Find the future value of an annuity due with an annual payment of $13,000 for three years at 3% annual interest using the simple interest formula. What is the future value of the annuity? How much was invested? How much interest was earned? What is the future value of the annuity?​

The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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Answer:

The values are missing in the question. They are : 16.3,12.8,13,32.2,28.1,34.4,46.4,53,15.4,18.2

Step-by-step explanation:

16.3,12.8,13,32.2,28.1,34.4,46.4,53,15.4,18.2

We calculate sample mean and std deviation from given data.

Sample Mean, \($ {\overset{-}X} =\frac{\Sigma (X)}{n} $\)   =269.8/10=26.98

Sample Variance, \($s^2= \frac{\Sigma(X-{\overset{-}X})^2}{(n-1)}$\)    =1859.496/9=206.610667

Sample std dev,s=\($\sqrt{s^2}$\)=√206.610667≈14.373958

We want to test two tailed hypothesis:

\($H_0$\) : σ=12

\($H_2$\) : σ≠12

Given: s=14.373958⇒ \($s^2$\) =206.610667,n=10

Significance level, a=0.1 Degrees of freedom, df=n-1=9

Since this is two tailed test, we need area of α=0.1 on either side of critical value. This means area of 0.05 on right of positive critical value.

Critical values are given by \($ X_{1-\alpha/2}^2 =X_{0.95}^2 \text{ and}\ X_{1-\alpha/2}^2 =X_{0.95}^2 $\)  with 9 degrees of freedom.

We can use chi-square table or following excel commands:

CHISQ. INV(0.95,9)=3.32511284307

CHISQ. INV (0.05,9)=16.9189776046

Critical Values, \($X_L^2$\)=3.325  and \($X_R^2$\)=16.919

Since this is two tailed test, the decision rule or rejection criteria is:

Reject null hypothesis if test statistic is less than or equal to left critical value OR more than or equal to right critical value, i.e,

Reject \($H_0$\)   if \($x^2$\)≤3.325  OR \($x^2$\)≥16.919

Test statistic is given by \($X^2=\frac{(n-1)s^2}{\sigma^2}$\) =((9)*206.610667)/144=12.913167    

Test statistic, \($x^2$\)=12.913

since test statistic is between two critical values, we (do not reject \($H_0$\)) (i.e, we fail to reject \($H_0$\).

Conclusion: There is (not sufficient) evidence to conclude that standard deviation is not equal to 12 .

Alternatively, we can use p-value approach. The decision rule or rejection criteria is: reject null hypothesis if p-value is less than or equal to significance level (α), i.e, reject \($H_0$\) if p-value ≤0.1

P-value is twice the (smaller) tail area of test statistic because this is two tailed test. We can use excel function to find this. 2*M IN (CHISQ.DIST (12.913167,9,  TRUE ) 1-CHISQ.DIST 12.913167,9,  TRUE ) =0.333149809868

P-value =0.3331

since p-value is greater than significance level (α),we (do not reject \($H_0$\)) (i.e, we fail to reject \($H_0$\)).

Conclusion: There is (not sufficient) evidence to conclude that standard deviation is different from 12 .

Answer:

The population standard deviation is 1.92.

Step-by-step explanation:

Population mean:

Sum of all values divided by the number of values. Thus:

\(M = \frac{2 + 3 + 5 + 7}{4} = 4.25\)

Population standard deviation:

Square root of the division between the sum of the difference squared of each value and the mean, and the number of values. Thus.

\(S = \sqrt{\frac{(2-4.25)^2 + (3-4.25)^2 + (5-4.25)^2 + (7-4.25)^2}{4}} = 1.92\)

The population standard deviation is 1.92.

Answer:

(2, 2)

Step-by-step explanation:

Since we know that y = x, we can substitute that into the first equation and solve for y.

-(y) + 3y = 4

2y = 4

y = 2

And once more, since we know that y = x, we now know that x is also 2.

Therefore, the solution is (2, 2).

Based on the information, we can infer that the salary a worker earns depends on the hourly wage they earn. In this case we will have to multiply the value of each hour by the number of hours worked. Additionally, I would agree to have a higher minimum wage to benefit workers.

