Find the compound amount and the interest earned when the given investment has continuous compounding.

$11,000 at 2.3% for 8 years

Answers

Answer 1

The compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.

What is compound interest?

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We know the formula for continuous compounding:

[tex]\rm A = P(e)^{rt}[/tex]

[tex]\rm A = 11000(e)^{0.023\times8}[/tex]

A = $13,222.17

I = A - P = 13,222.17 - 11000

I  = $2,222.17

Thus, the compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.

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Related Questions

A gas can hold 10 litters of gas.
How many could we fill 7 litters of gas?

Answers

Answer:

a gas can hold 7×10=70 litters of gas

Please I need help with this 2 calc questionssss. Thank you

Answers

Question 14

As we approaching from the negative side, [tex]|x-3|=3-x[/tex].

So, we have [tex]\lim_{x \to 3^{-}}=\frac{3-x}{x-3}=\frac{-(x-3)}{x-3}=\boxed{-1}[/tex]

and thus the limit exists at x=3.

Question 15

For the top part of the function, [tex](9-9)^{2}=0[/tex]

For the bottom part of the function, [tex]9-9=0[/tex]

As both one-sided limits are equal, L = 0, and thus the limit exists at x=9.

A chocolate bar measures 40 mm wide, 80 mm long, and 5 and 1 over 2 mm high. Will’s Wrapping Company is making a wrapper to cover the chocolate bar. Use the correct net and determine how much paper will be needed to make the wrapper.

Answers

Answer:

7720 mm²

Step-by-step explanation:

area = 2 × 80 mm × 40 mm + 2 × 80 mm × 5.5 mm + 2 × 40 mm × 5.5 mm

area = 7720 mm²

if anyone knows how to answer this do so please

Answers

Answer:

b = 5.3

A = 48.6

B = 41.4

Step-by-step explanation:

Attached is the Pics contain the Pythagoras Theorem and Trigonometric Identities.

So for our Right-Angled Triangle we have from Pythagoras Identity that

[tex]a^{2} +b^{2} =c^{2}[/tex]  ,, Then [tex]b^{2} =c^{2} -a^{2}[/tex]  where a=6 , c=8

by substituting,

[tex]b^2=8^2-6^2=28\\ b=\sqrt{28} =2\sqrt{7}=5.3[/tex]

Now to find A , we will use the Trigonometric Identities

Since    [tex]sin(A)=\frac{Opposite}{Hypotenuse}=\frac{a}{c} =\frac{6}{8}=\frac{3}{4} \\[/tex]

[tex]A=sin^{-1} (\frac{3}{4} )=48.6\\[/tex]

Since in any Triangle A+B+C=180

Then B=180-A-C=180-48.6-90=41.4

Select the procedure that can be used to show the converse of the Pythagorean theorem using side lengths chosen from 3 feet, 4 feet, 5 feet, and 6 feet.


A. Knowing that 32 + 42 = 52, draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle.


B. Knowing that 32 + 52 ≠ 62, draw the 3-foot side and the 5-foot side with a right angle between them. The 6-foot side will fit to form a right triangle.


C. Knowing that 32 + 42 = 52, draw any two of the sides with a right angle between them. The third side will fit to form a right triangle.


D. Knowing that 42 + 52 < 62, draw the 4-foot side and the 5-foot side with a right angle between them. The 6-foot side will fit to form a right triangle.

Answers

Using Pythagoras theorem,  we know that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle

How to use Pythagoras theorem to prove a right triangle?

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

Therefore,

c²= a²+ b²

where

c = hypotenuse sidea and b are the other legs.

Therefore,

3² + 4² = 5²

Hence,

Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle

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The question is down below 30 points

also I home school and have permission to post this question

Answers

The ratios for the surface area, volume and width respectively are:

Ratio of SA = 9:196.Ratio of V = 27:2,744.Ratio of W = 3:14.

What is ratio?

Ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this exercise, we are given the scale factor for this canoe is 3:14. Thus, the ratio of the surface area of the canoe model to the surface area of the original model would squared as follows:

Ratio of SA = 3²/14²

Ratio of SA = 9/196

Ratio of SA = 9:196.

