Help pls! The question is in the the photo.

For the function ƒ(x) = 2 (x − 10)² + 6 then F⁻¹ = [tex]\frac{x- 6}{2}[/tex] + 10 is the inverse of the given functions.

y = [tex]\frac{x - 6}{2}[/tex] + 10

F⁻¹ = [tex]\frac{x -6 }{2}[/tex] + 10

A function that is capable of reversing into another function is referred to as an inverse function or anti function. Simply put, if a function is denoted by "f" or "F," then the inverse function is denoted by "f-1" or "F-1." The inverse function returns the original value for which a function provided the output.

If any function "f" takes x to y, then the inverse of "f" will take y to x. A function that consists of its inverse retrieves the original value when considering functions, where f and g are inverses, and f(g(x)) = g(f(x)) = x. Then, the opposite of f(x) is g(y) = (y-5)/2 = x.

The equation of the inverse relation can be obtained by substituting every y in the equation for every x in the equation that describes the relation between the variables x and y.

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Thomas invested $3,000 into a bank account with a 5% interest return compounded annually. then the following equations indicates the total amount of money 3000(1.05)^1/16

Thomas invested $3,000 into a bank account with a 5% return compounded annually.

A: represents the current balance or compound amount in the account.

P: represents the principal (the original amount deposited).

R: annual interest rate (in decimal form).N: the number of times per year that interest is compounded .T: time in years the money has been invested.

The formula of interest is A=P (1+r)ⁿ

A=Final amount  

P= Principal ( deposit invested)  

r= interest rate

n= time

So,  in this case

P=$3,000

r= 5% or 0.05

n=1/ 16

Replacing

A=3000(1+0.05)^1/16

A=3000( 1.05)^1/16

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An equation that represents the number of miles, m, Enrique walks in w weeks will be N = 32T.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that every week, Enrique walks one mile each day for 4 days a week. He can usually walk 1 mile in about 14 to 16 minutes. Estimate the number of minutes Enrique will spend walking over an 8-week period.

The expression for the total time will be calculated as:-

N = 32 x T

Here, T is the time in minutes for running per mile.

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The missing value in the solution to the equation is 4. The value of x is 4 and y is -6 which is (4, -6).

A solution to an equation is a value or values that make the equation true. For example, if the equation is x + 3 = 7, then the solution to the equation would be x = 4.

To solve an equation, you must use a combination of addition, subtraction, multiplication, division, and algebraic manipulations to isolate the unknown variable. For instance, to solve the equation x + 3 = 7, you would subtract 3 from both sides of the equation to find x = 4.

It is important to note that an equation may have more than one solution. For example, the equation x2 + 4 = 0 has two solutions, x = 2 and x = -2.

In some cases, equations may not have a solution. This happens when the equation is not true for any value of the unknown variable. For example, the equation 0 = 1 is not true for any value of x, so it does not have a solution.

In summary, a solution to an equation is a value or values that make the equation true. To solve an equation, you must use a combination of addition, subtraction, multiplication, division, and algebraic manipulations to isolate the unknown variable. An equation may have multiple solutions or no solution at all.

The given equation is 4x + y = 10.

We have the value of y is -6,

To find the value of x, using the equation 4x + y = 10

4x - 6 = 10

4x = 10 +6

4x = 16

x = 4

The missing value in solution is 4.

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Answer:60 percent

Step-by-step explanation:

Step 1) 72 = 120% × Y

Step 2) 72 = 120/100× Y

Multiplying both sides by 100 and dividing both sides of the equation by 120 we will arrive at:

Step 3) Y = 72 × 100/120

Step 4) Y = 72 × 100 ÷ 120

Step 5) Y = 60

The word used incorrectly in the sentence is "envelopes".

The word used incorrectly in the sentence is "envelopes". The comment should be "envelopes" instead. This is because "envelopes" is a plural noun, referring to more than one envelope. The apostrophe in "envelopes" implies possession, indicating that the envelopes belong to someone or something, but it is not necessary for this context.

Hence, the correct sentence should be "The mailperson's job is to put the envelopes in every mailbox on the block."

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Answer:

it analyses how citizenship was different in the past

Answer:

82

Step-by-step explanation:

average class score=total number of test scores/number of test scores

sum up the scores 79+82+85+91+97+73+88+87+85+92+90+85+86+91+94+85+92

=1482÷18=82.33333

=82

Correlation: A correlation is a statement that suggests there is a relationship between two variables, where a change in one variable tends to follow or be associated with a change in another variable.

