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maksim [4K]
3 years ago
10

Parallelogram BCDE with vertices B(2, -3), C(6,-4), D(7.-6), and E(3.-5):

Mathematics
1 answer:
Klio2033 [76]3 years ago
5 0
Rotation 270 counterclockwise about origin is easy, swap the x and y then reverse the sign of the y
so (x, y) rotates to (y, -x)
Sadly to change the centre we need to translate the centre to the origin, rotate and the translate back.
In this case that means adding -1, 2 to x,y respectively, rotating, adding 1, -2 to x,y respectively

B(2, 3) translates to (1, 5) which rotates to (5, -1) and translates back to B’(6, -3)
C(6, -4) translates to (5, -2) which rotates to (-2, -5) and translates back to C’(-1, -7)
D(7, -6) translates to (6, -4) which rotates to (-4, -6) and translates back to (-3, -8)
E(3, -5) translates to (2, -3) which rotates to (-3, -2) and translates back to (-2, -4)

The translation is much easier simply moving each point 8 to the right
B’(2, 11), C’(6, 4), D’(7, 2) and E’(3, 3)

Using the grid will everything clear!
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Which set represents the domain of function shown? {(-3,6),(0,2),(4,7),(11,15)}
ValentinkaMS [17]

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{-3,0,4,11}

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3 years ago
The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of
Ipatiy [6.2K]

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

7 0
3 years ago
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