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

Who thinks ree kid,Joshdub Juicy and mully are super funny!

Answers

Answer:

me

Step-by-step explanation:

Answer:

I do! Juicy do be kinda cute too tho. EddieVR though is probably the most funny. Especially his Horror VR videos.

Step-by-step explanation:

What about Narrator? He seems like he'd be really nice and he's funn-

when Mully cuts him off, it's golden lolololol

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

Answers

Answer:

x - y = 4

Step-by-step explanation:

Hope this helped! :)

A river has a current of 2km per hour. Find the rate of Fred’s boat in still water if it travels 30 km downstream and the same time it takes to travel 14 km upstream.

Answers

Answer:

32km

Step-by-step explanation:

how many number of subsets in set D

Answers

Answer: A proper subset is a subset that is not identical to the original set—it contains fewer elements. You can see that there are 16 subsets, 15 of which are proper subsets. Listing the sets is fine if you have only a few elements.

85 miles on 8 gallons of gas

Answers

Answer:

11.6 miles per gallon

Step-by-step explanation:

Answer:

11.6 miles per gallon

Step-by-step explanation:

just divide

Simpty to create an ealent expression
8k-5(-5k+3)

Answers

Answer:

Tge answer:8k+25k-15

Hillary needs to know if the triangle shown is a right triangle. Which equation should she use to help?

Answers

Answer:

a2+b2=c2

Step-by-step explanation:

A right triangle is a triangle in which one of the angles is a 90∘ angle. A triangle can be determined to be a right triangle if the side lengths are known. If the lengths satisfy the Pythagorean Theorem (a2+b2=c2) then it is a right triangle.

Q13. A stone is dropped from a height of 5 km. The distance it falls through varies directly with the
square of the time taken to fall through that distance. If it falls 64 min 4 seconds. find the distance the
stone covers in the 5th second?
A. 36 m
B. 58 m
C. 72 m
D. 100 m

Answers

I’m not sure but I think it might be C so sorry if it’s wrong

Answer:

The stone covers 36 m in the 5th second. Correct choice: A.

Step-by-step explanation:

Proportions

Two variables are said to be proportional if one of them can be calculated by multiplying the other by a constant of proportionality. If y and x are those variables, then:

y=k.x

There are other similar proportions where the relation is not linear. For example, if y is proportional to the square of x, then:

[tex]y=k.x^2[/tex]

According to the conditions of the question, the distance traveled by a stone dropped from a height of 5 Km varies directly with the square of the time taken to fall through that distance. If d is the distance and t is the time, then;

[tex]d=k.t^2[/tex]

To find the value of k, we use the given condition: The stone falls d=66 meters in t=4 seconds. Substituting:

[tex]64=k.4^2=16k[/tex]

Solving:

[tex]k=64/16=4[/tex]

Substitute the value of k into the equation to get the complete model.

[tex]d=4.t^2[/tex]

Now we calculate the distance when t=5 seconds:

[tex]d=4\cdot 5^2=4\cdot 25=100[/tex]

The stone has covered 100 m in 5 seconds. But we need to find the distance covered in the 5th second, that specific interval between 4 sec and 5 sec.

Since we already know the distance for t=4 sec (64 m), and the distance for t=5 sec (100 m), then:

distance in the 5th second = 100 m - 64 m = 36 m

The stone covers 36 m in the 5th second. Option A.

A scuba diver swam 96 ft.
below the surface of the
lake. He then swims up 49
ft. What is his depth now?

Answers

Answer:

96-49=47

Step-by-step explanation:

he goes down then up so 47

Answer:

-47

Step-by-step explanation:

-96 + 49

-47

Identify the holes, vertical asymptotes, and horizontal asymptotes of the following.


[tex]f (x) = \frac{2}{x-3}[/tex]

Answers

Answer:

Horizontal asymptote: y = 0

Vertical asymptote: x = 3

Step-by-step explanation:

The vertical asymptote in this graph would be when x = 3 because it would make the denominator 0, which would make the equation undefined.

There will not be any holes in the graph, because there won't be any point undefined in the function except for when x = 3, but that's a vertical asymptote.

Now, for the horizontal asymptote, we see what value y approaches as x approaches plus and minus infinity. Since x is in the denominator, y will approach 0 when it's plus or minus infinity.

Horizontal asymptote: y = 0

Vertical asymptote: x = 3

The slope of a line is ¾. A different line passes through the points (6, 3) & (-1, 5). Are the lines parallel? Why or why not?

Answers

Answer:

B. They are not parallel because their slopes are not equal.

Step-by-step explanation:

Find the slope of the line that runs through points (6, 3) and (-1, 5):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-1 - 6} [/tex]

[tex] slope (m) = \frac{2}{-7} = -\frac{2}{7} [/tex]

Since the slope of the line that passes through points (6, 3) and (-1, 5) is not the same with line that has a slope of ¾, therefore, both lines cannot be parallel.

The answer is "B. They are not parallel because their slopes are not equal."

Mari claims that 2(to the fifth power) × 3² x 5 is a multiple of a number. Is she correct? Explain. ASAP

Answers

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The answer to [tex]2^{5} *3^{2} *5[/tex] is 1440.

