How much should you invest each month in order to have $800,000 if your rate of return is 2.8% compounded monthly and you want to achieve your goal in 40 years? How much interest will you earn? How much should you invest each month in order to have $800,000 if you want to achieve your goal in 20 years? If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?​

The three statements about his solution that are true include the following:

1. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2. He did not multiply the numerator and denominator by the correct number to equal 1,500.

5. He should have multiplied the numerator and denominator by 75, not 30,  because 20 × 75 = 1,500.

Based on the information provided, a mathematical expression which models the number of songs of each genre on Josiah's MP3 player to be 300 songs:

here, we have,

10/20 = x/1500

Multiplying the mathematical expression by 75, we have the following:

75 × (10/20) = x/1,500

750/1500 = x/1500

1,500x = (750 × 1,500)

x = (750 × 1,500)/1,500

x = 750.

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Answer:

Step-by-step explanation:  https://flexbooks.ck12.org/cbook/ck-12-middle-school-math-concepts-grade-6/section/6.15/primary/lesson/elapsed-time-msm6/

The system of equations are solved and the number of performers for the show A is 10,034

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as T

Now , the value of T is

The total number of performers in the two shows T = 16,756

A + B = 16,756

The number of performers in show A = 3312 + number of performers in show B

Substituting the values in the equation , we get

A = B + 3,312

On simplifying the equation , we get

A + A - 3,312 = 16,756

Subtracting 3,312 on both sides of the equation , we get

2A = 16,756 + 3,312

2A = 20,068

A = 10,034

Hence , the equation is A = 10,034

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The solution is Option D.

The derivative of the function is given by the equation f' ( x ) = -x / ( √5-x² )

In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately

Given data ,

Let the function be represented as f ( x )

Substituting the values in the equation , we get

f ( x ) = √ ( 5 - x² )

Now , the derivative of the function is f' ( x )

f' ( x ) = ( 1/2 ) 1 / √( 5 - x² ) ( d/dx ) ( -x² )

On simplifying the equation , we get

f' ( x ) = ( 1/2 ) 1 / √( 5 - x² ) ( -2x )

On further simplification , we get

f' ( x ) = ( -2x/2 ) 1 / √( 5 - x² )

f' ( x ) = -x / ( √5-x² )

Hence , the derivative of the function is f' ( x ) = -x / ( √5-x² )

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The length of segment AB is determined as 13 units.

The distance between two points is the length of the line segment that connects the two points in a plane.

here, we have,

The length of segment AB is the distance between point A and point B, which is calculated as follows;

|AB| = √[(x₂ - x₁)² + (y₂ - y₁)²]

where;

x₁ is the x - component of point A

x₂ is the x - component of point B

y₁ is the y - component of point A

y₂ is the y- component of the point B

|AB| = √[(x₂ - x₁)² + (y₂ - y₁)²]

|AB| = √[(-5 - 7)² + (5 - 10)²]

|AB| = √[144+25]

|AB| = 13 units

Thus, the length of segment AB is the distance between point A and B.

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The Canal's price/earnings ratio is 2.92.

To calculate Canal's price/earnings ratio, we need to find the earnings per share (EPS) first. The EPS can be calculated by dividing the net income by the weighted average number of common shares outstanding.

The weighted average number of common shares outstanding can be calculated as follows:

Weighted average number of common shares outstanding = Total number of common shares - Weighted average number of treasury shares

Weighted average number of common shares outstanding = 24,200 - 4,200 = 20,000

EPS = Net income / Weighted average number of common shares outstanding

EPS = $260,000 / 20,000 = $13

Finally, the price/earnings ratio can be calculated by dividing the market price per share by the EPS:

Price/earnings ratio = Market price per share / EPS

Price/earnings ratio = $38 / $13 = 2.92

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Answer:

There are two solutions:

[tex]\boxed{v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}}\\\\or\\\\\boxed{v = 1.3333.... \text{ and }v= 1.5}\\[/tex]

Step-by-step explanation:

The given equation is  :

[tex]\dfrac{2}{v-2}=-6\:+\:\dfrac {1}{v-1}\\\\[/tex]

Find the LCM of the denominators:

LCM = [tex]\left(v-2\right)\left(v-1\right)[/tex]

Multiply by LCM:
[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right)[/tex]

Simplify

[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right):\quad 2\left(v-1\right)[/tex]

[tex]\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right):\quad v-2[/tex]

So the equality becomes
[tex]2\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+v-2[/tex]

Expand the brackets:
[tex]2\left(v-1\right):\quad 2v-2[/tex]

[tex]\text {Right side becomes: }\\-6\left(v-2\right)\left(v-1\right)+v-2\\Expand \; \left(v-2\right)\left(v-1\right):\quad v^2-3v+2\\\\\text {Right side becomes}\\-6\left(v^2-3v+2\right) + v -2\\= -6v^2+6\cdot \:3v-6\cdot \:2 + v - 2\\\\\\= -6v^2+18v-12+v-2\\\\\text{Simplify}\\= -6v^2+19v-14\\\\\text{Left side}2(v-1= 2v-2\\\\\text{Finally we get}\\2v - 2 = 6v^2+19v-14\\\\[/tex]

