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Elena L [17]
3 years ago
7

Morgan Bowie is trying to determine the amount to set aside so that he will have enough money on hand in 3 years to overhaul the

engine on his vintage used car. While there is some uncertainty about the cost of engine overhauls in 3 years, by conducting some research online, Morgan has developed the following estimates.
Engine Overhaul Estimated Cash Outflow Probability Assessment
$390 10%
570 30%
750 50%
790 10%


How much should Keith Bowie deposit today in an account earning 6%, compounded annually, so that he will have enough money on hand in 6 years to pay for the overhaul?
Mathematics
1 answer:
Nostrana [21]3 years ago
6 0

Answer:

$468.09

Step-by-step explanation:

first we must calculate the expected future value of the engine overhaul:

($390 x 10%) + ($570 x 30%) + ($750 x 50%) + ($790 x 10%) = $39 + $171 + $375 + $79 = $664

now we must determine the present value of $664 using a 6% interest rate:

PV = FV / (1 + r)⁶ = $664 / 1.06⁶ = $468.09

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The speeds in miles per hour of seven randomly selected qualifiers for the Indianapolis 500 (in 2012) are listed below. Estimate
SSSSS [86.1K]

Answer:

Mean qualifying speed

= 224.5669mi/hr

Speed that passed the average/mean

= 226.240mi/hr ,224.037mi/hr 226.484mi/hr, 225.172 mi/hr

Step-by-step explanation:

Let's understand what mean is then understand what mean qualifying speed is.

First mean is like the average of the seven speed listed below.

So let's find the mean.

Mean = (223.684+ 222.929+ 226.240

+224.037 +226.484+ 225.172

+223.422)/7

Mean = 1571.968/7

Mean = 224.5669

So the mean qualifying speed is those speed that qualifies when the mean is taken, i.e the speed that crossed the average.

Mean qualifying speed are

=226.240 ,224.037,226.484

, 225.172

4 0
3 years ago
A ball is launched at 30 meters per second (m/s) from a 20-meter tall platform. The equation for the object's height s at time t
Juliette [100K]

The maximum height the ball reaches is 65.92 m.

The time taken for the ball to reach the maximum height is 3.06 seconds.

The time taken for the ball to hit the ground is 6.12 seconds.

<h3>maximum height the ball reaches</h3>

The maximum height the ball reaches is calculated as follows;

s(t) = -4.9t² + 30t + 20

at maximum height, final velocity = 0

v = 0

ds/dt = -9.8t + 30 = 0

9.8t = 30

t = 30/9.8

t = 3.06 seconds

s(3.06) = -4.9(3.06)²  + 30(3.06)  + 20

s(3.06) = 65.92 m

Thus, the time taken for the ball to reach the maximum height is 3.06 seconds.

<h3>Time of flight of the ball</h3>

The time taken for the ball to hit is the total time of flight = 2 x 3.06 seconds = 6.12 seconds.

Thus, the maximum height the ball reaches is 65.92 m.

The time taken for the ball to reach the maximum height is 3.06 seconds.

The time taken for the ball to hit the ground is 6.12 seconds.

Learn more about maximum height here: brainly.com/question/12446886

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4 0
2 years ago
A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 35 m². The surface area of the image is 315 m². T
Westkost [7]

The original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

<h3>How does dilation affect length, area, and volume of an object?</h3>

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

<u><em>L = k × M</em></u>

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by <u><em>k²</em></u><em> </em>to get each other corresponding quantity from their similar figures' quantities.

<u><em>So </em></u><u><em>area </em></u><u><em>of </em></u><u><em>first figure </em></u><u><em>= k² × area of second figure</em></u>

Similarly,

<u><em>Volume </em></u><u><em>of first figure = k³ × volume of second figure.</em></u>

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

For this case, we're given that;

  • Surface area of pre-image = 35 m²
  • Surface area of dilated image = 315 m²
  • Height of pre-image = 5.8 m
  • Height of dilated image.

Let the scale fator of dilation be k.

Then:

<u><em>So area of pre-image = k² × area of dilated image</em></u>

Thus, we get:

35 = k^2 \times 315\\\\k = \sqrt{\dfrac{35}{315}} = 1/3

(took positive root as scaling is done by non-negative factors as only magnitude matters mostly)

Thus, we get:

Height of pre-image = (1/3) × Height of dilated image (say h)

5.8 = (1/3) \times h\\h = 3 \times 5.8 = 17.4 \rm \: m

Thus, the original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

Learn more about dilation here:

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4 0
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What is the measure of RMN? ​
wariber [46]

Answer:

The Answer is: 63°

Step-by-step explanation:

The angle 117° is the key information. Across the line, the angle 117° is part of the 180° across the line. Angle RMN is equal to 180° - 117° =  63°

5 0
3 years ago
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Point V is on line segment UW. Given VW = 6 and UV = 14, determine the<br> length UW
SpyIntel [72]

Answer:  The length is 20.

Step-by-step explanation:

If UW is the line segment, then the length of VW and UV has to equal to the length of UW

VW = 6

UV  = 14

6 + 14 = 20

6 0
3 years ago
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