Chris and Jen decide to go apple picking at a local apple orchard. As the number of apples they pick increases the cost of the apples also increases. The function ff relates the varying cost of Chris and Jen's apples, cc , in terms of the varying number of pounds of apples that Chris and Jen pick, nn , where c=f(n)c=f(n) and ff is defined by f(n)=0.4n+6f(n)=0.4n+6.
Evaluate f−1(33) Note( this is F^-1)
Determine the rule for the function f^-1

Answers

Answer 1

Any relation that has an inverse is a function

The value of [tex]\mathbf{f^{-1}(33)}[/tex] is [tex]\mathbf{f^{-1}(33) = 67.5}[/tex]The rule of [tex]\mathbf{f^{-1}(n)}[/tex] is [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]

The function is given as:

[tex]\mathbf{f(n) = 0.4n + 6}[/tex]

(a) Evaluate [tex]\mathbf{f^{-1}(33)}[/tex]

First, we calculate the inverse function

We have:

[tex]\mathbf{f(n) = 0.4n + 6}[/tex]

Rewrite as:

[tex]\mathbf{y = 0.4n + 6}[/tex]

Subtract 6 from both sides

[tex]\mathbf{y -6= 0.4n + 6 - 6}[/tex]

[tex]\mathbf{y -6= 0.4n}[/tex]

Divide both sides by 0.4

[tex]\mathbf{\frac{1}{0.4}(y -6)= \frac{0.4n}{0.4}}[/tex]

[tex]\mathbf{\frac{1}{0.4}(y -6)= n}[/tex]

[tex]\mathbf{2.5(y -6)= n}[/tex]

Make n the subject

[tex]\mathbf{n = 2.5(y -6)}[/tex]

Rewrite as:

[tex]\mathbf{n = 2.5(f(n) -6)}[/tex]

So, the inverse function is:

[tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]

Substitute 33 for n to calculate [tex]\mathbf{f^{-1}(33)}[/tex]

[tex]\mathbf{f^{-1}(33) = 2.5(33 -6)}[/tex]

[tex]\mathbf{f^{-1}(33) = 2.5(27)}[/tex]

[tex]\mathbf{f^{-1}(33) = 67.5}[/tex]

(b) The rule of [tex]\mathbf{f^{-1}(n)}[/tex]

In (a), we have: [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]

Hence, the rule of [tex]\mathbf{f^{-1}(n)}[/tex] is [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]

Read more about functions and inverses at:

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Related Questions

please answer both questions​

Answers

Answer:

$24.63

Step-by-step explanation:

Surface area of a sphere = 4πr²

Surface area of the sphere

= 4π7²

= 196π

= 615.752... cm²

The total cost

= 0.04 × 615.752...

= $24.63 (rounded to the nearest hundredth)

A union of restaurant and foodservice workers would like to estimate the mean hourly wage, , of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate using the mean of the sample. What is the minimum sample size needed in order for the union to be confident that its estimate is within of

Answers

Answer:  the minimum sample size needed = 145

Step-by-step explanation:

Formula for sample size:

[tex]Sample \ size =(\dfrac{z^*\times standard\ deviation}{margin \ of \ error})^2[/tex]

, where z* = Critical z-value

Given: Standard deviation = 2.15

Margin of error = 0.35

Z* for 95% confidence = 1.96

Sample size = [tex](\frac{1.96\times2.15}{0.35})^2[/tex]

[tex]=(12.04)^2\\\\=144.9616\approx145[/tex]

Hence, the minimum sample size needed = 145

(125/64)-1/3 as a radical

-1/3 is square it should be and the top of 64 outside the bracket

Answers

9514 1404 393

Answer:

  ∛(64/125) = 4/5

Step-by-step explanation:

Maybe you want to express ...

  [tex]\displaystyle\left(\frac{125}{64}\right)^{-\frac{1}{3}}=\left(\frac{64}{125}\right)^{\frac{1}{3}}=\boxed{\sqrt[3]{\frac{64}{125}}}[/tex]

__

The denominator of the fractional exponent is the index of the radical. The other applicable rule of exponents here is a^-b = 1/a^b.

