Please help with the setup of the problem, thank you.
1 answer:
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<h3><u>Question:</u></h3>
Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units.
The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?
<h3><u>Answer:</u></h3>Dimensions of cylinder A are multiplied by to produce the corresponding dimensions of cylinder B
Cylinders A and B are similar solids.
The base of cylinder A has a circumference of units
The base of cylinder B has an area of units
Let "x" be the required factor
From given question,
Dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B
Therefore, we can say,
The circumference of base of cylinder (circle ) is given as:
Where "r" is the radius of circle
Given that base of cylinder A has a circumference of units
Therefore,
Thus the dimension of cylinder A is radius = 2 units
<h3><u>Cylinder B:</u></h3>The area of base of cylinder (circle) is given as:
Given that, the base of cylinder B has an area of units
Therefore,
Thus the dimension of cylinder B is radius = 3 units
Thus dimensions of cylinder A are multiplied by to produce the corresponding dimensions of cylinder B
Question:
According to Masterfoods, the company that manufactures M&M's, 12% of peanut M&M's are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. You randomly select peanut M&M's from an extra-large bag looking for a red candy.
If every student in a large Statistics class selects peanut M&M’s at random until they get a red candy, on average how many M&M’s will the students need to select? (Round your answer to two decimal places.).
Answer:
If every student in the large Statistics class selects peanut M&M’s at random until they get a red candy the expected value of the number of M&M’s the students need to select is 8.33 M&M's.
Step-by-step explanation:
To solve the question, we note that the statistical data presents a geometric mean. That is the probability of success is of the form.
The amount of repeated Bernoulli trials required before n eventual success outcome or
The probability of having a given number of failures before the first success is recorded.
In geometric distribution, the probability of having an eventual successful outcome depends on the the completion of a certain number of attempts with each having the same probability of success.
If the probability of each of the preceding trials is p and the kth trial is the first successful trial, then the probability of having k is given by
Pr(X=k) =
The number of expected independent trials to arrive at the first success for a variable Xis 1/p where p is the expected success of each trial hence p is the probability for the red and the expected value of the number of trials is 1/p or where p = 12 % which is 0.12
1/p = 1/0.12 or 25/3 or 8.33.