Answer:
(h o k) (3) = 3
(k o h) (-4b) = -4b
Step-by-step explanation:
An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.
This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.
Answer:
Step-by-step explanation:
Since the life of the brand of light bulbs is normally distributed, we would apply the the formula for normal distribution which is expressed as
z = (x - u)/s
Where
x = life of the brand of lightbulbs
u = mean life
s = standard deviation
From the information given,
u = 1300 hrs
s = 50 hrs
We want to find the probability that a light bulb of that brand lasts between 1225 hr and 1365 hr. It is expressed as
P(1225 ≤ x ≤ 1365)
For x = 1225,
z = (1225 - 1300)/50 = - 1.5
Looking at the normal distribution table, the probability corresponding to the z score is
0.06681
For x = 1365,
z = (1365 - 1300)/50 = 1.3
Looking at the normal distribution table, the probability corresponding to the z score is
0.9032
Therefore
P(1225 ≤ x ≤ 1365) = 0.9032 - 0.06681 = 0.8364
Answer:
a) 0.264
b) 48 cubit light-years
Step-by-step explanation:
For calculating a) What is the probability of 3 or more stars in 16 cubic light years?
a)
λ= 1 star/16 cubic light-years
t= measure t in units of 16 cubic light years.
E(Y) = λ t = (1/16)(16) = 1 star
P(X>=2) = 1 - P(X<2)
= 1 - [e^-1 + (e^-1)(1)/1!]
= 0.264
b)
P(X≥1) = 1 - P(X=0)
= 1 - e^-μ
0.95 = 1 - e^-μ
e^-μ = 1 - 0.95
e^-μ = 0.05
ln(e^-μ) = ln(0.05)
-μ = -3
μ = 3
Therefore 3 x 16 = 48 cubic light years of space
Answer:
B. 
in decimal form, it would be 0.015625
4(-2)^2(-1)^3
4 x 4 x -1
Correction answer D: -16
