You have a goal of saving to build up a nest egg of $625,357.24, and you are going to make regular deposits to an account that pays an APR of 7.2% compounded monthly. What monthly deposits are required to reach this goal in 40 years? (Round your answer to the nearest cent.)

Answer:

-7/3

Step-by-step explanation:

(-2-5)/(5-2)

-7/3

Answer:

C.

Step-by-step explanation:

Using Slope formula (y2-y1/x2-x1), we can plug these 2 coordinates in. -2-5/5-2= -7/3.

Or even by simply using rise over run, we can get the slope. Up 7 over 3, and we know that the slope is negative, so we add a negative sign in front.

-Hope this helped

The simplified form of the expression will be 1 / [2(x - 5)] and [(x - 4) / [x (x - 2)].

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The expression is given below.

⇒ [(3x) / (x² - 25)] · [(x² + 6x + 5) / (6x² + 6x)]

Simplify the expression, then we have

⇒ [(3x) / (x² - 25)] · [(x² + 6x + 5) / (6x² + 6x)]

⇒ [(3x) / (x² - 5²)] · [(x² + 5x + x + 5) / (6x² + 6x)]

⇒ {3x / [(x - 5)(x + 5)]} · {[(x + 5)(x + 1)] / [(6x)(x + 1)]}

⇒ 1 / [2(x - 5)]

The expression is given below.

⇒ [(x² - 2x - 3) / (x² + 2x + 1)] ÷ [(x³ - 5x² + 6x ) / (x² - 3x - 4)]

Simplify the expression, then we have

⇒ [(x² - 2x - 3) / (x² + 2x + 1)] ÷ [(x³ - 5x² + 6x ) / (x² - 3x - 4)]

⇒ {[(x - 3)(x + 1)] / [(x + 2)(x + 1)]} · {[(x - 4)(x + 1)] / [x(x - 3)(x - 2)]}

⇒ [(x - 4) / [x (x - 2)]

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The solution to the differentiation dy/dx =(1+x/1-x)^1/3 is  [tex]\frac{dy}{dx} = 1^\frac{1}{3}[/tex]

What is differentiation?

Differentiation is a method of finding the derivative of a function.

To find the derivation of the function Simplify

[tex]\frac{dy}{dx} = ( 1+ \frac{x}{1} - x)^ \frac{1}{3}[/tex]

Any expression divided by one remains the same

[tex]\frac{dy}{dx}= ( 1+ x-x) ^\frac{1}{3}[/tex]

Eliminate x

[tex]\frac{dy}{dx} =[/tex] 1 [tex]\frac{1}{3}[/tex]

Therefore, the solution to the differentiation is  [tex]\frac{dy}{dx} =[/tex] 1 [tex]\frac{1}{3}[/tex]

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Answer:

The [tex]x[/tex]-intercept

Step-by-step explanation:

The equation of line A is [tex]y=\frac{1}{3}x+1[/tex].

The equation of line B is [tex]y=x+3[/tex].

The lines share the same [tex]x[/tex] intercept, since when [tex]x=-3[/tex], [tex]y=0[/tex] for both lines.

Answer:

is 121.004 I hope I've helped!

The linear regression equation for the profit in x years after 1997 is of:

y = 20.5x + 142.

Using this equation, the estimate for the profit in 2006, is of: $326,500.

The linear regression equation is obtained inserting the points of the data, represented either in a table or in a scatter plot, into a linear regression calculator.

In the context of this problem, these points are given as follows:

(0, 131), (1, 168), (2, 202), (3, 193), (4, 221).

Inserting these points into a calculator, the equation is:

y = 20.5x + 142.

The estimate for the profit in 2006, that is, 9 years after 1997, is of:

y = 20.5(9) + 142 = 326.5 thousand dollars = $326,500.

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1. Triangle ABC with the vertices, A(0, 2), B(6, 4), and C(4, -2) is drawn and attached below.

2. The midsegment is EF. This is verified using the triangle midsegment theorem which states that EF = 1/2(AC).

The midsegment of a triangle is the line segment that joins the midpoints of two sides of a triangle together. Every triangle typically has three midsegments.

According to the triangle midsegment theorem, the length of the midsegment is half the length of the third side of the triangle that it is parallel to.

