Sophie invested $170 in an account paying an interest rate of 2\tfrac{3}{4}2 4 3 ​ % compounded continuously. Wyatt invested $170 in an account paying an interest rate of 3\tfrac{1}{8}3 8 1 ​ % compounded monthly. After 9 years, how much more money would Wyatt have in his account than Sophie, to the nearest dollar?

Answers

Answer 1

Answer:

$7

Step-by-step explanation:

Answer 2

Wyatt will have $7 more in his account than Sophie.

What is compound interest?

Compound interest is the interest you earn on interest.

Given that, Sophie invested $170 in an account paying an interest rate of [tex]2\tfrac{3}{4}[/tex]% compounded continuously.

Wyatt invested $170 in an account paying an interest rate of [tex]3\tfrac{1}{8}[/tex]% compounded monthly.

We need to find how much more money would Wyatt have in his account than Sophie after 9 years,

For compounded continuously = [tex]Amount = Principal \times e^{rt[/tex]

Sophie =

[tex]Amount = 170 \times e^{0.0275 \times 9[/tex]

A = $217.74

Therefore, Sophie will have $217.74 in her account after 9 years.

For Wyatt,

So, using the formula of CI,

[tex]Amount = Principal(1+r/n)^{nt[/tex]

So,

[tex]= 170(1.0026)^{108[/tex]

A = $225

Therefore, Wyatt will have $225 in his account after 9 years.

The amount Wyatt have more than Sophie = 225-217.74 = $7.26 ≈ $7.

Hence Wyatt will have $7 more in his account than Sophie.

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Related Questions

Help me with this please

Answers

Answer:

4*2*4 = 32

Answer = 32m3

please give brainliest

32m³

The formula for a rectangular prism is LxWxH which in this case would be 4x4x2. You may do it in any order you want to for the next part as long as you are multiplying the numbers: 4 x 4 = 16 x 2 = 32 or 4 x 2 = 8 x 4 = 32 .

I hope this will help you.

Tell me if I am incorrect and I will change my answer or take it down.

Cheers!^^

A penguin can dive 48 meters below the surface of the water to reach a fish. It dives 2% of the total depth every 1 second.

What is the total depth of the penguin after 4 seconds?

−3.84 meters
−0.96 meters
−1.92 meters
−2.88 meters

pls help

Answers

Answer:

8 becaus it dives. 2 meters second so if it dives to meters every second then all you have to do is add to to 4 seconds

is this reletion just a function? Justify your answer. A. Yes, because every x- and y-value is positive. B. no, because two points with the same y-value have different x-values. C. Yes because every x-value corresponds with a single y-value. D. Yes, because the number of x-values is the same as the number of y-values.

Answers

Answer:

The element 15 has two arrows pointing to both 7 and 9. This is a clear violation of the requirement to be a function. A function is well behaved, that is, each element in the domain must point to one element in the range. Therefore, this relation is not a function.

Step-by-step explanation:

Btw brainliest me plss

Solve for x. Show each step of the solution. 4.8(9-x)+36=102-2.5(2x+2)

Answers

4.8(9−x)+36=102−2.5(2x+2)

First we will expand the equation by removing those parenthesis. We can use the distributive property. An example is 4.8(9-x) is 43.2-4.8x

43.2-4.8x+36 = 102-5x-5

Then we simplify each side by combining like terms.

79.2-4.8x=97-5x

Then to isolate the variable, we will subtract 79.2 on both sides.

-4.8x=17.8-5x

Then add 5x on both sides

0.2x=17.8

Finally, divide both sides by 0.2 and you get

x=89

Answer:

x =89

Step-by-step explanation:

4.8(9-x)+36=102-2.5(2x+2)

Distribute

43.2 - 4.8x + 36 = 102 - 5x -5

Combine like terms

79.2 -4.8x = 97-5x

Add 5x to each side

79.2 -4.8x+5x = 97-5x+5x

79.2 + .2x = 97

Subtract 79.2 from each side

79.2 -79.2+ .2x = 97-79.2

.2x =17.8

Divide by .2

.2x/.2 = 17.8/.2

x =89

Expand and simplify (x-2)(x-1)

Answers

Answer:

(x - 3) x + 2

Step-by-step explanation:

1/4 (2 x - 3)^2 - 1/4

Does anyone know how to do this? I’m really confused on this question. Also please explain or show work on a piece of paper to get marked =]

Answers

(3*0.5)/2=0.75 in^2
The lines are just helping you to see that the shaded space is half of the rectangle

A hot-air balloon rises 150 feet every 5 second. Which equation represents the relationship between time and height?

