Celesta wants to go on a cruise in three years. She could earn 8.2 percent compounded monthly in an account if she were to deposit the money today. She needs to have $10,000 in three years. How much will she have to deposit today

Answers

Answer 1

Given:

Amount after three years = $10000

Rate of interest = 8.2 percent compounded monthly = 0.082

Time = 3 years

To find:

The principal value.

Solution:

Formula for amount is

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

where, P is principal, r is rate of interest, n is the number of times interest compounded in an year, t is number of years.

Substitute A=10000, r=0.082, n=12 and t=3 in the above formula.

[tex]10000=P\left(1+\dfrac{0.082}{12}\right)^{12(3)}[/tex]

[tex]10000=P\left(1+\dfrac{41}{6000}\right)^{36}[/tex]

[tex]10000=P\left(\dfrac{6041}{6000}\right)^{36}[/tex]

[tex]10000=P(1.27783)[/tex]

Divide both sides by 1.27783.

[tex]\dfrac{10000}{1.27783}=P[/tex]

[tex]7825.76712=P[/tex]

[tex]P\approx 7825.767[/tex]

Therefore, today she have to deposit $7825.767.


Related Questions

How will you write 4x + 23y into a statement

Answers

Answer:

Tom wants to go to disneyland this weekend with 23 adults including himself and 4 children Ashley 3, Leslie 1, Brit 4, Victor 2. Children under the age of 6 pay "x" amount while anyone older pay "y" amount. What equation can tom use to find out how much the tickets in total will be.

Step-by-step explanation:

Y = Adults pay y amount - There are 23 adults

X =kids under 6 pay x amount - there are 4 children

4x+23y

4 (kids under 6 ticket cost)+ 23 (Adults ticket cost)

How many solutions does this equation have

2x + 1 = 2x – 1

Answers

Wait by x do you mean times or? If you don’t mean times then it’s 4x

some wanna look at this and help me ?​

Answers

21x+1+14x+4=180
35x+5=180
35x=175
X=5
21(5)+1
105+1
Answer

A random sample of 17 hotels in Boston had an average nightly room rate of $165.40 with a sample standard deviation of $21.70. The critical value for a 98% confidence interval around this sample mean is ________.

Answers

Answer:

153.158 ; 177.642

Step-by-step explanation:

Given the following:

Sample mean (m) = 165.40

Sample standard deviation (s) = 21.70

Sample size (n) = 17

α = 98%

Confidence interval = m ± z(SE)

z at 98% = 2.326

SE = s/√n

SE = 21.70/√17 = 5.2630230

Hence,

Confidence interval = 165.40 ± 2.326(5.2630230)

165.40 - 12.241791498 OR 165.40 + 12.241791498

153.158 ; 177.642

Find the midpoint of the line segment joining the points ​R(3​,​3) and ​S(​-2,6​).

Answers

Answer: 2,9

(3,3) & (-2,6) midpoints

Answer:

(0.5,4.5)

Step-by-step explanation:

Use the midpoint formula to find the answer: ((x1+x2/2),(y1+y2/2))

((3-2/2),(3+6/2))

((1/2),(9/2))

(0.5,4.5)

Let z = z = 8 (cosine (StartFraction pi Over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) ) and w = 3 (cosine (StartFraction pi Over 6 EndFraction) + I sine (StartFraction pi Over 6 EndFraction) ).

Which statement describes the geometric construction of the product zw on the complex plane?

Stretch z by a factor of 3 and rotate StartFraction pi Over 2 EndFraction radians counterclockwise.
Stretch z by a factor of 3 and rotate StartFraction pi Over 6 EndFraction radians counterclockwise.
Stretch z by a factor of 24 and rotate StartFraction pi Over 2 EndFraction radians counterclockwise.
Stretch z by a factor of 24 and rotate StartFraction pi Over 6 EndFraction radians counterclockwise.

Answers

Answer:

c on edge

Step-by-step explanation:

fr

Answer:

(B) Stretch z by a factor of 3 and rotate π/6 radians counterclockwise.

Step-by-step explanation:

edge:2022 Happy new year!

The angles shown above form a linear pair. Show all of your work for full credit.
A. What is the angle relationship between these two angles?
B. Set up an equation and solve for n.
C. Substitute your values into the equation and find the measurements of both angles.

