If f(x) = 5x3 – 2 and g(x) = x+1, find (f - g)(x).

Answer:

$1,466.23 Will be your answer mate !!!!!!

Step-by-step explanation:

The present value is calculated by discounting each of the cash flows to the present therefore if we assume no salvage value:  

PV = $100 / 1.08 + $100 / 1.08^2 + $100 / 1.08^3 + $200 / 1.08^4 + $300 / 1.08^5 + $600 / 1.08^6  

PV = $923.98  

Technically, as we have assumed there are no salvage value then in the future value will be zero. If you are asking how much remains in the investment. If you are asking how much the investment has yielded, keep in mind that the cash flows are not by definition reinvested so the time value of those cash flows can't be accounted for. If you do not account for the time value of those cash flows then the future value is just:  

$100 * 3 + $200 + $300 + $500 = $1,300  

However if you use the 8% per annum effective rate as a discount rate to take into consideration the time value of the money which is basically saying that you can reinvest the cash flows at 8% per annum effective then the future value would be:  

$100 * 1.08^5 + $100 * 1.08^4 + $100 * 1.08^3 + $200 * 1.08^2 + $300 * 1.08 + 500 = $1,466.23

you'll get your answer as : $1,466.23 !

Final answer:

The present value of the investment with varying cash flows and an 8% discount rate is $943.28. The future value, assuming reinvestment at an 8% interest rate until the end of Year 6, is $1,466.23.

Explanation:

To calculate the present value of the investment with varying cash flows and an 8% discount rate (interest rate), we discount each cash flow to its present value using the formula [tex]PV = FV / (1 + r)^t,[/tex]where PV is present value, FV is future value, r is the annual interest rate, and t is the number of years until the payment.

Year 1:  [tex]\$100 / (1 + 0.08)^1 = $92.59[/tex]

[tex]Year 2: \$100 / (1 + 0.08)^2 = $85.73 \\Year 3: \$100 / (1 + 0.08)^3 = $79.38 \\Year 4: \$200 / (1 + 0.08)^4 = $150.26 \\Year 5: \$300 / (1 + 0.08)^5 = $220.08 \\Year 6: \$500 / (1 + 0.08)^6 = $315.24 \\[/tex]

The sum of these values is the total present value of the investment, which equals $943.28.

For the future value, we grow each cash flow by the interest rate for the remaining period it would be invested until the end of Year 6, since payments are made at the end of each year.

[tex]Year 1: \$100 * (1 + 0.08)^5 = $146.93 \\Year 2: \$100 * (1 + 0.08)^4 = $136.05 \\Year 3: \$100 * (1 + 0.08)^3 = $125.97 \\Year 4: \$200 * (1 + 0.08)^2 = $233.28 \\Year 5: \$300 * (1 + 0.08)^1 = $324.00 \\[/tex]

Year 6: $500 = $500.00

By adding all future values, the total future value of the investment is $1,466.23.

Answer:

8,000,000

Step-by-step explanation:

all you have to do is multiply the 4*2 then add the missing 0's for example so its 8 then add the six zeros behind the 8

The value of the multiplication is 8, 000 , 000

First, we need to know that multiplication is an arithmetic operation.

Also, PEDMAS is the mathematical acronym used to represent the different arithmetic operations.

They are given as;

From the information given, we have that;

2,000 times 4,000

This is represented as;

2000 ×4000

Multiply the values

8, 000 , 000

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Juan needs to sell 18 fruit baskets and 2 pencils to achieve his goal.

The number of items = (total price for the items)/(each price of the required item)

Given that,

Price of a fruit basket = $16.50

Price of a pencil = $1.50

His goal is to achieve $300

So,

The number of fruit baskets required to sell by the Juan = 300.00/16.50

⇒ 18.18 (rounding off)

⇒ 18 fruit baskets

And

Then 2 more pencils are to be sold to achieve his goal.

Therefore, 18 fruit baskets need to be sold by Juan.

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Answer:

A. 40 mph

Step-by-step explanation:

A bird flies 2/3 miles per minute. You are trying to solve miles per hour.

