<span>It is important to know that the sum of the three angles inside a triangle add up to 180 degrees. So then we get the following by adding up all three provided angle measures:
3x + (2x + 20) + (4x - 20) = 180
Some algebraic manipulation follows:
3x + 2x + 20 + 4x - 20 = 180
9x = 180
x = 180/9 = 20
The value of x is 20 degrees.</span>
Answer:
See below for answers and explanations
Step-by-step explanation:
<u>Part A</u>
Assuming that conditions have been met for the interval, we use the formula 
where 
represents the sample mean, 
represents the critical value, 
represents the sample standard deviation, and 
is the sample size.
The critical value of for an 80% confidence level with degrees of freedom 
is equivalent to 
Thus, we can compute the confidence interval:
Therefore, we are 80% confident that the true mean age of all customers is between 30.17 and 35.11 years.
<u>Part B</u>
The margin of error is 
Answer:
x = 5
Step-by-step explanation:
Simplify. First, combine like terms:
3x - x + 2 = 12
(3x - x) + 2 = 12
(2x) + 2 = 12
2x + 2 = 12
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
& is your order of operation.
First, subtract 2 from both sides:
2x + 2 (-2) = 12 (-2)
2x = 12 - 2
2x = 10
Next, divide 2 from both sides:
(2x)/2 = (10)/2
x = 10/2
x = 5
5 is your answer for x.
Check: Plug in 5 for x in the equation. Solve:
3(5) - (5) + 2 = 12
15 - 5 + 2 = 12
10 + 2 = 12
12 = 12 (True)
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