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Dovator [93]
3 years ago
6

According to a recent​ study, 9.3​% of high school dropouts are​ 16- to​ 17-year-olds. In​ addition, 6.4​% of high school dropou

ts are white​ 16- to​ 17-year-olds. What is the probability that a randomly selected dropout is​ white, given that he or she is 16 to 17 years​ old?
Mathematics
1 answer:
Finger [1]3 years ago
4 0

Answer:

0.688 or 68.8%

Step-by-step explanation:

Percentage of high school dropouts = P(D) = 9.3% = 0.093

Percentage of high school dropouts who are white = P(D \cap W) = 6.4% = 0.064

We need to find the probability that a randomly selected dropout is​ white, given that he or she is 16 to 17 years​ old. This is conditional probability which can be expressed as: P(W | D)

Using the formula of conditional probability, we ca write:

P(W | D)=\frac{P(W \cap D)}{P(D)}

Using the values, we get:

P( W | D) = \frac{0.064}{0.093} = 0.688

Therefore, the probability that a randomly selected dropout is​ white, given that he or she is 16 to 17 years​ old is 0.688 or 68.8%

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3 years ago
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What is the value of x?<br><br> Please help! Thanks!
leonid [27]

Answer:

x=75

Step-by-step explanation:

We can use proportions to solve this problem.  Put the side of the small triangle over the side of the large triangle.

42           50

------ = ----------

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42           50

------ = ----------

105          50+x

Using cross products

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8 0
3 years ago
WHAT IS THE REMAINDER WHEN <img src="https://tex.z-dn.net/?f=32%5E%7B37%5E%7B32%7D%20%7D" id="TexFormula1" title="32^{37^{32} }"
Feliz [49]

Recall Euler's theorem: if \gcd(a,n) = 1, then

a^{\phi(n)} \equiv 1 \pmod n

where \phi is Euler's totient function.

We have \gcd(9,32) = 1 - in fact, \gcd(9,32^k)=1 for any k\in\Bbb N since 9=3^2 and 32=2^5 share no common divisors - as well as \phi(9) = 6.

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where the c_i are positive integer coefficients from the binomial expansion. By Euler's theorem,

\left(32^{(\cdots)\right)^6 \equiv 1 \pmod9

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32^{37^{32}} \equiv 32\cdot1 \equiv \boxed{5} \pmod9

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2 years ago
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