At East Junior High School, there are a total of 1175 students in the 7th and 8th

Ella invested $2,700 in an account paying an interest rate of 5.4% compounded

Dmitry [639]

Answer:

The account will take 7 years to reach a value of $4,020

Step-by-step explanation:

Compound Interest

When it occurs interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

$A=P\left(1+{\frac {r}{n}}\right)^{nt}$

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Ella invested P=$2,700 in an account with an interest rate of r=5.4% (0.054) compounded monthly. Since there are 12 months in a year, n=12.

It will be calculated when will the account have a value of A=$4,020. Substituting all the values in the formula:

$4,020=2,700\left(1+{\frac {0.054}{12}}\right)^{12t}$

Calculating:

$4,020=2,700\left(1.0045)^{12t}$

Dividing by 2,700:

$\frac{4,020}{2,700}=\left(1.0045)^{12t}$

To solve this equation for t, we need to apply logarithms:

$\log\frac{4,020}{2,700}=\log\left(1.0045)^{12t}$

Applying the logarithm power rule:

$\displaystyle \log\frac{4,020}{2,700}=12t\log 1.0045$

Dividing by 12log 1.0045:

$\displaystyle t=\frac{\log\frac{4,020}{2,700}}{12\log 1.0045}$

Calculating:

t= 7.39 years

Rounding to the nearest year, the account will take 7 years to reach a value of $4,020

3 0

2 years ago

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A washer and dryer cost a total of $1014. The cost of the washer is two times the cost of the dryer. Find the cost of each item.

timurjin [86]

Answer:

Washer is $676

Dryer is $338

Step-by-step explanation:

1014 divide by 3 gives you 338.

338 x 2 = $676

676 is twice 338.

676 + 338 = 1014

8 0

2 years ago

You invest $4000 in a bank account with 5% interest compounded annually. You are wondering how long it would take for your money

SCORPION-xisa [38]

The formula for compound interest is written as $A = P(1 + \frac{r}{n})^{nt}$ , where P is the principal (initial amount), r is the rate of interest, n is the number of times it's compounded per year, and t is the time in years. With the values from this problem plugged in, it looks like:

$A = 4000(1.05})^{t}$

Since you're trying to find when your money will double, put 8000 for A and solve for t :

$8000 = 4000(1.05})^{t} \\ \\ 2 = (1.05})^{t} \\ \\ t=log_{1.05}2 \\ \\ t = 14.20669908289$

It will take approximately 14.21 years, or about 14 years, 2 months, and 16 days, for the money to double.

7 0

2 years ago

Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat’s weight is

prohojiy [21]

Answer:

Step-by-step explanation:

Hello!

You have the information of the net gain of weight of rats of three independent groups that were fed with three different formulas (A, B and C)

The objective is to determine if the population variance of the weight gain of the rats fed with formula C (feed by Javier) is the same as the population variance of the weight gain of the rats fed with formula A (feed by Linda)

Then you have two variables of interest:

X₁: Net weight gain of the rats fed with formula A (gr)

X₂: Net weight gain of the rats fed with formula C (gr)

Assuming that both variables have a normal distribution, the statistical test for this analysis is a variance ratio.

The hypotheses are:

H₀: σ₁²=σ₂²

H₁: σ₁²≠σ₂²

α: 0.10

$F= \frac{S_1^2}{S_2^2} * \frac{Sigma_1^2}{Sigma_2^2}~~F_{n_1-1;n_2-1}$

The sample variances are:

S₁²= 10.09gr

S₂²= 27.16

$F_{H_0}= \frac{10.09}{27.16} *1= 0.37$

Remember, another way of expressing the statistical hypotheses for this test is H₀: σ₁²/σ₂²= 1 vs. H₁: σ₁²/σ₂²≠ 1, the theoretical value for the ration of the population variances is one (considering that the null hypothesis is true).

The p-value of the test is 0.3605

Using the p.value approach, the decision rule is

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value is greater than α, the decision is to not reject the null hypothesis.

Using a level of 10%, there is no significant evidence to reject the null hypothesis. Then you can conclude that the population variance of the net weight gain of the rats fed by Javier is statistically the same as the population net weight gain of the rats fed by Linda.

I hope this helps!

7 0

2 years ago

LOOK AT THE BOTTOM MAKE SURE YOU ARE RIGHT ?????????????????????????????/

Kisachek [45]

V≈ 78.54units

V=π r² h/3 = π · 5² · 3/3 ≈ 78.53982

I hope this helps!

7 0

2 years ago

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