Based on the information in the graph, we can infer that workers will have wages of $5.2, $6.0, and $6.6. According to the above, the salary varies depending on the number of hours.

On the other hand, I believe that you would agree to a salary increase because this would benefit workers who would be better paid for each hour of work.

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Answer:

106 million tons

Step-by-step explanation:

Plastic takes up 24%, metal 8%, and 'other trash' 21%. Add those up and you get that those three take up a total of 53%. Now multiply 200 by 53% and you have 106 million tons.

Answer:

7x + 3

Step-by-step explanation:

3x + 4x + 3

7x + 3

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

B. 22.5

Step-by-step explanation:

Answer:

17$

Step-by-step explanation:

25-8=17

The Residual is -8.4 hours and the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.

A residual plot is a type of scatter plot where the horizontal axis represents the independent variable, or input variable of the data, and the vertical axis represents the residual values.

Now, looking at the given residual plot and using a calculator online, we can say that the equation of the least squares regression line is;

y^ = 180.8 + 15.2x

Now, for 2 tablespoons of sugar , we have x = 2. Thus;

y^ = 180.8 + 15.2(2)

y^ = 212.4 hours

Residual for 204 hours is;

Residual = 204 - 212.4 = -8.4 hours

Thus, the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.

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Complete question is;

Does adding sugar to the water in a vase help flowers stay fresh? To find out, two statistics students went to a flower shop and randomly selected 12 carnations. When they got home, the students prepared 12 identical vases with exactly the same amount of water in each vase. They put one tablespoon of sugarin 3 vases, two tablespoons of sugar in 3 vases, and three tablespoons of sugar in 3 vases.In the remaining 3 vases, they put no sugar. After the vases were prepared, the students randomly assigned 1 carnation to each vase and observed how many hours each flower continued to look fresh.

Calculate and interpret the residual for the flower that had 2 tablespoons of sugar and looked fresh for 204 hours.

Answer:

Step-by-step explanation:

Since you are reflecting about the x axis you keep the x coordinate the same and multiply the y coordinate by -1 so you have point (8,-4)

Answer:

y= -3/5x + 12/5

Step-by-step explanation:

Remember, the formula is y= mx + b

#1 So we're gonna put it into that order by subtracting 3x from both sides:

3x + 5y= 12

-3x           -3x

We are left with this:

5y= -3x + 12

#2 Now we will divide 5 to both sides to isolate the variable

5y/5= -3x/5 + 12/5

#3 Now that the variable is isolated we are left with the answer:

y= -3/5x +12/5

Hope this helps :)

Answer:

C

......................................................

Answer:

9.72

Step-by-step explanation:

1.8 x 1.8 x 3 = 9.72

The missing length from Fabian's measurement is 22.5

In this question, it is given that the scale factor is 2:5

And the widths are 6 and 15.

And the length is 9.

We have to find the measurement of the length after the scale factor .

And for that we multiply 9 with the scale factor, and on doing so, we will get

9 x 2.5 = 22.5

So the missing length from Fabian's measurement is 22.5

The concept of "scale factor" pertains to a numerical value which magnifies or scales the scale or dimension of an entity or system in a proportional manner. Resizing or rescaling objects while preserving their proportional relationships is a prevalent practice in multiple domains, such as mathematics, physics, engineering, and computer graphics.

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Fabian used a ratio table to show the original dimensions of a rectangle and the dimensions when the rectangle is changed by a scale factor. He forgot to enter the length of the new rectangle.

Scale factor

1

2.5

Width

6

15

Length

9

Which length is missing from Fabian’s table?

3.6

11.5

21.6

22.5

Answer:

0.5 or \(\frac{1}{2}\)

Step-by-step explanation:

Answer: 17873.75 dollars

Step-by-step explanation:

We can use the equation: l = p x r x t (Total Interest = principal x interest rate x years/time)

9050 will be the principal; it's the amount you deposit in the first place.

7.5% is the interest rate. You can convert it to 0.075 as a decimal.

13 is the years/time. If Marcus's parents put the college fund in when he was 5 and now he's 18, there has been 13 years in between.

9050 x 0.075 x 13 = 8823.75

8823.75 + 9050 = $17873.75

So in Conclusion, the total amount in the account when Marcus is 18 is 17873.75 dollars.