A correlation is a statement that suggests there is a relationship between two variables. It does not necessarily mean that a change in one variable will cause a change in the other variable, but that a change in one tends to follow or be associated with a change in the other. For example, a correlation could be made between the amount of rainfall a region receives and the number of plants that are able to grow there. If the rainfall increases, then the number of plants that can grow in the region is likely to increase as well. A correlation can be either positive or negative, with a positive correlation meaning that an increase in one variable will likely result in an increase in the other, and a negative correlation meaning that an increase in one variable will likely result in a decrease in the other. Correlation can be used to make predictions, but should not be confused with causation, as correlation does not necessarily imply causation.

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The complete question: which of the following refers to a statement that  there is a relationship between two variables that can change in one variable tends to follow or be associated with a change in another variable?

B and E are true.The regression output can be used to determine whether there is a relationship between Red Sox away games and daily revenue.

The output can also be used to calculate the average daily revenue for each scenario.

For the scenario where the Red Sox do not play away, the output will give the average daily revenue, which is $1,768.32. So, statement A is true.

For the scenario where the Red Sox play away, the output will give the average daily revenue, which is $2,264.57. So, statement B is true.

For the scenario where the Red Sox do not play away, the output will also give the average daily revenue, which is $1,272.07. So, statement D is false.

Finally, the output can be used to calculate the difference between the average daily revenue when the Red Sox play away and when they do not, which is $496.25. So, statement E is true.

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The Equation of the line which has a slope of 1/5 and passes through (-10,4) will be  [tex]y = \frac{1}{5} x + 6[/tex] .

Given, We have the slope of the line = 1/5 and a  point (-10,4) though which the line passes. We know that the form of a linear line is y=mx + c (slope intercept form) where m is the gradient/slope of the line and c is the point where it intercepts the y axis on the graph. We can directly put the value slope in the place of m.

To find C , we can put the coordinates of the given point in the equation to solve for C. Therefore :

⇒ y = mx + c

⇒y =  1/5 x + c

⇒4 = 1/5 x (-10) + c

⇒4 = -2 + c

⇒ 4 +2 = c

⇒c =  6

Putting all the values in equation gives us the linear equation of the line :  [tex]y = \frac{1}{5} x + 6[/tex]

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The complete question is :

What is the locus/ linear equation/ equation of the line that has a slope of 1/5 and passes through coordinates (-10,4)?

The value of [tex]P$$(2 < x < 10)$[/tex] is 0.5350

As per the Function, [tex]$P(x < x)=1-e^{-m x}$[/tex]

Where [tex]$x \sim E x p(0.2)$[/tex]

Therefore, [tex]$m=0.2$[/tex]

[tex]$$P(2 < x < 10)=P(x < 10)-P(x < 2)$$[/tex]

Applying all data

[tex]& \mathrm{P}\left(2 < \mathrm{x} < 10=\left(1-e^{0.2 \times 10}\right)-\left(1-e^{0.2 \times 2}\right)\right. \\[/tex]

=0.6703-0.1353=0.5350

The complete question is,

A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be

modelled by the following distribution: X-Exp(0.2)

Find [tex]$P(2 < x < 10)$[/tex].

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Answer: Sorry!

Step-by-step explanation:

Hello! I can help you if you can add the photo and fix the typos.  

For a family of linear functions with slope 2, the equation is y = 2x + b, where b is the y-intercept. For a family of linear functions such that f(2) = 1, the equation is y = x + b, where b is the y-intercept. Both families of linear functions have the same equation, y = x + b, and all functions belonging to both families have a slope of 1 and a y-intercept of b.

(a) The equation for the family of linear functions with slope 2 is y = 2x + b, where b is the y-intercept. To sketch several members of the family, plot several points (x, y) with the equation, then connect the points to form a line.

(b) The equation for the family of linear functions such that f(2) = 1 is y = x + b, where b is the y-intercept. To sketch several members of the family, plot several points (x, y) with the equation, then connect the points to form a line.

(c) The equation for both families of linear functions is y = x + b, where b is the y-intercept. All functions belonging to both families have a slope of 1 and a y-intercept of b.

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a) The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6

b) The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7.

c) The interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).

What is a function?

A function is a mathematical relationship between two variables, often denoted as "f(x)" or "y = f(x)". A function assigns a unique output to each input within its domain. In other words, for every value of x, there is a corresponding value of y, and each value of x can only correspond to one value of y.

a. To find the first four nonzero terms and the general term for the power series expansion of f(t) about t=0, we need to find the Taylor series of f(t) centered at 0. The general term of a Taylor series is given by:

f(t)^(n) / n! * (t-0)^n

The Taylor series of f(t) = 3/(1+t^2) centered at 0 is:

f(t) = 3 - 3t^2 + 3/3t^4 - 3/5t^6 + ...

