which function represents the inverse function below? please help ​

Answer:

#2 486

#3 25

#4 25

#5 1,000,000

Step-by-step explanation:

Sequences like this always have some rule that determines the next number, a pattern that needs to be followed. Sometimes the pattern is easy to find, sometimes really hard.

#2 One of the first things to check is the ratio of adjacent numbers. Here we have 2 then 6 then 18 then 54 etc.

The most prominent feature of these numbers is that the next number is always three times bigger than the previous. It's safe to assume that the missing number will be 162 • 3 = 486.

#3 Of course numbers can be arranged in the decreasing order as well. However, that does not change their ratio. In this example, carefully examining, we can see that each number in the sequence is exactly twice smaller than the previous:

800 -> 400 -> 200 -> 100  etc.

Following this pattern, we can say that the next number will be 50 / 2 = 25.

#4 Of course, ratio is not the only way to help us find the pattern. One of the very often used methods is also the difference between adjacent numbers. Let's subtract each adjacent pair:

4 - 1 = 3

9 - 4 =5

16 - 9 = 7

Longer the sequence is, greater are the chances to see the pattern, but from this we could conclude that the difference between adjacent numbers is always an odd number (3, 5, 7). We could say that the next odd number is 9, so the missing number is 16 + 9 = 25

There is another pattern that could be found. This sequence could also represent the sequence of squared numbers:

1^2, 2°2, 3°2, 4^2

In this case, the next number would be 5^2 which is also 25.

#5 Again, we can find a pattern established on the ratio of numbers, but this time with repetitive symbol L. After every L, the number is a thousand times bigger than the previous number:

0.001 -> 1 -> 1000

So, following this pattern, the missing number would be 1000 • 1000 which equals to 1000000 (a million).

Answer:

[tex]f=6.8[/tex]  

Step-by-step explanation:

Given equation:

[tex]88.1-2.3f=72.46[/tex]

To solve for the unknown variable [tex]f[/tex].

Solution:

In order to solve for [tex]f[/tex], we will isolate [tex]f[/tex] alone on one side by carrying out math operations to both sides.

We have:

[tex]88.1-2.3f=72.46[/tex]

Subtracting both sides by 88.1

[tex]88.1-88.1-2.3f=72.46-88.1[/tex]

[tex]-2.3f=-15.64[/tex]

Dividing both sides by -2.3

[tex]\frac{-2.3f}{-2.3}=\frac{-15.64}{-2.3}[/tex]

∴ [tex]f=6.8[/tex]    (Answer)

The system of inequalities is x+y≥250 and 3x+2y≤800.

Step-by-step explanation:

Given,

People to invite = at least 250

At least 250 means that the number can increase from 250.

Cups to be provided = only 800

It means the number cannot exceed 800.

Number of adults = A

Number of children = C

According to given statement;

x+y≥250

3x+2y≤800

The system of inequalities is x+y≥250 and 3x+2y≤800.

Keywords: linear inequalities, addition

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Answer:

The correct option:  x + y = 6

Step-by-step explanation:

In a Cartesian system or a coordinate system, the abscissa is the value of the horizontal (x) value and the ordinate is the value of the vertical (y) value.

So, The sum of the abscissa and the ordinate = x + y when written as an algebraic expression.

Since given that The sum of the abscissa and the ordinate is six

So,  the correct equation is x + y = 6

The original number is 64

Step-by-step explanation:

The given is:

We need to find the original number

Assume that the unit digit of the number is x and the ten digit is y

∵ The unite digit of the number is x

∵ The ten digit of the number is y

∵ The sum of the two digits is 10

- Add x and y, then equate the sum by 10

∴ x + y = 10 ⇒ (1)

∵ The value of the number is x + 10y

- Reverse the digits means y will be the unit digit and x will

   be the ten digit

∴ The new number is y + 10x

∵ The new number is 18 less than the original number

- That means their difference is 18, (the original number minus

   the new number = 18)

∴ (x + 10y) - (y + 10x) = 18

- Simplify the left hand side

∴ x + 10y - y - 10x = 18

- Add the like terms in the left hand side

∴ -9x + 9y = 18

- Divide both sides by 9

∴ -x + y = 2 ⇒ (2)

Now we have a system of equation to solve it

Add equation (1) and (2) to eliminate x

∴ 2y = 12

- Divide both sides by 2

∴ y = 6

- Substitute the value of y in equation (1) to find x

∵ x + 6 = 10

- Subtract 6 from both sides

∴ x = 4

∵ The original number is x + 10y

∵ x = 4 and y = 6

∴ The original number = 4 + 10(6) = 4 + 60 = 64

The original number is 64

To check the answer reverse the digits of the number

∵ The new number is y + 10x

∴ The new number = 6 + 10(4) = 6 + 40 = 46

∵ The original number is 64

∵ The new number is 46

∵ 64 - 46 = 18

∴ The new number is less than the original number by 18

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Answer:

The original number is 64.

