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4 years ago

Provide answers for part a,b, and c. Show work for part c.

Mathematics

1 answer:

schepotkina [342]4 years ago

6 0

Answer:

Step-by-step explanation:

PART A

The Pythagoras theorem is expressed as

Hypotenuse^2 = opposite side^2 + adjacent side^2

PART 2

The hypotenuse is the longest side of the triangle. Looking at the given triangle, the longest side is the side with the length of 7. Therefore, hypotenuse = 7

PART C

To determine x, we will apply the Pythagoras theorem as stated above.

Opposite side = √14

Adjacent side = x

Therefore

7^2 = x^2 + (√14)^2

49 = x^2 + 14

x^2 = 49-14 = 35

Taking square root of both sides of the equation, it becomes

x = √35

x = 5.92

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If g(x)=2(x-4), find the value of x if g(x) =20 A. 32 B. 12 C. 14 D. 10

SOVA2 [1]

I think it is 32, bc the value of x is 20 so your problem would look like this; 2 ( (20) - 4 )

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3 years ago

The average speed of a golden eagle is 30 mph and the average speed of a peregrine falcon is 48 mph. How far will the peregrine

Oliga [24]

Answer:

53 1/3 miles.

Step-by-step explanation:

Well the eagle would take 1 1/3 of an hour to fly 40 miles, so you multiply 1 1/3 to 48 to get your answer.

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3 years ago

Read 2 more answers

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

Anton [14]

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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3 years ago

The double number line shows that Toni can type 180 words in 2 minutes.

NeTakaya

Answer:

270 words per minute

Step-by-step explanation:

It is given 180 words in 2 minutes, this means Toni can type 180/2 = 90 words per minute (90wpm).

Thus, in the same ratio/rate, Toni would be able to type:

90 * 3 = 270 words per minute.

Correct answer 270 wpm

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3 years ago

Read 2 more answers

What is the value of 110% of 1/2 of 1/4 of 64.

Alex787 [66]

Step-by-step explanation:

110/1000*1/2*1/4*64/1

110*1*1*64=7040

1000*2*4*1=8000

7040/8000

704/800

3 0

3 years ago