Mathematics College

Suppose 6000 is placed in an account that pays 3% interest compounded each year. Assumed that no withdrawals are made from the account .

Find the amount at the end of one year ?

Find the amount in the account at the end of two year .

Answers

Answer 1
Find the amount at the end of one year? $6180
Find the amount in the account at the end of two year. $6365.4
Answer 2

Final answer:

With a principal amount of $6000 and a 3% annual interest rate compounded yearly, the account balance at the end of one year will be $6180, and at the end of two years, it will be $6365.40.

Explanation:

To calculate the amount of money in an account with compounded interest, we can use the formula [tex]A = P(1 + r/n)^{(nt)[/tex], where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times the interest is compounded per year, and t is the time the money is invested for in years.

For the student's case, with $6000 placed in an account at 3% interest compounded each year with no withdrawals:

To find the amount at the end of one year, we calculate it as [tex]A = 6000(1 + 0.03/1)^{(1\times 1)[/tex], which equals $6000 × 1.03 = $6180.To find the amount at the end of two years, [tex]A = 6000(1 + 0.03/1)^{(1\times 2)[/tex], giving us $6000 × 1.03² = $6365.40.

As such, after one year, the student would have $6180, and after two years, the balance would be $6365.40.

Related Questions

Select three rations that are equivalent to 7: 6.

Answers

14:12
21:18
28:24
............

Imagine a world in which only decimal,not fractions,are used.how would your life be different

Answers

This answer depends a bit on your age, the types of activities you partake in and the kind of work you do/are planning to do but here goes:

I am thinking of some uses of fractions where decimals are not typically used. One might be cooking. Often the ingredients (1/2 cup of four and so on) are measured using fractions. If you were in a world with decimals you might need to make (1/3) the servings of a recipe that calls for 1/4 of a cup of some ingredient and instead of 1/12 have to deal with a long repeating decimal that probably would need to be approximated so would not be precise.

While on the subject of food ordering pizza (1/2 with pepperoni, 1/4 mushrooms and 1/4 plain) would be doable after you got used to it but probably not as comfortable. Dividing up slices of pizza among friends (one slice is usually 1/8 of a pie) might be awkward though eventually doable.

Estimation - the biggest issue is exactitude versus estimation. When we use a fraction like 1/3 that is an exact value, but when we use .333 or .3333333 no matter how many 3s we use we are only estimating because the 3s go on forever and we can't write them forever. Yes, we can use .3 (with a bar over the 3, but now try to multiply that with .456565656 with a bar over the 56. This becomes practically impossible unless we estimate ... so the biggest issue would be that you would lose precision in many calculations and measurements and have to deal with answers that are good enough (but not exact).

Now say you work on some major car company or you design bridges or you are a scientist developing medicine that cures diseases, would not you want the ability to measure and compute precisely? If I split the pizza up wrong it is not a big deal. If I use a little more flour or a little less than I should in the recipe it might not make much of a difference in the end but if I am doing something that impacts the health, safety or well being of another human being, I would not want to live in a world where I have to estimate and can't count on having the exact, precise value.

Help with this math question please had to post picture side ways for it to fit thanks

Answers

Hello,
Please, see the attached files.
Thanks.

496 rounded to the nearest 10 is 500 true or false

Answers

True, It would round up to 500.
True if it was 495 then it would be 490 but because its 496 that's closer to 500

5.1 times 10 to the fourth power

Answers

The answer is 6,765,201. I apologize if I got this wrong.
5.1*10=51
so, 51*51*51*51=6765201

a motorboat travels 432 kilometers on 6 hours going upstream and 384 km in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current.
please help slove and steps

Answers

Going upstream: 432 km / 6 hours = 72 km/h
Going downstream: 384 km / 4 hours = 96 km/h
Going upstream against the current means that the effective speed is:
r_boat - r_current = 72
Meanwhile, going downstream with the current means;
r_boat + r_current = 96
Adding both equations (to cancel out r_current) gives:
2r_boat = 72 + 96
r_boat = 84 km/h
Substituting back into one of the original equations: r_current = 12 km/h.