Plz show work, this is a test. NO LINKS!!!

Answers

Answer:

surface area of the square pyramid

=(32×32)+(2×32×20)

=1024+1280

=2304 square feet

Find the missing length indicated. Please help!!!

Answers

C
because if you look at where the unmarked side is divided, the one you’re supposed to find is obviously bigger than the other.

Carrie walked 6 miles per day. Which table represents y, the number of miles Carrie walked in x days.

D. Says 1. 18
2. 36
3. 54
4. 72

Answers

Answer:

C

Step-by-step explanation:

Since Carrie walked 6 miles her day, the function that best suits this relationship is given by [tex]y=6x[/tex] where [tex]x[/tex] is the number of days she walked and [tex]y[/tex] is the number of miles.

Table C represents this function [tex]y=6x[/tex] because all y values are exactly 6 times the x value.

Answer:

The answer is C.

Step-by-step explanation:

18 ÷ 3 = 6 miles a day

36÷6 = 6 miles a day

54÷9 = 6 miles a day

72÷12 = 6 miles a day

In a group of five students, there are two boys and three girls. The instructor randomly selects one student to record for the group and another student to spy on the other groups. Find P(boy first and girl second), the probability of selecting one of the boys first, and then selecting a girl for the second role

Answers

Answer: The instructor randomly selects one student to record for the group and another student to spy on the other groups.

[tex]\color{yellow}{}[/tex]

question : Suppose you have VND 100 million to save orspend. If you lend, you will receive 112 million after a year. Inflation is 14% / year.
a. What is the nominal interest rate you get?
b. What is the real interest rate?
c. Should you save or spend that money?
d. Question (c) how will be answered if inflation is 10% / year, nominal interest rates do not change?

Answers

Answer:

Step-by-step explanation:

Ethan is 1.6 metres tall, Uzma is 154 cm tall.
Work out how much taller Ethan is than Uzma.

Answers

Answer:

1.6 metres is 160 centimetres

Ethan is 6 centimetres taller than Uzma

2x + 3y = 7 and x + y = 3? *

Answers

Answer:

1) 7/2 - 3/2y,

2) 3-y, y

Step-by-step explanation:

See Image below for steps:)

PLEASE PLEASE HELP!!!!

Find the volume of the triangular pyramid to the nearest whole number

A) 170in³
B) 340in³
C) 680in³
D) 1,020³

Answers

V=(l x w x h) / 3 ———> (10 x 12 x 17) / 3 ———> 2040/3 = 680 in^3, it’s C

Hank can see the top of a tree in a mirror that is placed 475 cm from the tree when he stands 190 cm from the mirror. What is the height of the tree?

Answers

Answer:

The height of the tree is 430cm

Step-by-step explanation:

Given

The attached illustration

Required

The height of the tree

Let:

[tex]h \to[/tex]  Hank's height

[tex]H \to[/tex] Tree height

[tex]d \to[/tex] distance between Hank and Mirror

[tex]D \to[/tex] distance between tree and Mirror

From the question, we have:

[tex]\angle 1 = \angle 2[/tex]

This means that:

[tex]\frac{H}{D} = \frac{h}{d}[/tex]

Make H the subject

[tex]H = \frac{h}{d} * D[/tex]

So, we have:

[tex]H = \frac{172cm}{190cm} * 475cm[/tex]

[tex]H = \frac{172* 475cm}{190}[/tex]

[tex]H = \frac{81700cm}{190}[/tex]

[tex]H = 430 cm[/tex]

Can someone help me

Answers

It’s Rational numbers

how many solution does this equation have 17+4h+2=19−5h+9h?

Answers

Answer:

h=0

Step-by-step explanation:

if you plug it it works

Answer:

The input is an identity, it is true for all values.