For the volume, we would take the cube:

Ratio of V = 3³/14³

Ratio of V = 27/2,744

Ratio of V = 27:2,744.

For the width, we have:

Ratio of W = 3/14

Ratio of W = 3:14.

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Solve inequality
58 - 10xs 20 + 9x.

Answers

Answer:

x>=2 so B

Hope this helps :)

+
120
A. Right
B. Obtuse
C. Acute
D. Equilateral
E. Scalene
OF. Isosceles

Answers

Answer:

See below

Step-by-step explanation:

Isosceles because two sides are same length

                 and

Obtuse because there is an interior angle greater than 90 °

Question 12
You are negotiating to make a 7-year loan of $20,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at
the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from
Year 4 through Year 7. Breck is essentially riskless, so you are confident the payments will be made. You regard 8% as an
appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the end of each of
the final 4 years, that is, what is X?
(A) $2,520.02
B) $2,831.49
$3,369.47
$2,491.71
0.5 Points
E $2,661.60

Answers

The required x = $2,831.49. Option B) is correct.

7-year loan of $20,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7.

What is invesment?

When some apply there money on something so that he can get higher value in returns of his money.

for the final 4 years

20000=2500/1.08+5000/(1.08^2)+7500/(1.08^3)+x/(1.08^4)+x/(1.08^5)+x/(1.08^6)+x/(1.08^7)

x = $2,831.49

Thus the required value of x = $2,831.49.


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Write the equation 2x + 4y = 12 in slope intercept form. Show your work.

Answers

Answer:

First we have to find the value of x;

then we have to find the value of y;

Step-by-step explanation:

here,

2x= 12

x = 12\2

x = 6

now,

4y = 12

y = 12\4

y = 3

° the value of x is 6

° ° the value of y is 3


The junior class sold 75% of the raffle tickets. They started with 100 raffle tickets.
How many tickets have been sold?

Answers

Answer:

75

Step-by-step explanation:

Since they sold 75% of the raffle tickets and the total is 100 raffle tickets, you simply need to find 75% of 100. To find x% of a, you simply convert x% to a decimal by dividing by 100 and then multiplying it by a. So the general formula to find x% of a would be: [tex]a*\frac{x}{100}[/tex]. In this case a=100, and x=75. So you have the equation: [tex]100*\frac{75}{100} = \frac{100 * 75}{100}=\frac{75}{1} = 75[/tex]

Answer: 75 tickets

Step-by-step explanation:

- percentages are out of 100, they are a rate, number, or amount in each hundred

- for example, (10/100) x 100 (because it’s out of 100) = 10%
- or it could be (6/40) x 100 (because it’s out of 100) = 15%

- so because they started with 100 tickets, it’s just (75/100) x 100 =75

hope this helps :)

Emma read the statement “the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5.” She translated it as shown below. 6 x = negative 2 x minus 4.5 What errors did Emma make? Select two options. She should have used division to represent the quotient of six and x. She should not have included an equal sign. She should have used parentheses to show that Negative 2 is multiplied by (x minus 4.5). She should have subtracted the difference (x minus 4.5) from Negative 2. She should have used parentheses to show that Negative 2 is multiplied by (4.5 minus x).

Answers

The errors Emma made are

She should have used division to represent the quotient of six and xShe should have used parentheses to show that - 2 is multiplied by (x - 4.5)

Writing an expression as an equation

From the question, we are to determine the errors that Emma made

The given statement is

"The quotient of six and a number, x, is the same as negative two times the difference of x and 4.5"

"The quotient of six and a number, x", can be expressed as

6/x

"Two times the difference of x and 4.5", can be expressed as

2(x - 4.5)

Hence, the errors Emma made are

She should have used division to represent the quotient of six and xShe should have used parentheses to show that - 2 is multiplied by (x - 4.5)

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I have redone this one assignment like 5 times and I keep getting it wrong help

Answers

3/10 * 9/9 = 27/90

5/9 * 10/10 = 50/90

77/90 which is about 3/4 mile!

The original price of a mountain bike was reduced by $125 . if p= the mountain bike's original price in dollars, which algebraic expression represents the reduced price?

Answers

The algebraic expression that represents the reduced price is p - 125

How to determine the reduced price?