Answers

Answer:

y=30x

Step-by-step explanation:

the slope would be the change in height/time so 150/5 which is 30feet/sec

thus using the form y=mx+b and assuming the balloon started on the ground (0) then y=30x

What is the value of 6(2b-4) when b=5?

Answers

Answer:

36

Step-by-step explanation:

6(2b-4)
6(2(5)-4)
6(10-4)
6(6)
36

the value of y is 20% more than the value of x. the ratio of x:y = 5

Answers

Answer:

x:y = 5:6

Step-by-step explanation:

y = x(20/100) + x

y = x (1/5) + x

Factorize X

y = x (1/5 + 1)

y = x (6/5)

5y = 6x

-----------------------------

ratio x:y = 5:6

The ratio is x:y = 5:6.

What is ratio?

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same sort and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is expressed as a: b.

Given:

value of y is 20% more than the value of x

So,

y = x(20/100) + x

y = x (1/5) + x

y = x (1/5 + 1)

y = x (6/5)

5y = 6x

Hence, the ratio is x:y = 5:6.

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who is the father of modern Biology?

Answers

Aristotle
Hope this helps

Answer:

hi

Step-by-step explanation:

i am not sure but i think Aristotle

hope it helps

have a great day

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U.S. residents and 40 Australians is obtained. Consider the random variables described below:

X: the number of U.S. residents with blood type AB
Y: the number of Australians with blood type AB

Required:
What is the probability that exactly 2 of the U.S. residents have blood type AB?

Answers

8 percent. Could I please get brainliest?

Which of the following rational functions is graphed below?

A. F(x) =(x-2)/(x+5)

B. F(x) =1/(x-2)(x + 5)

C. F(x) =1/(2x + 5)

D. F(x)= 1/(x+2)(x-5)

Answers

You can try predicting the graph on some special points and will see it quickly the function which is plotted on the graph.

The rational function which is graphed below is given by

Option D: F(x)= 1/(x+2)(x-5)

How to find the function which was used to make graph?

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph  of a function is rising upwards after a certain value of x, then the  function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

How to do analysis of the given graph to find the function it represents?

Since the graph is almost zero always except x = -2 and x = +5 ( since 5 lines are denoting 10,thus lines on x axis are made on two two intervals), thus the function must be such that as input increases, the output decreases quickly but stays above or below the x axis as per the interval.

The graph goes to +infinity or - infinity(depending on the sign of the function) as the input value x = -2 or + 5, this shows that there can be some value like (x + 2)(x- 5) in the denominator so that as x tends to -2 or +5, the denominator shrinks fast and therefore the function gets immensely big numbers.

I chose them since

[tex](x+2)(x-5)|_{x=-2} \: = (-2+2)(-2-5) = 0 \times -7 = 0\\\\(x+2)(x-5)|_{x=5} \: = (5+2)(5-5) = 7 \times 0 = 0[/tex]

As denominator goes to zero, the function will have big and big values.

We can see that when x < -2, the denominator [tex](x+2)(x-5)[/tex] is positive, and the function tends to upside, and when -2 < x < 5, the function is negative and when 5 < x, the function is positive again.

This shows that the function is having signs just like the denominator.

Thus, out of the options available, the fourth option seems so fit.

Thus,

The rational function which is graphed below is given by

Option D: F(x)= 1/(x+2)(x-5)

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What is the ratio of all flowers in the vase to daisies?
What is the ratio of daisies to roses?

Answers

Can you please add an image?

Please help me with the following problem.

Answers

Answer:

No, Yes, No, No.

Step-by-step explanation:

"It is not the case that x is equal to 100." This means that x ≠ 100.

"x is not equal to 300." The problem has nothing to do with 300. We know that x ≠ 100, but the fact that x ≠ 300 doesn't prove or deny anything about the statement x ≠ 100.

"x is equal to 100." This is the complete opposite of the original statement! If x = 100, then this completely denies or negates the fact that x ≠ 100.

"It is not the case that x is equal to 400." Again, 400 has nothing to do with the statement x ≠ 100, so the statement neither proves nor denies the statement x ≠ 100.

"x is equal to 300." Same story: 300 has nothing to do with x ≠ 100, so it doesn't change anything about x ≠ 100.

The distance that a person drives at a constant speed varies directly with the amount of time they have been
driving. If, at a particular speed, a person drives 107 miles in two hours, then how far will they drive, at the
same speed, in 14 hours?

