Find f (2) and f (3) if f (n) is defined recursively by f (n +1) = (n) ⁄ (n − 1) , f (0) = f (1) = 1 and for n = 1, 2, 3, …​

Hence its proven that f and g are inverse of one another

What is a Function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Given,

f(x)= 2x-3/2

g(x)= 2x+3/2

Step 1: show that fog=x

f(g(x))

[2((2x + 3) / 2) - 3]/2

[(2x + 3) - 3] / 2

(2x + 3 - 3) / 2

2x / 2

x , which is equals to x

Now, for Step 2: gof = x

g(f(x))

g((2x - 3)/2)

[2((2x - 3)/2) + 3]/2

[(2x - 3) + 3]/2

(2x - 3 + 3)/2

2x/2

x , which is equals to x

Since, both fog(x) and gof(x) equals to x

Hence, its proven that f and g are inverse of one another

To learn more about Function ckick on the link

https://brainly.com/question/10439235

#SPJ1

Answer: 60 minutes

Step-by-step explanation:

x=time Madison spent at the mall

2x + 15 = 135

2x = 135-15

x = 120/2 = 60

Answer:

  4.  121,800

  5.  591 3/32

  6.  1/4

Step-by-step explanation:

You want the sum of the first 200 terms of the arithmetic sequence starting 12, 18, 24, ....

The sum of the first n terms of an arithmetic sequence is given by the formula ...

  Sn = (2·a1 +d(n -1))(n/2)

where a1 is the first term and d is the common difference. Your sequence has first term 12 and common difference 18-12 = 6. The desired sum is ...

 S200 = (2·12 +6(200 -1))/(200/2) = (24 +1194)(100) = 121,800

You want the sum of the first 8 terms of the geometric sequence starting 12, 18, 27, ....

The sum of the first n terms of a geometric sequence is given by the formula ...

  Sn = a1·(r^n -1)/(r -1)

where a1 is the first term and r is the common ratio. Your sequence has first term 12 and common ratio 18/12 = 3/2. The desired sum is ...

  S8 = 12·((3/2)^8 -1)/(3/2 -1) = 24·6305/256 = 591 3/32

For this sequence, a1 = 1/12 and r = 2/3. When the sum is infinite and |r| < 1, the sum formula becomes ...

  S = a1/(1 -r)

The desired sum is ...

  S = (1/12)/(1 -2/3) = (1/12)/(4/12) = 1/4

Answer:

[tex]\textsf{4.} \quad 121,800[/tex]

[tex]\textsf{5.} \quad \dfrac{18915}{32}=591.09375[/tex]

[tex]\textsf{6.} \quad \dfrac{1}{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given arithmetic sequence:

The first term of the given sequence is 12.

The common difference can be found by subtracting the first term from the second term:

[tex]\implies d=a_2-a_1=18-12=6[/tex]

Therefore:

To find the sum of the first 200 terms, substitute n = 200, a = 12 and d = 6 into the formula:

[tex]\begin{aligned}S_{200}&=\dfrac{1}{2}(200)[2(12)+(200-1)(6)]\\&=100[24+(199)(6)]\\&=100[24+1194]\\&=100[1218]\\&=121800\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given geometric sequence:

The first term of the given sequence is 12.

The common ratio can be found by dividing the second term by the first term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{18}{12}=1.5[/tex]

Therefore:

To find the sum of the first 8 terms, substitute n = 8, a = 12 and r = 1.5 into the formula:

[tex]\begin{aligned}\implies S_{8}&=\dfrac{12(1-1.5^8)}{1-1.5}\\\\&=\dfrac{12\left(1-\frac{6561}{256}\right)}{-0.5}\\\\&=\dfrac{12\left(-\frac{6305}{256}\right)}{-0.5}\\\\&=\dfrac{-\frac{18915}{64}}{-0.5}\\\\&=\dfrac{18915}{32}\\\\&=591.09375\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given geometric sequence:

The first term of the given sequence is ¹/₁₂.

The common ratio can be found by dividing the second term by the first term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{\frac{1}{18}}{\frac{1}{12}}=\dfrac{2}{3}[/tex]

Therefore:

To find the sum of the infinite geometric sequence, substitute a = ¹/₁₂ and r = ²/₃ into the formula:

[tex]\begin{aligned}\implies S_{\infty}&=\dfrac{\frac{1}{12}}{1-\frac{2}{3}}\\\\&=\dfrac{\frac{1}{12}}{\frac{1}{3}}\\\\&=\dfrac{1}{12} \times \dfrac{3}{1}\\\\&=\dfrac{3}{12}\\\\&=\dfrac{1}{4}\end{aligned}[/tex]

Answer: C & E

Step-by-step explanation: A is a lie, function 1 is pos

B is a lie function 1 is pos

C is true

D is a lie

E is true

The probability that three cards have the same number, using the hypergeometric distribution, is of:

0.0448 = 4.48%.