Note that there are 60 minutes in an hour. Multiply 2/3 with 60:

2/3 x 60 = (2 * 60)/3 = (120)/3 = 40

A. 40 mph is your answer.

~

Answer:

k(x)=5x+2

k(4)=5(4) +2 =22

k(1)= 5(1) +2 =7

k(4) - k(1) = 22 - 7 = 15

The answer is:

A). 15

Answer:

145,146,147

Step-by-step explanation:

Let x be the first number

x+1 is the next number

x+1 +1 is the next number

The sum of these three number is

x + x+1 + (x+1+1) = 438

Combine like terms

3x +3 = 438

Subtract 3 from each side

3x+3-3 = 438-3

3x= 435

Divide by 3

3x/3=435/3

x = 145

x+1 =146

x+1+1 = 147

Answer:

10/60 as a decimal is:

0.166666667

Step-by-step explanation:

To get 10/60 converted to decimal, you simply divide 10 by 60.

Please mark brainliest and have a great day!

Answer:

0.166666666666667

Step-by-step explanation:

Answer:

The product of  [tex](x^2+3x+1)(x^2+x+2)[/tex] is [tex]x^3+4x^3+6x^2+7x+2[/tex]

Step-by-step explanation:

We need to find the product of [tex](x^2+3x+1)(x^2+x+2)[/tex]

We need to multiply the first term with the second term.

Multiplying:

[tex](x^2+3x+1)(x^2+x+2)\\=x^2(x^2+x+2)+3x(x^2+x+2)+1(x^2+x+2)\\=x^4+x^3+2x^2+3x^3+3x^2+6x+x^2+x+2\\Adding\,\,like\,\,terms\,\,\\=x^4+x^3+3x^3+2x^2+3x^2+x^2+6x+x+2\\=x^3+4x^3+6x^2+7x+2\\[/tex]

So, the product of  [tex](x^2+3x+1)(x^2+x+2)[/tex] is [tex]x^3+4x^3+6x^2+7x+2[/tex]

Solution:

A

Step-by-step explanation:

It's y =-2x³

Hope it helps you..☺

The graph of y = x³ is transformed as y = -6x³.

It's a unique type of connection with a predetermined domain and range, and every value in the domain exists associated with precisely one value in the range, according to the function.

The given equation exists, y = x³

The graph of y = x³ describes the transformed function.

Therefore, the correct answer is option B. y = -6x³.

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Answer:

12

Step-by-step explanation:

Volume of cylinder is pi*r^2*h    (this is equal to 540pi in this case)

So we have 540pi=pi*r^2*h  

this means that 540=r^2*h   (I just divided both sides by pi since both sides were being multiplied by pi)

The height,h, is 15 so plug in 540=r^2*15

Divide both sides by 15 giving 540/15=r^2

So r^2=36

So r=6

The diameter,d, is twice the radius, r.

So d=2(6)=12

Answer:

b. 12

Step-by-step explanation:

The volume of a cylinder is

[tex]\pi {r}^{2} h[/tex]

Let us compose an equality and solve for the radius.

540pi = pi × r^2 × 15.

Divide both sides of the equation by 15pi.

r^2 = 36

r = +/- 6.

Length cannot be negative, so r = 6.

diameter = 2 × r. In this case,

d = 2 × 6 = 12.

The diameter is 12 ft.

Answer:

0.3.

Step-by-step explanation:

The residual of a data point is equal to the observed value minus the predicted value. (Stat Trek)

What's the predicted y-value of a point with [tex]x = 5[/tex] based on this best-fit regression line?

[tex]y = -0.2\times 5 + 1.7 = 0.7[/tex].

The observed value here is [tex]y = 1[/tex]. As a result, the residual for this point is [tex]1 - 0.7 = 0.3[/tex].

Answer: 0.2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

edge 2021

The polynomial that is in standard form is 13x^5 + 11x - 6x^2 + 5.