Answers

Answer:

749 miles

Step-by-step explanation:

I divided 107 by 2 and then multiplied that by 14

a person drives 53.5 at that particular speed so they keep driving that amount of miles each hour so it's 749

The distance they will drive, at the same speed, in 14 hours is 749 miles.

Given the following data:

Distance A = 107 milesTime A = 2 hoursTime B = 14 hours

To find how far (distance) will they drive, at the same speed, in 14 hours, we would apply direct proportion:

By using direct proportion:

107 miles = 2 hours

X miles = 14 hours

Cross-multiplying, we have:

[tex]2X = 107 \times 14\\\\2X = 1498\\\\X = \frac{1498}{2}[/tex]

X = 749 miles

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Eight times the sum of 8 and some number is 80. What is the number?

Answers

Answer: 8(8+x)=80

Step-by-step explanation: 8 times is shown in parenthesis, 8+x is the sum, and 80 is the answer

There are 6 pizzas cut into 48 equal pieces.

What is the equation that represents the number of slices, ​x , for each pizza?

Answers

X=8
8 slices per pizza
Hope this helps

Answer:

y=8x

Step-by-step explanation:

In the year 2000 Florida's population was 16 million. since 2000, the state's population has grown about 2% each year. this means that Florida's population is growing exponentially. Find Florida's population in 2006​

Answers

Yes yes I will love to see if you get it right it is 12050

someone please answer!!!

Answers

Answer:

Step-by-step explanation:

1 60

2 120

3 60

4 120

5 30

6 30

A coin is tossed 12 times. What is the probability of obtaining five heads and seven tails?

Answers

Answer:

it is likely to happen, this is because both sides have an even chance of being landed on, the chance of both sides is 1/2.

Use the formula for simple interest to find the interest rate if a deposit of $1400 earned $490 of interest after 5 years,

Answers

Given the simple interest formula:

I = P•R•T

where:
I = interest
P = principal
R = interest rate
T = time (in years)

We can isolate R algebraically to find out the interest rate:

I = P•R•T

Divide both sides by P•T:

I / (P•T) = (P•R•T)/(P•T)

The formula for the interest rate is:
R = I / (P•T)

Substitute the given values into this formula to solve for the interest rate (R):

R = I / (P•T)

R = $490/ ($1,400 • 5 years)
R = $490 / $7,000
R = 0.07 or 7%

Therefore, the interest rate is 7%.

Please mark my answers as the Brainliest if you find my explanations and solution helpful :)

A rectangular garden is 23 feet long and 11 feet wide. A brick walk way with uniform width is going to be constructed around the garden. The brick walk way will have an area of 126 square feet. What should be the width of the brick walk way? Type in your answer to the nearest thousandth. The width of the walk way should be___feet wide.

Answers

Answer:

92 is da correct answer okk that is find da question say happy always

the width of a rectangular window is 24 inches. the area is 624 square inches. What is the length?

Answers

Answer:

Using the formula

A=wl

Solving forl

l=A

w=624

24=26in

Answer:

26 inches

Step-by-step explanation:

624/24 =

Someone help pleasee

Answers

Answer:

Step-by-step explanation

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Find the value of x if 81=3x

Answers

Answer:

here ,

81=3x

or , 81/3=x

or,27=x

hence ,the value of x=27

Answer:

×=27

Step-by-step explanation:

81/3=3×

27=×

hence

×=27

Dante it by 15 pounds of metal for $36 which purchase would have the same cost per pound is Dante purchase

Answers

36 dollars worth of metal

5.67+42.4561 Now, I need help I dont even know what that means and its extra points!​

Answers

Answer:

jrhn nd jdhdjidhdjduhihdnidhdhdidbdkjx

Step-by-step explanation:

thanks sa points

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Here's the solution :

[tex]5.67 + 42.4561[/tex]

[tex]5.6700 + 42.4561[/tex]

[tex]48.1261[/tex]

Plz show ur work! Ty if u do. Will give brainilest!

Answers

Answer:

12/32 divide by 4 and get 3/8 you can’t simplify any further after that

Step-by-step explanation:

Convert 4feet to inches

Answers

4 x 12 = 48
48 inches :)

Answer:

48

Step-by-step explanation:

multiply the length value by 12

the length is 4ft so you multiply it by 12

so

4×12=48

so the answer is 48

What is the estimated sum of fifty-five, sixty, and sixty-five using compatible numbers?

Answers

Answer:

escapingdatprison445

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