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andrey2020
2 months ago
12

A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Descri

be how a sequence can be used to determine the height of the ball when it reaches its fourth peak.
Mathematics
2 answers:
Zina [12.3K]2 months ago
9 0

Sample response from E2020:

The successive heights drop by a factor of 2/3, so the series of peak heights is geometric: 27, 18, 12. Taking two-thirds of 12 yields 8, so the ball will reach 8 feet on the fourth peak.

I hope this is helpful :)

~ V.

tester [12.3K]2 months ago
4 0
A geometric sequence models the bounce heights:
Use the formula
A (subscript n) = Ar(n-1)
a = the first-term value
n = the index of the term you want (for the fourth peak, n = 4) 
r = common ratio, found by dividing the second term by the first
Here r = 18/27 = 2/3 because 27×(2/3) = 18, and similarly 18×(2/3) = 12
For the fourth peak n = 4
Compute: 4th term = 27(2/3)^(4-1) = 8
Therefore the height at the fourth peak is 8
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Answer:

Ben could have sold a maximum of 6 turkey sandwiches.

Step-by-step explanation:

Turkey sandwiches are priced at $2.50, while veggie wraps cost $3.50 at the snack stand.

Our goal is to determine the largest number of turkey sandwiches Ben might have sold.

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4 veggie wraps were sold (y).

Thus, the inequality is: 2.50x + 3.50(4) < 30

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- 14 - 14

2.50x < 16

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Ultimately, Ben could sell a maximum of 6 turkey sandwiches.

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2 months ago
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One sphere has a radius of 5.10 cm; another has a radius of 5.00cm. What is the difference in volume (in cubic centimeters) betw
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The line width of a tool used for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micromete
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Answer:

a. 0.82%

b. 71.11%

c. 0.564 micrometer

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To find the z value for each measurement, we must calculate and determine the percentage they correspond to, and the difference will give us the percentage between those two statistics.

The equation for z is:

z = (x - m) / (sd)

Here, x is the value being evaluated, m denotes the mean, and sd represents the standard deviation.

a.

For 0.62 copies, we calculate:

z = (0.62 - 0.5) / (0.05)

z = 2.4

This translates to 0.9918.

Therefore, p (x > 0.62) = 1 - 0.9918

p (x > 0.62) =  0.0082 = 0.82%

b.

For 0.47 copies, we have:

z = (0.47 - 0.5) / (0.05)

z = -0.6, which equates to 0.2742.

For 0.63 copies:

z = (0.63 - 0.5) / (0.05)

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c.

For x copies, we find:

p = 0.9 corresponds to z = 1.28.

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From which we derive:

x = 1.28*0.05 + 0.5

x = 0.564 micrometer

4 0
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