The polynomial that is in standard form is 13x5 + 11x - 6x2 + 5. In standard form, the polynomial is arranged by descending order of exponents. The terms are written with the coefficient in front of each variable.

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Answer:$0.08 per pen

Step-by-step explanation:

$1.60/20=0.08

Hope this helps :)

Answer:

x=-1 or (-1,0)

Step-by-step explanation:

(-4 +- sqrt(4^2-4(5)(-1)))/2*5

(-4 +- sqrt(16+20))/10

(-4 +- sqrt(36))/10

(-4 +- 6)/10

x= (-4+6)/10 = 2/10 = 1/5 = 0.2

x= (-4-6)/10 = -10/10 = -1

x-intercepts: (0.2,0), (-1,0)

SA = (l x w x 2) + (l x h x 2) + (w x h x 2)

SA = (6 x 4 x 2) + (6 x 2 x 2) + (4 x 2 x 2)

SA = 48 + 24 + 16

SA = 88

The answer is 88 square units.

Answer:

A. 88 square units.

Step-by-step explanation:

Volume formula:

 ↓

[tex]V=L*W*H[/tex]

[tex]6*4*2=48[/tex]

[tex]L*H*2[/tex]

[tex]6*2*2=24[/tex]

[tex]W*H*2[/tex]

[tex]4*2*2=16[/tex]

Add the numbers from left to right.

48+24=72

72+16=88

88 is the correct answer.

Explicit formula [tex]a_{n} =8n+15[/tex]

Recursive formula [tex]\left \{ {{a_{1} =23} \atop {a_{n}=a_{n-1}+8 }} \right.[/tex]

To solve this problem we have to use an arithmetic sequence. The cost of renting a kayak for 1 hour is $23, each additional hour is $8 more. So, the first element of the secuence will be 23 for one hour, then each addittional hour will be 23 + 8, making the secuence:

{23, 31, 39, 47, 55,.....,n}

Writing a recursive formula of the form [tex]a_{n} =a_{n-1} +d[/tex] where [tex]a_{n}[/tex] is the nth term, n the number of terms, and d the common difference in the secuence.

The common difference of the secuence {23, 31, 39, 47, 55,.....,n}. So, the first term is [tex]a_{1} =23[/tex], and the common diffenece is d = 8 which is the difference between each term.

[tex]\left \{ {{a_{1} =23} \atop {a_{n} =a_{n-1}+8 }} \right.[/tex]

Writing a explicit formula of the form [tex]a_{n} =a_{1} +d(n-1)[/tex] where where [tex]a_{n}[/tex] is the nth term, n the number of terms, [tex]a_{1}[/tex] the first term of the secuence, and d the common difference in the secuence.

With [tex]a_{1}=23[/tex], and d = 8:

[tex]a_{n} =23+8(n-1)[/tex]

[tex]a_{n} =23+8n-8[/tex]

[tex]a_{n} =8n+15[/tex]

Answer:

[(-15, 21), (-6, 12).(-1, 7)}

Step-by-step explanation:

we have

x+y=6

Find the values of y for XE (-15, -6, -1)

so

For x=-15

-15+y=6 --->y=21

therefore

a solution is the point (-15,21)

For x=-6

-6+y=6 --->y=12

therefore

a solution is the point (-6,12)

For x=-1

-1+y=6 --->y=7

therefore

a solution is the point (-1,7)

The set of ordered pairs that are solutions is

[(-15, 21), (-6, 12).(-1, 7)}

Final answer:

The correct set of ordered pairs, which are the solutions to the equation x + y = 6 given x in {-15, -6, -1}, is {(-15, 21), (-6, 12), (-1, 7)}.

Explanation:

To determine which set of ordered pairs are solutions to the given equation x + y = 6, we need to plug the x-values into the equation and solve for y.

The correct set of ordered pairs is therefore {(-15, 21), (-6, 12), (-1, 7)}.

Step-by-step explanation:

Let's do the volume first. Volume of any prism is the area of the base times the height.

