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2 years ago

The function f(t)= 15000(1.08)^t models the value of an investment t years from now. What is the meaning of the value of f(10)

Mathematics

1 answer:

guajiro [1.7K]2 years ago

4 0

in the f(t) = 15000(1.08)ᵗ, which is a form of a compounded interest formula, t = years, so

f(t) = 15000(1.08)¹⁰ , is the value of it when t = 10, after 10 years.

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General Hospital has noted that they admit an average of 9 patients per hour.

serious [3.7K]

Answer:

(a) The probability that during the next hour less than 3 patients will be admitted is 0.00623.

(b) The probability that during the next two hours exactly 8 patients will be admitted is 0.00416.

Step-by-step explanation:

The complete question is: General Hospital has noted that they admit an average of 8 patients per hour.

(a) What is the probability that during the next hour less than 3 patients will be admitted?

(b) What is the probability that during the next two hours exactly 8 patients will be admitted?

The above situation can be represented through Poisson distribution as it includes the arrival rate of the pattern. So, the probability distribution of the Poisson distribution is given by;

$P(X = x) = \frac{e^{-\lambda} \times \lambda^{x} }{x!} ; x = 0,1,2,......$

Here X = Number of patients admitted in the hospital

$\lambda$ = arrival rate of patients per hour = 9 patients

So, X ~ Poisson( $\lambda$ = 9)

(a) The probability that during the next hour less than 3 patients will be admitted is given by = P(X < 3)

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= $\frac{e^{-9} \times 9^{0} }{0!} + \frac{e^{-9} \times 9^{1} }{1!} + \frac{e^{-9} \times 9^{2} }{2!}$

= $e^{-9} +(e^{-9} \times 9)+ \frac{e^{-9} \times 81}{2}$

= 0.00623

(b) Here, $\lambda = 9 \times 2$ = 18 because we have to find the probability for the next two hours and we are given in the question of per hour.

So, X ~ Poisson( $\lambda$ = 18)

Now, the probability that during the next two hours exactly 8 patients will be admitted is given by = P(X = 8)

P(X = 8) = $\frac{e^{-18} \times 18^{8} }{8!}$

= 0.00416

3 0

2 years ago

Dori filled her car with 26.5 gallons at the start of her trip. Upon arrival she

scoray [572]

Answer:

1726 miles.

Step-by-step explanation:

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2 years ago

Read 2 more answers

A 90 percent confidence interval is to be created to estimate the proportion of television viewers in a certain area who favor m

Dominik [7]

Answer:

This means that the first interval, with 9000 viewers, is 3 times as narrower as the second interval, with 1000 viewers.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The width of the interval is:

$W = 2z\sqrt{\frac{\pi(1-\pi)}{n}}$

In this sample:

Two 90% intervals, with different lenghts. So both have the same values for z an $\pi$

Interval A:

9000 viewers.

So the width is

$W_{A} = 2z\sqrt{\frac{\pi(1-\pi)}{9000}}$

Interval B:

100 viewers

So the width is

$W_{B} = 2z\sqrt{\frac{\pi(1-\pi)}{1000}}$

Relationship between the widths:

$R = \frac{W_{A}}{W_{B}} = \frac{2z\sqrt{\frac{\pi(1-\pi)}{9000}}}{2z\sqrt{\frac{\pi(1-\pi)}{1000}}} = \frac{\sqrt{1000}}{\sqrt{9000}} = \frac{\sqrt{1}}{\sqrt{9}} = \frac{1}{3}$

This means that the first interval, with 9000 viewers, is 3 times as narrower as the second interval, with 1000 viewers.

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2 years ago

Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes si

Semmy [17]

Step-by-step explanation:

Tracie’s bus travels towards her home at an average speed of StartFraction one-half EndFraction mile per minute.

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2 years ago

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Julli [10]

Because she needs 3 blankets and it takes 15 day per blanket(rate is given), she needs 3x15 or 45 days. She has 60 days so she can volunteer at most 15 days.

answer: s≤15

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2 years ago