Suppose that a function pairs elements from set A with elements from set B . Recall that a function is called onto if every element in B is paired with at least one element in A .
b. What are the domain and range of the function?

A composite function exists as a function that depends on another function. The value for  (f⁰f)(0) = - 4/3

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the two functions be g(x) = 3x + 2 and f(x) = x - 2/3

Now, (f⁰f)(x) = f[f(x)]

f(x) = x - 2/3

(f⁰f)(x) = f( x - 2/3)

simplifying the above equation, we get

(f⁰f)(x) = (x - 2/3) - 2/3  

(f⁰f)(0) = - 2/3 - 2/3

(f⁰f)(0) = - 4/3

Therefore, the value of (f⁰f)(0) = - 4/3.

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The common rate of both expressions are equal, so the expressions 64,96 and 60,90 are proportional

The expressions are given as

64,96 and 60,90

Rewrite the expressions as

(x, y) = (64,96) and (60,90)

As a general rule

Proportional expressions have the same constant rate

The constant rate (r) of the expressions is then calculated as

r = y/x

For the expression (64, 96), we have the following computation

r = 96/64

Evaluate the quotient

So, we have

r = 1.5

For the expression (60, 90), we have the following computation

r = 90/60

Evaluate the quotient

So, we have

r = 1.5

The common rate of both expressions are equal i.e. 1.5

Hence, the expressions 64,96 and 60,90 are proportional

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n-2 is the next larger odd integer if the number represented by n-3 is an odd number.

Parity, in mathematics, is the characteristic of an integer that determines whether it is even or odd. If an integer is a multiple of two, it is even; otherwise, it is odd. For instance, 4, 0, and 82 are even. 3, 5, 7, and 21 are odd numbers in comparison.

Whole numbers that cannot be divided perfectly into pairs are referred to as odd numbers. When two is divided by an odd number, one is left over.

based on the available facts;

Formulate based on the conditions stated:

(n-3)+1

Rearrange and group related terms:

n+(-3+1)

Calculate the sum or difference:

n-2

Answer is n-2

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The function that relates the sales and the number of muffins is :

S = 2.5 m

The sales amount can be find by the total sales. That is , if there are n products to sell and selling amount is x rs. then we can easily find the total sales by multiplying them and by this total sales we can easily find the number of items sold per units and vice versa.

In the question given,

amount (A) = $ 250.00

Now take any of two values from table ,

Choose any two points and calculate the slope:

slope = [tex]\frac{50 - 20}{20 - 8}[/tex] =  2.5

thus, y = 2.5x

Hence we can say the function that relates the sales and the number of muffins is :

S = 2.5 m

where, S = sales amount

           m = number of muffins to be sell

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The complete question is:

In a bake sale, you recorded the number of muffins sold and the amount of sales in a table as shown.

a. What is a function that relates the sales and the number of muffins?

b. How many muffins would you have to sell to make at least $ 250.00 in sales?

Answer:

2x>8

Step-by-step explanation:

this should be right

Answer:

14

Step-by-step explanation:

To solve [tex]\frac{ab^2-4}{10}[/tex]

We need to know what [tex]ab^2[/tex] is.

[tex]ab^2 = a*b^2 = 4 * 6^2 = 4*36 = 144[/tex]

[tex]\frac{144-4}{10} = 140/10 =14[/tex]

Hope this helps :)

Have a great day!

Answer:

square = width*height,

circle=pi*r^2

triangle = w * h * 0.5

Step-by-step explanation:

square = width*height,

circle=pi*r^2

triangle = w * h * 0.5

The exponential expression [tex]6^{-3}[/tex]/ [tex]3^{-2}[/tex] * 6² is equivalent to the exponential expression is 3² / [tex]6^{5}[/tex] which is option 2 and not option 1

The Exponential expression given to us is 6^-3/3^-2x6^2 or we can write it as

[tex]6^{-3}[/tex]/ [tex]3^{-2}[/tex] * 6²

There is a rule for solving exponents that when we reciprocate the fractions with exponential powers the signs of powers get changed from negative to positive and positive to negative

for example

[tex]x^{-2}[/tex] is written as [tex]\frac{1}{x^{2} }[/tex]

So, we can write the above  exponential expression as

3² / 6³ × 6²

Also, when two same numbers with different powers then the base remains same and powers get added.

3² / [tex]6^{3+5}[/tex]

3² / [tex]6^{5}[/tex]

So, the exponential expression [tex]6^{-3}[/tex]/ [tex]3^{-2}[/tex] * 6² is equivalent to the exponential expression is 3² / [tex]6^{5}[/tex] which is option 2 and not option 1

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Answer:

Hi the answer to that question is 2

Answer:The answer to your question is

I bought

12

hardcover books and

24

softcover books.

Explanation:

We shall represent the hardcover books purchased by

x

and the softcover books purchased by

y

. From the details we can write two equations:

x

+

y

=

36

8

x

+

2

y

=

144

From the first equation we can calculate the value of

y

.

x

+

y

=

36

Subtract

x

from each side.

y

=

36

−

x

Now, in the second equation, substitute

y

with

(

36

−

x

)

.

