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mezya [45]
3 years ago
13

Question text You have just won the lottery. The Lottery Corporation offers you two options: 1. a lump-sum payment of $400,000,

or 2. an annuity of $800,000 to be received in equal installments over the next 20 years. At what interest rate, r, will you be indifferent between the two options?
Mathematics
1 answer:
igomit [66]3 years ago
6 0
Use present value equation.
If present value of annuity equals 400,000, then you are indifferent.

PV = A(v + v^2 + ...v^{20}) \\  \\ PV = A\frac{v(1-v^{20})}{1-v}

where v = 1/(1+r) and  A = annual payment = 800,000/20 = 40,000

PV = 400,000
After subbing in the numbers, the equation is:
10 = \frac{v(1-v^{20})}{1-v} \\  \\ 10 - 10v = v - v^{21} \\  \\ v^{21} - 11v+10 = 0 \\  \\ v = 0.928034 \\  \\ \frac{1}{1+r} = 0.928034 \\  \\ r = 0.0775

Therefore at interest rate of about 7.75% you are indifferent.
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Triangle QRS is dilated according to the rule DO,2 (x,y).
Gemiola [76]

The correct options about the dilation are; Options A, B and E

<h3>How to interpret Dilated Objects?</h3>

From the given information, find attached a dilated image.

The scale factor is 2

QRS → Q'R'S' = (x,y) → 2(x,y)

The coordinates of ∆QRS are; Q (-3, 3), R (2, 4) and S (-1, 1)

To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In other words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.

2(x, y) = (2x, 2y)

The coordinates of ∆Q'R'S' becomes: Q' (-6, 6), R' (4, 8), S' (-2, 2)

To determine the statements that are true about the image ΔQ'R'S,

Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.

A) DO, 2 (x, y) = (2x, 2y)

A dilation about the origin with a scale factor 2 is described using the above notation.

Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)

R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)

S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)

Thus Option A is correct.

B) Side Q'S' lies on a line with a slope of -1

Q' (-6, 6)

S' (-2, 2)

coordinate (x, y)

Slope = m = (change in y)/(change in x)

m = (6-2)/[-6-(-2)]

m = 4/(-6+2) = 4/-4

m = -1

Option B is correct

c) QR is longer than Q'R'

Length of QR (-3 to 2) = 5

Length of Q'R' (-6 to 4) = 10

QR is not longer than Q'R'

Option C is false

d) The vertices of the image are closer to the origin than those of the pre-image.

From the diagram, the vertices of the preimage are closer to the origin than those of the dilation image.

Option D is False

e) The distance from Q' to the origin is twice the distance from Q to the origin.

The distance from Q' to the origin (6 to 0) = 6

The distance from Q to the origin (3 to 0) = 3

The distance from Q' to the origin = 2(the distance from Q to the origin)

Option E is correct.

Read more about Dilated Objects at; brainly.com/question/10253650

#SPJ1

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Answer:

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