Answer:
10
Step-by-step explanation:
So we have the expression:
First, evaluate within the absolute value bars. 3 times -4 is -12. Thus:
Now, subtract:
The absolute value of -10 is positive 10. So:
And we're done!
Answer:
n = 8 or n = −6
Explanation:
First, isolate the absolute value:
5 − |n − 1| = −2
7 − |n − 1| = 0
7 = |n − 1|
Then, split this into two equations, since the result of the absolute value could be positive or negative:
7 = n − 1 7 = −(n − 1)
8 = n 7 = −n + 1
n = −6
Answer:
a) 0.4121
b) $588
Step-by-step explanation:
Mean μ = $633
Standard deviation σ = $45.
Required:
a. If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount?
We solve using z score formula
= z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
For x = $646
z = 646 - 633/45
z = 0.22222
Probability value from Z-Table:
P(x<646) = 0.58793
P(x>646) = 1 - P(x<646) = 0.41207
≈ 0.4121
b. How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16? (Round your answer to the nearest dollar.)
Converting 0.16 to percentage = 0.16 × 100% = 16%
The z score of 16%
= -0.994
We are to find x
Using z score formula
z = (x-μ)/σ
-0.994 = x - 633/45
Cross Multiply
-0.994 × 45 = x - 633
-44.73 = x - 633
x = -44.73 + 633
x = $588.27
Approximately to the nearest dollar, the amount should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.16
is $588
Imagine A'V' is part of the dilated figure, and AV is part of the original figure.
A'V' = 3.2
AV = 3.2 + 4.8 = 8
A'V'/AV = 3.2/8 = 2/5
Answer: First choice, 2/5.