V = Ah

The base is a large square with a smaller rectangle cut from the corner, so its area is:

A = (14)(14) - (7)(10)

A = 126

So the volume is:

V = (126)(6)

V = 756 m^3

Now the surface area of a prism is the area of the bases plus the base perimeter times the height:

S = 2A + Ph

We already found the area of the base. Now we just have to add the perimeter times height.

S = 2(126) + (14 + 14 +7 + 10 + 7)(6)

S = 480 m^2

Final answer:

To solve the equation 9x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b, isolate x on one side of the equation, subtract 4 from both sides, then divide both sides by 9.

Explanation:

To solve the equation 9x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b, we need to isolate x on one side of the equation. Here's how to do it:

Therefore, the solution to the equation is x = 7/9.

Step one: 3x+4y=20; 10=40-3y

Step two: 3y=40-10, so y=(40-10)/3=10

Step three: 3x+4*10=20

Step four: 3x=20-40=-20, so x=-20/3=-6.66666...~ -6.67

Answer:

f(2) = -4

Step-by-step explanation:

Plug in 2 for x:

f(x) = 4x - 12

f(2) = 4(2) - 12

Remember to follow PEMDAS. (PEMDAS = Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction) PEMDAS is what you follow to solve these questions.

First, Multiply:

f(2) = 4(2) - 12

f(2) = (4 * 2) - 12

f(2) = 8 - 12

Next, subtract:

f(2) = 8 - 12

f(2) = -4

f(2) = -4 is your answer.

~

Answer:

-4

Step-by-step explanation:

put 2 into all the x values in the equation.

4(2) - 12 = -4

Answer:

So, the inverse of function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex] is [tex]f^{-1}(x)= 4x^2-3[/tex]

Step-by-step explanation:

We need to find the inverse of the given function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex]

To find the inverse we replace f(x) with y

[tex]y = \frac{-1}{2} \sqrt{x+3}[/tex]

Now, replacing x with y and y with x

[tex]x = \frac{-1}{2} \sqrt{y+3}[/tex]

Now, we will find the value of y in the above equation

Multiplying both sides by -2

[tex]-2x = \sqrt{y+3}[/tex]

Taking square on both sides

[tex](-2x)^2 = (\sqrt{y+3})^2[/tex]

[tex]4x^2 = y+3[/tex]  

Finding value of y

[tex]y = 4x^2-3[/tex]

Replacing y with f⁻¹(x)

[tex]f⁻¹(x)= 4x^2-3[/tex]

So, the inverse of function

[tex]f(x) = \frac{-1}{2} \sqrt{x+3}[/tex] is [tex]f^{-1}(x)= 4x^2-3[/tex]

ANSWER

[tex]f^{ - 1} (x) =4 {x}^{2}- 3[/tex]

EXPLANATION

A function will have an inverse if and only if it is a one-to-one function.

The given function is

[tex]f(x) = - \frac{1}{2} \sqrt{x + 3} \: \: where \: \: x \geqslant - 3 [/tex]

To find the inverse of this function, we let

[tex]y=- \frac{1}{2} \sqrt{x + 3}[/tex]

Next, we interchange x and y to get,

[tex]x=- \frac{1}{2} \sqrt{y+ 3}[/tex]

We now solve for y.

We must clear the fraction by multiplying through with -2 to get;

[tex] - 2x = \sqrt{y + 3} [/tex]

Square both sides of the equation to get:

[tex](- 2x)^{2} = (\sqrt{y+ 3}) ^{2} [/tex]

[tex]4x^{2} = y + 3[/tex]

Add -3 to both sides

[tex]4 {x}^{2} - 3 = y[/tex]

Or

[tex]y = 4 {x}^{2}- 3[/tex]

This implies that,

[tex]f^{ - 1} (x) =4 {x}^{2}- 3[/tex]

This is valid if and only if

[tex]x \geqslant - 3[/tex]

Answer:

y = -2x - 6

Step-by-step explanation:

4y = -8x - 24

y = -2x - 6

Answer:

y = -6 - 2x

Step-by-step explanation:

8x + 4y = -24

4y = -24 - 8x

y = (-24 - 8x) / 4

  = -[tex]\frac{24}{4}[/tex] - [tex]\frac{8}{4}[/tex]

  = -6 - 2x (ans)  or -(6 + 2x)

Answer:

The ratio of their surface areas is 4:49

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

In this problem the scale factor is equal to the ratio 2:7

and

Remember that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

therefore

In this problem the ratio of their surface areas is (2:7)^2 = 4:49

The ratio of their surface areas is,

⇒ 4 : 49

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

\

We know that;

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor.

