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3 years ago

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2) Portia deposited $16,879.35 into a savings account paying 9.6% interest compounded annually for 3 years. How much money will

Portia have after 3 years?

1 answer:

Monica [59]3 years ago

7 0

Answer:

is 20,000

Step-by-step explanation:

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Suppose n people, n ≥ 3, play "odd person out" to decide who will buy the next round of refreshments. The n people each flip a f

blondinia [14]

Answer:

Assume that all the coins involved here are fair coins.

a) Probability of finding the "odd" person in one round: $\displaystyle n \cdot \left(\frac{1}{2}\right)^{n - 1}$ .

b) Probability of finding the "odd" person in the $k$ th round: $\displaystyle n \cdot \left(\frac{1}{2}\right)^{n - 1} \cdot \left( 1 - n \cdot \left(\frac{1}{2}\right)^{n - 1}\right)^{k - 1}$ .

c) Expected number of rounds: $\displaystyle \frac{2^{n - 1}}{n}$ .

Step-by-step explanation:

<h3>a)</h3>

To decide the "odd" person, either of the following must happen:

There are $(n - 1)$ heads and $1$ tail, or
There are $1$ head and $(n - 1)$ tails.

Assume that the coins here all are all fair. In other words, each has a $50\,\%$ chance of landing on the head and a

The binomial distribution can model the outcome of $n$ coin-tosses. The chance of getting $x$ heads out of

The chance of getting $(n - 1)$ heads (and consequently, $1$ tail) would be $\displaystyle {n \choose n - 1}\cdot \left(\frac{1}{2}\right)^{n - 1} \cdot \left(\frac{1}{2}\right)^{n - (n - 1)} = n\cdot \left(\frac{1}{2}\right)^n$ .
The chance of getting $1$ heads (and consequently, $(n - 1)$ tails) would be $\displaystyle {n \choose 1}\cdot \left(\frac{1}{2}\right)^{1} \cdot \left(\frac{1}{2}\right)^{n - 1} = n\cdot \left(\frac{1}{2}\right)^n$ .

These two events are mutually-exclusive. $\displaystyle n\cdot \left(\frac{1}{2}\right)^n + n\cdot \left(\frac{1}{2}\right)^n = 2\,n \cdot \left(\frac{1}{2}\right)^n = n \cdot \left(\frac{1}{2}\right)^{n - 1}$ would be the chance that either of them will occur. That's the same as the chance of determining the "odd" person in one round.

<h3>b)</h3>

Since the coins here are all fair, the chance of determining the "odd" person would be $\displaystyle n \cdot \left(\frac{1}{2}\right)^{n - 1}$ in all rounds.

When the chance $p$ of getting a success in each round is the same, the geometric distribution would give the probability of getting the first success (that is, to find the "odd" person) in the $k$ th round: $(1 - p)^{k - 1} \cdot p$ . That's the same as the probability of getting one success after $(k - 1)$ unsuccessful attempts.

In this case, $\displaystyle p = n \cdot \left(\frac{1}{2}\right)^{n - 1}$ . Therefore, the probability of succeeding on round $k$ round would be

$\displaystyle \underbrace{\left(1 - n \cdot \left(\frac{1}{2}\right)^{n - 1}\right)^{k - 1}}_{(1 - p)^{k - 1}} \cdot \underbrace{n \cdot \left(\frac{1}{2}\right)^{n - 1}}_{p}$ .

<h3>c)</h3>

Let $p$ is the chance of success on each round in a geometric distribution. The expected value of that distribution would be $\displaystyle \frac{1}{p}$ .

In this case, since $\displaystyle p = n \cdot \left(\frac{1}{2}\right)^{n - 1}$ , the expected value would be $\displaystyle \frac{1}{p} = \frac{1}{\displaystyle n \cdot \left(\frac{1}{2}\right)^{n - 1}}= \frac{2^{n - 1}}{n}$ .

7 0

2 years ago

90+8=x+k<br> x=72<br> k=?<br> help please

quester [9]

Answer:

k = 26

Step-by-step explanation:

90 + 8 = x + k

x = 72

90 + 8 = 72 + k

90 + 8 = 98

98 = 72 + k

98 = 72 + k

-72 -72

98 - 72 = 26

72 + k - 72 = k

26 = k

k = 26

8 0

3 years ago

Read 2 more answers

Maggie has a container in the shape of a right prism. The formula for its surface area is SA = Ph + 2B. Solve for h.

mart [117]

Answer:

Step-by-step explanation:

We have been given a formula for the surface area of a container in shape of right prism. We are asked to solve for h for our given formula.

First of all, we will switch sides for our given equation as:

Now, we will subtract 2B from both sides of our equation.

Now, we will divide both sides of our equation by P.

Therefore, option A is the correct choice.

<em>PLS MARK BRAINLIST </em>

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2 years ago

Which variable is most important to the following problem? At 9:45 a.m. a patient’s temperature was 101.5 degrees at 10:41, the

statuscvo [17]

Answer:

Option A is the important variable.

Step-by-step explanation:

Given is - At 9:45 a.m. a patient’s temperature was 101.5 degrees at 10:41, the nurse took the patients temperature again and found it was 105.8 degrees, the highest ever recorded.

The variable that is most important here is A: the number of minutes it took for the to reach its peak.

Firstly it is not mentioned if 10:41 is am or pm.

If its am, then such a temperature rise in less than an hour is very dangerous.

So, the important variable is option A.

6 0

3 years ago

Resuelve el siguiente problema de fracciones y escoge la alternativa correcta: Jaime compra una propiedad en 84000 dólares y des

Kryger [21]

Answer:

$21,000

Step-by-step explanation:

Solve the following fraction problem and choose the correct alternative: Jaime buys a property for $ 84,000 and after one year sells it earning 1/4 of the purchase price. How much was the profit? *

The amount of profit is calculated as

1/4 of the purchase price

Purchase price = $84,000

= 1/4 of $84,000

= 1/4 × $84,000

= $21,000

Therefore, the amount of the profit = $21,000

5 0

3 years ago