Answer:

Step-by-step explanation:

l = -2.4t + 75

what this equation is saying is that the initial height of the anchor is 75 meters (thats also ur y intercept), and it drops at a rate of 2.4 meters per second.

another way u could look at it is the initial height is before u drop the anchor....0 seconds...meaning sub in 0 for t

l = 2.4(0) + 75

l = 0 + 75

l = 75 meters <=====

Answer:

Step-by-step explanation:

X + 61° = 90° {right angle}

X = 90° - 61°

X = 29°

Answer:

23/12x+7

Step-by-step explanation:

2 3/4=11/4

8 2/5=42/5

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

11/4x-5/6(x-42/5)

11/4x-5/6x+210/30

11/4x-5/6x+7

33/12x-10/12x+7

23/12x+7

Answer:

The total amount that Beyonce will pay for the chair is $9100.

Step-by-step explanation:

The Principal amount of chair  = $6500

Rate of interest  = 8%

Time = 5 years

Now, SIMPLE INTEREST  = [tex]\frac{P\times R \times T}{100}[/tex]

So, here calculating the interest on the chair, we get:

[tex]SI = \frac{6500 \times 5 \times 8}{100} = 2600[/tex]

So, the interest on the amount of chair for 5 years  is $2600.

Total amount of chair  = Original Amount of Chair + Interest Amount

                                      = $6500 + $2600 = $9100

Hence, the total amount that Beyonce will pay for the chair is $9100.

To find the total amount, calculate the interest and add it to the principal amount.

Simple interest is calculated using the formula: I = P * r * t, where I is the interest, P is the principal amount (loan), r is the annual interest rate, and t is the time in years. In this case, the principal amount (loan) is $6500, the annual interest rate is 8%, and the time is 5 years. So, the interest can be calculated as: I = 6500 * 0.08 * 5 = $2600.

To find the total amount that Beyonce will pay for the chair, we need to add the interest to the principal amount. The total amount is given by the formula: Total Amount = Principal + Interest. Therefore, Total Amount = 6500 + 2600 = $9100.

So, Beyonce will pay a total amount of $9100 for the chair, including the principal amount and interest.

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Answer:

x=0.9

Step-by-step explanation:

1. You first have to isolate the x term so you subtract 6.814 from both sides which makes the equation 1.54x=1.386

2. Then, to isolate "x", you divide 1.54 on both sides to get rid of the 1.54 which makes x=.9

Answer:

Part a) see the explanation

Part b) The graph in the attached figure

Step-by-step explanation:

The complete question is

The length of a snake in a video game doubles every minute. the function f(x)=10*(2)^x represents the length of the snake in centimeters. the time x=0 represents when the game started.

a) label the correct axes with "length (cm)" and"time (minutes)"

b) graph f(x)=10*(2)^x

Part a) we know that

we have a exponential function of the form

[tex]f(x)=a(b^x)[/tex]

where

f(x) -----> the length of a snake in a video game in centimeters

x ----> the time in minutes

a is the initial value or y-intercept of the linear equation

b is the base of the exponential equation

In this problem

[tex]f(x)=10(2^x)[/tex]

so

[tex]a=10\ cm[/tex] ---> initial value, value of y when the value of x is equal to zero[tex]b=2[/tex] ----> factor growth

[tex]b=(1+r)\\r=b-1=2-1=1[/tex]

[tex]r=100\%[/tex] ----> percent rate of change

Is a exponential growth function

Part b) Graph the function

To graph the function we need different points

assume different values of x and find the values of f(x)

For x=0 ---->  [tex]f(0)=10(2^0)=10[/tex] ----> point (0,10)

For x=1 ---->  [tex]f(1)=10(2^1)=20[/tex] ----> point (1,20)

For x=2 ---->  [tex]f(2)=10(2^2)=40[/tex] ----> point (2,40)

For x=3 ----> [tex]f(3)=10(2^3)=80[/tex] ----> point (3,80)

For x=4 ---->  f(4)=10(2^4)=160 ----> point (4,160)

Plot the points, connect them and draw the graph

see the attached figure

Answer:

Area = π×(3.5)^2+ π×(3.5)^2

=76,96902001295 inch²

The intersection of the sets of outcomes of events A and B is the set of all outcomes that are common in both events A and B. This is a concept from set theory in mathematics.