In this problem the scale factor is equal to the ratio 2/7,

Hence, If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

therefore,

In this problem the ratio of their surface areas is ,

⇒ (2 / 7)²

⇒ 4 / 49

⇒ 4 : 49

Thus, The ratio of their surface areas is,

⇒ 4 : 49

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Answer:

[tex]x=3\\y=-1\\\\(3,-1)[/tex]

Step-by-step explanation:

We have the following system of equations

[tex]4x-3y=15\\2x+2y=4[/tex]

To solve the system of equations multiply the second equation by -2 and add it to the first equation

[tex]-2*(2x+2y)=-2*4[/tex]

[tex]-4x - 4y=-8\\4x-3y=15[/tex]

-------------------

[tex]-7y = 7\\y=-1[/tex]

Now substitute the value of y in any of the two equations and solve for the variable x

[tex]4x-3(-1)=15[/tex]

[tex]4x+3=15[/tex]

[tex]4x=15-3[/tex]

[tex]4x=12[/tex]

[tex]x=\frac{12}{4}[/tex]

[tex]x=3[/tex]

Finally the solution is:

(3, -1)

Answer:

B

Step-by-step explanation:

24 times 4 is 96 legs

196-96=100 divided by 2 is 50 humans

50 plus 24 is 74

Answer:

B 24 horses and 50 humans

Step-by-step explanation:

Let x = humans

y = horses

Each horse and human has 1 head, for a total of 74 heads

x+y = 74

Each human has 2 leags, 2x  and each horse has 4 legs, 4y for a total of 196 legs

2x+4y = 196

We have a system of equations

x+y = 74

2x+4y = 196

Multiply the first equation by -2

-2(x+y) = -2*74

-2x -2y - 154

Add the modified first equation to the second equation

-2x-2y = -154

2x+4y = 196

-----------------------

2y = 48

Divide by 2

2y/2 = 48/2

y = 24

There are 24 horses

x+y = 74

We know there are 24 horses

x+24 = 74

x+24-24 = 74-24

x=50

There are 50 humans

Range is all the y values in this case that would be...

{-1, 4, 11, 13}

Keep in mind that there are different ways to show range. The one I showed it just one of them

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where

[tex](h, k)[/tex] - center

[tex]r[/tex] - radius

We have:

[tex](x-7)^2+(y-10)^2=4[/tex]

Therefore

[tex]h=7,\ k=10,\ r^2=4\to r=\sqrt4\to r=2[/tex]

The standard form of the equation of a circle is

(x - h)2 + (y - k)2 = r2

Where (h, k) is the center,

r is the radius

(x - 7)2 + (y - 10)2 = 4 [Given]

This is rewritten as (x - 7)2 + (y - 10)2 = 22

Comparing it with the standard form

(h, k) = (7, 10)

The radius of the circle r = 2 units

The radius of a circle is  Option A. 2 units

The diameter is a straight line that passes through the center of the circle. The radius is half of the diameter. It starts from a point on the circle, and ends at the center of the circle.

A straight line extending from the center of a circle or sphere to the circumference or surface: The radius of a circle is half the diameter. the length of such a line.

The radius of a circle is the distance from the center of the circle to any point on its circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.

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Answer:

y = 1/4 x - 1.

Step-by-step explanation:

The slope (from the 2 given points) =  (0 - -1) / (4 - 0) = 1/4.

The y-intercept is at y = -1, so the equation is:

y = 1/4 x - 1.