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Nataly [62]
3 years ago
11

Mr.Gork has square sheet of aluminum that measure 24 in. On each side.What is the area of the largest circular disk that he can

cut from this sheet of aluminum
Mathematics
1 answer:
kolbaska11 [484]3 years ago
4 0

Answer:

The area of the largest circular disk that he can cut from this sheet of aluminum is <u>452.16 in²</u>.

Step-by-step explanation:

Given:

Mr.Gork has square sheet of aluminum that measure 24 in on each side.

Now, to find the area of the largest circular disk that he can cut from this sheet of aluminum.

<u><em>As, the side of the square sheet of aluminum is given 24 in.</em></u>

<u><em>So, the  diameter of the largest circular disk that he can cut from this sheet of aluminum is 24 in.</em></u>

Now, we get the radius of the circular disk:

Radius (r) = Diameter ÷ 2

Radius (r) = 24\div2 = 12\ in.

And, now to get the area of the circular disk we put formula:

Area=\pi r^2

( Taking, π = 3.14 )

Area=3.14\times (12)^2\\\\Area=3.14\times 144\\\\Area=452.16\ in^2.

Therefore, the area of the largest circular disk that he can cut from this sheet of aluminum is 452.16 in².

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Sonya and her family went to dinner. The cost of the meal was $47.28. They left a 15% tip. What was the total amount sonyas fami
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Step-by-step explanation:

First, need to find 15% of 47.28.

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Then we add that to the original cost.

47.28+7.092 = 54.372

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3 years ago
Seventy-two percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of th
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Answer:

a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) 0.064 = 6.4% probability that 7 of them are discovered.

Step-by-step explanation:

For itens a and b, we use conditional probability.

For item c, we use the binomial distribution along with the conditional probability.

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

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.

a) If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator

Event B: Not located.

Probability of having an emergency locator:

66% of 72%(Are discovered).

20% of 100 - 72 = 28%(not discovered). So

P(A) = 0.66*0.72 + 0.2*0.28 = 0.5312

Probability of having an emergency locator and not being discovered:

20% of 28%. So

P(A cap B) = 0.2*0.28 = 0.056

Probability:

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.056}{0.5312} = 0.105

0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) If it does not have an emergency locator, what is the probability that it will be discovered?

Probability of not having an emergency locator:

0.5312 of having. So

P(A) = 1 - 0.5312 = 0.4688

Probability of not having an emergency locator and being discovered:

34% of 72%. So

P(A \cap B) = 0.34*0.72 = 0.2448

Probability:

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2448}{0.4688} = 0.522

0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

p is the probability of being discovered with the emergency recorder:

0.5312 probability of having the emergency recorder.

Probability of having the emergency recorder and being located:

66% of 72%. So

P(A \cap B) = 0.66*0.72 = 0.4752

Probability of being discovered, given that it has the emergency recorder:

p = P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4752}{0.5312} = 0.8946

This question asks for P(X = 7) when n = 10. So

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

P(X = 7) = C_{10,7}.(0.8946)^{7}.(0.1054)^{3} = 0.064

0.064 = 6.4% probability that 7 of them are discovered.

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