Hannah would like to make an investment that will turn 8000 dollars into 33000 dollars in 7 years. What quarterly rate of interest, compounded four times per year, must she receive to reach her goal?

Answers

Answer 1

Answer:

20.76%

Step-by-step explanation:

[tex]33000=8000(1+\frac{i}{4})^{4*7}\\4.125=(1+\frac{i}{4})^{28}\\\sqrt[28]{4.125}=1+\frac{i}{4} \\i= .207648169[/tex]

which rounds to 20.76%

Answer 2

Answer:

About 0.2076 or 20.76%.

Step-by-step explanation:

Recall that compound interest is given by the formula:

[tex]\displaystyle A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]

Where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is applied per year, and t is the number of years.

Since Hannah wants to turn an $8,000 investment into $33,000 in seven years compounded quarterly, we want to solve for r given that P = 8000, A = 33000, n = 4, and t = 7. Substitute:

[tex]\displaystyle \left(33000\right)=\left(8000\right)\left(1+\frac{r}{4}\right)^{(4)(7)}[/tex]

Simplify and divide both sides by 8000:

[tex]\displaystyle \frac{33}{8}=\left(1+\frac{r}{4}\right)^{28}[/tex]

Raise both sides to the 1/28th power:

[tex]\displaystyle \left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}= 1+\frac{r}{4}[/tex]

Solve for r. Hence:

[tex]\displaystyle r= 4\left(\left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}-1\right)[/tex]

Use a calculator. Hence:

[tex]r=0.2076...\approx 0.2076[/tex]

So, the quarterly rate of interest must be 0.2076, or about 20.76%.


Related Questions

An office manager buys 2 office chairs and 4 file cabinets for $380. Next year she buys 4 office chairs and 6 file cabinets for $660. What is the cost of each office chair, c? What is the cost of each file cabinet, f? Explain how you fond the cost of each chair and file cabinet.

Answers

Answer:

16.5

Step-by-step explanation:

Answer:

file cabinet = 50

chair = 90

Step-by-step explanation:

x = chair

y = file cabinet

1st year, solve for x

2x+4y = 380

2x = 380 - 4y

x = 190 - 2y

2nd year

Now substitute x = 190 - 2y in your 2nd year formula

4x+6y = 660

4(190-2y)+6y = 660

760 - 8y + 6y = 660

-2y = -100

y = 50

The cost of the filling cabinet is 50 each

Now use the value for y (50) in your first formula to get x

2x+4y=380

2x+4*50=380

2x=380-200

2x=180

x=90

Please help solve and explain this thank you

Answers

Answer:

hi

Step-by-step explanation:

A town recently dismissed 5 employees in order to meet their new budget reductions. The town had 4 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that no more than 1 employee was over 50

Answers

Answer:

0.7513 = 75.13% probability that no more than 1 employee was over 50

Step-by-step explanation:

The employees are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

4 + 16 = 20 employees, which means that [tex]N = 20[/tex]

4 over 50, which means that [tex]k = 4[/tex]

5 were dismissed, which means that [tex]n = 5[/tex]

What is the probability that no more than 1 employee was over 50?

Probability of at most one over 50, which is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,20,5,4) = \frac{C_{4,0}*C_{16,5}}{C_{20,5}} = 0.2817[/tex]

[tex]P(X = 1) = h(1,20,5,4) = \frac{C_{4,1}*C_{16,4}}{C_{20,5}} = 0.4696[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2817 + 0.4696 = 0.7513[/tex]

0.7513 = 75.13% probability that no more than 1 employee was over 50

The lifespan, in years, of a certain computer is exponentially distributed. The probability that its lifespan exceeds four years is 0.30. Let f(x) represent the density function of the computer's lifespan, in years, for x>0. Determine an expression for f(x).

Answers

Answer:

The correct answer is "[tex]0.300993e^{-0.300993x}[/tex]".