Can you please explain this

Answers

1st triangle is isoceles triangle as one as two angles are equal due to the equal sides......
2nd triangle is equilateral triangle as all sides are same
The two triangles are not congruent because we do not know if the third sides of both triangles are congruent. We can see that the first and second sides are congruent to their corresponding sides in the 2nd triangle. However, if we do not know that the third side in the first triangle is congruent to its corresponding side in the second triangle, then we cannot conclude that the two sides are congruent.

A town has two fire engines, a and b, that operate independently. the probability that engine a is available when needed is 0.96. the probability that engine b is available when needed is also 0.96. 12. what is the probability that neither fire engine is available when needed?

Answers

P(both unavailable) = P(A unavailable)*P(B unavailable) = 0.04^2 = 0.0016

translated 2 units left and 9 units down

Answers

Move 2 times to the left and go down 9 times i think....

The translation of the given expression is "[tex]\bold{y=(x+2)^2-9}[/tex]"

Translation of equation:

Given:

"translated 2 units left and 9 units down".

we assume the equation is "y" so, the translation of the above-given expression is equal to "[tex]\bold{y=(x+2)^2-9}[/tex]".

Please find the attached diagram for the translated expression.

Find out more information about the translation here:

brainly.com/question/24649944

What is the arc length of a circle (in meters) with a radius of 2 meters that has an arc angle of 90°? A 2π B π C 2 D 4π

Answers

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad de grees\\ ------\\ r=2\\ \theta =90 \end{cases}\implies s=\cfrac{(90)\pi (2)}{180}\implies s=\pi [/tex]

Buying something in order to increase social status is known as _____ consumption.

1 Conspicuous
2 Emotional
3 Research
4 Wise

Answers

1) conspicuous consumption

1) Conspicous Consumption

Which of the following is the same as 5(2 − 1)?

a 5 − 2 − 1

b 5 × 2 × 1

c 10 − 1

d 10 − 5

e one of the above

Answers

I believe it would be D

Distance between New York and San Francisco is 2539.79 MI a train travels at an average speed of 90 miles per hour what equation shows the relationship between distance traveled (Dl speed (s) and time taken (t)

Answers

D = s*t . . . . . . . distance is the product of speed and time

_____
If you want to know the time it takes to get from New York to San Francisco, you can substitute the given values and solve for t.
  2539.79 = 90t
  2539.79/90 = t ≈ 28.2199 . . . . hours

Lee associates borrowed $60,000. The company plans to set up a sinking fund that will pay back the loan at the end of 12 years. Assuming a rate of 8% compounded semiannually, the amount to be paid into the fund each period is?

Answers

If your choices are the following:
A. $1,350
B. $1,536
C. $1,653
D. $5,163
E. None of these

Then the answer is B. $1,536.

Solution:
$60,000 x .0256
=1,536

what do i do?? i just have to find what the the question marks show.

Answers

------------------------------------------------------
Given information
------------------------------------------------------
100%  = $27.60

------------------------------------------------------
Rewriting it
------------------------------------------------------
[tex]\$27.60 = 100 \%[/tex]
[tex]\$1 = 100 \div 27.60 \%[/tex]
[tex]\$1 = \frac{250}{69} \%[/tex]

------------------------------------------------------
Find $4.14 in percentage
------------------------------------------------------
[tex]\$1 = \frac{250}{69} \%[/tex]
[tex]\$4.14 = \frac{250}{69} \times 4.14[/tex]
[tex]\$4.14 = 15%[/tex]

------------------------------------------------------
Answer: 15%
------------------------------------------------------


------------------------------------------------------
Find $31.74 in percentage
------------------------------------------------------
[tex]\$1 = \frac{250}{69} \%[/tex]
[tex]\$31.74 = \frac{250}{69} \times 31.74[/tex]
[tex]$31.74 = 115%[/tex]

------------------------------------------------------
Answer: 115%
------------------------------------------------------

Admission to the state fair costs $5 and each ride costs $0.75. If Ahmed wants to spend no more than $14 at the fair, how many rides can he ride? 
-Show All Work Please- 

Answers

14-5= 9

9 divided by .75 = 12

He can ride 12 rides.

