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2 answers:
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Answer:
-4 4 4.5 8 20.5 32
Step-by-step explanation:
f g(x) = f(g(x))
Given, f(x) = 2x²
and g(x) = x - 2
Now f(g(x)) = f(x - 2) = 2(x - 2)²
We know that (a - b)² = a² - b² + 2ab
Using this we expand f(g(x)). We get:
f(g(x)) = 2{x² - 4x + 4}
Similarly, g(f(x)) = g(2x²) = 2x² - 2
Now, f(g(-2)) = 2[(-2)² - 4(-2) + 4] = 2(16) = 32.
Also, g(f(-2)) = 2[(-2)² - 2] = 2(2) = 4.
f(g(3.5)) = 2{(3.5)² -4(3.5) + 4} = 2[12.25 - 14 + 4] = 2(2.25) = 4.5.
g(f(3.5)) = 2{(3.5)² -2} = 2{12.25 - 2} = 2(10.25) = 20.5.
f(g(0)) = 2{0 - 4(0) + 4} = 2(4) = 8.
g(f(0)) = 2{0 - 2} = 2(-2) = -4.
Arranging them in ascending order, we get:
-4 4 4.5 8 20.5 32 would be the sequence.
Answer:
a) 2.5 shots
b) 59.4 shots
c) 4.87 shots
Step-by-step explanation:
Probability of making the shot = 0.6
Probability of missing the shot = 0.4
a) The expected number of shots until the player misses is given by:
The expected number of shots until the first miss is 2.5
b) The expected number of shots made in 99 attempts is:
He is expected to make 59.4 shots
c) Let "p" be the proportion shots that the player make, the standard deviation for n = 99 shots is:
The standard deviation is 4.87 shots.