Step-by-step explanation:

According to the question,

⇒ [tex]P(x>4)=0.3[/tex]

We know that,

⇒ [tex]P(X > x) = e^{(-\lambda\times x)}[/tex]

⇒     [tex]e^{(-\lambda\times 4)} = 0.3[/tex]

∵ [tex]\lambda = 0.300993[/tex]

Now,

⇒ [tex]f(x) = \lambda e^{-\lambda x}[/tex]

By putting the value, we get

           [tex]=0.300993e^{-0.300993x}[/tex]

Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save money at the monthly rate to buy the item for its cash price.
A bunk bed with a cash price of $1,998, at $143 per month for 15 months

Answers

Answer:

$2,145 ; $147 ; 14 months

Step-by-step explanation:

Given that :

The cash price, that is, the amount that would be paid if customer is to pay the entire amount item is worth at once = $1998

Monthly payment = $143

Period = 15 months

The total installment price ; total amount paid on a monthly pay for 15 months :

(monthly payment * period)

($143 * 15)

= $2,145

The carrying charge :

Installment pay - Cash amount

$(2,145 - 1,998)

= $147

The number of month needed to save at Monthly rate to buy item at it's cash price :

Cash price / monthly payment

$1998 / $143

= 13.97

= 14 months

HELP HELP QUICK QUICK

Answers

Answer:

multiplication by -1 will reflect over the x-axis

multiplication by a positive number will "scale" or "stretch" the function

Step-by-step explanation:

On Friday Evelyn sold 9 dresses and 20 pairs of pants. On Saturday she sold twice as many dresses and 10 more pants than Friday. How many dresses did Evelyn sell on Friday and Saturday?

Answers

Answer: 27 Dresses and 50 Pants

Step-by-step explanation:

If she sold 9 pairs of pants and

9 x 2 = 18

18 + 9 = 27

20 + 10 = 30

30 + 20 = 50

Evelyn sold 9 dresses and 20 pairs of pants on Friday, and on Saturday, she sold 18 dresses and 30 pairs of pants.

Evelyn's sales of dresses and pants over two days, Friday and Saturday. We'll use some mathematical expressions and reasoning to find out how many dresses Evelyn sold on each day.

Let's start by assigning some variables to represent the number of dresses and pants Evelyn sold on Friday and Saturday. We'll use "F" for Friday and "S" for Saturday. So, let [tex]D_F[/tex] be the number of dresses sold on Friday, [tex]D_S[/tex] be the number of dresses sold on Saturday, [tex]P_F[/tex] be the number of pants sold on Friday, and [tex]P_S[/tex] be the number of pants sold on Saturday.

According to the problem, on Friday, Evelyn sold 9 dresses, which can be expressed as:

[tex]D_F[/tex] = 9

She also sold 20 pairs of pants on Friday:

[tex]P_F[/tex] = 20

Now, let's move on to Saturday's sales. It says she sold twice as many dresses as Friday, which means the number of dresses on Saturday is double that of Friday's sales:

[tex]D_S = 2 * D_F[/tex]

Additionally, she sold 10 more pairs of pants on Saturday compared to Friday:

[tex]P_S = P_F + 10[/tex]

We already know that [tex]D_F = 9[/tex], so we can find the number of dresses sold on Saturday by substituting this value into the equation for [tex]D_S[/tex]:

[tex]D_S = 2 * 9 = 18[/tex]

Next, we'll calculate the number of pants sold on Saturday using the given information. Since [tex]P_F = 20[/tex], we can find [tex]P_S[/tex]:

[tex]P_S = 20 + 10 = 30[/tex]

So, to summarize, Evelyn sold 9 dresses and 20 pairs of pants on Friday, and on Saturday, she sold 18 dresses and 30 pairs of pants.

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-3xy^2+5xy^2
Operations with polynomials

Answers

9514 1404 393

Answer:

  2xy^2

Step-by-step explanation:

The terms are "like" so can be combined. It might be helpful to think of this as an application of the distributive property.