The probability mass function for the hypergeometric distribution is defined as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the function are listed below:

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

N = 28, k = 4, n = 5, x = 3.

Hence for one color, the probability that three cards have the same number is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,28,5,4) = \frac{C_{4,3}C_{24,2}}{C_{28,5}} = 0.0112[/tex]

There are four colors, hence the probability is:

p = 4 x 0.0112 = 0.0448 = 4.48%.

More can be learned about the hypergeometric distribution at https://brainly.com/question/14741653

#SPJ1

If he has 2 more pennies than nickels. the number of pennies is  10.6  and the number of nickels that Levi has is  12.6.

n = number of nickels

n-2 = number of pennies

Hence,

5n +1(n -2) = 74

Collect like terms

6n = 76

Divide both side by 6n

n = 76/6

n = 12.6 ( nickels)

Pennies

n-2

= 12.6 -2

= 10.6

Therefore Levi  has 10.6 pennies and 12.6 nickels.

Learn more about pennies and nickels here:https://brainly.com/question/16204831

#SPJ1

Answer:

Step-by-step explanation:

Jb

Answer: 1. 0.1333 2. 1

Step-by-step explanation:

Step 1: 2/15 is the same as 2 divided by 15 which is 1.33333333333333333333333333333333333333333333333333 and so on.

Step 2: Clearly, the only number that is repeating is the 3.

The number of dinners that should be prepared to maximize profit is 1200.

The maximum profit is $1040

We know that,

y = ax²+ bx + c

The expression has the greatest value at x = -b/2a

From the question, we have

y=-0.001x² +2.4x-400

x = -b/2a

= -2.4/2*(-0.001)

=1200

substituting the value  we get

y=-0.001x² +2.4x-400

y=-0.001*1200² +2.4*1200-400

y=$1040

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

To learn more about multiplication visit: https://brainly.com/question/5992872

#SPJ1

Answer: 1/8x - 5/6

Step-by-step explanation:

Let's move the similar terms of the problem together.

So first we have:

-3/4x + 7/8x

And then we have:

-1/3 - 1/2

So to add/subtract fractions, the denominators have to be equal. We can change the -3/4 into -6/8 by just multiplying by 2/2 which is just 1. (Anything multiplied by 1 is just itself). So then we have:

-6/8x + 7/8x ---> 1/8x

Next, the second part.

Since neither denominators (3 or 2) can turn into one another by multiplying them with a number, we'll just multiply them with the opposite denominator.
So then we have:

-1/3 * (2/2) = -2/6
-1/2 * (3/3) = -3/6

-2/6 - 3/6 = -5/6

So finally we have:

1/8x - 5/6

Answer:god is good

Step-by-step explanation:if u put this 1 stars u hate god

if u give 5 stars u love god

Answer of the why did George Washington caution against the formation of political parties?

What potential risks do political parties pose towards democracy? Do you think that the country should have followed his advice are as follows :  

(a) He believes that the government was undermined by differences between the political parties. Additionally, he argues that "the alternate domination" of one party over another and concurrent attempts to exact revenge on their rivals have resulted in terrible atrocities and "is itself a frightful despotism."

(b)The democratic theory's main tenet is that democracies force administrations to take citizens' preferences into account. Every contemporary democracy is organized by political parties, and some observers contend that parties are what makes democracies responsive. Others, however, contend that parties give extremists a platform and make governments less receptive to the needs of the populace. As newly established democracies around the world grapple with concerns of representation and governability, the discussion of parties and democracy assumes fresh prominence.

To learn more about George Washington here:

https://brainly.com/question/14598321

#SPJ1

Answer:

the equation is 37.45-5.35v=0

Step-by-step explanation:

37.45-5.35v=0

minus 37.45 to both sides

-5.35v=-37.45

divide -5.35 from both sides

v=7

after 7 days she will finish the card

The distance travelled before their first gas stop is 76.68 miles.

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

Consider that the distance covered before their first stop for gas be 'x'

The Total distance travelled is 372 miles

WE have given that after stopping for gas they travelled  65 1/4 miles and then tripled their distance. The equation is;

x + 261/4 + 3x = 372

4x + 261/4 = 372

16x + 261 = 1488

16x = 1227

x = 76.68 miles

To know more about fraction visit:

brainly.com/question/21449807

#SPJ1

The difference in the amount of money earned by Beth and Bartley is $40.25.