Answers

Answer:

A. [tex] (4n + 22) + (8n - 10) = 180 [/tex]

B. [tex] n = 14 [/tex]

C. 78° and 102°

Step-by-step explanation:

A. The relationship between the two angles that are a linear pair is: their sum gives us 180°. That is:

[tex] (4n + 22) + (8n - 10) = 180 [/tex]

B. [tex] (4n + 22) + (8n - 10) = 180 [/tex]

Solve for n.

[tex] 4n + 22 + 8n - 10 = 180 [/tex]

Collect like terms

[tex] 12n + 12 = 180 [/tex]

Subtract 12 from both sides

[tex] 12n + 12 - 12 = 180 - 12 [/tex]

[tex] 12n = 168 [/tex]

Divide both sides by 12

[tex] \frac{12n}{12} = \frac{168}{12} [/tex]

[tex] n = 14 [/tex]

C. Plug in the value of 14 to get the measurement of both angles

[tex] (4n + 22) = 4(14) + 22 = 56 + 22 = 78 [/tex]

[tex] (8n - 10) = 8(14) - 10 = 112 - 10 = 102 [/tex]

Find mWYZ as well Find mACB please help with both. Thank you every much! Triangles, Need help, right now I’m does adding more stuff so it can stop saying 20 characters.

Answers

Answer:

m<WYZ = 23°

m<ACB = 87°

Step-by-step explanation:

Problem 1: Find WYZ

Given,

m<WVX = (3x - 7)°

m<VYZ = (16x - 3)°

∆WYZ ~ ∆WVX, therefore:

m<WYZ = m<WVX (corresponding angles of similar triangles are congruent)

m<WYZ = (3x - 7)° (substitution)

Create an equation to find the value of x.

m<WYZ + m<VYZ = 180° (linear pair)

(3x -7)° + (16x - 3)° = 180° (substitution)

Solve for x

3x - 7 + 16x - 3 = 180

Add like terms

19x - 10 = 180

Add 10 to both sides

19x - 10 + 10 = 180 + 10

19x = 190

Divide both sides by 19

19x/19 = 190/19

x = 10

m<WYZ = (3x - 7)

Substitute x = 10

m<WYZ = 3(10) - 7 = 30 - 7

m<WYZ = 23°

Problem 2: Find m<ACB

Given,

m<A = 62°

m<AED = (11x - 2)°

m<B = (6x + 13)°

∆ADE ~ ∆ACB, therefore:

m<AED = m<B (corresponding angles of similar ∆s are congruent)

(11x - 2)° = (6x + 13)°

Solve for x

11x - 2 = 6x + 13

Collect like terms

11x - 6x = 2 + 13

5x = 15

Divide both sides by 5

5x/5 = 15/5

x = 3

m<ACB + m<B + m<A = 180° (sum of ∆)

m<ACB + (6x + 13) + 62° = 180° (substitution)

Plug in the value of x and solve

m<ACB + (6(3) + 13) + 62° = 180°

m<ACB + (6(3) + 13) + 62° = 180°

m<ACB + (18 + 13) + 62° = 180°

m<ACB + 31° + 62° = 180°

m<ACB + 93° = 180°

Subtract 93 from both sides

m<ACB = 180° - 93°

m<ACB = 87°

Which of the following lists the numbers shown below in order from least to
greatest? Please hurry

Answers

-63/8, -7.8, 4 √5, √51

Find mo 8 5 m n o
Mo=

Answers

Answer:

MO is 13 units

Step-by-step explanation:

If point lies on a segment, then this point divides the segment into two parts, the sum of their lengths equals the length of the segment

Point N ∈ segment MO

→ That means point N divide segments MO to two parts MN and NO

∴ Point N divides segment MO into two parts MN and NO

→ That mans the length of segment MO equals to the sum of

   lengths of MN and NO

MO = MN + NO

∵ MN = 8 units

∵ NO = 5 units

∴ MO = 8 + 5

MO = 13 units

Determine wheather the given lines are parallel or not. Write the reasons .​

Answers

Answer:

yes it is parallel because the alternate interior angles are equal

* Which answer choice describes y = -3x² +7x - 2​

Answers

This is the answer for that question:
Y=-(3x-1)(x-2)

Answer:

y = -[tex]3^{2}[/tex] + 7x - 2

Step-by-step explanation:

-9-2= -11

y = -11 +7x

+11

y+11 = 7x

/7

1.57142857143= x

Help me please help

Answers

I think it’s roast beef

What equation is equivalent to 3x+6=4x+7

Answers

Answer:

x=-1

Step-by-step explanation:

The first thing we can do is subtract 3x from both sides (it makes solving the equation easier if you get rid of the variable first).