  -3xy^2 +5xy^2 = (-3 +5)xy^2 = 2xy^2

PLEASE HELPPPP WILL GIVE BRAINLIESTTTT

Factor the following expressions completely. Show and check all work on your own paper.
9x2-18x+9

Answers

Hi there!

[tex]\large\boxed{9(x - 1)^{2}}[/tex]

9x² - 18x + 9

We can begin by factoring out a 9 from each term:

9(x² - 2x + 1)

Now, find two terms that add up to -2 and equal 1 when multiplied. We get:

9(x - 1)(x - 1)

Or:

9(x - 1)²

Please HELP!

How many pairs (A, B) are there where A and B are subsets of {1, 2, 3, 4, 5, 6, 7, 8} and A ∩ B has exactly two elements?

Answers

Answer:

There are 256 pairs in all.

-5(8a+1)+6=281
Does anyone know the answer

Answers

Step 1: Distribute

-40a - 5 + 6 = 281

Step 2: Combine Like Terms

-40a + 1 = 281

Step 3: Move Variables and Constants to Different Sides

-40a = 280

Step 4: Divide

a = -7

Hope this helps!

a = -7

Step-by-step explanation;

-5 ( 8a + 1 ) + 6 = 281

Step 1 :- Distribute -5 through parantheses.

-5 × 8a + 5 × 1 + 6 = 281-40a - 5 + 6 = 281

Step 2 :- Combine like terms.

-40a + 1 = 281

Step 3 :- Move constant to right-hand side and change their sign.

-40a = 281 - 1

Step 4 :- Subtract the numbers.

-40a = 280

Step 5 :- Divie both side by -40 .

-40a / -40 = 280 / -40a = -7


Which law would you use to simplify the expression
(P/q)^3?

power of a power
power of a quotient
quotient of powers
power of a product

Answers

Answer: Power of a quotient

Step-by-step explanation:

The power of quotient basically is:

[tex](\frac{P}{q})^{3} =\frac{P^3}{q^3}[/tex]

-3/8 divided by -1/4

Answers

Flip the -1/4, cross deduct and should get 3/2

Answer:

It might be 3/2 or 1 and 1/2.

i need helpp pleaseee

Answers

To plot the point (3,-7) start at the origin (0,0) and move right three (3) units and then down seven (7) units.

According to the Venn Diagram below and given that P(A) = .4 as well as
P(B) = .3 what is P(AUB)?

Answers

Hello,

P(A)=0.4

P(B)=0.3

P(AUB)+P(A∩B)=P(A)+P(B)

P(AUB)=0.4+0.3-0.1=0.6

Answer C

The correct answer is option (C).

P(A ∪ B) = 0.6

Formula to find P(A ∪ B):

If A, B are two different events then P(A U B) = P(A) + P(B) - P(A ∩ B)

We have been given, P(A) = 0.4, P(B) = 0.3

From given Venn diagram,

P(A ∩ B) = 0.10

Now, P(A U B) = P(A) + P(B) - P(A ∩ B)

⇒ P(A U B) = 0.4 + 0.3 - 0.10

⇒ P(A ∪ B) = 0.6

Therefore, the correct answer is option (C) .6

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HELP ME WITH THIS TO EARN BRAINLIEST!!!!!!

Answers

Answer:

Step-by-step explanation:

answer C looks good  

Answer:

option c is answer

Step-by-step explanation:

as we can see r^2 =(d/2)^2

r^2=(6/2)^2

r^2=36/4=9

A=πr^2

A=9π

Simplify -|-5 + 2|
someone help quick

Answers

Answer:

-3

Step-by-step explanation:

Indicate the method you would use to prove the triangles congruent. If no
method applies, enter "none."
O SSS
k O SAS
O ASA
© None

Answers

Step-by-step explanation:

I suspect we don't see the full information for the problem here.

all listed 3 methods are typically used to prove that triangles are congruent (= when turned to have the same orientation, they would simply cover each other completely - no overhanging parts from either triangle).

