Answer:
The probability that a jar contains more than 466 g is 0.119.
Step-by-step explanation:
We are given that a jar of peanut butter contains a mean of 454 g with a standard deviation of 10.2 g.
Let X = <u><em>Amount of peanut butter in a jar</em></u>
The z-score probability distribution for the normal distribution is given by;
Z =
~ N(0,1)
where,
= population mean = 454 g
= standard deviation = 10.2 g
So, X ~ Normal(
)
Now, the probability that a jar contains more than 466 g is given by = P(X > 466 g)
P(X > 466 g) = P(
>
) = P(Z > 1.18) = 1 - P(Z
1.18)
= 1 - 0.881 = <u>0.119</u>
The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.
Answer:
YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.
Step-by-step explanation:
Given
Given that the function f(x) and g(x) are inverse functions.


To determine
Let us determine whether f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.
<u>Determining the inverse function of f(x) </u>
A function g is the inverse function of f if for y = f(x), x = g(y)

Replace x with y

Solve for y

Therefore,
YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.
Let's assume that the faster car has a 2 mile "head start".
The faster car is 1.2 times faster (48/40) than the slower car.
It will take five 2 mile trips to "catch" the other car.
Five 2 mile trips will take 5 * 40 seconds = 200 seconds.
Answer: $59313.58
Step-by-step explanation:
We know that formula we use to find the accumulated amount of the annuity ( ordinary annuity interest is compounded ) is given by :-
, where A is the annuity payment deposit, r is annual interest rate , t is time in years and n is number of periods.
Given : Annuity payment deposit :A= $4500
rate of interest :r= 6%=0.06
No. of periods : m= 1 [∵ its annual]
Time : t= 10 years
Now we get,

∴ the accumulated amount of the annuity= $59313.58