Step-by-step explanation:

17 + 4h + 2 = 19 - 5h + 9h

19 + 4h = 19 - 5h + 9h

19 + 4h = 19 + 4h

19 - 19 + 4h = 19 - 19 + 4h

4h = 4h

4h ÷ 4 = 4h ÷ 4

h = h

The input is an identity, it is true for all values.

How to solve a problem.

Answers

a) [tex]\log \left(\dfrac{A^3B}{C} \right) = 3\log A + \log B - \log C[/tex]

b) [tex]\log \left(\dfrac{\sqrt{A}}{B^2} \right) = \frac{1}{2}\log A - 2\log B[/tex]

simplify 16 + 15 - 5​

Answers

31 - 5
Or
26 I hope this is ok

Determine the value of x.

1) 14.75
2)15.25
3)11.92
4)18.56

Answers

Opposite angles are supplementary, the sum is 180 degrees.
6x+10+81.5=180
Combine like terms:
6x+91.5=180
Subtract 91.5 to both sides:
6x=88.5
Divide 6 to both sides:
x=14.75
The answer is 1) 14.75
Hope this helped!

Please help me i need help

Answers

Answer:

H

E

A

R

T

S

Step-by-step explanation:

easy

A survey result shows that cell phone usage among teenagers rose from 63% in 2006 to 71% in 2008.
Of the following choices, which statement about cell phone use among teenagers is true?
a. Cell phone usage rose by 11.2 percentage points.
b. Cell phone usage rose by 12.7 percentage points.
c. Cell phone usage rose by 12.7%.
d. Cell phone usage rose by 8%.

Answers

Answer:

d. Cell phone usage rose by 8%.

Explanation:

71 - 63 = 8

The statement that is true about percentage increase in cell phone use among teenagers is; c. Cell phone usage rose by 12.7%.

How to calculate percentage increase?

We are given;

Percentage of teenagers using cell phone in 2006 = 63%

Percentage of teenagers using cell phone in 2008 = 71%

Thus;

Percentage increase = (71% - 63%)/63%

Percentage increase = 12.7%

Read more about Percentage Increase at; https://brainly.com/question/11360390

#SPJ6

The serum cholesterol levels (in mg/dL) of 18 individuals are

220, 203, 211, 191, 257, 259, 242, 218, 186, 298, 228, 201, 206, 240, 189, 198, 247, 222

Find the 25th and 90th percentile s for these cholesterol levels.​

Answers

Answer:

228 and 222

Step-by-step explanation:

if the average of 6 numbers is 60, what is their sum?

Answers

Answer:

10

Step-by-step explanation:

The average of a dataset is the mean value of the dataset. It is calculated by dividing the sum of the dataset by the number of items in the dataset. The sum of the 6 numbers is 360.

Given that:

[tex]Average = 60[/tex]

[tex]n = 6[/tex] --- the number of data in the dataset

The average of a dataset is represented as:

[tex]Average = \frac{Sum}{n}[/tex]

Make Sum the subject

[tex]Sum = Average * n[/tex]

This gives:

[tex]Sum = 60 * 6[/tex]

[tex]Sum = 360[/tex]

Hence, the sum of the 6 numbers is 360.

Read more about averages at:

https://brainly.com/question/16480181

Is segment ST tangent to circle P1

Answers

Answer:

B . Yes

Step-by-step explanation:

Recall: a tangent of a circle is perpendicular to the radius of a circle, forming a right angle at the point of tangency.

Therefore, if segment ST is tangent to circle P, it means that m<T = 90°, and ∆PST is a right triangle.

To know if ∆PST is a right triangle, the side lengths should satisfy the Pythagorean triple rule, which is:

c² = a² + b², where,

c = longest side (hypotenuse) = 37

a = 12

b = 35

Plug in the value

37² = 12² + 35²

1,369 = 1,369 (true)

Therefore we can conclude that ∆PST is a right triangle, this implies that m<T = 90°.

