Mathematics College

Logan starts an IRA (Individual Retirement Account) at the age of 24 to save for retirement. He deposits $300 each month. Upon retirement at the age of 65. his
retirement savings is $1,510,293.29. Determine the amount of money Logan deposited over the length of the investment and how much he made in interest upon
retirement.

Answers

Answer 1

Total deposited = $147600

Interest earned = $1362693.29

Total no. of years for saving = 65-36-24 = 41

years saving no. of months = 41 x12

= 492 Month

deposit for 1 month = $300 deposit for 492 month = 492 x $300

= $147600

Total deposited = $147600

Total saving after retirement = $1,510,293.29 interest = total saving - total deposit

= $1,510,293.29 - $147600

= $1362693.29

What is the Interest Rate ?

Interest is a periodically paid interest amount related to the amount borrowed, deposited or borrowed (the so-called capital amount). The total interest on the amount borrowed or borrowed depends on the principal amount, the interest rate, the frequency of the interest and the time of loan, deposit or borrowing.

Annual interest is interest for one year. Other interest rates apply to different periods of time, such as a month or a day, but are usually calculated annually.

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Related Questions

Sarah enrolled $10,000 worth of debt with National Debt Relief. We negotiated with the creditors and reduced the debt by 50%. Sarah’s fee for our services was 25% of the enrolled debt ($10,000). How much did Sarah end up saving after reducing her debt and paying us our fee?*

Answers

Answer:

7500$

Step-by-step explanation:

Provide the correct reason for the statement in line 1. (please help)

Answers

Answer:

d) given

Step-by-step explanation:

nothing has been done yet, the statement is given as stated above the statement

The equation for the line that has a slope of -3/8 and passes through (0, 10) is: y = -3/8x + 10 : y = 3/8 x - 10

Answers

The standard form of expression equation of a straight line is;

[tex]y\text{ = mx+c}[/tex]

where;

m is the slope

c is the intercept

Given

slope m = -3/8

Next is for us to get the y- intercept of the line. This is done by subtituting the slope and the point (0,10) given into the equation y = mx+c and calculating c as shown;

[tex]\begin{gathered} y\text{ = mx+c} \\ 10\text{ = -3/8(0)+c} \\ 10\text{ = 0+c} \\ c\text{ = 10} \end{gathered}[/tex]

Next is to get the equation of the line by substituting m = -3.8 and c= 10 into the standard form of the equation as shown;

[tex]\begin{gathered} y\text{ = mx+c} \\ y\text{ = -}\frac{3}{8}x+10 \end{gathered}[/tex]

Hence the first option is correct

12. The perimeter of a triangle with sides 5x-1, 5x-1, 2.2x +10, and the perimeter of a square with a side length of 6.5x -11.8 are the same. What is the value of x?

Answers

The value of x is 4.

The perimeter of any shape is the sum of lengths of all its sides.

We are provided with the sides of triangle i.e., 5x-1, 5x-1 and 2.2x +10.

So, The perimeter of a triangle = sum of length of all three sides = (5x-1) + (5x-1) + (2.2x +10)

The perimeter of a triangle = 12.2x + 8 equation 1

Also, we are provided with the side of square i.e., 6.5x -11.8.

The perimeter of a square = 4 (side) = 4 (6.5x - 11.8)

The perimeter of a square = 26x - 47.2 equation 2

As per question,

Perimeter of a triangle = Perimeter of a square

12.2x + 8 = 26x - 47.2

13.8x = 55.2

x = 4

So we can write, the value of x is 4.

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the original price of an article was 240.00. The price is increased by 12½%. The new price of the article is?

Answers

Answer:

The new price of the article is $270

Step-by-step explanation:

270-240/240

x 100% = 12.5%

12.5x240/100

= 30

Please help me I was sick today and missed out on class and I don’t understand this question

Answers

Answer: 72 i think

Step-by-step explanation:

Through how many radians does the minute hand of a clock rotate from12:40 PM to 1:10 PM?o10- 10The minute hand rotates through radians.(Simplify your answer. Type an exact answer in terms of Use integers orfractions for any numbers in the expression)-10

Answers

As you can see in the given figure the minute hand of a clock rotate from 12:40 to 1:10 formig a straigth angle.

A straight angle in radians is π radians.

Then, the minute hand rotates π radians

find the answer to this problem (15/16) - ( -3/16)

A. 3/4
B. -3/4
C. -1 1/8
D. 1 1/8

Answers

Answer;D.
First you would do change change and it would be (15/16)+3/16,then do 15+3=18,then put it over 16,18/16,then you simplify and it would be 9/8,but you can’t have a bigger numerator over a denominator,so you would divide 9/8 and it would be 1 1/8.

a student has 200 Naira if someone gives her 160 Naira how much will she have if someone gives her x Naira how much would she have

Answers

Answer:

360 naira hope it will be helpful

Step-by-step explanation:

A teacher is organizing binders for her students. She has 54 pieces of lined paper, 36 pieces of grid paper, and 72 dividers. What is the greatest number of identical binders that she can make? Please help!

