a.
has an average value on [5, 11] of

b. The mean value theorem guarantees the existence of
such that
. This happens for

Answer:
x = 2
Step-by-step explanation:

In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we divided by 2 only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.

→ Expand the brackets

→ Multiply everything by 12 to make solving the equation easier
6x - 6 - 2x - 2 = 0
→ Simplify equation
4x - 8 = 0
→ Add 8 to both sides to isolate 4x
4x = 8
→ Divide by 4 on both sides to isolate x
x = 2
⇒ We can substitute x = 2 back into the equation to see if the solution is correct, if we get 0 on both sides then x = 2 is correct

⇒ Substitute in the values

⇒ Simplify

⇒ Simplify further

0 = 0
The solution x = 2 is correct
Answer:
x = - 14
Step-by-step explanation:
23 + 4 + x = 25 - 12
Combine like terms on both sides of the equation (by adding 23 and 4 on the left-hand side, and subtracting 12 from 25 on the right-hand side):
23 + 4 + x = 25 - 12
27 + x = 13
Next, subtract 27 from both sides to solve for x:
27 - 27 + x = 13 - 27
x = - 14
Please mark my answers as the Brainliest if you find this explanation helpful :)
Answer:
Claim is false
Step-by-step explanation:
Claim : A credit reporting agency claims that the mean credit card debt in a town is greater than $3500.

n = 20
Since n <30
So we will use t test
Formula : 
s = standard deviation = 391
x = 3600
n = 20


Degree of freedom = n-1 = 20-1 = 19
α=0.10
So, using t table
= 1.72
t critical > t calculated
So we accept the null hypothesis
Hence we reject the claim that the mean credit card debt in a town is greater than $3500.