The midpoint of a line is its middle, which can be calculate using the formula:

M(x, y) = [tex](\frac{x_2 - x_1}{2}, \frac{y_2 - y_1}{2})[/tex].

1. The coordinate of the three vertices that is used to draw a triangle are:

A(0, 2), B(6, 4), and C(4, -2).

The triangle is in the attachment below.

2. To plot the midsegment of the triangle, determine the midpoints of AB and BC, then plot the coordinate where both midpoints would be joined.

Midpoint of AB = (x, y) = (0+6)/2, (2+4)/2

= (6/2, 6/2)

= (3, 3) (let this be point E)

Midpoint of AB = (x, y) = (4+6)/2, (−2+4)/2

F = (5, 1)

The midsegment will have the endpoints, E(3, 3) and F(5, 1).

To verify the segment draw is the midsegment according to the triangle midsegment theorem, find the length of the midsegment, EF, and the length of the third side, AC using the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

EF = √[(5−3)² + (1−3)²]

EF = √8 units

AC = √[(4−0)² + (−2−2)²]

AC = √32 units

Based on the triangle midsegment theorem:

EF = 1/2(AC)

Plug in the values:

√8 = 1/2(√32)

√8 = 1/2(4√2)

√8 = 2√2

2√2 = 2√2 (true)

This means that EF is a midsegment of triangle ABC.

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The completion of the inventory table is as follows:

A = $48

B = $264

C = $420

D = $304.

What methods are used for inventory?

Utilizing some of the inventory procedures, the aforementioned inventory table is finished.

The First-in, First-out (FIFO) principle presupposes that the physical flow of products sold corresponds to the order in which they were acquired.

The Last-in, First-out method (LIFO) bases the cost of products sold on the most recent inventory acquisitions.

The weighted-average technique calculates the ending inventory and cost of goods sold using the average cost of goods.

Allocating the expenses of products sold and ending inventory are not based on any presumptions in Specification Identification. It substitutes specified expenses instead.

Inventory Table:

                                    Units    Unit Cost    Total Cost

Jan. 1      Beg. Inventory   8        $6.00            $48 ($6 x 8)

April 11    Purchases        24       $11.00          $264 ($11 x 24)

May 17    Purchases        30      $14.00          $420 ($14 x 30)

Dec. 5    Purchases         19      $16.00          $304 ($16 x 19)

Total                                 81                         $1,036

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The equation of circle (x-4)² + (y+11)² = 64

What is a Circle?

All points in a plane that are at a specific distance from a specific point, the center, form a circle. Alternatively, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Here we know that (h,k)=(4,-11) but we are not given the radius.

However, we can find the radius by using the distance formula.

Therefore,

r = √[(x2 - x1)² + (y2 - y1)²]

r = √[(4 - 4)² + (-3 + 11)²]

r = √[(0)² + (8)²]

r = √(8²)

r = 64

An equation of the circle with center (h,k) and radius r is

(x−h)^2 +(y−k)^2=r^2

Substitute the values in the equation of circle as follows:

(x-4)² + (y+11)² = 8²

(x-4)² + (y+11)² = 64

Therefore, the equation of the circle is (x-4)² + (y+11)² = 64

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An equation 7x+3x+10= -2[-5x +(-5)] has infinite solutions and an equation 7x+3x+10= -2[-5x + (-4)] has no solution.

Given that:

7x+3x+10 = -2 (_x + _)

=> 10x + 10 = -2 (_x + _)

Putting in the blank -5 so as to satisfy the equation that has an infinite solution.

=> 10x + 10 = -2(-5x + -5)

This is the equation that shows that it has infinite solutions and they are in the same line.

For no solutions

7x+3x+10 = -2 (_x + _)

In no solution, the value of b is not equal to -5.

For equation:

7x+3x+10 = -2 (-5x + b) [If putting value in first blank = -5]

Therefore, -2 (-5x + b) is parallel to 10x+10 for any value of b not equal to -5. Parallel lines never intersect. So solutions are no solution.

Putting the value of b = -4

7x+3x+10 = -2 [-5x + (-4)]

This is the equation that shows that it has infinite solutions and they are in the same line.

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The measure of the ∠DBC is 52°.

Because in this (∠DBC ) type of the situation we always consider the center alphabet for the angle.