The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6

b. To find the first four nonzero terms and the general term for the power series expansion of g(x) = ∫f(t)dt about x=0, we need to integrate the Taylor series of f(t) term by term.

g(x) = ∫f(t)dt = (3t - 3/3t^3 + 3/5t^5 - ...) from 0 to x

g(x) = 3x - 3/3x^3 + 3/5x^5 - ...

The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7

c. The interval of convergence of a power series is the set of values of x for which the series converges. To find the interval of convergence for g(x), we can use the ratio test.

The ratio test states that if the limit of |a(n+1)x^(n+1)|/|a(n)x^n| as n approaches infinity is less than 1, the series converges for all x.

|3/7x^7|/(|3/5x^5|) = |x^2|/(|3/5|) < 1 when |x| < sqrt(5/3)

So, the interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).

Hence,

a) The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6

b) The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7.

c) The interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).

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In a single triangle, there is a 40-degree and a 60-degree angle.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.

Triangles of the scalene, isosceles, and equilateral varieties differ from one another in terms of side length. The triangle is a scalene triangle if the lengths of the three sides are all different. An isosceles triangle is one with all three sides having equal lengths.

A 40-degree and a 60-degree angle are both present in one triangle. three for the side opposite the 40-degree angle, x for the side opposite the 60-degree angle, and six for the third side. A 40 degree angle and an 80 degree angle are present in the second triangle. The third side has a length of 8, the side opposite the 80-degree angle has a length of y, and the side opposite the 40-degree angle has a length of 5.

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The rebound velocity of the ball, vfx, is 10.0 m/s, calculated using the equation vfx = 2vix - viy, where vix is the initial velocity along the x-axis (4.0 m/s) and viy is the initial velocity along the y-axis (-2.0 m/s).

Using the equation vfx = 2vix - viy, the rebound velocity of the ball is calculated as follows:

vfx = 2(4.0 m/s) - (-2.0 m/s) = 10.0 m/s

1. Identify the initial velocity, vix, of the ball along the x-axis, which is 4.0 m/s.

2. Identify the initial velocity, viy, of the ball along the y-axis, which is -2.0 m/s.

3. Use the equation vfx = 2vix - viy to calculate the rebound velocity of the ball, vfx.

4. Calculate vfx = 2(4.0 m/s) - (-2.0 m/s) = 10.0 m/s.

The rebound velocity of the ball is 10.0 m/s.

The rebound velocity of the ball, vfx, is 10.0 m/s, calculated using the equation vfx = 2vix - viy, where vix is the initial velocity along the x-axis (4.0 m/s) and viy is the initial velocity along the y-axis (-2.0 m/s).

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The function g(16) = -1/2 x + 5 is solved by substitution to get -3

The process of changing an algebraic letter to it's value corresponds to the procedure known as substitution.

In the problem, the equation g(16) = -1/2 x + 5,

Considering the equation, the value of x is 16. The letter x will be replaced by 16 in the equation

g(16) = - 1/2 x + 5

g(16) = - 1/2  * 16 + 5

g(16) = - 8 + 5

g(16) = -3

Substituting x = 16 in the equation g(16) = -1/2 x + 5 results to a solution of -3

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Length (in ft) x Width (in ft) = area in sq. ft

Hope this helps

I'm not good at math so I got this from my notes :)

If it doesn't help then it was worth an attempt...

Answer: A

Step-by-step explanation:

Present value of F (P) = Compound amount (F) (1+periodic rate)

Answer: 3,-5

Step-by-step explanation:

Answer: (3, -5)

......................................

A Prime factor is a natural number that has only two factors namely 1 and the number itself. One is not a prime number. Prime factors are odd in nature except for 2 because 2 is the only even prime factor. Example of prime factors are 2,3,5,7,11 etc

def print_prime_factors(number):

 factor = 2

 while factor <= number:

   # Check if factor is a divisor of number

   if number % factor == 0:

     # If it is, print it and divide the original number

     print(factor)

     number = number / factor

   else:

     # If it's not, increment the factor by one

    factor+=1

 return "Done"

print_prime_factors(100)

Complete question- Above mentioned is the correct code with all blanks filled.

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Mary owes $13564 income tax.

Governments apply income taxes as a sort of tax on the income produced by people and businesses under their control. Government duties, public services, and citizen goods are all paid for through income tax revenue.

Given that the taxable income is $68,562.

