<span>9a + -3(2a + -4) = 15
Reorder the terms:
9a + -3(-4 + 2a) = 15
9a + (-4 * -3 + 2a * -3) = 15
9a + (12 + -6a) = 15
Reorder the terms:
12 + 9a + -6a = 15
Combine like terms: 9a + -6a = 3a
12 + 3a = 15
Solving
12 + 3a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 3a = 15 + -12
Combine like terms: 12 + -12 = 0
0 + 3a = 15 + -12
3a = 15 + -12
Combine like terms: 15 + -12 = 3
3a = 3
Divide each side by '3'.
a = 1
Simplifying
a = 1</span>
The answer is Always true. because A is greater than B so put it this way if A=2 and B =1 then 2>1 same goes for C>D so if A+C would have to be greater than B+D for instance 2+2>1+1 or 4>2 so
<span>If A>B and C>D, then A+C>B+D Always true.
</span>
Answer:
If we divide both sides by 
we got:
And we can use the normal distribution table or excel to find the probabilites and we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the area of a population, and for this case we know the distribution for X is given by:
Where 
and 
We select a a sample of n =4 and since the distribution for X is normal then we know that the distribution for the sample mean 
is given by:
And we want to find this probability:
If we divide both sides by we got:
And we can use the normal distribution table or excel to find the probabilites and we got:
Answer:
Total cost is $205328
Step-by-step explanation:
Given data:
cost C(q) = 0.1 q^3 - 0.5 q^2 + 500 q + 200
current units q = 4 ( 4000 units )
The current level of production is 4000 ( 4 )units, and manufacturer is planning to upgrade this to 4100 ( 4.1 ) units
C'(q) = 3 * 0.1 q^2 - 2 * 0.5 q + 500
C'(q) = 0.3 q2 - q + 500
C(4.1) - C(4) ≈ C’(4) x Δq
≈ C’(4) x 0.1
≈ ( 0.3 * 4^2 - 4 + 500 ) x 0.1
≈ ( 0.3 * 16 - 4 + 500 ) x 0.1
≈ 500.8 x 0.1 ≈ 50.08
total cost = 4100 x 50.08 = $205328