3 over 5 is 30% of what number?

Answers

3/5 = 0.3 * x
3/5 is 30% of x - This is how they match up from the word problem to a number sentence

So to solve it...
3/5 = 0.3x
x = 3/5 ÷ 0.3 = 2

What number lies between 7x8/10=

Answers

the number that lies between that is 7
the number that  between 7x8/10 is:

7x8=56
56/10= 5.6

therefore the answer is 5.6


hope this helps

-Rachael
(yahtzee05)


If the correlation between height and weight of a large group of people is 0.75​, find the coefficient of determination​ (as a​ percent) and explain what it means. assume that height is the predictor and weight is the​ response, and assume that the association between height and weight is linear.

Answers

Independent variable is the predictor variable which is the height and dependent variable is the response variable which is weight in this scenario.

The square of correlation coefficient gives the coefficient of determination. It is denoted by R² (R squared).

We are given:
R = 0.75

So,
R²  = 0.75²

R² = 0.5625

R²  = 56.25 %
The coefficient of determination tells how much of the trend of dependent data can be explained by the independent data using the linear regression model. So in the given case, Height can explain 56.25% of the trend in the weight.

Answer:

Step-by-step explanation:

Given that  the correlation between height and weight of a large group of people is 0.75

Coefficient of determination = [tex]R^2 =0.75^2 =0.5625=56.25%[/tex]

Coefficient of determination gives us the strength of association between two variables and how much the variability of the response variable i.e. weight is due to the variability of the predictor variable i.e. height

When there is a linear association correlation coefficient square gives us the reason for the variability and percentage due to the variability in predictor variable

Liliana used 4 dark power crystals to raise 14 zombie soldiers. She wants to know how many zombie soldiers (z) she can raise with 10 dark power crystals. How many zombie soldiers can Liliana raise with 10 power crystals?

Answers

4c = 14z.
1c = 3.5z.
10c = 35z.
So she can raise 35 with 10 power crystals. Hope it helps !:)

Answer:- Liliana can raise 35 zombie soldiers with 10 power crystals.


Explanation:-

Let the number of zombie soldiers raised by 10 dark power crystals be 'x'.

Zombie raised by 4 power crystals = 14

Since the number of zombie and power crystals are in direct proportion.

Therefore, we get

[tex]\frac{x}{10}=\frac{14}{4}[/tex]

Multiply 10 on both the sides, we get

[tex]\Rightarrow\ x=\frac{14}{4}\times10=35[/tex]

Liliana can raise 35 zombie soldiers with 10 power crystals.

Which is greater 320 fl oz of 18 pt

Answers

16 ounces = 1 pint
320/16 = 20 pints

320 fl oz is greater than 18 pt

How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3?

Answers

infinitely many solutions. Since your slope and Y axis values are the same on both sides no matter what you fill in for x your answer will be true.

how do you graph y=2sin(2x)

Answers

Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.
on the a axis, you set the x value at 0, π/4, π/2, 3π/4, π
2sin0=0, 2sin(π/2)=2, 2sinπ=0, 2sin(3π/2)=-2, 2sin(2π)=0
so the y values are 0, 2, 0, -2, 0 respectively
locate the points and connect
extend the pattern left and right if there is no limit for x. It should look like a wave

At a certain time of day the angle of elevation of the sun is 30 a tree has a shadow that is 25 feet long find the tree to the nearest foot

Answers

If we draw out this scenario, we can see that it is a 30-60-90 right triangle, and the tree shadow is the leg opposite of the 60 degree angle. The problem asks for the length of the tree, which is the leg opposite of the 30 degree angle. In a 30-60-90 triangle, the leg opposite of the 30 degree angle has length “x”, and the leg opposite of the 60 degree angle has length “x times sqrt 3” (or “x rad 3”). We know the leg opposite of the 60 degree angle is 25 feet, so we can setup the equation “x rad 3 = 25”. We divide sqrt of 3 on both sides and end up with “x = 25/sqrt 3”. The problem asked for the leg opposite of the 30 degree angle, which we set as “x”. The problem asks for the length to the nearest foot. When put into a calculator, “25/sqrt 3” ends up being about 14 feet, which is our final answer.