The reduction is given as:

Reduction = $125

The original price is given as:

Original = P

The reduced price is calculated as:

Reduced price = original - reduction

This gives

Reduced price = p - 125

Hence, the algebraic expression that represents the reduced price is p - 125

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Find the slope of the line that contains the points:
(-4, 3) and (4, 9)
a) 3/4
b) -3/4
c) 4/3
d) -4/3

Answers

Step-by-step explanation:

ATTACHED IS THE SOLUTION!!!

Answer:

The answer would be A. 3/4

Step-by-step explanation:

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

A cash card has a starting value of $25. If the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month.

Answers

Using linear function concepts, we have that from the information given:

The relationship is linear.The independent variable is the number of months.The dependent variable is the value of the card.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.x is the independent variable.y is the dependent variable.

From the information given, the y-intercept is of 25 and the slope is of $2.50, hence the value after t months is given by:

V(t) = 25 - 2.5t.

Thus:

The relationship is linear.The independent variable is the number of months.The dependent variable is the value of the card.

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In each part (a)-(d) below, some additional assumptions about the
picture are given. In each problem, determine whether the given
assumptions are enough to prove that the two triangles are similar; and
if so, what the correct correspondence of vertices is. If the two triangles
must be similar, prove this result by describing a sequence of similarity
transformations that maps one triangle to the other. If not, explain why
not.
a. The lengths AX and XD satisfy the equation 2AX = 3XD.
AX
b. The lengths AX, BX, CX, and DX satisfy the equation A
c. Lines AB and CD are parallel.
d. Angle XAB is congruent to angle XCD.
=
DX
CX

Answers

In the triangle, the fact that wee are given 2AX = 3XD isn't enough to prove similarity.

How to explain the triangle?

a. In the question, we are given 2AX = 3XD. An arbitrary triangle AXB can be drawn where one extends AX and choose a point D on the extended line in order for 2AX = 3XD. Also, extend BX and choose a point C on the line so that 2BX = XC. Even though they both satisfy the condition, they're not similar.

b. We are given that AX/BX = DX/CX. When this is rearranged, we'll have AX/DX = BX/CX. In this case, let AX/DX = k. DX and AX will align upon rotation of 180°. The triangle can then be dilated by a factor of k. This brings about the mapping of triangle DXC to AXB. Therefore, the original triangle DXC is similar to AXB.

c. Lines AB and CD are parallel. Here, the dilation moves line CD onto line AB. Here, since the dilation moves D to a point on ray XA, D must move to A. Therefore, the rotation of triangle DXC is similar to AXB. Therefore, DXC is similar to AXB.

d. Here, angle XAB is congruent to angle XCD. This shows similarity and in this case, XCD is similar to XAB.

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If an object moves along the y-axis (marked in feet) so that it’s position at time X (in seconds) is given by f(x) = 108x -12x^2 , find the following:

Answers

The velocity equation is:

[tex]v(x) = 108 - 24x[/tex]

Such that:

[tex]v(0) = 108 ft/s\\v(2) = 60ft/s\\[/tex]

And the velocity is zero for x = 4.5

How to find the velocity equation?

We know that the position equation is:

[tex]f(x) = 108*x - 12*x^2[/tex]

To get the velocity, we need to differentiate with respect to x, so we get:

[tex]v(x) = \frac{df(x)}{dx} = 108 - 2*12*x = 108 - 24*x[/tex]

Now we want to get the velocity for x = 0 and x = 2, we will get:

[tex]v(0) = 108 - 24*0 = 108\\\\v(2) = 108 - 24*2 = 60[/tex]

Then, when x = 0, the velocity is 108 ft/s, when x = 2 the velocity is 60 ft/2.

Finally, we need to solve:

[tex]v(x) = 108 - 24*x = 0\\\\x = 108/24 = 4.5[/tex]

The velocity is zero when x = 4.5

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The step function f(x) is graphed. -54-3 -2 -1 4 3 EXO 4 4 y 1 CHELLEREN 2 3 What is the value of f(0)? O -2 O -1 0 0 1​

Answers

Answer: -2

Step-by-step explanation:

When x = 0, y = -2.

