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Answer:
x = - 2, x = 6
Step-by-step explanation:
Given f(x) = 18 we require to solve
3 | x - 2 | + 6 = 18 ( subtract 6 from both sides )
3 | x - 2 | = 12 ( divide both sides by 3 )
| x - 2 | = 4
The absolute value function always returns a positive value, however, the expression inside can be positive or negative, thus
x - 2 = 4 ( add 2 to both sides )
x = 6
OR
- (x - 2) = 4
- x + 2 = 4 ( subtract 2 from both sides )
- x = 2 ( multiply both sides by - 1 )
x = - 2
As a check substitute these values into the left side of the equation and if equal to the right side then they are the solutions
x = 6 → 3|6 - 2| + 6 = 3|4| + 6 = 3(4) + 6 = 12 + 6 = 18 ← True
x = - 2 → 3|- 2 - 2| + 6 = 3|-4| + 6 = 3(4) + 6 = 12 + 6 = 18 ← True
Hence solutions are x = - 2, x = 6
Answer:
14
Step-by-step explanation:
H. 4,8,12,16 will be your answer (: hope this helps!
Answer:
P = 0.0438 ; We reject the Null and conclude that there is significant evidence that the discharge limit per gallon of waste has been exceeded.
Due to the small sample size.
Step-by-step explanation:
H0: μ = 500
H1 : μ > 500
Test statistic :
(xbar - μ) / S.E
Tstatistic = (1000 - 500) / 200
= 500 / 200
= 2.5
Pvalue from Test score ; df = 4 - 1 = 3 ; using calculator :
Pvalue = 0.0438
At α = 0.05
Pvalue < α ; We reject the Null and conclude that there is significant evidence that the discharge limit per gallon of waste has been exceeded.
The test above has a very small sample size, and for a distribution to be approximately Normal, the sample size must be sufficiently large enough according to the Central limit theorem.
For a two sided analysis ; the Pvalue is twice that for the one sided, hence, Pvalue = (0.0438 * 2) = 0.0876 yielding a less strong evidence against the Null.