Answers

Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.

What is the highest common factor?

The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.

We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.

We can see that the highest common factor is 18.

When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2. When you divide 72 by 18, the result is 4.

The number of lined paper = 54 pieces

The number of grid paper = 36 pieces

The number of dividers = 72 dividers

The common factors of 54, 36, and 72 are 2, 9, and 18.

The highest common factor of 54, 36, and 72 is 18.

Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.

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Can you check work please?

Answers

When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.

[tex]\begin{gathered} K(-4,-3)\rightarrow K^{\prime}(4,3) \\ L(-3,-1)\rightarrow L^{\prime}(3,1) \\ M(0,-3)\rightarrow M^{\prime}(0,3) \end{gathered}[/tex]

If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is
given by y = 88t - 16t².
When does the ball reach its maximum height? (Round to two decimal places)

Answers

If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.

Maximum height

Given equation:

y = 88t - 16t²

Maximum height dy/dt = 0

88-32t = 0

32t = 88

t = 88/32sec

t = 2.75sec

Hence,

Maximum height attained by the ball :

Maximum height attained by the ball = 88(2.75)-16(2.75)²

Maximum height attained by the ball = 242 - 121

Maximum height attained by the ball = 121 feet

Therefore the maximum height is 121 feet.

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Solve the equation for x.
6(x + 3) - 8 = 4x + 2(4 + x)

Answers

===============================Solve the Equation - Solution and Explanation===============================

Hello! So...

We are given the following to solve:

Solve for x.

[tex]6(x+3)-8=4x+2(4+x)[/tex]

_______________________________________________________

1. Expand both sides of the equation.

[tex]6(x+3)-8=6x+10[/tex]

[tex]4x+2(4+x)=6x+8[/tex]

[tex]6x+10=6x+8[/tex]

______________________________

2. Subtract 10 from both sides.

[tex]6x+10-10=6x+8-10[/tex]

_______________________________

3. Simplify.

[tex]6x=6x - 2[/tex]

_______________________________

4. Subtract 6x from both sides.

[tex]6x-6x=6x-2-6x[/tex]

_______________________________

5. Simplify.

[tex]0=-2[/tex]

^Notice, the sides are not equal in the solution. This being said, there would be no solution.

___________________________________________________

Hope this helps! If you need anything else, feel free to comment below. Thanks and good luck!

find all real and complex zeros for f(x)=x^3-x^2+3x-3

Answers

The real and complex zeros for the function given as .f(x) = x³ - x² + 3x - 3 are x = 1 and x = ±i√3, respectively

How to determine the zeros of the function?

The equation of the function is given as

f(x) = x³ - x² + 3x - 3

Group the terms of the function in two's

So, we have the equation

f(x) = (x³ - x²) + (3x - 3)

Factor each group in the function

f(x) = x²(x - 1) + 3(x - 1)

Factor out x - 1

f(x) = (x² + 3)(x - 1)

Set to 0

(x² + 3)(x - 1) = 0

This gives

x² = - 3 and x = 1

Evaluate the roots

x = ±i√3 and x = 1

Hence, the zeros of the equation are x = ±i√3 and x = 1

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1. Write the regression2.r =3. what does the r mean?I predict there will be a [blank] relationship between [blank] and [blank] I think it’s because [blank] and I’m gonna send a photo about my graphing points

Answers

First of all, we have to find the mean of x values.

According to the given graph, the x values are: 0, 1, 2, 2, 3, 3, 4, 5, 6, 7.

So, the mean is

[tex]\bar{x}=\frac{0+1+2+2+3+3+4+5+6+7}{10}=\frac{33}{10}=3.3[/tex]

The mean of x values is 3.3.

The y values are: 2, 2, 3, 4, 4, 4, 5, 6, 8, 9.

The mean would be

[tex]\bar{y}=\frac{2+2+3+4+4+4+5+6+8+9}{10}=\frac{44}{10}=4.4[/tex]

The mean of y values is 4.4.

Now, we find the standard deviation for x values and y values.

[tex]undefined[/tex]

hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 26∘ and 30∘.
How high (in feet) is the ballon?

Answers

The height of balloon is 1.99 miles above the ground.

What is angle of depression ?

In the event when the line of sight is directed downhill from the horizontal line, an angle is created with it. Angle of depression is the angle produced between the horizontal line and the observer's line of sight when the object being observed is below the level of the observer.

Let's give the balloon's height above the earth and the distance it is from the first milepost horizontally a name.