Given that, Beth makes $10.25/hour and Bartley makes $11.50 an hour.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

If Beth worked for 23 hours

Money earned by Beth is

10.25×23=$235.75

If Bartley worked for 17 hours

Money earned by Bartley is

11.50×17 =$195.5

So, difference of money = 235.75-195.5

= $40.25

Hence, the difference in the amount of money earned by Beth and Bartley is $40.25.

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ1

Answer:

least

- 1/4 ft

- 14 3/4 ft

- 15 1/2 ft

- 20 3/5 ft

greatest

Answer:

- 20 3/5 ft

- 15 1/2 ft

- 14 3/4 ft

- 1/4 ft

I the number is larger looking but have a negative symbol, then it is smaller.

For example, -1 is greater than -6. Also -1/4 is greater than -20 3/5.

Trust me, I am a year ahead in school, so trust me.

I hope this helped.

Answer:

slope: 1

y-intercept: (0,2)

the second point to plot: (1,3)

Step-by-step explanation:

Points to plot

(0,2),(1,3),(-2,0)

The measure of central angle is 45°

Here, arc length S = 5π/4

radius r = 5

We need to find central angle θ

Using the formula of arc length,

S = r * θ

5π/4 = 5 * θ

θ = π/4

θ = 45°

Therefore, the measure of central angle is 45°

Learn more about the central angle here:

https://brainly.com/question/1577784

#SPJ1

The subject of the equation is x and it can be written as x = t/6.

Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. The equation's solution is the value of the variable for which the equation is true. An equation remains the same even when the LHS and RHS are flipped. The solution is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are dealing with, we can solve it. There are various types of equations, including linear, quadratic, rational, and radical ones.

The given equation is

6x = t

Divide both sides by 6

6x/ 6 = t/ 6

x = t/ 6

So, the subject of the equation is x - t/6.

To know more about the subject of an equation, visit:

https://brainly.com/question/14780696

#SPJ1

The domain is  {-5, -4, -2, 0, 1} and range is {4, -1, 1, 4, 3}

The given relation is {(−5,4), (−4, −1), (−2,1), (0,4), (1,3)

We need to find its domain and range

Domain of the set is {-5, -4, -2, 0, 1}

Range of the set is {4, -1, 1, 4, 3}

If in an relation every input has an single output, it is said to be a function

Here, every element of the domain has a single element in range, so it is a function

The given relation is  {(−3, −4), (−1,2), (0,0), (−3,5), (2,4)}

We need to find its domain and range

Domain of the set is {-3, -1, 0, -3, 2}

Range of the set is {-4, 2, 0, 5, 4}

If in an relation every input has an single output, it is said to be a function

Here, every element of the domain has a single element in range, so it is a function

Therefore, the domain is  {-5, -4, -2, 0, 1} and range is {4, -1, 1, 4, 3}

To learn more about functions refer here

https://brainly.com/question/2328150

#SPJ1

The equivalent multiplication sentence that shows associative property is 3x(1×6)

Associative property is defined as, when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped.

This means that if a,b,c are real numbers then a×(b×c)=b×(a×c)

using the associative property,1×(3×6)= 3×(1×6)

To verify the statement,let's find out

solving the parentheses first

1×(3×6)=1×18= 18

3×(1×6)= 3×6= 18

this means that 1×(3×6) and 3×(1×6) are associative

therefore 1×(3×6)=3×(1×6)

learn more about associative property from

https://brainly.com/question/13181

#SPJ1

The vertex of the equation y=x^2-12x+7 is (6,-29) and the graph is given below.

In the given question we have to find the graphing form of y=x^2-12x+7.

The given equation is y=x^2-12x+7.

To graph the given equation we firstly express that equation in the standard form of parabola.

y=a(x-h)^2+k

Add and subtract 36 in the given equation;

y=x^2-12x+36-36+7

y=x^2-2×6×x+(6)^2-29

y=(x-6)^2-29

The vertex of the given equation is (6,-29).