In this the center alphabet is B, and there are some values given in the equation for a, b, c, d angles.

So, we can find the value of angle B which is 52°.

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The value of dy/dx is -27/8 for 1=5x³+2y²+4xy  at (-1,3).

A differential equation is an equation that contains one or more functions with its derivatives.

Given,

The equation is 1=5x³+2y²+4xy

We need to differentiate the given equation

5.3x²+4ydy/dx+4(xdy/dx+y)=0

15x²+4ydy/dx+4(xdy/dx+y)=0

15x²+4ydy/dx+4xdy/dx+4y=0

15x²+dy/dx(4y+4x)+4y=0

dy/dx(4y+4x)=-15x²-4y

dy/dx=-15x²-4y/4y+4x

Now plug in x =-1 and y=3

dy/dx=-15(-1)²-4(3)/4(3)+4(-1)

=-15-12/12-4

=-27/8

Hence, the value of dy/dx is -27/8 for 1=5x³+2y²+4xy  at (-1,3).

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Answer:

Step-by-step explanation:

x= a. 60

y = I. 15

angle c = b. 45

angle DBC = h. 105

angle CBA = g. 75

Answer:

x=60° y=15° m∠c=45° ∠DBC=105° ∠CBA=75°

Step-by-step explanation:

Since it shows that 7y and 5y make 180 degrees, 12y=180 and y=15

So m∠c=45 degrees and ∠CBA is 75 degrees.

180-(45+75)=60 degrees.

So ∠DBC is 105 degrees. :D

The missing values in the ratios are 2/3 and 16/3 in the set of 1, _ , _.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given are two sets of ratios 2, _, _ and 3, 1, 8.

If we observe the first value of the first and second ratio we see that

The second set of ratios is (3/2) or 1.5 times larger than the first set of ratios.

So the second and the third value of the first set of ratios are (1/3/2) = 2/3 and 8/(3/2) = 16/3.

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Answer:

2 dollars

Step-by-step explanation:

You divide 18 by 9 and get 2. That is the unit rate. :)

The area of the final polygon is 8x² + 4x - 16

From the question, we are to determine the area of the final polygon.

From the given information,

"A polygon with an area of (4x^2 + 2x - 16) square units is combined with a rectangle that has a width of (6x + 2) units and a length of (x - 5) units."

First, we will determine the area of the rectangle.

Area of the rectangle = (6x + 2)(x - 5)

Area of the rectangle = 6x² - 30x + 2x - 10

Area of the rectangle = 6x² - 28x - 10

Now, we will add it to the area of the polygon

4x² + 2x - 16 + 6x² - 28x - 10

= 4x² + 6x² - 28x + 2x - 10 - 16  

= 10x² - 26x -26

Also,

From the given information,

"a polygon with an area of (2x^2 - 30x - 10) square units is removed"

Then,

The area of the final polygon = 10x² - 26x - 26 - (2x² - 30x - 10)

Area of the final polygon = 10x² - 26x - 26 - 2x² + 30x + 10

Area of the final polygon = 10x² - 2x² + 30x - 26x + 10 - 26

Area of the final polygon = 8x² + 4x - 16

Hence, the area is 8x² + 4x - 16

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The polynomial graph has only one relative maximum at point b.

A function's graph can be used to determine the relative peaks and minima of the function. A relative maximum or minimum is a point that is higher than the points directly adjacent to it on both sides. The opposite is true for a relative maximum or minimum. When drawing a curve, relative maxima and minima are crucial spots that can be discovered using either the first or second derivative test.

Given, a polynomial function by observing the graph itself we conclude that the graph has no absolute maxima as it is going towards negative and positive infinity but it has a relative maximum a point b.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

a² - 3x - 10

a(a -3) (x - 10)

According to the give triangle ABC, the length of the line segments

BD is 5.5

CD is 13.5

AC is 10.5

Triangle:

Triangle refers a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees.

Given,

AD is a median in ΔABC, if BD = 5x - 8, CD = 3x + 12, and AC = 7x -14.

Here we need to find the length of the all three segments.​

We know that, the length of BC is the sum of BD and CD.

Thus can be written as,

BC = BD + CD

Now, we have to apply the values on the equation, then we get,

Length of BC is x.