We can state the following if the angle of this milepost's depression is 24 degrees:

Tan(24)=[tex]\frac{h}{b}[/tex]

b = [tex]\frac{h}{tan(24)}[/tex]

We can state the following for the following milepost as there will be (b+1)miles horizontal distance of and a 20 degree depression at that location.

tan(20)=[tex]\frac{h}{b+1}[/tex]

b +1 = [tex]\frac{h}{tan(20)}[/tex]

Therefore, substituting equation 1

[tex]\frac{h}{tan(24)}[/tex] = [tex]\frac{h}{tan(20)} -1[/tex]

1 = [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex]

1 = h× ( [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex] )

h = 1.99 miles

Consequently, the height of balloon is 1.99 miles above the ground.

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The graph of a linear function is given below.What is the zero of the function ?A. -3B. -3/2C. -2/3D. -2

Answers

Using the graph, we can deduce the following:

• x-intercept: x = -2

• y-intercept: y = -3

Let's determine the zero of the function.

The zero of a function can be said to be the root of the function. It is also called the x-intercept of the function.

The zero of a function is the point the line crosses the x-axis.

From the graph the x-intercept is at x = -2.

Therefore, the zero of the function is:

x = -2

ANSWER:

D. -2

y= −2x+8
x-intercept:
Enter as a coordinate: such as
(a,b)
y
-intercept:
Enter as a coordinate: such as
(a,b)

Answers

For given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)

In this question, we have been given an equation y = -2x + 8

We need to find the x-intercept and y-intercept. Also, we need to write it as a coordinate (a, b)

To find the x-intercept we need to substitute y = 0 in the above equation.

0 = -2x + 8

2x = 8

x = 4

So, the x-intercept is (4, 0)

To find the y-intercept we need to substitute x = 0 in the above equation.

y = -2(0) + 8

y = 0 + 8

y = 8

So, the y-intercept is (0, 8)

Therefore, for given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)

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Find the equation for the circle with a diameter whose endpoints are (5,5) and (3,−5).

Answers

The equation of the circle in standard form whose center is at (h, k) = (4, 0) is (x - 4)² + y² = 26.

How to derive the standard equation of the circle based on the coordinates of diameter endpoints

In this question we find the coordinates of the endpoints of the diameter of the circle, then, the center of the circle is the midpoint of the line segment. The center of the circle is found by midpoint formula:

(h, k) = 0.5 · (5, 5) + 0.5 · (3, - 5)

(h, k) = (4, 0)

And the radius of the circle is determined by Pythagorean theorem:

r = √[(4 - 5)² + (0 - 5)²]

r = √[(- 1)² + (- 5)²]

r = √26

Then, the equation of the circle in standard form is describe below:

(x - h)² + (y - k)² = r²

If we know that (h, k) = (4, 0) and r = √26, then the equation of the circle is:

(x - 4)² + y² = 26

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7. On February 12th, a fire occurred at a local dry cleaning plant and the inpatient service days for the localhospital (120 beds) was reported to be 130. What is the bed occupancy rate for February 12th? Round toone decimal place.

Answers

We can use the following formula:

[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{\#_{\text{ }}of_{\text{ }}inpatient_{\text{ }}days_{\text{ }}for_{\text{ }}a_{\text{ }}given_{\text{ }}period}{_{\text{ }}avalaible_{\text{ }}beds\times\#_{\text{ }}days_{\text{ }}in_{\text{ }}the_{\text{ }}period}_{}\times100[/tex]

So:

[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{130}{120\cdot365}\times100[/tex]

Answer:

0.3%

i need help the problem is
solve for y
2x+y=3

Answers

Answer:

y = 3 - 2x

Step-by-step explanation:

Subtract 2x from both sides of the equation.

Answer:

y = x or 1x

Step-by-step explanation:

x as a variable can also be expressed as 1x.

so we can say that 2x + 1x

because x & y are two different type of variables. you think of y as a question mark ( ? ).

Now the new equation is

y = ?

so 1x + ? = 3

because x is the same thing as a 1x you can say that 2x + 1x = 3

Classify the following functions as growth or decay: f(x) = 10 (6/7)^x, g(x)= 1/3e^x, h(x)=5e^-x, k(x)= -10(6/7)^x

Answers

It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.

Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.

Now let's analyze the functions from the problem.

[tex]\text{ Let }f(x)=10\cdot(\frac{6}{7})^x[/tex]

Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.

Use these rules to find whether each function is increasing or decreasing.

Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.

[tex]3-\sqrt{x} 5[/tex]

Answers

The value of the expression given as 3 - √x⁵ is 3 - x^2√x

What are expressions?

Expressions are mathematical statements that are represented by variables, coefficients and operators

How to evaluate the expression?

The expression is given as

3 - √x⁵

Express 5 as the sum of 4 and 1