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3 years ago

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If an object is dropped from a height of 144 feet, the function h(t)=-16t^2+144 gives the height of the object after t seconds.

When will the object hit the ground
A. 3s
B. 6s
C. 1.5 s
D. 9s

1 answer:

shtirl [24]3 years ago

5 0

Answer:

A. 3s

Step-by-step explanation:

The height of the object after t seconds is given by:

$h(t) = -16t^2 + 144$

When will the object hit the ground?

It hits the ground after t seconds, and t is found when $h(t) = 0$ . So

$h(t) = -16t^2 + 144$

$0 = -16t^2 + 144$

$16t^2 = 144$

$t^2 = \frac{144}{16}$

$t^2 = 9$

$t = \sqrt{9}$

$t = 3$

3 seconds, so the correct answer is given by option a.

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Suppose approximately 75% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introvert

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Answer:

$P(x \ge 5) = 1.000$ ---- At least 5 from marketing departments are extroverts

$P(x=15) = 0.013$ ---- All from marketing departments are extroverts

$P(x = 0) = 0.002$ ---------- None from computer programmers are introverts

Step-by-step explanation:

See comment for complete question

The question is an illustration of binomial probability where

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$(a):\ P(x \ge 5)$

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$p = 75\%$ --- proportion that are extroverts

Using the complement rule, we have:

$P(x \ge 5) = 1 - P(x < 5)$

So, we have:

$P(x < 5) =P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)$

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$P(x = 2) = ^{15}C_{2} * (75\%)^2 * (1 - 75\%)^{15 - 2} = 105* (0.75)^2 * (0.25)^{13} = 8.80 * 10^{-7}$

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$P(x = 4) = ^{15}C_{4} * (75\%)^4 * (1 - 75\%)^{15 - 4} = 1365 * (0.75)^4 * (0.25)^{11} = 0.000103$

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Recall that:

$P(x \ge 5) = 1 - P(x < 5)$

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$(b)\ P(x = 15)$

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$(c)\ P(x = 0)$

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$p = 70\%$ --- proportion that are introverts

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$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x = 0) = ^{5}C_0 * (70\%)^0 * (1 - 70\%)^{5-0}$

$P(x = 0) = 1 * 1 * (0.30)^5$

$P(x = 0) = 0.002$

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