Prove that f(x)=2x+4 and g(x)= (x-4)/2 are inverses of each other. Show your work.
1 answer:
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Answer:
b) LeBron is relatively taller because he has a larger z-score.
Step-by-step explanation:
Z-score:
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
LeBron James:
Height of 81 inches, while the average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, which means that we have to find Z when
Candace Parker:
Height of 76 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. This means that we have to find Z when
Who is relatively taller?
Due to the higher z-score, LeBron James, and thus, the correct answer is given by option b.
Answer:
10
Step-by-step explanation:
Here it's given that the area of the shaded region is 48 u² and we need to find out the value of x .
The given figure is made up of two rectangles where the smaller one is inscribed into the bigger one .
- The area of shaded region will be equal to the difference of the areas of the two rectangles , that is equal to 48 u² .
- The area of rectangle is length × breadth .
- The dimensions of bigger rectangle is (x+3)(x-4) and that of smaller one is 3 × x .
So that ,
ar(bigger) - ar(smaller) = 48
[ (x+3) (x-4)] - 3(x) = 48
[ x² - 4x +3x -12 - 3x ] = 48
x² -4x -12 -48 = 0
x² - 4x - 60 = 0
x² - 10x + 4x - 60 = 0
x( x -10) +4(x -10) = 0
(x +4)(x-10) = 0
x = -4,10
- Since sides can't be negative ,
x = 10