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Ede4ka [16]
3 years ago
7

You deposit $400 into an account that pays 2% annual interest compounded quarterly.

Mathematics
2 answers:
muminat3 years ago
4 0

Step-by-step explanation:

Part A

The exponential model that describes the situation

The formula is

Y (x)=400 (1+0.02/4)^4x

Y (x)=400 (1+0.005)^4x

Y (x)=400 (1.005)^4x

Where x is the number of years

Part B

The value of the account after 5 years

Y (5)=400×(1.005)^(4×5)

Y (5)=441.96

Read more on Brainly.com - brainly.com/question/4656074#readmore

Ad libitum [116K]3 years ago
3 0
Part A
The exponential model that describes the situation
The formula is
Y (x)=400 (1+0.02/4)^4x
Y (x)=400 (1+0.005)^4x
Y (x)=400 (1.005)^4x
Where x is the number of years

Part B
The value of the account after 5 years
Y (5)=400×(1.005)^(4×5)
Y (5)=441.96

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Answer:

Final answer is x=\frac{\pi}{3} and x=\frac{5\pi}{3}.

Step-by-step explanation:

Given equation is 1-\cos\left(\theta\right)=\frac{1}{2}

Now we need to find the solution of  1-\cos\left(\theta\right)=\frac{1}{2} in given interval [0, 2\pi ].

1-\cos\left(\theta\right)=\frac{1}{2}

-\cos\left(\theta\right)=\frac{1}{2}-1

-\cos\left(\theta\right)=-\frac{1}{2}

\cos\left(\theta\right)=\frac{1}{2}

which gives x=\frac{\pi}{3} and x=\frac{5\pi}{3} in the given interval.

Hence final answer is x=\frac{\pi}{3} and x=\frac{5\pi}{3}.

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You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proporti
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Answer:

We need a sample size of at least 369.

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 margin of error is:

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

For this problem, we have that:

\pi = 0.32

90% confidence level

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

How large of a sample size is required?

We need a sample size of at least n.

n is found when M = 0.04. So

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

0.04 = 1.645\sqrt{\frac{0.32*0.68}{n}}

0.04\sqrt{n} = 1.645\sqrt{0.32*0.68}

\sqrt{n} = \frac{1.645\sqrt{0.32*0.68}}{0.04}

(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.32*0.68}}{0.04})^{2}

n = 368.02

Rounding up

We need a sample size of at least 369.

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3 years ago
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