Thus, segment ST is a tangent to circle P.

i need help with this one plz! (marking BRAINLIST) :) ​

Answers

Answer:

x=22

Step-by-step explanation:

the triangle in which x is in is an equilateral triangle.

44 is an exterior angle to that triangle.

an exterior angle is always equal to tbe sum of the opposite 2 interior angles.

because that triangle is equilateral

x =44 ÷ 2

x=22

A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:

f(n) = 12(1.03)n

What is the average rate of change of the function f(n) from n = 3 to n = 10, and what does it represent? (4 points)

Answers

Answer:

The average of rate was of 0.4314 cm/day, which means that on average, during this interval, the plant grew by 0.4314 cm each day.

Step-by-step explanation:

Average rate of change:

The average rate of change of a function f(x), from x = a to x = b, is given by:

[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]

In this question:

[tex]f(x) = 12(1.03)^n[/tex]

From n = 3 to n = 10

[tex]a = 3, b = 10[/tex]

[tex]f(b) = f(10) = 12(1.03)^{10} = 16.13[/tex]

[tex]f(a) = f(3) = 12(1.03)^{3} = 13.11[/tex]

Average rate of change:

[tex]A = \frac{f(b)-f(a)}{b-a} = \frac{16.13-13.11}{10-3} = 0.4314[/tex]

The average of rate was of 0.4314 cm/day, which means that on average, during this interval, the plant grew by 0.4314 cm each day.

Select 3 sides that can form a right triangle.

Answers

Answer: 14, 48, 50

Step-by-step explanation:

14^2+48^2=50^2

(select all the correct answers) Which function are correctly graphed

Answers

9514 1404 393

Answer:

  A, D

Step-by-step explanation:

The first and last functions are correctly graphed here. The others suffer from misplaced solid/open dots. When the inequality is < or > and does not include the "or equal to" bar (as in ≤ or ≥), then the corresponding end dot is an open circle.

HELP PLS!!

A circle has been divided into 4 equal angles. is each angle acute, obtuse or right?

Answers

Answer:

Right

Step-by-step explanation:

360/4 = 90

90° is a right angle

I’ll give brainliest

Answers

Answer:

C. C = 3P

Step-by-step explanation:

C = total costs

P = number of popsicles

Unit price of 1 popsicle = $3

To get the total cost of popsicles, we need to multiply the number of popsicles bought by the price of each popsicles

Total cost of popsicles = number of popsicles × unit price

Thus, the question would be written as:

C = 3P

Find the area of the triangle to the nearest tenth . Pleaseeee help

Answers

Answer:

15.8 cm²

Step-by-step explanation:

Please see attached photo for diagram.

We'll begin by calculating the angle A. This can be obtained as follow:

B = 56°

C = 78°

A =?

A + B + C = 180 (Sum of the angle in triangle)

A + 56 + 78 = 180

A + 134 = 180

Collect like terms

A = 180 – 134

A = 46°

Next, we shall determine the value of b by using the sine rule. This can be obtained:

Side opposite angle C (c) = 7.2 cm

Angle C = 78°

Angle B = 56°

Side opposite angle B (b) =?

b/Sine B = c/sine C

b/Sine 56 = 7.2/Sine 78

Cross multiply

b × Sine 78 = 7.2 × Sine 56

Divide both side by Sine 78

b = 7.2 × Sine 56 / Sine 78

b = 6.1 cm

Finally, we shall determine the area of the triangle. This can be obtained as follow:

Side opposite angle C (c) = 7.2 cm

Side opposite angle B (b) = 6.1 cm

Angle A = 46°

Area (A) =?

A = ½bcSineA

A = ½ × 6.1 × 7.2 × Sine 46

A = 15.8 cm²

Therefore, the area of the triangle is 15.8 cm²

Use the order of operations to simplify the expression
(5.4)² - 5.4²

Answers

Answer is 0 for the question

Answer:

0

Step-by-step explanation:

(5.4)^2 - 5.4^2

= 5.4^2 - 5.4^2

= 5,4^2(1 - 1)

= 5.4^2(0)

= 0

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