Answer:
A. x = 5
Step-by-step explanation:
3x + 9 = 24
→ Minus 9 from both sides
3x = 15
→ Divide both sides by 3
x = 5
Step-by-step explanation:
The translation vector v can be resolved into its x and y components, where x² + y² = 10 (Pythagoras' Theorem) and y = 3x
(parallel to y = 3x - 2, slope = 3).
We have x² + (3x)² = 10,
=> x² + 9x² = 10, 10x² = 10, x = 1 or x = -1.
When x = 1, y = 3. When x = -1, y = -3.
Therefore 2 possible translation vectors
are (1, 3) or (-1, -3).
First new C' = (2 + (1), 3 + (3)) = (3, 6).
Second new C'= (2 + (-1), 3 + (-3)) = (1, 0).
The possible images are (3, 6) and (1, 0).
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
Answer:d
Step-by-step explanation: I got it right
