P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955$

$P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637$

$P = P(X = 1) + P(X = 2) = 0.3955 + 0.2637 = 0.6592$

There is a 65.92% probability that she gets exactly 1 or exactly 2 questions right.

(c) What is the probability that she gets the majority of the questions right?

That is the probability that she gets 3, 4 or 5 questions right.

$P = P(X = 3) + P(X = 4) + P(X = 5)$

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 3) = C_{5,3}.(0.25)^{3}.(0.75)^{2} = 0.0879$

$P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0146$

$P(X = 5) = C_{5,5}.(0.25)^{5}.(0.75)^{0} = 0.001$

$P = P(X = 3) + P(X = 4) + P(X = 5) = 0.0879 + 0.0146 + 0.001 = 0.1035$

There is a 10.35% probability that she gets the majority of the questions right.

6 0

3 years ago

For the standard normal probability distribution, the area to the right of the mean is:

sveticcg [70]

The answer is 0.5. I hope this is helpful.

7 0

3 years ago

The length of one leg or a right triangle is 4 meter, and the length of the hypotenuse is 15 meters. Find the exact length of th

Roman55 [17]

You'd be using Pythagorean theorem for this.

4 0

3 years ago

Read 2 more answers

Graph the following lines and using the graph determine several values of x for which the graph is positive (negative): y=−4x+3

True [87]

Answer:

Step-by-step explanation:

Given line is,

y=-4x+3

when, x=-1 , y=-4(-1)+3=4+3=7

when, x=0 , y=-4(0)+3=0+3=3

when, x=1 , y=-4(1)+3=-4+3=-1

So, we got the points (-1,7) , (0,3) , (1,-1)

Now, putting the points in the graph and adding them , we will get the graph of given line.

Please check image for the graph.

Now for the second part-

The graph is positive means- it will be above the x-axis, that is y value will be positive.

From the graph we can see that, if x<0 , then y is positive.

So, any value of x which is less than 0 , will give the positive graph here.

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3 years ago

Write 3.11 as a mix number and a improper fraction?

steposvetlana [31]

3 plus 11/10 (mix number, you can get it by simplifying 300/100=3 with 11/100 left over)
311/100 (improper fraction=a fraction where the numerator is bigger than the denominator, you get it by just taking the last decimal place which is a houndredth here so you take the whole thing over 100 basically)

7 0

3 years ago