The correct answer to the given question is option B.

The correct statement that best describes the intersection of the sets of outcomes of events A and B is 'The intersection of the sets is the set of all outcomes in events A and B'.

In mathematical terms, the intersection of two sets, often denoted as A ∩ B, is the set of elements which are in both A and B.

Thus, the intersection of two sets of outcomes of events A and B, would consequently be the set of all outcomes that are common in both events A and B.

This is mainly a concept from set theory, a fundamental part of mathematics that deals with the study of sets, which are collections of objects.

For instance, if the set A = {1, 2, 3} and the set B = {2, 3, 4}, then A ∩ B = {2, 3}. In this example, 2 and 3 are the outcomes that are common in both events A and B.

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Answer:

2 BTUs/cubic foot.

Step-by-step explanation:

Suppose that 2 people exercising in an enclosed room are each generating about 2,400 BTUs of body heat per hour.

So, 2 people will produce (2400 × 2) = 4800 BTUs for 1 hour.

Now, the volume of the room with dimensions (20 ft by 12 ft by 10 ft) will be (20 × 12 × 10) = 2400 cubic feet.

Therefore, the number of BTUs per cubic foot will be produced  by [tex]\frac{4800}{2400} = 2[/tex] BTUs/cubic foot. (Answer)

Answer:

1.12*10^(-15)

Step-by-step explanation:

Answer:

1.12e-15

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Option A

[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6}) = 6.9977 \times 10^{-3}[/tex]

Solution:

Given expression is:

[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6})[/tex]

To evaluate the expression, let us make the exponent of 10 same

[tex]2.3 \times 10^{-6} = 0.0023 \times 10^{-6+3} = 0.0023 \times 10^{-3}[/tex]

[ Here, decimal point is moved three times left, so add 3 ]

Therefore,

[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6}) = (7 \times 10^{-3}) - (0.0023 \times 10^{-3})[/tex]

[tex]\text{Take the } 10^{-3} \text{ as common }[/tex]

[tex](7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 10^{-3}(7-0.0023)\\\\\text{ Solve for terms inside the bracket }\\\\(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 10^{-3} \times 6.9977\\\\\text{Therefore, the simplified expression is: }\\\\(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 6.9977 \times 10^{-3}[/tex]

Thus Option A is correct

Answer:

D) 24.

Step-by-step explanation:

The solution is 24 routes. To determine the number of different routes we multiply the routes for each part of the trip. 4(3)(2) = 24 routes.

He can take 24 different routes for his trip

The correct option is option D)

What is permutation and combination?

an arrangement of objects in a definite order is known as permutation. The members or elements of sets are arranged here in a sequence.  a combination is a selection of items from a set which has distinct members, and the order of selection does not matter. even though the terms are used together they are different and formula for calculating them is also different

We are given that,

Jacksonville to Atlanta: 4 routes

Atlanta to Knoxville: 3 routes

Knoxville to Indianapolis: 2 routes

Also Sammy is traveling from Jacksonville to Atlanta to Knoxville to Indianapolis

To find the different routes sammy can take can be computed as

4*3*2=24ways

Hence Sammy can take 24 routes

The correct option is option D)

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Answer:

Step-by-step explanation:

Convert into improper fractions

Add numerators and denominators

Simplify

Hope this helps :)

Answer:

The number of comic books did they have in all   = 56

Step-by-step explanation:

The ratio of comics with Susan : Abe = 3 : 5

Let us assume the common factor on this ratio = m

So, the number of comics Susan has  = 3 m

The number of comics Abe has  = 5 m

Also, given:  Abe had 14 more comic books than Susan

So, the number of comics Abe had  = 14 + 3 m

⇒  5 m  =  3 m + 14

or,   2 m = 14, or m = 7

So, the number of books Susan has = 3 m = 3 x 7 = 21 books

The number of books Abe has  = 5 m = 5 x 7 = 35

So, the book they have in all = 21 +  35 = 56

Answer:

Step-by-step explanation:

Let the number be x and y

xy = 378.......(1)

x + y = 41......(2)

Making y as subject in (2)

y = 41 - x......(3)

Substitute it in (1)

x(41 - x) = 378

41x - x² = 378

x² - 41x + 378 = 0

x² - 27x - 14x + 378 = 0

(x² - 27x) - (14x - 378) = 0

x(x - 27) - 14(x - 27) = 0

(x -14)(x - 27) = 0

x - 14 = 0 or x - 27 = 0

x = 14 or x = 27

And y = 41 - x

When x = 14

y = 41 - 14 = 27

y = 27

When x = 27

y = 41 - 27 = 14

y = 14

The two numbers are 14 and 27.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Let the numbers are x and y.