3x+6=4x+7

-3x    -3x

6=x+7

All we need to do now is subtract 7 on both sides.

6=x+7

-7    -7

-1=x  or  x=-1  (they both mean the same thing!)

Hope this helps!! Have a wonderful day c:

What’s the height of the building if it 77% of 596

Answers

Approximately 459 ; 458.92 to be exact
458.92 is the height

Can someone please help me, ty!! (Will mark brainliest)

Answers

Answer:

im gonna say 4 if im wrong its my fault

If x^(y)=5^(x-y) then dy/dx=​

Answers

First, rewrite

[tex]x^y=e^{\ln x^y}=e^{y\ln x}[/tex]

[tex]5^{x-y}=e^{\ln5^{x-y}} = e^{\ln(5)(x-y)}[/tex]

Now, differentiate both sides using the chain rule:

[tex]\dfrac{\mathrm d\left(e^{y\ln x}\right)}{\mathrm dx}=\dfrac{\mathrm d\left(e^{\ln(5)(x-y)}\right)}{\mathrm dx}[/tex]

[tex]e^{y\ln x}\dfrac{\mathrm d(y\ln x)}{\mathrm dx}=e^{\ln(5)(x-y)}\dfrac{\mathrm d(\ln(5)(x-y))}{\mathrm dx}[/tex]

[tex]x^y\left(\dfrac{\mathrm dy}{\mathrm dx}\ln x+y\dfrac{\mathrm d(\ln x)}{\mathrm dx}\right)=\ln(5)5^{x-y}\left(\dfrac{\mathrm d(x)}{\mathrm dx}-\dfrac{\mathrm dy}{\mathrm dx}\right)[/tex]

[tex]x^y\left(\ln x\dfrac{\mathrm dy}{\mathrm dx}+\dfrac yx\right)=\ln(5)5^{x-y}\left(1-\dfrac{\mathrm dy}{\mathrm dx}\right)[/tex]

[tex]\left(x^y\ln x+\ln(5)5^{x-y}\right)\dfrac{\mathrm dy}{\mathrm dx}=\ln(5)5^{x-y}-yx^{y-1}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\ln(5)5^{x-y}-yx^{y-1}}{x^y\ln x+\ln(5)5^{x-y}}[/tex]

Which number line shows 1/3 and its opposite

Answers

Where are the number lines?
You forgot to attach a picture

15 men can dig a ditch in 10 days, how many day
Will 10men take working at the same rate​

Answers

Answer:

If 10 men dig a ditch in 12 days .

Total man-days required to dig the ditch

= 10 men × 12 days

= 120 man-days

how long would 15 men take to dig it?

No of days required to finish the job by 15 men

= 120 men-days / 15 men

= 8 days

Answer: 8 days will be required to finish the job by 15 men

Step-by-step explanation:

Hope this helps u

Crown me as brainliest:)

An ice sculpture is melting at a constant rate. Its weight changes -1 4/5 pounds every hour. What is the total change in weight of the sculpture after 3 1/2 hours

Answers

Answer:it said i was wrong and the correct answer should have been -6 3/10

Step-by-step explanation:

The total change in weight of the sculpture after [tex]3\frac{1}{2}[/tex] hours is, [tex]\bold{-6\frac{3}{10}}[/tex] pounds.

What is rate of change of function?

"The rate of change function is the rate at which one quantity is changing with respect to another quantity."

Given: The weight of an ice sculpture changes [tex]-1\frac{4}{5}[/tex] pounds every hour.

We need to find the total change in weight of the sculpture after [tex]3\frac{1}{2}[/tex] hours.

i.e., the rate of change of an ice sculpture per hour is -1 4/5 pound.