Income tax is the tax charged on an individual's or entity's income

Using the table as a guide, $68,562 falls within the income range $31,850 - $77,100

So, the tax is $4386 added to 25% of the excess over $31850

This is calculated as:

tax = $4386 + 25%(income - 31,850)

In our case,

income = $68562

Substitute $68,562 for income

Tax = $4386 + 25%(68,562 - 31,850)

Solve the expression in the bracket

tax = 4386 + 9178

Add the terms of the expression

tax = 13,564

therefore, Mary owes $13564 in income tax.

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The change in elevation of the scuba diver after 8 minutes is -24.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers. Unknown variables, numbers, and arithmetic operators make up an algebraic expression. It contains no equality or inequality symbols.

The expression (8)(2)(-1.5) represents the change in the scuba diver's elevation after 8 minutes.

To determine the change in elevation, we need to evaluate the expression.

(8)(2)(-1.5) = (16)(-1.5) = -24

Thus, the change in elevation is -24.

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Answer:

FV = $1,200 * e^(0.09*10)

Step-by-step explanation:

The equation used to calculate the future value of an investment compounded continuously is:

FV = PV * e^(r*t)

where:

FV = future value

PV = present value (initial investment) = $1,200

r = annual interest rate (9% = 0.09)

t = number of years (10 years)

So, the future value of the investment would be:

FV = $1,200 * e^(0.09*10)

Answer :

0.783

Step-by-step explanation:

We know that,

sin^2 (x) + cos^2 (x) = 1

Thus,

[tex] \sin^{2} (A) + cos^{2} (A) = 1 \\ cos^{2} A =1 - sin^{2} A \\ cos^{2} A = 1 - (0.622)^{2 } \\ cos^{2} A = 1 - 0.386884 \\ cos A = \sqrt{0.613116} \\ = 0.783[/tex]

It is discovered that the phrase under the division symbol is 3x2 - (b - 2)x - c, meaning that b = 5 and c = 3.

find the roots of  x2 - x - 1  =  0    

--->     Using the quadratic formula, the roots are  [ 1 + sqrt(5) ] / 2   and   [ 1 + sqrt(5) ] / 2.

Placing these values into the equation  x5 - bx - c  =  0,  we get:

x  =  [ 1 + sqrt(5) ] / 2   --->   ( [ 1 + sqrt(5) ] / 2 )5   -  b( [ 1 + sqrt(5) ] / 2 )  -  c  =  0

--->    [ 176 + 80sqrt(5) ] / 32  -  ( [ 1 + sqrt(5) ] / 2 )b  -  c  =  0

multiplying by 32     --->    176  +  80sqrt(5)  -  16b  -  16sqrt(5)b  -  32c  =  0

Using the same steps for x  =  [ 1 - sqrt(5) ] / 2 , we get:     176  -  80sqrt(5)  -  16b  +  16sqrt(5)b  -  32c  =  0

Now, let's combine these two results:      176  +  80sqrt(5)  -  16b  -  16sqrt(5)b  -  32c  =  0

   176  -  80sqrt(5)  -  16b  +  16sqrt(5)b  -  32c  =  0

Subtract the lower equation from the upper:      160sqrt(5)  -  32sqrt(5)b  =  0   --->     160sqrt(5)  =  32sqrt(5)b     --->     b  =  5

Now, substitute this value for b into  176  +  80sqrt(5)  -  16b  -  16sqrt(5)b  -  32c  =  0

--->176  +  80sqrt(5)  -  16(5)  -  16sqrt(5)(5)  -  32c  =  0    

--->176  +  80sqrt(5)   - 80  -  80sqrt(5)  - 32c  =  0

--->96  -  32c  =  0

--->c  =  3

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Answer: It is 36cm the height of it and the length W times L

Step-by-step explanation:

Answer:

-2.5, -2.02, -11/4

Step-by-step explanation:

Any number beginning with -2 will be the answer. -11/4 is -2.75 when converted to a decimal!

Scale of the model is found to be 1 : 30 using the ratio method.

A model of a car is 4 inches long.

The actual car is 10 feet long.

 4 in. = 10 ft. ( since given )

Divide both sides by 4, we get

∴ 1 in. = 2.5 ft.

We use the ratio here to compare the lengths of the actual car and its model.

A ratio scale is a quantitative measurement scale that is used to compare numbers.

The model is 4 inches long while the actual car is 10 feet long.

One foot is equal to 12 inches. Therefore the car in terms of inches is:

10 feet × 12 inches = 120 inches

The ratio scale is the length of the model of the car : length of the actual car

= 4 : 120

= 1 : 30

Therefore the scale of the model is 1: 30.

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