what is the inverse of the following function? 50 points

The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let f(n) represent the total cost of shoe rentals for n games, hence:

The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.

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[tex]\square[/tex] The function is continuous. [False]

Both pieces of the function are continuous, so the overall continuity of [tex]g(x)[/tex] depends on continuity at [tex]x=0[/tex].

We have

[tex]\displaystyle \lim_{x\to0^-} g(x) = \lim_{x\to0} \left(\frac1{2^x} + 3\right) = 1 + 3 = 4[/tex]

and

[tex]\displaystyle \lim_{x\to0^+} g(x) = \lim_{x\to0} (-x^2+2) = 2[/tex]

The one-sided limits do not match, so [tex]g[/tex] is not continuous at [tex]x=0[/tex].

[tex]\square[/tex] As [tex]x[/tex] approaches positive infinity, [tex]g(x)[/tex] approaches positive infinity. [False]

[tex]g(x)[/tex] is a large negative number when [tex]x[/tex] is very large, so [tex]g(x)[/tex] is approaching negative infinity.

[tex]\boxed{\checkmark}[/tex] The function is decreasing over its entire domain. [True]

This requires [tex]g'(x) \le 0[/tex] on the entire real line. Compute the derivative of [tex]g[/tex].

[tex]g'(x) = \begin{cases}-\ln(2)\left(\dfrac12\right)^x & x<0 \\\\ ? & x=0 \\\\ -2x & x>0 \end{cases}[/tex]

• [tex]\left(\frac12\right)^x > 0[/tex] for all real [tex]x[/tex], so [tex]g'(x)<0[/tex] whenever [tex]x<0[/tex].

• [tex]x^2\ge0[/tex] for all real [tex]x[/tex], so [tex]-x^2\le0[/tex] and [tex]-x^2+2\le2[/tex]. Equality occurs only for [tex]x=0[/tex], which does not belong to [tex]x>0[/tex].

Whether the derivative at [tex]x=0[/tex] exists or not is actually irrelevant. The point is that [tex]g(b) < g(a)[/tex] if [tex]b>a[/tex] for all real [tex]a,b[/tex].

[tex]\boxed{\checkmark}[/tex] The domain is all real numbers. [True]

There are no infinite/nonremovable discontinuities, so all good here.

[tex]\boxed{\checkmark}[/tex] The [tex]y[/tex]-intercept is 2. [True]

When [tex]x=0[/tex],

[tex]g(0) = -0^2 + 2 = 2[/tex]

Step-by-step explanation:

Let take the first derivative

[tex] \frac{d}{dx} ln(x)) = x {}^{ - 1} [/tex]

The second derivative

[tex] - {x}^{ - 2} [/tex]

The third derivative

[tex]2 {x}^{ - 3} [/tex]

The fourth derivative

[tex] - 6 {x}^{ - 4} [/tex]

The fifth derivative

[tex]24 {x}^{ - 5} [/tex]

Let create a pattern,

The values always have x in it so

our nth derivative will have x in it.

The nth derivative matches the negative nth power so the nth derivative so far is

[tex] {x}^{ - n} [/tex]

Next, lok at the constants. They follow a pattern of 1,2,6,24,120). This is a factorial pattern because

1!=1

2!=2

3!=6

4!=24

5!=120 and so on. Notice how the nth derivative has the constant of the factorial of the precessor

so our constant are

[tex](n - 1)[/tex]

So far, our nth derivative is

[tex](n - 1)!x {}^{ - n} [/tex]

Finally, notice for the odd derivatives we are Positve and for the even ones, we are negative, this means we are raised -1^(n-1)

[tex] - 1 {}^{n -1} (n - 1) ! {x}^{-n} [/tex]

That is our nth derivative

Answer:

width = 34 inches

length = 16 inches

Step-by-step explanation:

Given:

1.)The length of a rectangle is two more than double the width

2.)The perimeter is 100 inches

Let's analyze the first part,

The length is 2 more than double the width so if we let x represent the length the width would be 2x + 2

Now the second part,

the perimeter is calculated by the following formula:

2*(w+l)

(w: width, l: length)

2*(x+2x+2) first do inside the parenthesis by adding like terms

x+2x+2 = 3x + 2 now multiply both terms with 2

2*(3x+2) = 6x + 4 this is the perimeter of the rectangle, now write another equation using this

6x + 4 = 100 subtract 4 from both sides

6x = 96 divide both sides by 6

x = 16 this the length and the width would be

2x + 2 = 2*16 + 2 = 34

The computation shows that the the hospital in-patient admission rate for the employees of the Prendergast Corporation is 104.5 admissions per 1000 employees.

