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3 years ago

5

A small train at an amusement park is carrying passengers. Half of the passengers are 4 years old, 1/10 are 5 years old, 3/10 ar

e 6 years old, and 1/10 are 7 years old.
What is the expected age for one of the passengers on the train?

A. 5 years
B. 5.5 years
C. 6 years
D. 6.1 years

1 answer:

solniwko [45]3 years ago

6 0

In order to find the expected age, we must multiply the probability of picking each child by their age, then add them all up. Like this:

E(x) = 4(1/2) + 5(1/10) + 6(3/10) + 7(1/10)
E(x) = 5 years

By doing this we are giving each age group a percentage of the entire population.

Hope this helps!

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Quadrilateral ABCD is dilated by a scale factor of 3/2 to create quadrilateral A'B'C'D'. If quadrilateral ABCD has an area of 30

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Answer:

67.5

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the enlargement or reduction of an object by a factor.

The area of ABCD = AB * BC = 30

As a result of the dilation to form A'B'C'D', A'B' = 3/2 * AB, B'C' = 3/2 * BC, C'D' = 3/2 * CD and A'D' = 3/2 * AD. Hence:

Area of A'B'C'D' = A'B' * B'C' = 3/2 * AB * 3/2 * BC = 9/4 * (AB * BC) = 9/4 * 30 = 67.5

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3 years ago

F(x) = x + 4 and g(x) = 2x + 3, evaluate each expression.

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Answer:

$15.~f(g(2))=\Large\boxed{11}\\$

$16.~g(f(2.5))=\Large\boxed{16}$

$17.~g(f(-5))=\Large\boxed{1}$

$18.~f(g(-5))=\Large\boxed{-3}$

Step-by-step explanation:

<h3>Given information</h3>

$f(x)=x+4$

$g(x)=2x+3$

<h3>Question 15. f(g(2))</h3>

<u>Substitute values into the first function</u>

$g(2)=2(2)+3$

$g(2)=4+3$

$g(2)=7$

<u>Substitute the values of the first function into the second</u>

$f(g(2))=f(7)$

$f(7)=(7)+4$

$f(7)=\Large\boxed{11}$

<h3>Question 16. g(f(2.5))</h3>

<u>Substitute values into the first function</u>

$f(2.5)=(2.5)+4$

$f(2.5)=6.5$

<u />

<u>Substitute the values of the first function into the second</u>

$g(f(2.5))=g(6.5)$

$g(6.5)=2(6.5)+3$

$g(6.5)=13+3$

$g(6.5)=\Large\boxed{16}$

<h3>Question 17. g(f(-5))</h3>

<u>Substitute values into the first function</u>

$f(-5)=(-5)+4$

$f(-5)=-1$

<u>Substitute the values of the first function into the second</u>

$g(f(-5))=g(-1)$

$g(-1)=2(-1)+3$

$g(-1)=-2+3$

$g(-1)=\Large\boxed{1}$

<h3>Question 18. f(g(-5))</h3>

<u>Substitute values into the first function</u>

$g(-5)=2(-5)+3$

$g(-5)=-10+3$

$g(-5)=-7$

<u>Substitute the values of the first function into the second</u>

$f(g(-5))=f(-7)$

$f(-7)=(-7)+4$

$f(-7)=\Large\boxed{-3}$

Hope this helps!! :)

Please let me know if you have any questions

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