Then,

the system of equations

xy = 378  {equation 1}

x + y = 41   {equation 2}

y = 41 - x

Then

x(41 - x) = 378

41x - x² = 378

x² - 41x + 378 = 0

x² - 27x - 14x + 378 = 0

(x² - 27x) - (14x - 378) = 0

x(x - 27) - 14(x - 27) = 0

(x -14)(x - 27) = 0

x - 14 = 0 or x - 27 = 0

x = 14 or x = 27

And y = 41 - x

When x = 14

y = 41 - 14 = 27

y = 27

When x = 27

y = 41 - 27 = 14

y = 14

Therefore, the  14 and 27 are the numbers.

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Answer:

The rate of change for the interval shown in the table is 1 , so the function is a linear function.

Step-by-step explanation:

See the table attached.

The table shows selected points from a function.

Now, the given interval is x = 1 to x = 4.

For, x = 1, f(x) = 2 and for x = 4. the function f(x) = 5.

Therefore, the rate of change for the interval shown in the table i.e slope of the line is [tex]\frac{5 - 2}{4 - 1} = 1[/tex] and it is constant throughout the interval so the function is a linear function. (Answer)

The rate of change for the interval shown in the table is constant , so the function is a linear function.

Note the following important points:

1. Linear Function:

If the difference between y values remains constant for any pair of consecutive points ([tex]y_2-y_1 = y_3-y_2 = y_4-y_3,[/tex]and so on), the function exhibits a constant rate of change, indicating a linear function. In this case, the rate of change would be the difference between two y values divided by the difference between their corresponding x values (e.g., [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]).

2. Non-Linear Function:

If the difference between y values varies between consecutive points, the function would be non-linear. The specific type of non-linear function (e.g., quadratic, exponential) would require further analysis with more data points or additional information about the function's behavior.

In this case, as shown in the attached table, it is clear that

For [tex]x_1=1, y_1=f(x)=2[/tex].

For [tex]x_2=2, y_2=f(x)=3[/tex].

For[tex]x_3=, y_3=f(x)=4[/tex].

For [tex]x_4=, y_4=f(x)=5[/tex], and so on.

Thus the rate of change for the interval shown in the table or its slope is constant as evident from the following calculation.

[tex]\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{3-2}{2-1}=1\\ \frac{(y_3-y_2)}{(x_3-x_2)}=\frac{4-3}{3-2}=1\\\frac{(y_4-y_3)}{(x_4-x_3)}=\frac{5-4}{4-3} =1[/tex].

So it is clear that, the rate of change for the interval shown in the table is constant , so the function is a linear function.

Introduction

Wrestling is a wonderful activity with many advantages for the student-athlete. It is a sport that is highly

competitive, exciting and satisfying. It is a sport that provides for individual and team competition. It is -

and should be - fun. Unfortunately, the practice of losing weight by not eating, restricting fluid intake and

over-exercising reduces the sport's fun. This information is presented to help clear up misconceptions

regarding wrestling and weight loss. I also hope to give some guidance to those who desire to manage

their weight properly in preparation for and during the wrestling season.

History and Stigma

For too long, the wrestling community has unthinkingly accepted the myth that to be a good wrestler, you

must cut weight. The generally accepted thinking is something like this: if your natural weight is 135

pounds, you may be a good wrestler at 135 pounds. But if you wrestle at 130 pounds, you'll be a better

wrestler. And if you can make it down to 125, you'll be a state champion. No facts support that widely held

view, yet wrestlers and parents subscribe to that faulty reasoning. Looking further back, many remember

the days that losing excessive weight was a specific practice and expectation among wrestlers. It was

supposed to teach sacrifice, commitment, and the idea of “No Pain, No Gain.”

Regardless of the current attitude of the majority of the wrestling community, the stigma that an unhealthy

loss of weight is a requirement of wrestling among outside observers sticks. The Virginia High School

League has followed national guidelines to establish rules that encourage healthy weight management

among wrestlers.