The in-patient admission rate for Ramsey Manufacturing company = 100 admissions per 1000 employees.

It is given that the in-patient rate of Prendergast will be 10% higher than Ramsey's.

So, in-patient rate of Prendergast:

= 100 + 10% of 100

= 110 admissions

Now, it is also given that out of total in-patients, 5% are for tonsillectomies (which are not in-patient).

So, in-patient admission rate for Prendergast:

= 110 - 5% of 110

= 110 - 5.5

= 104.5 admissions per 1000 employees

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Complete question:

The hospital in-patient admission rate for employees of the Ramsey Manufacturing Company is 100 admissions per 1000 employees per year.

The Prendergast Corporation has older employees and is told that its hospital in-patient admission rate will be 10% higher than Ramsey’s. At the same time, however, all tonsillectomies will be done in the hospital’s outpatient department instead of requiring the patient to be admitted as an in-patient. Given that 5% of all in-patient admissions are for tonsillectomies, what is the hospital in-patient admission rate for the employees of the Prendergast Corporation?

A. 110.0 B. 115.0 C. 109.5 D. 100.0 E. 104.5 F. 117.0

the range that would be the most appropriate to represent the numerical data on the vertical axis is B. 20 to 100.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

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The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

Bar graph :

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data

The range that would be the most approximately to represent the numerical data on the vertical axis is B. 20 to 100.

because

it is not possible to have zero number of cars that have a particular color,

in That way, we can eliminate options C and D .

in option A the range is too small which is not possible.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

Work Shown:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.2 + 0.8 - 0.07

P(A or B) = 0.93

The domain of the function is the set of all real numbers and the range of the function is the set of all values greater than -2

The function is given as:

f(x) = 2(x -4)^2 - 2

A quadratic function can take any real number as its input.

So, the domain of the function is the set of all real numbers

The vertex of the above function is:

Vertex = (4, -2)

And the leading coefficient is:

a = 2

The y value of the vertex is;

y = -2

Because the value of a is positive, then the vertex is a minimum.

This means that the range of the function is the set of all values greater than -2

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The monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be better option.

Given that for $200,000 loan Option 1 is a 30-year loan at an APR of 10% Option 2 is a 15-year loan at an APR of 9.5%.

A concept that implies that the future value of money will be lower than its present value due to several factors such as inflation is known as TVM(time of value money).

Monthly Payments

Option 1

Loan Amount = $200,000

Number of payments = 30×12 = 360

Monthly interest rate = 10%/12 = 0.008333333

Monthly payment = Loan amount (1+ monthly interest rate)ⁿ×monthly interest rate/[(1+monthly interest rate)ⁿ- 1]

Monthly payment=200,000×(1+0.008333333)³⁶⁰×(0.008333333)/[(1+0.008333333)³⁶⁰-1]

Monthly payment=33062.328/18.83739

Monthly payment=$1755.144

Option 2

Loan Amount = $200,000

Number of payments = 15 x 12=180

Monthly interest rate = 9.5%/12=0.00792

Monthly payment = 200,000(1+0.00792)¹⁸⁰(0.00792)/[(1+0.00792)¹⁸⁰-1]

Monthly payment=6553.096/3.137

Monthly payment=$2088.97

Total Payments

Option 1

As we've found out the monthly payments, we now need to multiply it by the number of months.

$1755.144×360 = $631851.84

Option 2

$2088.97×180 = $376014.6

Conclusion

Option 2 will always be the better option economically as it saves $255837.24 ($631851.84 - $376014.6) in total payments.

Hence, For $200,000 loan Option 1 a 30-year loan at an APR of 10% Option 2 a 15-year loan at an APR of 9.5% is the monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be the better option.

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These are the laws of indices. You just have to memorise it, sorry : (

Hope it helps : )

Answer:

[tex]2xy^2(xy-1)(xy-3)[/tex]

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

Given expression

[tex]2x^3y^4-8x^2y^3+6xy^2[/tex]

The greatest common factor of all three terms is [tex]2xy^2[/tex].