=> 5x - 8 + 3x + 12

=> 8x - 4

=> 8x = 4

=> x = 1/2

Now, we have to apply the value of x as 1/2, on the line segments, then we get,

BC = 5(1/2) - 8

BC = 5/2 - 8

BC = 11/2 = 5.5

So, the value of CD is,

CD = 3(1/2) + 12

CD = 3/2 + 12

CD = 27/2

CD = 13.5

Then the value of AC is,

AC = 7(1/2) - 14

AC = 7/2 - 14

AC = 21/2

AC = 10.5

Therefore, the line segments BC is 5.5, CD is 13.5 and AC is 10.5.

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The number of stuffed animals Lakeview shipped to each store is 31

The Lakeview Toy Factory produced 180 stuffed animal

It donated 25 of the stuffed animals to a local e

After donation the number of stuffed toys left = 180 - 25 = 155

Lakeview shipped the rest to 5 store

Each of the stores received the same number of stuffed animals

Number of stuffed animals each store recieved = total toys/ number of store

= 155/ 5 = 31

Therefore,  the number of stuffed animals Lakeview shipped to each store is 31

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Answer:

- 4x3=12

12x2=24

so, 24 = 24

Answer:

144y²-120y+25

Step-by-step explanation:

(12y-5)²

(12y-5)(12y-5)

12y(12y-5)-5(12y-5)

144y²-60y-60y+25

144y²-120y+25

The value of 3 over one thirds minus one forth is 8 3/4.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, 3 over one thirds minus one forth. This will be:

= 3 /(1/3) - 1/4

= (3 × 3) - 1/4

= 9 - 1/4

= 8 3/4

The value is 8 3/4.

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The volume of the cylindrical water tank that has a length of 20 feet and a radius of 12 feet is about 9,048 cubic feet.

The correct option is option d;

d. 9,048

The volume of a solid indicates the amount of space the solid takes at a location.

The formula for finding the volume of the cylindrical tank is presented as follows;

V = π·r²·L

Where;

r = The radius of the tank

L = The length of the tank

From a similar question on the website, we have;

The length of the tank, L = 20 feet

Therefore;

The volume of the tank, V = π × 12² × 20 ≈ 9048

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8 more than s stripes:

equation: s + 8

They needed 4 more games to have same number of hits which is 26 hits

The answer to the common factor is?

Factors that are shared by two or more numbers are referred to as common factors in mathematics. To put it another way, a common factor is a number that will divide a group of two or more numbers exactly.

Given That:
Player 1 average hits = 2 hit per game
Player 1 Total hits this season = 18
Player 1 total game this season = 18/2 = 9

Player 2 average hits = 1 hit per game
Player 2 Total hits this season = 22
Player 2 total game this season = 22/1 = 22

If we add 4 game for each player than

Player 1 total hits = 18 + 4(2) = 26

Player 2 total hits = 22 + 4 = 26

Hence they needed 4 more games to have same number of hits which is 26 hits

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The population of Springfield in 2046, given the growth rate, can be found to be  251, 940 people

When given the starting population, and the population growth rate, the growth in population can be found by the formula:

= Starting population x ( 1 + population growth rate ) ^ number of years

The number of years would be:
= 2046 - 2019

= 27 years

The population in 2046 would be:

= 202, 628 x ( 1 + 0.81 % ) ²⁷

= 251, 940 people

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3x + 4 is the expression that gives the same value as (3x-2x) + 2(2x-x) + 4

The Given Expression is : (3x-2x) + 2(2x-x) + 4

⇒ 1(x) + 2(x) + 4

⇒ x + 2x + 4

⇒ 3x + 4

Hence, the equivalent expression for the given expression is 3x + 4.

An Expression is composed only of variables, operators (or) symbols, and numbers. There will be no equality(=) sign in an expression.

If there is an equality(=) sign, then it is called an equation.

The value of given expression at x = 2 is :

(3(2) - 2(2)) + 2(2(2) - 2) + 4

= (6 - 4) + 2(4 - 2) + 4

= 2 + 2(2) + 4

= 2 + 4 + 4

= 10

The value of the equivalent expression is :

3(2) + 4

= 6 + 4

= 10

Both the expressions gave the same value.

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