8

x

+

2

y

=

144

8

x

+

2

(

36

−

x

)

=

144

Open the brackets and simplify.

8

x

+

72

−

2

x

=

144

6

x

+

72

=

144

Subtract

72

from both sides.

6

x

=

72

Divide both sides by

6

.

x

=

12

Now in the first equation, substitute

x

with

12

.

x

+

y

=

36

12

+

y

=

36

Subtract

12

from both sides.

y

=

24

Step-by-step explanation:

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The angle of A when the polygon slides 4 units left and 3 units up on the coordinate plane is 75°.

From the information, Polygon AVC’s slides 4 units left and 3 units up on the coordinate plane. If the original measure of angle A was 75 degrees.

It should be noted that translation doesn't change the angle. Therefore, the number will be the same as the translation is stationary.

Therefore, the angle of A when the polygon slides 4 units left and 3 units up on the coordinate plane is 75°

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The trace of water left on the floor is the circumference of 565.2 cm.

Water traces are seen on the floor from a wet bicycle tire.

The bicycle wheel makes three complete rotations before coming to a stop, circumference  and the tire has a radius of 30 cm.

The circle of the cycle is indicated by the water stain left on the floor.

Given the radius = 30 cm

So,

C = 2 × 3.14 × 30

C = 188.4

Given that a bicycle wheel turns three times before pausing to pick up a trace of water, the answer is,

3 x 188.4 = 565.2 cm

the floor has a 565.2 centimeter trace of water.

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Aqil have 88 stickers.

Let Ryan have x stickers initially. Then Aqil will have (352-x) stickers. Ryan lost 25% of his stickers i.e., x-(25% of x)

= x- 25x/100

= x-x/4

= 3x/4

After Ryan lost 25% of his stickers, the ratio of Ryan's stickers to Aqil's stickers was 9:4 i.e.,

3x/4 : (352-x) = 9 : 4

⇒ 3x/4/(352-x) = 9/4

⇒3x/4 x 4 = 9 x (352-x)

⇒3x = 3168-9x

⇒3x+9x = 3168

⇒12x = 3168

⇒x = 3168/12

⇒x = 264

∴ Ryan have 264 stickers of the total 352 stickers and Aqil will have (352-x) i.e., 88 stickers.

Hence, Aqil have 88 stickers out of the 352 stickers.

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We can buy 9 programs after buying the laptop if we want to spend $ 500 at most on the laptop.

The cost of the laptop = $ 319

The maximum money we have = $ 500

Money left after purchasing the laptop will be calculated by using subtraction.

Money left = $ 500 - $ 319 = $ 181

Now, cost of each program = $ 20

The number of programs we can buy = $ 181 / $ 20

The number of programs we can buy = 9.05

That means 9 programs.

Therefore, we get that, we can buy 9 programs after buying the laptop if we want to spend $ 500 at most on the laptop.

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An expression for the combined total dollar amount he earned this month:

Total Earning = 15b + P(N - b)

where, b is the total hours worked as a tutor

P is the amount earned by Ryan per hour as a waiter

N is the total number of possible hours Ryan can work in a month

In this question,

Ryan works as a tutor for $15 an hour and as a waiter for $10 an hour. This month, he worked a combined total of 81 hours at his two jobs.

Let the number of hours Ryan works daily as a waiter be x

and the number of hours worked daily as a tutor be y

Ryan earns $15 per hour as tutor.

So, we get an expression for the daily earnings on tutoring = 15y

Let Ryan earns $P per hour as waiter.

so, we get an expression for the daily earning as a waiter = Px

The total possible hours Ryan can work in a month is dependent on conditions not specified.

Assuming 24 working days (6 days weekly for 4 weeks) in a month with maximum approved work hours of 12 hours daily, the total hours Ryan can work will equal 24 x 12 = 288 hours

This 288hrs is an estimate and can change based on applicable hours of work daily and number of working days in a month; it can also be represented as N

If b is the total hours Ryan worked as a tutor this month, the hours Ryan can work as a waiter in a month is equal to 288 - b

So, in a month, Ryan will earn 15b as a tutor and P(288-b) as a waiter or optionally P(N - b)

So, the combined dollar amount earned in a month is:

Total Earning = 15b + P(N - b)

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Answer:

Step-by-step explanation:

Convert 9 feet into meters:

Round 2.7432 meters:

There are 24 possible arrangements that begin with letter R

Combinations are used to determine the number of selections of an item within another while permutation is used for arrangements

The arrangements of the digits is an illustration of factorials

The word is given as: SHREK

If the first letter begins with the letter R, then we have the following possible arrangements

The number of arrangement is the product of the above values

So, we have

Arrangement = 1 * 4 * 3 * 2 * 1

Evaluate

Arrangement = 24

Hence. there are 24 possible arrangements that begin with letter R

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Answer:

$29.40

Step-by-step explanation:

Answer:

He would have $100 in his bank account from the information provided

Step-by-step explanation:

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(10,8)

Equation Form:

x=10,y=8

Step-by-step explanation:

Using the properties of logarithm the value of the expression is  [tex]log_{6} 12 + log_{6} 3 = 2[/tex]

A logarithm is the power to which a number must be raised in order to get some other number.