Switch sides:
[tex]-6v^2+19v-14=2v-2[/tex]

Move 2 from right to left(sign changes)
[tex]-6v^2+19v-14 + 2 =2v\\\rightarrow -6v^2+19v-12=2v\\\\[/tex]

Move 2v to left side(sign changes)

[tex]-6v^2+19v-12-2v = 0\\\\\rightarrow -6v^2+17v-12=0\\\\[/tex]

This is a quadratic equation which can be solved with a quadratic equation calculator. I used a calculator to solve this:

The solutions are:
[tex]v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}\\\\\\\text{In decimal these would be}\\\\v = 1.3333.... \text{ and v}= 1.5\\[/tex]

The solution for the One-Variable Addition Equations is,

1: d = 0.6,  2:  k = 11,  and 3: y = 3.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given 1: d  + 3.2 = 6.3 - 2.5

subtract 3.2 from both sides

d = 6.3 - 2.5 - 3.2

d = 0.6

2: 25 + k + 4(1/4) = 37

divide 4/4 = 1

25 + k + 1 = 37

k = 37 - 26

k = 11

3: 4(1/2) + y = 10(1/2)

so 4/2 = 2 and 10/2 = 5

2 + y = 5

y = 3

Hence d  = 0.6, k = 11,  and y = 3.

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The solution of the inequality 3x < 13 is x < 4.33.

None of the given option is correct.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

3x < 13.

Simplifying,

x < 4.33

The graph is given in the attached image.

Therefore, the solution is x < 4.33.

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Answer:

see below

Step-by-step explanation:

60+75=135

BOC =180 -135 =45

DOE = BOA =60

AOE =180-DOE =120

The domain is the second option:

(2, 8]

For a function y = f(x), we define the domain as the set of the possible inputs for the function.

Here we have a piecewise function that is defined in the 3 regions:

2 < x  ≤ 4

4 < x < 8

x ≥ 8

So the domain is the set of any value larger than 2, and we can write that as:

(2, 8]

We end it at "8" becase is the last defined value and that is the only option that makes sense.

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Answer: It's the fourth option; f^-1(x)=x^3/125 -7

The area of a 7 by 10 grid would be 70 square units.

This is calculated by multiplying the length (7 units) by the width (10 units), resulting in 7 x 10 = 70.

The equation which models the product is, A = 6 x 8

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

Given that,

A area model,

which has 6  box in column arrangement and 8  box in row arrangement,

Suppose, each box has 1 unit square area

Now, area of a model can be written as,

Area = Number of box in column x Number of box in row

Number of box in column  = 6

Number of box in row = 8

Each box has 1 unit square area,

So,

A = 6 x 8

   = 48 unit square

Hence, it can be represented as, A = 6 x 8

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The cost of the book in Naira is N 24.99  

Mr. Awolowo needs to pay N 4165 at the post office.  

An exchange rate determines the value of one unit of currency in relation to another type of money. Which means exchanging the price from one currency to another currency.

People use the exchange rates when they want to travel abroad and It is necessary to convert cash into local currency in order to do purchases locally.

Here we have

The book costs £3. If the rate of exchange is £ 1 = N 8.33  

Cost of the book in Naira = 3 × N 8.33  

= N 24.99  

Mr Awolowo wants to send £500 to his brother in the United Kingdom  

As we know the rate of exchange, is £ 1 = N 8.33    

=>  £500 = 500 × 8.33  = N 4165  

Therefore,

The cost of the book in Naira is N 24.99  

Mr. Awolowo needs to pay N 4165 at the post office.  

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The required number of Barnes & Noble stores in 2009 is 725.28.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

To determine the number of Barnes & Noble stores in 2009, we need to evaluate the piecewise function for t = 2009.

Since 2009 is between the interval 6 ≤ t < 12, the number of stores is given by the first piece of the function:

y = -3.692 × x² + 65.28 × x + 437.30

put x = 9 for the year 2009

y = -3.692 × 9² + 65.28 × 9 + 437.30 = 725.28

So, there were 725.28 Barnes & Noble stores in 2009.

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The eigen values of matrix A  [tex]\left[\begin{array}{ccc}1&2&1\\0&2&1\\0&0&3\end{array}\right][/tex] are respectively, 1, 2, 3

In mathematics, the eigen values are characteristic roots of the equation

| A - λI |,

where,  A is matrix and λ is eigen value of the matrix

Properties of matrix,

1.  Sum of diagonal elements = Sum of eigen values

2. Determinant of matrix  = Product of eigen values

Given that,

Matrix A =    [tex]\left[\begin{array}{ccc}1&2&1\\0&2&1\\0&0&3\end{array}\right][/tex]

The eigen values of A = ?