The graph of the given equation is given below:

To learn more about the graph of equation link is here

brainly.com/question/12703381

#SPJ1

The value of the expression given as (7/4x - 5) - (2y - 3.5) - (-1/4x + 5) is 2x - 2y - 6.5

In this question, the representation of the expression is given as

(7/4x - 5) - (2y - 3.5) - (-1/4x + 5)

Start by removing the brackets in the expression

So, we have

7/4x - 5 - 2y + 3.5 + 1/4x - 5

Evaluate the fractions in the expression

The expression becomes

1.75x - 5 - 2y + 3.5 + 0.25x - 5

Collect the like terms

1.75x + 0.25x - 2y - 5  + 3.5  - 5

Evaluate the like terms

2x - 2y - 6.5

Hence, the solution is 2x - 2y - 6.5

Read more about expressions at

https://brainly.com/question/4344214

#SPJ1

The probability that the family had at least 3 girls is 0.6367

This is a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:

P(x = r) = nCr . p^r . q^n-r

Given: n= 8, probabibility of sucess (p) = 0.5, x≥3 (at least 3 girls)

The failures can be calculated using q = 1 - p = 1 - 0.5 = 0.5

P(x≥3) = 1 - P(x≤3) = 1 - ( P(x= 0) + P(x= 1) + P(x= 2) + P(x= 3) )

Using the formula:

P(x≥3)  = 1 - ( (8C0 x 0.5⁰  x 0.5⁸⁻⁰) +(8C1 x 0.5¹  x 0.5⁸⁻¹) + (8C2 x 0.5²  x 0.5⁸⁻²)  +  (8C3 x 0.5³  x 0.5⁸⁻³) )

          = 1 - ( (1/256) + (1/32) + (7/64) + (7/32) )

         = 0.6367

Therefore, the probability that the Wilson family had at least 3 girls is 0.6367

Learn more about binomial probability distribution on:

brainly.com/question/28954930

#SPJ1

Answer:

Slope = -2

Y-intercept = -8

Step-by-step explanation:

Hello!

Slope-Intercept Form: y = mx + b

The m variable in this equation would be -2, and it is also the slope of the equation.

The b variable in this equation is -8, which is the y-intercept of the equation.

Answer:

y intercept -8

slope -2

Step-by-step explanation:

y = -2x-8

This is written in slope intercept form

y = mx+b

The slope is m  which is -2

The y intercept is b which is -8

Answer: This is a 1 by 5 rectangle

perimeter = 12 units

========================================================

Work Shown:

Label the vertices A,B,C,D

A =  (1, 4)

B = (1, 5)

C = (6, 5)

D = (6, 4)

The x coordinates of points A and B are the same (x = 1). The difference in y values of these points is 5-4 = 1 unit. This is the height of the rectangle. In other words, it's the length of segment AB.

Points B and C have the same y coordinate (y = 5). The difference in x value is 6-1 = 5 which is the horizontal length of the rectangle. This is the length of segment BC.

In short, this is a 1 by 5 rectangle. It's one unit tall and five units across.

--------

Perimeter = 2*(length+width)

Perimeter = 2*(5+1)

Perimeter = 2*6

Perimeter = 12 units

Or you can add up the four sides (1,5,1 and 5) to get the same result.

The number which is as represented on the calculator display is; Choice A; 0.000001231151

It follows from the task content that the number which is represented on the calculator display is to be identified.

By checking, The display of the calculator is; 1.231151 E-⁶.

The number above can be represented as follows;

1.231151 × 10-⁶.

Since a negative exponent on the number ten indicates a shift leftwards, it follows that the number represented on the calculator display is;

0.000001231151.

Therefore, the correct number represented on the calculator display is; Choice A; 0.000001231151.

Read more on exponents of 10;

https://brainly.com/question/4957644

#SPJ1

Answer: A

Step-by-step explanation: A

A

Using the proportionality theorem, the values are:

x = 3

y = 2

The proportional theorem states that if two triangles are similar to each other, then their corresponding side lengths have the same ratios.

The triangles above are similar to each other, therefore, their corresponding sides will have lengths that are proportional or have the same ratios.

Therefore:

3/1.5 = 6/x

Cross multiple

3x = (1.5)(6)

3x = 9

3x/3 = 9/3

x = 3

Find y:

3/1.5 = 4/y

3y = (1.5)(4)

3y = 6

3y/3 = 6/3

y = 2

Learn more about proportionality theorem on:

https://brainly.com/question/8160153

#SPJ1

The measure of the required angle ∠VUT = 80 degrees

Given : A triangle with angle measures as :

∠RTU = 50°

exterior angle ∠UVR = 120°

To find : ∠VUT

In the given triangle we can use the exterior angle sum property

which states that the angle opposite to the inside of the triangle and the angle outside the triangle

The angle outside the triangle is 120 degrees

120 = ∠VUT  + 50

thus on subtracting 50 both sides we will get

∠VUT = 120 - 50

∠VUT = 80 degrees

To know more about triangles and angles you may visit the link which is mentioned below:

https://brainly.com/question/27682397

#SPJ1