Factor this out:

[tex]2xy^2(x^2y^2-4xy+3)[/tex]

Complete the square:

[tex]2xy^2(x^2y^2-4xy+4-1)=[/tex]

[tex]2xy^2((xy-2)^2-1)[/tex]

Factorize further using the identity for the difference of squares:

[tex]2xy^2(xy-2+1)(xy-2-1)=[/tex]

[tex]2xy^2(xy-1)(xy-3)[/tex]

let's firstly convert the mixed fraction to improper fraction and then take it from there, keeping in mind that the whole is "x".

[tex]\stackrel{mixed}{5\frac{5}{6}}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{3}x~~ = ~~5\frac{5}{6}\implies \cfrac{7}{3}x~~ = ~~\cfrac{35}{6}\implies 42x=105\implies x=\cfrac{105}{42} \\\\\\ x=\cfrac{21\cdot 5}{21\cdot 2}\implies x=\cfrac{21}{21}\cdot \cfrac{5}{2}\implies x=1\cdot \cfrac{5}{2}\implies x=2\frac{1}{2}[/tex]

The province's population is growing at the rate of  58.34 %

Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. The calculation for ROC is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period.

Given:

Initial Population = 4.2 million

Population after 20 years = 6.65 million

Change in population = 6.65 - 4.2 = 2.45 million

Rate at which the province's population growing is

= [tex]\frac{Change in population}{Inital Population}[/tex] x100 %

= [tex]\frac{2.45}{4.2}\\[/tex] x 100%

= 58.34 %

Thus the province's population is growing at the rate of  58.34 %

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Solving a quadratic function, it is found that the ball has a height of 19 feet at t = 0.72 seconds and t = 1.22 seconds.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

In this problem, the function is:

h(t) = -16t² + 31t + 5

The height is of 19 feet when h(t) = 19, hence:

19 = -16t² + 31t + 5

16t² - 31t + 14 = 0.

Then:

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Considering the given graph, the meaning of point A is given by:

A can with an 11 cm diameter has an 18 cm height.

The graph gives the height of the can as a function of the diameter. Both measures are in cm. Then, the axis are given as follows:

Point A has coordinates (11,18), that is, x = 11, y = 18, hence the interpretation is:

A can with an 11 cm diameter has an 18 cm height.

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Answer:

A

Step-by-step explanation:

just took the quiz and can confirm the other guy is valid :D

The number of bacteria when t = 8 is approximately 66 bacterias

Given the function that gives the number of bacteria in a population as a function of time in hour expressed as:

P=48∙e^((0.045t))

If the value of t is 8, hence;

P=48∙e^((0.045(8))

P = 48e^0.36

P = 65.933

Hence the number of bacteria when t = 8 is approximately 66 bacterias

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The procedure for solving -275+156-(-293)-157 = 17 is to follow bodmas operation

-275+156-(-293)-157 = 17

Using BODMAS

-275+156-(-293)-157 = 17

= -275 + 156 + 293 - 157

= 17

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Answer:

B. quadratic function graph

Answer:

b

Step-by-step explanation:

(-4(-1)-8)(3(2)^2+2=4-8×12+2

-4×14=-56

-3x is a term in the expression -3x - 7(x+4)

The expression is given as:

-3x - 7(x+4)

Considering the following expression

Ax + B(x  - b)

The terms in the expressions are Ax and B(x  - b)

This means that -3x is a term in the expression -3x - 7(x+4)

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Answer:

slope = 11/2

Step-by-step explanation:

If you are given two points, you can find the slope using the point-slope equation. The equation looks like this:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope, "x₁" and "y₁" represent the values from one point, and "x₂" and "y₂" represent the values from the other point. You can plug the values from the points into the equation and simplify to find the slope.

Point 1: (-4, 7)                Point 2: (-6, -4)

x₁ = -4                              x₂ = -6

y₁ = 7                               y₂ = -4

y₁ - y₂ = m(x₁ - x₂)                               <----- Point-slope form

7 - (-4) = m(-4 - (-6))                            <----- Insert values

11 = m(2)                                             <----- Simplify

11/2 = m                                             <----- Divide both sides by 2

[tex]\huge\boxed{\frac{11}{2}}[/tex]

The slope is equivalent to vertical change divided by horizontal change, otherwise known as "rise over run".