I guess there is a diagram with 2 triangles and what is known about them.

and since we cannot see them, we cannot tell you which method would apply here.

just remember

SSS means all 3 sides of one triangle are exactly the same as the 3 sides of the other triangle. if you know the lengths of all 3 sides, there is only one triangle you can create. you can only orient it differently.

SAS means two sides and the enclosed angle are the same. again, only one triangle can be created with that information.

ASA means one side and the 2 angles at the end points of that side are known. again, only one triangle can be created with that information.

What value of x will make the equation true?

Answers

Answer:

5

Step-by-step explanation:

When a square root of an expression is multiplied by itself, the result is that expression

5=x

Round 100.9052 to the nearest hundredths

Answers

To round 100.952 to the nearest tenth consider the hundredths’ value of 100.952, which is 5 and equal or more than 5. Therefore, the tenths value of 100.952 increases by 1 to 0.

100.952 rounded to the nearest tenth = 101.0

an interest expense of $125 has been incorrectly debited to utilities expense.

Answers

Answer:

125x=(62.50+(62.50)×0

TRUE or FALSE: The regression equation is always the best predictor of a y value for a given value of x. Defend your answer.

Answers

Answer:

FALSE

Step-by-step explanation:

The regression equation is a prediction model which is generated for a given independent, x and dependent, y variable. The regression model is usually ideal when both the dependent and independent variables are numerical. The regression equation cannot be generated if either the x or y value is non-numeric. In such situation, classification models may be better suited for such cases especially if there is no efficient method of converting the non-numeric column into a numeric variable.


A boat travels 8 miles north from point A to point B. Then it moves in the direction S 40°W and reaches point Finally, it turns S 40°E and returns to point A
The total distance covered by the boat is______miles

A. 14.95
B. 18.44
C. 20.04
D. 25.88

Answers

Answer:

B.18. 44 miles

Step-by-step explanation:

We are given that

Distance between A and B=8 miles

Angle B=Angle BCQ=40 degree (Alternate interior angles)

Angle ACB=180-Angle ACP-Angle BCQ

Angle ACB=180-40-40=100 degree

In triangle ABC

Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property

Substitute the values

[tex]\angle A+40+100=180[/tex]

[tex]\angle A+140=180[/tex]

[tex]\angle A=180-140[/tex]

[tex]\angle A=40[/tex] degree

Angle A=Angle B

When two angles are equal of a triangle then the triangle is isosceles triangle.

Therefore, triangle ABC is an isosceles triangle.

[tex]\implies BC=AC [/tex]

Now, Sine law

[tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]

Using the sine law

[tex]\frac{BC}{sin 40}=\frac{AB}{sin 100}[/tex]

[tex]\frac{BC}{sin 40}=\frac{8}{sin 100}[/tex]

[tex]BC=\frac{8\times sin40}{sin 100}[/tex]

BC=5.22

AC=BC=5.22 miles

Now, total distance covered by the boat=AB+BC+AC

Total distance covered by the boat=8+5.22+5.22=18.44 miles

Hence, option B is correct.

Find the measure of of RA.

Answers

Answer:

RA = 24

Step-by-step explanation:

Since the triangle is isosceles ( 2 equal sides ) , then LU is a perpendicular bisector , so

AU = RU , that is

4r = 18 - 2r ( add 2r to both sides )

6r = 18 ( divide both sides by 6 )

r = 3

Then

RA = 18 - 2r + 4r = 18 + 2r = 18 + 2(3) = 18 + 6 = 24

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with A random sample of 12 sample specimens has a mean compressive strength of psi. Round your answers to 1 decimal place. (a) Calculate the 95% two-sided confidence interval on the true mean compressive strength of concrete. Enter your answer; 95% confidence interval, lower bound Enter your answer; 95% confidence interval, upper bound (b) Calculate the 99% two-sided confidence interval on the true mean compressive strength of concrete.

