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Katena32 [7]
3 years ago
12

Your friend deposits $6000 in an investment account that earns 7.3% annual interest. Find the balance after 18 years when the in

terest is compounded quarterly.
Mathematics
1 answer:
marusya05 [52]3 years ago
4 0

Answer: $22,063.2

Step-by-step explanation:

quarterly means that 4 times per year this interest, the balance can be find by the equation:

A = P*(1 + r/4)^(4*t)

Where P is the initial value, r is the rate of increase (7.3% in this case, but remember that you must use the decimal form; 0.073) and t is the number of years:

so we have:

B = $6,000*( (1 + 0.073/4)^(4*18) = $22,063.2

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A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyl
LuckyWell [14K]

Answer:

A sample of 16577 is required.

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 z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

99% confidence level

So \alpha = 0.01, z is the value of Z that has a p-value of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

She wants to estimate the proportion using a 99% confidence interval with a margin of error of at most 0.01. How large a sample size would be required?

We have no estimation for the proportion, and thus we use \pi = 0.5, which is when the largest sample size will be needed.

The sample size is n for which M = 0.01. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.01 = 2.575\sqrt{\frac{0.5*0.5}{n}}

0.01\sqrt{n} = 2.575*0.5

\sqrt{n} = \frac{2.575*0.5}{0.01}

(\sqrt{n})^2 = (\frac{2.575*0.5}{0.01})^2

n = 16576.6

Rounding up:

A sample of 16577 is required.

8 0
3 years ago
In the diagram below, P is circumscribed about quadrilateral ABCD. What is the value of x?
alexira [117]
We know that
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So,
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(x+20) + 110 = 180 \\ x+130=180 \\ x=180-130 \\ x=50degrees

therefore

the answer is
x=50degrees
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4.5

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