pete's dog weighed 30 pounds . then lost 16% of its weight , how much weight did the dog loose

Answers

The dog would now way 25.2 pounds, having lost 4.8 pounds.
the dog had lost 4.8

Compare and contrast y=square root of x and f(x)=square root of x

Answers

 For this case we have the following functions:
 y = square root of x
 f (x) = square root of x
 Rewriting the functions we have:
 [tex]y = x ^ {(1/2)} f (x) = x ^ {(1/2)}[/tex]
 We observed that:
 The functions are exactly the same.
 The difference is that when writing f (x) we know that the function depends on x.
 When writing the letter y, we have two variables:
 y: dependent variable.
 x: independent variable.

Answer:

Step-by-step explanation:

Given are two functions

[tex]y=\sqrt{x} :\\f(x) =\sqrt{x}[/tex]

We have to compare and contrast these two functions.

On comparing we have both are the same.

FIrst one is written as y = form while second function is written as function of x

Sometimes we use y and sometimes we use f(x) in practice.

In both the cases, x is the independent variable and normally marked on x axis and y or f(x) the dependent variable marked on vertical y axis.

-4x-2y=-12 and 4x+8y=-24 using addition/eliminatin method

Answers

Use the elimination method:

-4x - 2y = -12
+4x + 8y = -12
--------------------
 0  + 6y = -24

6y = -24
6y/6 = -24/6
y = -4

Plug in -4 for y in one of the equations
-4x - 2y = -12
-4x - 2(-4) = -12
-4x + 8 = -12
-4x + 8 (-8) = -12 (-8)
-4x = -20
-4x/-4 = -20/-4
x = 5

x = 5, y = -4

hope this helps
elimination method is best because one equation has 4x and the other has -4x. Add the two equations together.

 -4x - 2y = -12
+4x + 8y = -24
----------------------
   0 + 6y = - 36

divide by 6 both sides 
y = -6 

use this to find x in either equation.
4x + 8(-6) = -24
4x  - 48 = -24
4x = -24 + 48
4x = 24
x = 6

how would you graph y=| x-2|-4

Answers

To graph ty function simply make a table of values, where you choose any value for x and substitute that value in the function.

Then take the absolute value of the expression in the square bracket.

It is always positive, the absolute value of -6 is 6 etc.

Then graph the resulting points.

Another way to do it is simply draw the graph of y = |x| then move it 2 spaces to the right and 4 spaces down, I believe.

when using fraction strips how do you know that two fractions are equivalent

Answers

The same strip area is covered by equivalent fractions. That's what makes them equivalent.
She is correct. The first person that answered

Carlisle is testing different types of planting soil to determine which type is most effective in growing blueberry bushes. He purchases 2 different brands of planting soil from a local store. Carlisle applies Brand A to an area of the yard that receives full sunlight and Brand B to another area of the yard that is in partial shade. He waters both areas daily. At the end of the study, Carlisle concludes Brand A is more effective in growing blueberry bushes. Why is his conclusion not valid?

Answers

This conclusion is not valid because BOTH SOIL BRANDS WERE NOT SUBJECTED TO THE SAME CONDITIONS. 
Carlisle applied brand A to the part of the yard that received full sunlight while brand B was applied to the area of the yard which received partial sunlight. This implies that the soils were subjected to different conditions and this ought not to be so, since sunlight is a very important factor, which the soils need.
His conclusion is not valid because his dependent variables weren't the same. When testing out an independent variable, which is the soil in this case, all the other factors of the experiment has to remain the same in order to provide a correct conclusion. Since Carlisle was testing out two different types of soils, he had to set all the other conditions of the plants exactly the same, including the amount of lights that the plants receive. Brand B received full sunlight whereas brand A received less. This could definitely have impaired the results of this experiment, therefore, making it invalid.
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