Current Regulations

Preseason weight certification is accomplished with three steps. The first is determining each wrestler’s

body fat percentage using skin fold calipers. Next, the wrestler completes a hydration test, to insure

against a dehydrated weight measurement, and the wrestler weighs in. The third step is the calculation of

the wrestler’s minimum wrestling weight based on 7% body fat for males and 12% for females. The

wrestler may not wrestle at a weight class below his minimum weight during the season. The wrestler is

also restricted from losing more then 1.5% body weight loss per week (official weigh-ins at certification,

matches, and tournaments are used for this calculation). A one-pound per month growth allowance is

provided to allow for the natural growth of this age group. The VHSL advises, and we have instituted,

daily weigh-ins before and after practice to monitor weight-loss and dehydration.

Additionally, the National Federation of State High School Associations has adopted several other rules to

guide coaches and wrestlers while managing their weight. Wrestlers are discouraged from wrestling at a

weight class more then one weight class above their certified weight.

The equation that models the situation of a wrestler's varying weight is w = x +/- 3.2, with x representing the normal weight. The minimum weight is 164.8 pounds and the maximum weight is 171.2 pounds.

To write an equation that models the situation, we can use the variables x and w to represent the normal weight and the varying weight, respectively. The equation can be written as w = x +/- 3.2, where the +/- sign represents that the weight can vary by as much as 3.2 pounds. Given that the normal weight is 168 pounds, the minimum weight would be 168 - 3.2 = 164.8 pounds, and the maximum weight would be 168 + 3.2 = 171.2 pounds.

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-8, 3.5, -1.15. -9 1/4

I hope this helped!

huh cant see nun............

Answer:

Step-by-step explanation:

buys it for $ 45

well...you know the business is gonna want to make a profit...so they would have to sell it for more then they bought it for.

I would say $ 60 or $ 80

Final answer:

Given the wholesale price of $45, the sensible retail prices to charge customers would be $60 and $80, as they both allow for covering costs and earning a profit, unlike $20 and $40, which would incur losses.

Explanation:

The question involves understanding wholesale and retail prices, essential concepts in economics and business mathematics. When a company buys an item at a wholesale price, it usually marks up the price when selling it at retail to cover costs and generate profit. Given the wholesale price of $45, the retail prices that make sense to charge customers would be those higher than $45 because selling at a lower price would result in a loss.

Both $60 and $80 are above the wholesale price and would allow the company to cover additional costs and earn a profit. $20 and $40 would not make sense as they are below the wholesale price, leading to a loss per item sold.

Answer:

186.111111111

Step-by-step explanation:

Answer: the answer is 186.111111

The expression of multiplication used will be 26x = 1300.

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 Miranda was asked to solve the problem 1300 divided by 26. The expression will be written as,

26x = 1300

x = 1300 / 26

x = 50

Hence, the expression of multiplication used will be 26x = 1300.

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Miranda can solve 1300 divided by 26 by using multiplication – specifically, by finding what number multiplies with 26 to result in 1300. She can break down the number 26 into smaller factors for easier estimation, using inverse operations to eventually find that 50 is the correct answer.

Using Multiplication to Solve Division Problems

Miranda was asked to solve the problem 1300 divided by 26. To use multiplication to solve this division problem, she can apply the reciprocal approach. Essentially, she can multiply 1300 by the reciprocal (the inverse) of 26. The reciprocal of a number 'a' is 1/a, so the reciprocal of 26 is 1/26. However, finding the reciprocal of 26 directly can be challenging, so we can use intuitive steps that simplify the problem.

For example, we could productively think about what number, when multiplied by 26, gives us 1300. This is a form of inverse operations. One way to approach this is to break down 26 into factors like 2 and 13, which might lead to simpler multiples to work with. She may start by estimating and refining her estimations by multiplying different numbers by 26 and seeing how close she gets to 1300. It’s a trial and error process, but eventually, she will find the correct answer of 50, as 26 multiplied by 50 equals 1300.

Answer

overlapping

explanation:

This is overlapping set because at least one common element (5) is present in both set.

Answer:

28

Step-by-step explanation:

Plug in the corresponding numbers to the corresponding variables. Note that:

m = 7

r = 8

t = 2

mr/t = (7 * 8)/2

(7 * (8/2)) = 7 * 4 = 28

28 is your answer.

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