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2 years ago

15

A toy rocket is launched from a platform 33 feet above the ground at a speed of 83 feet per second. The height of the rocket in

feet is given by the polynomial −16t2 + 83t + 33, where t is the time in seconds. How high will the rocket be after 3 seconds?
a. 2586 feet
b. 234 feet
c. 138 feet
d. 105 feet

1 answer:

yanalaym [24]2 years ago

3 0

Answer:

c. 138 feet

Step-by-step explanation:

h(t) = −16t^2 + 83t + 33

At3 seconds

h(3) = -16(3^2) + 83(3) + 33

h(3) = -16(9) + 249 + 33

h(3) = -144 + 249 + 33

h(3) = 138

c. 138 feet

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a. $f_X(x) = \dfrac{1}{3.5}8.5$

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Step-by-step explanation:

From the given information;

Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

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From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

$f_X(x) = \dfrac{1}{12-8.5}8.5$

$f_X(x) = \dfrac{1}{3.5}8.5$

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The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

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F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

$P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx$

$P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}$

$P(X\geq11) = {\dfrac{1}{3.5}} (12-11)$

$P(X\geq11) = {\dfrac{1}{3.5}} (1)$

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d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

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