So, f(0) = -2.

Consider triangle ABC with the measure of an angle B = 60゚ and sidelinks a equal 4 &c equal 5 what option listed is an expression that is equivalent to the length of side B

Answers

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The correct option is B.

What is the Law of Cosine?

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

The length of the sidelink b using the cosine rule can be written as,

[tex]b = \sqrt{a^2+c^2-2ac\cos(\angle B)}\\\\b = \sqrt{4^2+5^2 - 2(4)(5)(\cos 60^o)}\\\\b = \sqrt{16+25-20}[/tex]

Hence, the correct option is B.

The complete question is:

Consider ABC with the measure of angle B equal to 60 degrees, and side lengths a=4 and c=5. Which option lists an expression that is equivalent to the length of side b?

Options are given in the image below.

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Use the trigonometric ratios sine, cosine, and tangent to answer the following questions

Answers

Answer:

Step-by-step explanation:

When you brush your wig will all the hair come off the wig completely or will it still be the same in a year

Answers

Answer:

no

Step-by-step explanation:

Yes, brush it… not too much though. Try a wide comb/wig brush.

(05.05 HC) Figure ABCD has vertices A(-3, 2), B(2, 2), C(2, -4), and D(-3, -2). What is the area of Figure ABCD?​

Answers

Answer:

I don't know how to answer this, sorry!

Step-by-step explanation:

.



Keisha borrowed money from a bank to buy a fishing boat.
She took out a personal, amortized loan for $19,500, at an interest rate of 4.75%, with monthly payments for a term of 5 years.

(a) Find Keisha's monthly payment.
(b) If Keisha pays the monthly payment each month for the full term,
find her total amount to repay the loan.
$0
(c) If Keisha pays the monthly payment each month for the full term,
find the total amount of interest she will pay.
$0

Answers

Answer:

Your $19,513 loan has 60 monthly payments of $366.00 at 4.75%.

If you make all of your payments on this loan, and do not prepay any of the principal, the total interest for this loan is $2,447.26.

Step-by-step explanation:Loan Summary

Total payments $21,960.26

Total interest paid $2,447.26

Loan amount $19,513

Monthly payment $366.00

Interest rate 4.75%

Term 60 monthly payments

Huilans age is three times Thomas age The sum of their ages is 76 what is Thomas age

Answers

Answer:

let x be thomas age

3x for huilans age since huilans age is 3 time thomas age

both of their ages add to 76

ie. x + 3x =76

solve for x

4x = 76

x = 76 ÷ 4

x = 19. thomas age

to get huilans age : take 19 × 3 = 57

Pls help! I need to finish quickly.

Answers

The inverse of the function f(x) = 2x + 5 is; f⁻¹(x) = (x - 5)/2

How to find the Inverse of a Function?

An inverse function in mathematics is function which reverses the another function.

We want to find the inverse of the function; f(x) = 2x + 5

Thus;

Step 1; y = 2x + 5

Step 2; Subtract 5 from both sides to get;

y - 5 = 2x

Step 3;  Since we want to find the inverse of f(x), then we now have;

x - 5 = 2y

Step 4: Divide both sides by 2 to get;

(x - 5)/2 = y

Step 5; Thus, we have;

f⁻¹(x) = (x - 5)/2

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Which of the following is the most profitable investment for a candy shop that earns $1 revenue per pound of candy? (5 points) Group of answer choices Worker at $10 per hour, producing eight pounds of candy per hour Worker at $12 per hour, producing 16 pounds of candy per hour Machine with $5 per hour operating cost, producing 10 pounds of candy per hour Machine with $8 per hour operating cost, producing 14 pounds of candy per hour

Answers

Then the most profitable investment is the first machine (third option) because for each dollar, it produces 2 pounds of candy.

Which of the following is the most profitable investment?

The first option is a worker that costs $10 per hour and produces 8lb, then this worker gives:

8lb/$10= 0.8 pounds per dollar.

The second worker costs $12 per hour, and produces 16lb per hour, so this worker gives:

16lb/$12 = 1.33 pounds per dollar.

The third option is a machine that cost $5 per hour and produces 10lb per hour, then:

10lb/$5 = 2 pound per dollar.