Hope this helps!

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Jessica has the higher score because her z score on the SAT is 1.05, which is greater than Ashley's z score on the ACT, which is 1.02.

Jessica scores 1830 on the SAT.

Ashley scores 27 on the ACT.

Assuming that both tests measure the same thing, then we have to determine who has the higher score.

Consider the z-score for Jessica's SAT score of 1830.

z = (x - μ)/σ

z = (1830 - 1498)/316

z = 332/316

z = 1.05

Consider z for Ashley, who has an ACT score of 27.

z = (27 - 21.5)/5.4

z = 5.5/5.4

z = 1.02

Jessica has the higher score because her z score on the SAT is 1.05, which is greater than Ashley's z score on the ACT, which is 1.02.

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The reason that completes the proof for step 6 is given as follows:

D. Definition of midpoint.

The midpoint between two points is the halfway point between them, hence it is found obtaining the mean of the coordinates of each endpoint.

Thus the coordinates of P' are obtained as follows:

(applying the mean of the coordinates of x and y for the endpoints of the segment P').

The coordinates of R' are obtained as follows:

The coordinates of Q' are obtained as follows:

Meaning that the correct option is given by option D.

The problem is given by the image presented at the end of the answer.

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Answer:

2 apples and 4 bananas

Step-by-step explanation:

Given info:

Question given:

Determine the number of apples, x, and the number of bananas, y, that Juan bought.

Solution:

Since, we know that;

apples = x

bananas = y

Cost of each apple = $1 & Cost of each banana = $ 0.50

Total = 6

The equation that represents the following information:

x + y = 6

x + 0.5y = 4

We can multiply the top equation by -1 so it becomes -x -y = 6

-x - y = 6

x + 0.5y = 4

Now, we can use elimination to cancel out the x.

-0.5y = -2

y = 4

Because y=4, x must be 2 since x+y=6. So,

x = 2 and y = 4

Which means;

Juan bought 2 apples and 4 bananas.

~kavinsky

The total gross salary for FICA taxes is $4896 with the tax rates 6.2% and 1.45%.

The amount you earn each month before taxes and other deductions is referred to as your monthly gross income. In other words, it's your annual salary divided by 12. It's only a simple metric to aid in budgeting and other routine financial computations.

Annual Salary Amount / Number of Pay Periods = Gross Pay.

Gross pay equals the number of hours worked in a pay period multiplied by the hourly rate (+ overtime hours multiplied by the hourly overtime rate).

Given,

Tax rate=6.2%

=64000(6.2/100)

=3968

And also given another tax rate is 1.45%

=64000(1.45/100)

=92.8

Total=3968+928

=$4896

Therefore, the total gross salary for FICA taxes is $4896.

The total gross salary for FICA taxes is $4896 with the tax rates 6.2% and 1.45%.

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Answer: 39.62

Explanation: usual speed be x

today's speed = x+4

difference in time = 1/3 hours ( 20 min)

Usual time - today's time = 1/3

144%2Fx+-+144%2F%28x%2B4%29+=+1%2F3

multiply equation by 3x(x+4)

144%2A3%28x%2B4%29-144%2A3%2Ax=+x%28x%2B4%29

432x+1728-432x=x^2+4x

x^2+4x-1728=0

solve this you will get the usual speed which is

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Step 1: 12 divided by 3 = 4. 12+4 = 16.

I need to know what ⅓ of 12 is so I can continue the problem without messing up.

Step 2: 16*2 = 32.

Half of however many are left is 16.

Step 3: 32 divided by 4 is 8. 32+8 is 40. Two dozen is 24. 40 + 24 = 64.

Now we know the answer.

Boom.

Explanation:

FD and BC are congruent

FD = 6.2

BC = 6.2

AC = AB + BC

AB and BC are congruent due to the three tick marks on both of them

AB = BC = 6.2

AC = 6.2 + 6.2

AC = 12.4

∠BDF = 26°

BD = hypotenuse, FD = 6.2

cos 26 = FD/BD

cos 26 = 6.2/BD

BD = 6.2/cos 26 = 6.2/0.8988 = 6.898

BD = 6.9