It is known that,

For the upper and lower triangular matrix, eigen values of the matrix are diagonal elements,

given matrix is, upper triangular,

Diagonal elements are  1, 2, 3

So, The eigen values will be 1, 2, 3

Thus, the eigen values are  1, 2, 3

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Answer:

a) C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)
b) 39.22
c)  143.69

Step-by-step explanation:

(a) We can write a piecewise function to describe the cost C(n) of n CDs purchased:

C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)

(b) The cost of 53 CDs is:

C(53) = 0.74 * min(53, 100) + 0.69 * max(53 - 100, 0) = 0.74 * 53 = 39.22

(c) The cost for 201 CDs is:

C(201) = 0.74 * min(201, 100) + 0.69 * max(201 - 100, 0) = 0.74 * 100 + 0.69 * 101 = 74 + 69.69 = 143.69

Answer:

The range of acceptable length is between 35.28 inches and 36.72 inches.

To calculate the range of acceptable length:

Lower bound: 36 in. - (36 in. x 0.05) = 35.28 in.

Upper bound: 36 in. + (36 in. x 0.05) = 36.72 in.

The linear function for the population in t years after 2000 is given as follows:

P(t) = 2200t + 44000.

The estimate for the population in 2010 is given as follows:

66,000.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Two points for the function are given as follows:

(5, 55000) and (8, 61600).

Dividing the change in the output by the change in the input, the slope m is given as follows:

m = (61600 - 55000)/(8 - 5)

m = 2200.

Hence:

P(t) = 2200t + b.

When x = 5, y = 55000, hence the intercept b is given as follows:

55000 = 2200(5) + b

b = 55000 - 2200(5)

b = 44000.

Hence the function is:

P(t) = 2200t + 44000.

2010 is 10 years after 2000, hence the estimate is given as follows:

P(10) = 2200(10) + 40000

P(10) = 66,000.

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The maximum value of the function z = 5x + 3y subjected to the constraints is given as follows:

48.1665.

The function for this problem is defined as follows:

z = 5x + 3y.

The constraints are given as follows:

x has a higher multiplier than y, hence the value of y should be minimized to obtain the maximum value, hence:

y = 3.

Then the value of x is obtained as follows:

6x + 7(3) = 68

6x = 47

x = 7.8333.

Then the maximum value of the function is given as follows:

z = 5(7.8333) + 3(3)

z = 48.1665.

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Answer:

Step-by-step explanation: A rectangle's perimeter formula is P=2(l+w), therefore,

P=2(21.9+18.3)

P=2(40,2)

P=80,4

You will need 80,4 inches of fondant to cover all the edges of the cake

Answer:

Below

Step-by-step explanation:

See diagram

.158384 = height/x      <======   x = height/.15838

.061162 = height /(11+x)    <====sub in x from above into here

.061162 = height /(11+height/.158384)      solve for height

.672789 + .386163 height = height

height = 1.1 mi high

From the audio, what is inferred from the fairy's action is that she was appreciative. The Option A is correct.

A fairy tale is a story, typically intended for children, that features fantastic and wondrous characters such as elves, goblins, wizards, and even, but not always, fairies. The term "fairy" tale appears to refer to a story's fantastic and magical setting or magical influences, rather than the presence of a fairy character within that story.

Fairy tales are frequently traditional; many were passed down from storyteller to storyteller before being written down in books. Examples of Fairy Tale includes Snow White, Cinderella, Rip Van Winkle, The Twelve Dancing Princesses, Rumpelstiltskin, Thumbelina

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Answer: She was vengeful

Step-by-step explanation:

The audio states that the other fairies were giving the princess positive spells while a fairy that wasn't invited to the party casted an evil spell on the princess, making her sleep for a 100 years. (It's based on the sleeping beauty story)

Answer: a) To make apple crumble for 16 people, Farid will need to double the ingredients as compared to serving 8 people. Hence, he will need:

700g * 2 = 1400g of apples

240g * 2 = 480g of sugar

180g * 2 = 360g of flour

So, Farid needs 360g of flour to make apple crumble for 16 people.

b) To make apple crumble for 2 people, Amal will need to use 1/8 of the ingredients as compared to serving 8 people. Hence, she will need:

700g / 8 = 87.5g of apples

240g / 8 = 30g of sugar

So, Amal needs 30g of sugar to make apple crumble for 2 people.

c) To make apple crumble for 6 people, Shahina will need to adjust the ingredients based on the apples she has available. To calculate the amount of sugar and flour required, she can use the ratio of sugar and flour to apples as follows:

Sugar: 700g / 8 = 87.5g per serving * 6 people = 525g

Flour: 700g / 8 = 87.5g per serving * 6 people = 525g

Since Shahina has plenty of the other ingredients, including butter, she can make apple crumble for 6 people with the amount of apples she has available. So, the answer is Yes, Shahina can make apple crumble for 6 people.

Step-by-step explanation:

The value of the given expression, -50 + 5/13p, when p = -26 is -60

From the question, we are to evaluate the given expression for the given value of p

The given expression is

-50 + 5/13p

and

The given value of p is p = - 26

Substitute the given value of p into the given expression

That is,

-50 + 5/13p

When p = -26, the expression becomes

-50 + 5/13(-26)

Simplify

-50 + 5(-2)

-50 - 10

= - 60

Hence, the value of the expression is -60

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Answer:

Step-by-step explanation:

If 3<y<7 then,

0 < 14-2y < 8

14 - 2(3) = 8

14 - 2(7) = 0