The last option costs $8 per hour, and produces 14 pounds per hour, then:

14lb/$8 = 1.75 pounds per dollar.

Then the most profitable investment is the first machine (third option) because for each dollar, it produces 2 pounds of candy.

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A home cleaning service takes more time to clean larger spaces. The table shows the number of minutes it takes for the service to clean a certain number of square feet within a home. Square Feet and Cleaning Time Number of Square Feet, x 50 80 100 150 Time in Minutes, y 20 32 40 60 Based on the table, how many minutes would it take for the service to clean 200 square feet? 20 minutes 80 minutes 125 minutes 400 minutes

Answers

The time required to clean 200 square feet will be 80 minutes. Option B is correct.

What is the surface area?

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

Let x be the cleaning time for the 200 square feet area;

From the table, it is observed that for a 1 sq. foot area the time needed to clean will be 0.4 minutes.

1 square feet = 0.4 minute

200 square feet = 200 × 0.4

200 square feet  = 80 minute

The time required to clean 200 square feet will be 80 minutes.

Hence, option B is correct.

The table is attached in the attachment.

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Identify the algebraic expression for the following: the quotient of 12 and a number y increased by 7

Answers

The algebraic expression for the given word problem is 12/y + 7

Writing an expression

From the question, we are to write the algebraic expression for the given word problem

The given word problem is

"the quotient of 12 and a number y increased by 7"

First,

"the quotient of 12 and a number y" can be expressed as

12/y

Then,

"the quotient of 12 and a number y increased by 7" becomes

12/y + 7

Hence, the algebraic expression for the given word problem is 12/y + 7

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do synethtic wig curls only come out if you put heat on it Answer Asap for brainlist
Yes or no

Answers

Answer:

There is no definitive answer to this question since different wigs are made with different kinds of synthetic fibers. Some synthetic fibers are more resistant to heat than others, so it really depends on the specific wig. In general, however, it is generally not recommended to use heat on synthetic wigs, as it can damage the fibers.

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Also, due to the height of the warehouse ceiling, boxes can only be stacked 4 levels high. The factory director has asked for your help in answering some questions about these boxes.a. Explain how you would find the weight of each stacked box if you knew the weight of the bottom box. Find the weight of each box in a stack of 4 boxes if the bottom box weighs 10 pounds.b. Eventually, these stacks of boxes will go onto pallets for shipping. We need to know how much each stack weighs in order to know how many stacks we can put on each pallet, but the bottom boxes do not necessarily weigh 10 pounds. In fact, we dont know how much they weigh at all! Write and simplify an expression to find the weight of one stack of 4 boxes based on the unknown weight of the bottom box.c. Each stack needs to weigh less than 100 pounds. Write and solve an inequality to find the maximum weight of the bottom box. What would be the possible range of weights for this box? It may help you to consider a graph of the solution to your inequality.I rlly need help for c, I got the other 2. approximately how many visitors does Shanghai receive per year (average) Passage OneCoral reefs that are falling apart are only one problem affecting ocean environment. Skeletons of dead coral animals make up coral reefs. Because living corals do not thrive without sun, they attach to the top of the reef. Without specific amounts of light, temperature, and oxygen, the coral reef cannot continue to support life. If the problems of erosion and pollution continue, there will not be a suitable home for sea life.Passage TwoThousands of fish would not have anywhere to live without coral reefs. Beautiful white, sandy beaches would not exist without any reef. There is nowhere that is better for diving because of the brilliant and beautiful marine life that lives among the reefs. But only a few parks have been established to protect the fragile environment of coral reefs.Which of the following is not true about the two passages?Both authors suggest that something must be done to save the reefs.Both authors state that coral reefs are polluting the ocean floor.Both authors suggest that coral reefs are fragile.Both authors state that coral reefs are threatened. Question 1 (5 points) SavedWhy do flights have layovers?To improve landing timesTo distribute flights to the big city hubsTo generate more lost luggageTo introduce passengers to flights to different cities in the hub-and-spoke modelQuestion 2 (5 points) SavedAirport security checks are designed toO frighten foreign travelers.Osell more products in the airport Which of the following pairs of lines are perpendicular to each other?