Answer:
a) X has a mean of 25 and a variance of 8.
b) The probability that the total weight X is between 22 and 28 oz is 0.711.
Step-by-step explanation:
We have to calculate the mean and variance of a sum of random normal variables.
We can apply the rule for mean and variance for sum of independent variables:

Then, the mean and variance of X is:

We can calculate the probability that X is between 22 and 28 as:

<h3>
Answer:</h3>
System
Solution
- p = m = 5 — 5 lb peanuts and 5 lb mixture
<h3>
Step-by-step explanation:</h3>
(a) Generally, the equations of interest are one that models the total amount of mixture, and one that models the amount of one of the constituents (or the ratio of constituents). Here, there are two constituents and we are given the desired ratio, so three different equations are possible describing the constituents of the mix.
For the total amount of mix:
... p + m = 10
For the quantity of peanuts in the mix:
... p + 0.2m = 0.6·10
For the quantity of almonds in the mix:
... 0.8m = 0.4·10
For the ratio of peanuts to almonds:
... (p +0.2m)/(0.8m) = 0.60/0.40
Any two (2) of these four (4) equations will serve as a system of equations that can be used to solve for the desired quantities. I like the third one because it is a "one-step" equation.
So, your system of equations could be ...
___
(b) Dividing the second equation by 0.8 gives
... m = 5
Using the first equation to find p, we have ...
... p + 5 = 10
... p = 5
5 lb of peanuts and 5 lb of mixture are required.
Answer:
Step-by-step explanation:
<h3>Given</h3>
- f(x) = 2^x + 5x and g(x) = 3x - 5
<h3>To find </h3>
<h3>Solution</h3>
- (f+ g)(x) =
- f(x) + g(x) =
- 2^x + 5x + 3x - 5 =
- 2^x + 8x - 5
Number 1 would be the correct answer :)
Step-by-step explanation:
2m+m=10+8
3m=18 /3
M=6