Total change in weight of the sculpture after t hours

= change in the weight of the sculpture per hour × t

= [tex](-1\frac{4}{5}) \times (3\frac{1}{2} )[/tex]

= [tex](-\frac{9}{5} ) \times (\frac{7}{2} )[/tex]

= [tex]-\frac{63}{10}[/tex]

= [tex]\bold{-6\frac{3}{10}}[/tex] pounds

Therefore, the total change in weight of the sculpture after 3 1/2 hours is, [tex]\bold{-6\frac{3}{10}}[/tex] pounds.

Learn more about rate of change here:

https://brainly.com/question/11499305

#SPJ2

Write 81% as a fraction. There is no need to simplify your answer.​

Answers

Answer:

81/100

Step-by-step explanation:

Answer:

81/100

Step-by-step explanation:

1. How many numbers less than 10,000 are there which are divisible
by 21, 35 and 63?​

Answers

Answer:

31

Step-by-step explanation:

To solve this problem, we must find the lowest common multiple of 21, 35 and 63

   Find the prime factors of the number;

 Prime factors of 21  = 3 x 7

                            35 = 3 x 5

                            63 = 3 x 3 x 7

  The lcm = 3 x 3 x 5 x 7 = 315

The numbers between  1 and 10, 000 divided by these three numbers;

   First number  = 315

    Last number  = 9765

Now the total number:

      = [tex]\frac{first number - last number }{315} + 1[/tex]

      = [tex]\frac{9765 - 315}{315}[/tex] + 1

     = 30 + 1

     = 31

The equation of a circle is (x−2)2+(y+6)2=100. Find the equation of a circle that is externally tangent to the given circle and has a center at (18, −6).

Answers

Answer:

(x-18)^2+(y+6)^=36

Step-by-step explanation:

circle basic equation is (x-h)^2+(y-k)^2=r^2

center is (18,-6) it is also externally tangent

so

(x-18)^2+(y+6)^2=36 answer

The equation of a circle that is externally tangent to the given circle and has a center at (18, −6) is [tex](x-18)^2+(y+6)^=36[/tex]

What is an equation of a circle?

A circle can be characterized by its center's location and its radius's length. Let the center of the considered circle be at (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Given that the circle basic equation is [tex](x-2)^2+(y+6)^2=100[/tex]

The center is (18,-6) it is also externally tangent;

Therefore,

[tex](x-18)^2+(y+6)^2=36[/tex]

Therefore, the equation of a circle that is externally tangent to the circle is; [tex](x-18)^2+(y+6)^2=36[/tex]

Learn more about equation of a circle here:

https://brainly.com/question/10165274

#SPJ2

Which statement is true

Answers

Answer:

b

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

The large Ferris wheel makes a revolution in 60 seconds. The small Ferris wheel makes one revolution in 20 seconds. How many seconds will pass before Jeremy and Deborah are both at the bottom again?

Answers

Answer:

120 seconds

Step-by-step explanation:

60         20

120        40

180       60

            80

            100

            120

A survey showed that 82% of kids play video games at home. What fraction of kids play video games at home?

Answers

Answer:

8.2/10

Step-by-step explanation:

Answer:

42/50

Step-by-step explanation:

How many liters are in 120 quarts?

1 qt ≈ 0.95 L

Answers

Answer:

114 liters

Step-by-step explanation:

120 x 0.95 = 114

A architect made a scale drawing of a house to be built. The scale is 2 inches to 3 feet. The house in the drawing is 24 inches tall. How tall is the actual house?

Answers

Answer:

36 feet.

Step-by-step explanation:

2 goes into 24 12 times, 12 times 3 is 36 therefore the actual house is 36 feet tall.

Simplify powers of i.
ASSIGNMENT
Simplify each of the following powers of i.
I^32

Answers

Answer:

i^15=-i

i^32=1

1^99=-i

i^22=-1

hope this helps :)

im sorry for the late answer, i put all the answers incase some one needs them, have a nice day!

Step-by-step explanation:

Answer: The answer is "1".

Step-by-step explanation:

Correct on edgen.

calculate doudle of 15.5
show the workout​

Answers

15.5*2= 31 double is two times
15.5 x 2 (double) = 31
Or 15.5+15.5 = 31 It’s double the same number...
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