Did Help , Have No I Deal What To Do

Emmet has $90 in a savings account that earns 10% interest, compounded annually.

STatiana [176]

Answer:

108.90

Step-by-step explanation:

You start with finding

10

%

of

90

.

$

90

⋅

.1

=

$

9

You add the money and the interest to get

$

99

for the first year. However, the next year is different. It's compound interest, so you have to multiply

10

%

by

$

99

.

$

99

⋅

.1

=

$

9.90

$

99

+

$ 9.90

= $ 108.90 The total would then be $

108.90 i think lol

3 0

3 years ago

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 104 eligible vot

crimeas [40]

Answer:

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this case, assume that 104 eligible voters aged 18-24 are randomly selected.

This means that $n = 104$ .

Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.

This means that $p = 0.22$

Mean and standard deviation:

$\mu = 104*0.22 = 22.88$

$\sigma = \sqrt{104*0.22*0.78} = 4.2245$

Probability that exactly 27 voted

By continuity continuity, 27 consists of values between 26.5 and 27.5, which means that this probability is the p-value of Z when X = 27.5 subtracted by the p-value of Z when X = 26.5.

X = 27.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{27.5 - 22.88}{4.2245}$

$Z = 1.09$

$Z = 1.09$ has a p-value of 0.8621

X = 26.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{26.5 - 22.88}{4.2245}$

$Z = 0.86$

$Z = 0.86$ has a p-value of 0.8051

0.8621 - 0.8051 = 0.057

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

5 0

3 years ago

Percentages: Decrease 253 by 42%

Mariana [72]

146.74 because 42% of 253 is 106.26, and take that away from 253 = 146.74

4 0

3 years ago

A restaurant has 18 tables and 54 chairs. The

luda_lava [24]

Answer:

The ratio is 1:3

Step-by-step explanation:

Let

x -----> the number of tables in the restaurant

y ----> the number of chairs in the restaurant

we know that

To find out the ratio of tables to chairs in the restaurant, divide the number of tables by the number of chairs

we have

$x=18\ tables\\ y=54\ chairs$

so

The ratio is equal to

$\frac{18}{54}$

Simplify

Divide by 18 both numerator and denominator

$\frac{1}{3}$

therefore

The ratio is 1:3

6 0

3 years ago

A random sample of 9 fields of corn has a mean yield of 38.2 bushels per acre and standard deviation of 9.66 bushels per acre. D

shtirl [24]

Answer:

The critical value that should be used is T = 1.397.

The 80% confidence interval for the true mean yield is between 24.705 bushels per acre and 51.695 bushels per acre.

Step-by-step explanation:

We have the standard deviation of the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 9 - 1 = 8

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.8}{2} = 0.9$ . So we have T = 1.397. This is the critical value that should be used.

The margin of error is:

M = T*s = 1.397*9.66 = 13.495

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 38.2 - 13.495 = 24.705 bushels per acre.

The upper end of the interval is the sample mean added to M. So it is 38.2 + 13.495 = 51.695 bushels per acre.

The 80% confidence interval for the true mean yield is between 24.705 bushels per acre and 51.695 bushels per acre.

7 0

3 years ago