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3 years ago

5

Calculate the amount of money you'll have at the end of the indicated time period, assuming that you earn simple interest. You

deposit $3400 in an account with an annual interest of 4.5 % for 20years. The amount of money you'll have at the end of the years is

1 answer:

weeeeeb [17]3 years ago

7 0

Answer:

The amount of money you'll have at the end of the years is 6460 dollars

Step-by-step explanation:

The total principal sum of money deposited = $3400$ dollars

The annual rate of interest is $4.5$ %

The time period for which the amount is invested $= 20$ years

As we know

$A = P (1 + rt)$

where A is the amount after 20 years

P is the principal sum of money

r is the rate of interest and

t is time period in years

Substituting the given values in above equation, we get -

$A = 3400 (1 + \frac{4.5}{100} * 20)\\A = 6460$ dollars

You might be interested in

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assig

Keith_Richards [23]

Answer:

1. Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C$

2. D. 36

3. C. 34

4. B. 1.059

5. B. 8.02

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part 1

The hypothesis for this case are:

Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C$

Part 2

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

If we assume that we have $p$ groups and on each group from $j=1,\dots,p$ we have $n_j$ individuals on each group we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

And we have this property

$SST=SS_{between}+SS_{within}$

We need to find the mean for each group first and the grand mean.

$\bar X =\frac{\sum_{i=1}^n x_i}{n}$

If we apply the before formula we can find the mean for each group

$\bar X_A = 27$ , $\bar X_B = 24$ , $\bar X_C = 30$ . And the grand mean $\bar X = 27$

Now we can find the sum of squares between:

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

Each group have a sample size of 4 so then $n_j =4$

$SS_{between}=SS_{model}=4(27-27)^2 +4(24-27)^2 +4(30-27)^2=72$

The degrees of freedom for the variation Between is given by $df_{between}=k-1=3-1=2$ , Where k the number of groups k=3.

Now we can find the mean square between treatments (MSTR) we just need to use this formula:

$MSTR=\frac{SS_{between}}{k-1}=\frac{72}{2}=36$

D. 36

Part 3

For the mean square within treatments value first we need to find the sum of squares within and the degrees of freedom.

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

$SS_{error}=(20-27)^2 +(30-27)^2 +(25-27)^2 +(33-27)^2 +(22-24)^2 +(26-24)^2 +(20-24)^2 +(28-24)^2 +(40-30)^2 +(30-30)^2 +(28-30)^2 +(22-30)^2 =306$

And the degrees of freedom are given by:

$df_{within}=N-k =3*4 -3 = 12-3=9$ . N represent the total number of individuals we have 3 groups each one with a size of 4 individuals. And k the number of groups k=3.

And now we can find the mean square within treatments:

$MSE=\frac{SS_{within}}{N-k}=\frac{306}{9}=34$

C. 34

Part 4

The test statistic F is given by this formula:

$F=\frac{MSTR}{MSE}=\frac{36}{34}=1.059$

B. 1.059

Part 5

The critical value is from a F distribution with degrees of freedom in the numerator of 2 and on the denominator of 9 such that we have 0.01 of the area in the distribution on the right.

And we can use excel to find this critical value with this function:

"=F.INV(1-0.01,2,9)"

And we will see that the critical value is $F_{crit}=8.02$

B. 8.02

5 0

3 years ago

Can someone walk me through it

Gre4nikov [31]

Answer: x = 123
--------------------------------------------
--------------------------------------------

Here are the basic steps:

Step 1) Find the measure of angle 7 (near the 35 degree angle)
Step 2) Find angle 6 (in the center; bottom angle)
Step 3) Use angle 6 to find the value of x
-----------------
Let's go through those steps mentioned
-----------------
Step 1) Finding the measure of angle 7

We see that the 35 degree angle and angle 7 combine to form a 90 right angle. So they must add to 90 degrees

(angle 7) + 35 = 90
(angle 7) + 35 - 35 = 90 - 35
angle 7 = 55

So angle 7 is 55 degrees. We'll use it on the next step
-----------------
Step 2) Finding the measure of angle 6

We'll use the result from step 1. The triangle with angle 7, angle 6, and the 68 degree angle will be focused on here. Recall that for any triangle, the three angles must add to 180 degrees.

So,
(angle 7) + (angle 6) + 68 = 180
(55) + (angle 6) + 68 = 180
(angle 6) + 55 + 68 = 180
(angle 6) + 123 = 180
(angle 6) + 123 - 123 = 180 - 123
angle 6 = 57

So we now know that angle 6 is 57 degrees
-----------------
Step 3) Find x

We now use the fact that angle 6 and angle x are a linear pair. They combine to form a straight line, or straight angle. In other words they add to 180 degrees (they are supplementary angles)

So,
(angle 6) + x = 180
(57) + x = 180
x + 57 = 180
x + 57 - 57 = 180 - 57
x + 57 - 57 = 123
x = 123
-----------------
Side note: we can use the exterior angle theorem to skip over step 2. To do this, we add up angle 7 (which was 55 degrees) to 68 to get 123 degrees which is the same answer.

6 0

2 years ago

A chemist is mixing a 50% salt solution with an 18% salt solution to make 40 L of a new solution that will contain 30% salt. How

Karolina [17]

Answer:

See below

Step-by-step explanation:

Sum of ingredients = sum of final solution

.50 x where x = 50 percent amount then 40 - x = 18% amount

.50 x + .18(40 - x) = .30 ( 40 )

.50 x + 7.2 - .18x = 12

.32x = 4.8

x = 15 L of 50% 25 liters of 18%

3 0

2 years ago

SOMEONE PLEASE HELP ME ASAP

IceJOKER [234]

Answer:

Letter A i think not sure

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Describe how to determine the average rate of change between x=1 and x=3 for the function f(x)=3x^3+1. Include the average rate

icang [17]

Answer:

39.

Step-by-step explanation:

We subtract f(1) which is the value of f(x) when x = 1 from f(3), then we divide by 3 - 1.

It is [(f3) - f(1]) / (3 - 1), so

Average rate of change = (3(3)^3 + 1) - (3(1)^3 + 1) / (3 - 1)

= (82 - 4) / 2

= 78 / 2

= 39.

7 0

3 years ago