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Volgvan
3 years ago
11

Seniors at a certain high school took a survey regarding future plans. All plan to attend college some time; however, 77% plan t

o go to college immediately following high school. Of those who plan to attend college immediately following high school, 18% plan to major in Math. Of those who do not plan to attend college immediately following high school, 11% plan to major in Math. What is the probability that a randomly chosen senior does not plan to attend college immediately following high school and plans to major in Math.
a) 0.1386
b) 0.1800
c) 0.8900
d) 0.0253
e) 0.1100
f) None of the above.
Mathematics
1 answer:
IgorC [24]3 years ago
6 0

Answer:

The correct option is d) 0.0253

Step-by-step explanation:

Consider the provided information.

When two events, X and Y, are dependent, then the probability of both occurring is: P(X \cap Y)  =  P(X) \cdot P(Y|X)

All plan to attend college some time; however, 77% plan to go to college immediately following high school.

Let X represents the Plan to go to college.

P(X) = 0.77

P(X') = 1 - 0.77 = 0.23

Of those who plan to attend college immediately following high school, 18% plan to major in Math. Of those who do not plan to attend college immediately following high school, 11% plan to major in Math.

Let Y represents Major in Math.

P(Y|X) = 0.18 and P(Y|X') = 0.11

Therefore the required probability is:

P(X'\cap Y) = P(X')P(Y|X') \\P(X'\cap Y)= 0.11\times 0.23 = 0.0253

Hence, the correct option is d) 0.0253

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Ilia_Sergeevich [38]

Answer:

The length of legs lm, mn, and lk is 32 while that of kn is 36.

Step-by-step explanation:

The diagram is attached in the answer.

As both the angles are equal thus the two forms isosceles triangles. This is true because the converse of base angle theorem is applicable here. The theorem clearly states that when a trapezoid is divided by the diagonal, it forms two set of angles where m<1=m<2 and m<lmk=m<nmk

This leads the two set of legs such as

\dfrac{lm}{kn}=\dfrac{8}{9}

Or this could be written as

lm=8x\\kn=9x

Now the remaining two sides are given as

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lk=8x

Similarly

mn=lm\\

Or

mn=8x

Now the perimeter is given as

\text{perimeter}=lm+mn+kn+lk\\

Here perimeter is given as 132 so this gives:

\text{perimeter}=lm+mn+kn+lk\\132=8x+8x+8x+9x\\132=33x\\x=\dfrac{132}{33}\\x=4

So the four legs are of length as given below:

lm=8x=8\times 4=32\\mn=8x=8\times 4=32\\lk=8x=8\times 4=32\\kn=9x=9\times4=36

So the length of legs lm, mn, and lk is 32 while that of kn is 36.

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Step-by-step explanation:

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