Answers

Answer:

95%: (3278.354 ; 3270.083)

99% : (3221.646 ; 3278.354)

Step-by-step explanation:

Given :

Sample size, n = 12

Mean, xbar = 3250

Sample standard deviation = √1000

The 95% confidence interval :

Mean ± Margin of error

Margin of Error = Tcritical * s/√n

Tcritical at 0.05, df=12-1 = 11 ;

Tcritical at 95% = 2.20

Hence,

Margin of Error = (2.20 * √1000/√12) = 20.083

Confidence interval : 3250 ± 20.083

Lower boundary = 3250 - 20.083 = 3229.917

Upper boundary = 3250 + 20.083 = 3270.083

2.)

The 99% confidence interval :

Mean ± Margin of error

Margin of Error = Tcritical * s/√n

Tcritical at 0.01, df=12-1 = 11 ;

Tcritical at 99% = 3.106

Hence,

Margin of Error = (3.106 * √1000/√12) = 28.354

Confidence interval : 3250 ± 28.354

Lower boundary = 3250 - 28.354 = 3221.646

Upper boundary = 3250 + 28.354 = 3278.354

Expand (2x - 4)2 using the square of a binomial formula.
(x)2 + 2(x)(4) + 42
O (2x)2 + 2(2x)(4) - 42
O(x2 - 2(x)(4) - 42
(2x)2 - 2(2x)(4) + 42

Answers

Step-by-step explanation:

We have to expand,

[tex]\longrightarrow [/tex] (2x 4)²

(a ― b)² = a² + b² ― 2ab

[tex]\longrightarrow [/tex] (2x)² + (4)² ― 2(2x × 4)

[tex]\longrightarrow [/tex] 4x² + 16 ― 2(8x)

[tex]\longrightarrow [/tex] 4x² + 16 ― 16x

[tex]\longrightarrow [/tex] 4x² ― 16x + 16

Hence, solved!

Answer:

D is the correct answer (2x)2 – 2(2x)(4) + 42

Step-by-step explanation:

If [infinity]∑n=0cn9n is convergent, does it follow that the following series are convergent? (a) [infinity]∑n=0cn(−3)n

Answers

Given: The series ∑cₙ[tex]9^n[/tex] is convergent

To find: The series ∑cₙ[tex](-3)^n[/tex] is convergent or not.

Solution: If the radius of convergence R the we can conclude that R≥4

So, the series will converge as -3<9.

what is the answer to 10% of 900​

Answers

Answer:

90 cause 90 times 10 is 900 and 10% times 10 is 100%

Step-by-step explanation:

Answer: 90

Step-by-step explanation: 900 × .10 = 90

Can someone help me with this question an also the rest of my school work?

Answers

Answer:

I think this one is B

Step-by-step explanation:

A movie theater has a seating capacity of 283. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2060 on a sold out night, how many children, students, and adults attended

Answers

Answer: adults = 79

children = 158

student = 46

Step-by-step explanation:

Let a = adults

Let c = children

Let s = student

From the information given,

a + c + s = 283 ....... i

c/a = 2, c = 2a ....... ii

5c + 7s + 12a = 2060 ...... iii

Put the value of c = 2a into equation i

a + c + s = 283

a + 2a + s = 283

3a + s = 283

s = 283 - 3a

Note that c = 2a

From equation iii

5c + 7s + 12a = 2060

5(2a) + 7(283 - 3a) + 12a = 2060

10a + 1981 - 21a + 12a = 2060

10a + 12a - 21a = 2060 - 1981

a = 79

Note c = 2a

c = 2 × 79 = 158

Since a + c + s = 283

79 + 158 + s = 283

s = 283 - 237

s = 46

adults = 79

children = 158

student = 46

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