According to the question we have been given the logarithmic expression as

                        = [tex]log_{6} 12 + log_{6} 3[/tex]

The properties of logarithm that we are going to use are :

  [tex]log(x*y) = logx + logy[/tex]   and   [tex]log_{a} a = 1[/tex]

Also we can see that the base are same so we can use the property of logarithm in the given equation.

Now solving it step by step using the properties of logarithm we get

                    [tex]= log_{6} (12*3)\\= log_{6} 36\\= log_{6} 6^{2} \\= 2* log_{6} 6\\= 2*1\\ = 2[/tex]                      

Hence using the properties of logarithm the value of the expression is [tex]log_{6} 12 + log_{6} 3 = 2[/tex]

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The equation of the line is y = -(1/3)x + 5,

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

We have,

The line is perpendicular to y = 3x - 2 and passes through (3, 4).

The slope of the line and the slope of y = 3x - 2 is:

[tex]m_{1} m_{2}[/tex] = -1

Where [tex]m_{2}[/tex] = 3

[tex]m_{1}[/tex] = -1/3

The equation for the line that passes (3, 4) is given by:

y - 4 = -1/3 ( x - 3)

y = -1/3x + 1 + 4

y = -(1/3)x + 5

Thus the equation of the line is y = -(1/3)x + 5,

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The complete question is:

What is the equation of the line perpendicular to y = 3x − 2  and passes through point (3,4)?

Caroline and Rodney, on their way to the canoe livery, stopped to eat lunch at the point on their map with coordinates of (-2, -1).

The coordinates of a point on a two dimensional plane are two numbers that define its location.

The given coordinates of the journey are;

Required; The coordinates of the map where Caroline and Rodney stopped for lunch.

Solution:

The coordinates of a point (x, y), which is a proportion, t, of the distance between two points (a, b), and (c, d) is given by the formula;

x = a•(1 -t) + c•t

y = b•(1 -t) + d•t

The location where they had lunch is therefore;

x = -4×(1 - (1/3)) + (1/3)×2 = -2

y = -3×(1 - (1/3)) + (1/3)×3 = -1

The points is therefore; (-2, -1)

The coordinates on the map where Caroline and Rodney stopped for lunch is (-2, -1)

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Answer: 1/23

Step-by-step explanation:

x=multiplicative inverse of 23

23*x=1

23x=1

23x/23=1/23

x=1/23

The only graph that has a slope of -¹/₃ and a y-intercept of -4 that represents the inequality y > -¹/₃x - 4 is the graph represented by option C.

We want to find the graph that represents the inequality;

y > -¹/₃x - 4

Now, the general form of equation for a linear equation is;

y = mx + c

where;

m is slope

c is y-intercept

Now since the inequality is greater than, it means that it must be shaded at the top and must be a broken or dashed line. Thus, the only graph that has a slope of -¹/₃ and a y-intercept of -4 is the graph represented by option C.

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Taking into account the definition of probability, the probability for a customer to pick at least one item is 14/15.

Probability is the possibility that a phenomenon or an event will happen, given certain circumstances and it is expressed as a percentage.

The probability of any event A is defined as the ratio between the number of cases in which event A may or may not occur and the total number of possible cases. This is called Laplace's Law:

P(A)= number of favorable cases÷ total number of posible cases

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event is verified when one of the two, A or B, or both occurs and it is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B.

In first place, let's define the following events:

So you know:

In this case, considering the definition of union of events, the probability for a customer to pick at least one item is calculated as:

P(M∪F)= P(M) + P(F) -P(M∩F)

P(M∪F)= 17/30 + 5/6 -7/15

P(M∪F)= 14/15

Finally, the probability for a customer to pick at least one item is 14/15.

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The required ratio of the input value to the output value is 1:3.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given:

Input   Output

 2             6

 3             9

 6             18

Now, the ratio is

2/6 = 1/3

and,  3/9 = 1/3

6/18 = 1/3

Hence, the ratio is 1:3.

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The linear equation in slope intercept form is y = -2x + 1

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The table represents the given parameters

On the table, we have the following points

(x, y) = (0, 1) and (1, -1)

A linear equation is represented as

y = mx + c

Substitute (x, y) = (0, 1) and (1, -1) in y = mx + c

So, we have

1 = 0 * m + c

-1 = 1 * m + c

This gives

1 = c

-1 =m + c

Rewrite 1 = c as

c = 1

Substitute c = 1 in -1 =m + c

-1 =m + 1

Evaluate

m = -2

Substitute m = -2 and c = 1 in y = mx + c

y = -2x + 1

Hence, the linear equation in slope intercept form is y = -2x + 1

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