Therefore, the slope can be represented with the following equation, where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are your points:

[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values and simplify to find the answer.

[tex]\dfrac{(-4)-7}{(-6)-(-4)}[/tex]

[tex]\dfrac{-4-7}{-6+4}[/tex]

[tex]\dfrac{-11}{-2}[/tex]

[tex]\boxed{\frac{11}{2}}[/tex]

Using the z-distribution, it is found that she should take a sample of 46 students.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence, by the Empirical Rule the standard deviation is found as follows:

[tex]6\sigma = 800 - 200[/tex]

[tex]6\sigma = 600[/tex]

[tex]\sigma = 100[/tex]

The sample size is n when M = 29, hence:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]29 = 1.96\frac{100}{\sqrt{n}}[/tex]

[tex]29\sqrt{n} = 196[/tex]

[tex]\sqrt{n} = \frac{196}{29}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{196}{29}\right)^2[/tex]

n = 45.67.

Rounding up, a sample of 46 students should be taken.

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The equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.

Given the expression; (z−3)4z−6

First, we apply distributive property.

(z−3)4z−6

(z−3)4z−6

z(4z) - 3(4z) - 6

We remove the parentheses

4z² - 12z - 6

Therefore, the equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.

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Using an exponential function, the expected mass of the sample in the year 2001 would be of 16 mg.

The function is:

[tex]A(t) = A(0)e^{-kt}[/tex].

In which:

The information given is as follows:

A(0) = 440, A(8) = 40.

Hence:

[tex]A(t) = A(0)e^{-kt}[/tex].

[tex]40 = 440e^{-8k}[/tex].

[tex]e^{-8k} = 0.09090909[/tex]

[tex]\ln{e^{-8k}} = \ln{0.09090909}[/tex]

[tex]-8k = \ln{0.09090909}[/tex]

[tex]k = -\frac{\ln{0.09090909}{8}[/tex]

k = 0.29973691

Then the function is:

[tex]A(t) = 440e^{-0.29973691t}[/tex]

2001 is 11 years after 1990, hence the amount is:

[tex]A(11) = 440e^{-0.29973691 \times 11} = 16[/tex]

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Answer:

1/21

Step-by-Step Explanation:

Let's solve your equation step-by-step.

3(1−5x)=2(3x+1)

Step 1: Simplify both sides of the equation.

3(1−5x)=2(3x+1)

(3)(1)+(3)(−5x)=(2)(3x)+(2)(1)(Distribute)

3+−15x=6x+2

−15x+3=6x+2

Step 2: Subtract 6x from both sides.

−15x+3−6x=6x+2−6x

−21x+3=2

Step 3: Subtract 3 from both sides.

−21x+3−3=2−3

−21x=−1

Step 4: Divide both sides by -21.

-21x/-21=-1/-21

x=1/21

[tex]\boldsymbol{\sf{3(1-5x)=2(3x+1)}}[/tex]

Reorder terms

Distribute

Subtract 3x from both sides.

Simplify

Subtract 6x from both sides.

Simplify

Divide both sides by the same factor

Simplify

Answer:

$4800

Step-by-step explanation:

Let's use the simple interest formula, P(1+rt), to find the final amount of the loan

10000(1+.12*4) = 14800, the final amount

14800 - 10000 = 4800 total in interest

Using the simple interest formula, it is found that the APR for the loan is of 4.472%.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

The parameters for this problem are:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

We solve the equation for r to find the APR.

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]3067.08 = 3000(1 + 0.5r)[/tex]

[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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Answer:

3) 194 feet

Step-by-step explanation:

The other house:

"a house that is 33 ft wide and 50 ft long"

area = LW = (33 ft)(50 ft) = 1650 ft²

This house:

LW = A

L × 22 ft = 1650 ft²

L = 75 ft

P = 2(L + W)

P = 2(75 ft + 22 ft)

P = 194 ft

Answer: 3) 194 feet

Answer:

3) P = 194 ft.

Step-by-step explanation:

[tex]A=wl[/tex]

[tex](30)(50)=22l[/tex]

[tex]1650=22l[/tex]

[tex]l=1650/22=75[/tex]

the dimensions of the house are: (22 × 75)

Perimeter:

[tex]p=2(22)+2(75)=44+150=194[/tex]

Hope this helps