I believe she is correct because 1440 can be divided by another number without any remainders.

A mug is 3/7 full. The mug contains 1/2 cup of water. Find the capacity of the mug

Answers

Answer:

7/6 cups of water is the mug's capacity

Step-by-step explanation:

Capacity refers to how much a container can contain.

Let x be the capacity of the mug.

According to the question, the mug is 3/7 full. This means that the mug contains 3/7 × x = 3x/7 of water.

It was further stated that the mug contains 1/2cup of water. This means that:

1/2 cup of water = 3x/7 of water in the mug

Hence;

1/2 = 3x/7

3x × 2 = 7 × 1

6x = 7

x = 7/6

Therefore, the capacity of that mug is 7/6 cups of water.

The capacity of the the mug if it is 3/7 full and contains 1/2 cup of water is 7/6 cup

Capacity

Given:

Quantity of the mug = 1/2 cup

let

x = full capacity of the mug

Water in the mug = 3/7 of x

= 3/7x

Note:

Water in the mug = 1/2 cup

So,

3/7x = 1/2

divide both sides by 3/7

x = 1/2 ÷ 3/7

= 1/2 × 7/3

= 7/6

Therefore, the full capacity of the mug is 7/6 cup

Learn more about fraction:

https://brainly.com/question/2929160

which integer represents 19°F bellow

Answers

Answer:   -19

Draw out a vertical number line. Positive values are above 0, and negative values are below zero.

please answer asap!!

Answers

Answer:

∠QPR = 40°

Step-by-step explanation:

According to the question the line PQ ⊥ PS which means that they both are perpendicular angles. Perpendicular angles are always 90°, so,

∠QPR + ∠RPS = 90°

=> 7x - 9° + 4x + 22° = 90°

=> (7x +  4x) +(22 - 9)° = 90°

=> 11x + 13° = 90°

=> 11x  = 90° - 13°

=> 11x = 77°

=> x = 77/11

=> x = 7

So, now that we have x, we can find ∠QPR,

7x - 9°

=> (7 * 7 - 9)°

=> (49 - 9)°

=> 40°

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

1. You are eating on a Tootsie Roll Lollipop that is in the shape of a sphere. It is giving up volume at a steady rate of 0.25 in3 /min. How fast will the radius be decreasing when the Tootsie Roll Pop is .75 inches across?

Answers

Answer:

Step-by-step explanation:

Since the Tootsie Roll lollipop is a sphere

volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]

the negative sign indicates that the volume is decreasing

upon differentiating

as the diameter given is =0.75 so radius will be = 0.375

[tex]dV/dt = 4piR^2*dR/dt[/tex]

so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]

So the radius is decreasing at the rate of dR/dt= 0.142in/min

Mackenzie has one candy bar to share equally with her best friend. What portion of the candy bar does Mackenzie give to her best friend.

Answers

Answer:1/2

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation: if each of you get part of the candy bar and you need to share it equally, both of you get 1/2 of it.

34(8x – 6) – 2 = 12 – x

Answers

Answer:

sorry for my handwriting

i think this is the correct answer

A set of history exam scores are normally distributed with a mean of 83.2 points and a standard deviation
of 8 points.
What proportion of exam scores are between 82 and 89.2 points?
You may round your answer to four decimal places.

Answers

Answer: .3330

Step-by-step explanation:

The proportion of exam scores are between 82 and 89.2 points is 0.3330.

What is standard deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

When comparing data sets that may have the same mean but a different range, it is helpful.

The mean of the two numbers 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30 for instance, is the same. The second, though, is obviously more dispersed.

Given:

mean = 83.2 points and

standard deviation = 8 points.

So, the proportion is

P(82 ≤ x ≤ 89.2)

=P( 82- 83.2 / 8 ≤ z ≤ 89.2 - 83.2/8)

=P (0.75) - P(-0.15)

=0.7734 -(0.4404)

= 0.3330

Learn more about standard deviation here:

https://brainly.com/question/13905583

#SPJ2

Elena’s bedroom door is 1.2 m wide. How wide should the door be on the scale drawing? Explain how you know.

Answers

Answer:

0.016cm

Step-by-step explanation:

I would convert 2cm in terms of meters

2cm/1 = 1m/100cm

since there are cm on top and bottom it cancels out

2•1 /1m• 100 = 2m/100 = .02 m

now you solve using proportions

x/.8 = .02/1

x= (.8)(.02) cross multiples)

x= 0.016

SOMEBODY HELP !!!!!!!

Answers

Answer:

i got

[tex] - \frac{11}{12} [/tex]

I do not know if I'm right please tell me me if I'm wrong

Find both the greatest common factor and the least common multiple of 24 and 30.

