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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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8 0
2 years ago
Simplify and verify the results for
KatRina [158]

Answer:

21440

Step-by-step explanation:

<h2>Simplify:</h2>
  • (7x³ + 8x² - 3)(x² - 5)

Start by multiplying 7x³ by x² and -5.

  • 7x⁵ - 35x³ + (8x² - 3)(x² - 5)    

Multiply 8x² by x² and -5.

  • 7x⁵ - 35x³ + 8x⁴ - 40x² + (-3)(x² - 5)

Multiply -3 by x² and -5.

  • 7x⁵ - 35x³ + 8x⁴ - 40x² -3x² + 15

Combine like terms together.

  • 7x⁵ - 35x³ + 8x⁴ - 43x² + 15

Rearrange the terms in descending power order.

  • 7x⁵ + 8x⁴ - 35x³ - 43x² + 15  
<h2>Verify (I): </h2>

Substitute x = 5 into the above polynomial.

  • 7(5)⁵ + 8(5)⁴ - 35(5)³ - 43(5)² + 15

Evaluate the exponents first.

  • 7(3125) + 8(625) - 35(125) - 43(25) + 15

Multiply the terms together.

  • 21875 + 5000 - 4375 - 1075 + 15

Combine the terms together.

  • 21440

This is the answer when substituting x = 5 into the simplified expression.

<h2>Verify (II):</h2>

Substitute x = 5 into the expression.

  • [7(5)³ + 8(5)² - 3][(5)² - 5]

Evaluate the exponents first.

  • [7(125) + 8(25) - 3][(25) - 5]

Multiply the terms in the first bracket next.

  • [875 + 200 - 3][25 - 5]

Evaluate the expressions inside the brackets.

  • [1072][20]

Multiply these two terms together.

  • 21440

This is the answer when substituting x = 5 into the original (unsimplified) expression.

3 0
2 years ago
If m&lt; BOE = 130 degrees and m&lt; cob = 80 degrees
hjlf

Answer:

then what?

Step-by-step explanation:

do we have to find the angle?

all I know is every right triangle is equal to 90°

6 0
3 years ago
In 6 years, John will be 3 times the age he was 2 years ago. What is his current age?
Vladimir79 [104]

Answer:

John is currently 6 years old.

Step-by-step explanation:

2 years ago: x years

Current time: x+2

In 6 years: x+8

EQUATION:

3(x)=x+8= 3x=x+8

(subract x from both sides)

2x=8

x=4

Therefore, John is 6 years old in current time

7 0
2 years ago
A parabola and a circle are graphed into the standard (x,y) coordinate plane. The circle has a radius of 4 and is centered at (1
Gala2k [10]

Answer:

Correct answer: Two point of intersection and one touch point.

Step-by-step explanation:

Cartesian form of parabola is: y= a(x-1)² + 5  and point named A(2,4)

when we replace the coordinates of the point A in the formula we get

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God is with you!!!

6 0
3 years ago
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