Answers

Answer:

24 = 2, 3 , 4, 6, 8, 12, 24

30 = 2, 3, 5, 6, 10, 15, 30

Step-by-step explanation:

Least common for both is 2

Greatest common factor for both is 6

Solve each proportion for x. Round to the nearest tenth.
117/45=x/95

Answers

Answer: x=247

Step-by-step explanation:

1. Set up the equation

117/45=x/95

2. Cross multiply

117(95) = 11115

45(x)= 45x

3. Set both equal to each other

11115=45x

4. Divide 45 on each side

11115/45 = 45x/45

5. Solve for x

x=247

Hope this helps :)

-Morgan

What is the value of p?

Answers

I pretty sure it’s 50

A and B are complementary angles. If mA = (2x + 30)° and mB = (7x – 3), then find the measure of B.

Answers

Answer:

mB=46

Step-by-step explanation:

2x+30+7x-3=90

Combine like terms

9x+27=90

Subtract by 27 on both sides

9x=63

Divide by 9 on both sides

x=7

mB=(7x-3)

Substitute 7 for x

mB= 7(7)-3

mB= 49-3

mB=46

Answer:

The measure of B is 46°

Step-by-step explanation:

To solve this equation, you need to add the two equations, and set them equal to 90° since they are complementary angles

2x+30+7x-3=90

You also need to add like terms, so 2x+7x and 30+-3, or 30-3

9x+27=90

Then you need to isolate the variable by subtracting 27 from both sides

9x+27-27=90-27

=

9x=63

Then you need to divide both sides by 9 to get x=7

Since we know what x is, we plug x into the equation (7x-3) and we will now have 7(7)-3.

To solve this, we multiply 7 and 7, and subtract 3 to get 46.

So the answer is mB=46

I hope this helps!!

   

5. Paul is x years old.
Rebecca is four times older than Paul.
Gemma is 10 years older than Paul.
the sum of their ages is 82 Years.
(a) Form a simplified equation in terms of x
(b) Solve the equation and work out each persons age.

Answers

Answer:  A) The equation will be     x + 4x + x + 10 = 82   B) Paul's age is 12, Rebecca's age is 48  and Gemma's age is 22.

Step-by-step explanation:

We will represent Paul's age by    the equation  p= x  where p is Paul

We will represent Rebecca's age by the equation  r = 4x  Where r is Rebecca

We will represent Gemma's age by the equation g = x + 10  where g is also Gemma's age.

We given that the sum of their ages is 82 years so meaning that  x + 4x + x + 10  has to equal 82.

A) The equation will be     x + 4x + x + 10 = 82  

Solve for the x equation to find Paul age because his age is x.

B)  (x) + (4x) + (x+10) = 82   combine like terms on the left side

    6x + 10 = 82

           -10    -10

   6x = 72

   x= 12  

Paul age is 12.  

r= 4(12)

r = 48

Rebecca's age is 48.

g= 12 +10

g= 22

Gemma's age is 22.  

What is 5/8 divided by 1/4?​

Answers

Answer: 2.5

Step-by-step explanation: If you do 5/8 divided by 1/4 in the calculator it is 2.5.

Find 8% of $40 answers with the nearest penny

Answers

Answer:

3.20

Step-by-step explanation:

Sorry i had the same question and i asked the teacher if he could help and he did but he sorta juts gave me the answer so cant really give an explanation so sorry.

Write the rational number as a decimal -4 2/3

Answers

Answer:

- 4.(6)

Step-by-step explanation:

Hi there !

- 4  2/3 =

= - 4  6/9

= - 4.(6)

Good luck !

Pick three numbers to make a fact family when write each fact family

5 7

2 4



Answers

Answer: Maybe it is 2,4

Step-by-step explanation:

A fact family is a group of math facts using the same numbers. In the case of addition and subtraction, you use three numbers and get four facts.

For example, you can form a fact family using the three numbers 3, 10, and 13: 10 + 3 = 13, 3 + 10 = 13, 13 − 10 = 3, and 13 − 3 = 10.

Addition facts − Here the sum of two of the three given numbers is the remaining third number. This sum is expressed in two possible orders. Thus, there are two addition facts for any three given numbers

For 3, 10 and 13, the two addition facts are:

3 + 10 = 13;

10 + 3 = 13

Subtraction facts − Here the difference of two of the three given numbers is the remaining third number. There are two such differences. Thus, there are two subtraction facts for any three given numbers.

For 3, 10 and 13, the two subtraction facts are:

13 − 10 = 3;

13 − 3 = 10

We use fact families to reinforce the connection between addition and subtraction, and to help students learn and memorize the basic addition & subtraction facts.

Problem 1:

Make four related number sentences using each set of 3 numbers.

10, 7, 3:

There should be two additions and two subtractions.

Solution

10, 7, 3:

Step 1:

The addition facts using above three numbers are:

7 + 3 = 10;

3 + 7 = 10;

Step 2:

The subtraction facts using above three numbers are:

10 – 7 = 3;

10 – 3 = 7

Problem 2:

Make four related number sentences using each set of 3 numbers.

13, 8, 5

There should be two additions and two subtractions.

Solution

13, 8, 5

Step 1:

The addition facts using above three numbers are:

5 + 8 = 13;

8 + 5 = 13;

Step 2:

The subtraction facts using above three numbers are:

13 – 5 = 8;

13 − 8 = 5

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