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Injective function is a type of function which relates an element of a given set with a distinct element of another set. An injective function is also referred to as a one-one function.

Let's start by listing supposition and their respective reasons.

Suppose,

g О f is injective then f : A → B is also injective.

As we are dealing with injective functions, we can rightly proceed.

The functions f(x) = f(y) when x,y ∈ A

g(f(x)) = g(f(y))

Given the fact that g О f ,then x = y

Thus, we can say that since g О f , f : A is an injective function too (one to one function)

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The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.

Volume of a solid plain:

The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.

Given in the question:

y = 2 - 1/2x

y = 0 , x = 1 and x = 2

As we know that:

[tex]\int\limits^2_1 {\pi (2 - \frac{1}{2}x - 0 })^2 \, dx[/tex]     ------------------------------ (1)

Simplifying,

      [tex]\pi \int\limits^2_1 {(2 - \frac{x}{2} )}^2 \, dx[/tex][tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]

⇒ [tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]

⇒ [tex]\pi [ 4x - x^2 + \frac{x^3}{12}]_1^2[/tex]

⇒ [tex]\pi [(8 - 4+ \frac{8}{12} ) - ( 4 - 1 + \frac{1}{12} )[/tex]

⇒ [tex]\pi (1 + \frac{7}{12})[/tex]

⇒ [tex]\frac{19\pi }{12}[/tex]

We can write 19π / 12 as

   (19× 22/7 )÷ 12

=  209/ 42

= 4.97 ≈ 5 cm³

Therefore, the volume is 5 cm³

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The value of x is 56 and the value if the unknown angle is 106°

Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line. The law of angle on a straight line states that the sum of angle on a straight line is 180°

This means that (2x-6)°+74= 180

(2x-6)°= 180-74

(2x-6)° = 106

add 6 to both sides

2x= 106+6

2x= 112

x= 112/2

x= 56

therefore the unknown angle = 2(56)-6 = 112-6= 106°

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After solving the given expression it will be equivalent to [tex]8^\frac{x}{3}[/tex]. Hence,  option C is correct.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the given expression in the question,

[tex]\sqrt[3]{8}^x[/tex]

So, this form is written as power/root

Then, then it can be written as  [tex]8^\frac{x}{3}[/tex].

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Answer: it should be C.

Step-by-step explanation: because its ascking to describe the formation.

The sample type is option (D) Systematic random sample

Here they randomly select one of the first 25 users each day and show them a message asking for a donation

They also show the message to every 25th user from that point on

The random sample is the selecting one from a large population

The systematic random sample is defined as the probability sampling method from a large population, the random samples are selected periodically. The periodical selection of random variable means the random variables are selected in regular interval.

Here the random samples are selected as one of the first 25 users each day

Therefore, the random sample is systematic random sample

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Answer:

have her do the number times each number every time so if the number is seven and there is a four on top, add or multiply or subtract 7 by 4

Step-by-step explanation:

Answer:

82.35

Step-by-step explanation:

91.5-(91.5*0.1)=

91.5-9.15=82.35

Slope: −34

y-intercept: (0,−14)

[IF ITS WRONG TELL ME]

The number of items 125 they will sell if the price per item is $3.50. They will sell 125 items if the price is $3.50.

In the given question, a manufacturing company finds that they can sell 275 items at $2.50 per item and 350 items at $2.00 per item.

If the relationship between the number of items sold i and the price per item p is a linear one then we have to find a formula that gives x in terms of p, x =

Now we have to use the formula to find the number of items they will sell if the price per item is $3.50. They will sell items if the price is $3.50.

Let’s find the slope using

m = {y(2)-y(1)}/{x(2)-x(1),

where

x(1) = 2.5      y(1)=275

x(2) = 2         y(2)=350

m = (350-275)/(2-2.5)

m = 75/(-0.5)

m = -150 is the slope

Point slope form to find the equation:

y - y1 = m(x-x1)

y - 275 = -150(x - 2.5)

y - 275 = -150x + 375

y = -150x + 275 + 375

y = -150x + 650,

But they want to have x = items sold and p = the price

So we have to write the equation where x is in terms of p

x = -150p + 650:

then use the formula to find the number of items they will sell if the price per item is $3.00.

x = -150(3.5) + 650

x = -525 + 650

x = 125 items sold when the price is $3.5

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f(5) = 7 is another to say a point at (5 , 7)

f(2) = 0 is another to say a point of (2 , 0)

to get the equation of any straight line, we simply need two points off of it, let's use those two above

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{5}}} \implies \cfrac{ -7 }{ -3 } \implies \cfrac{ 7 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{ 7 }{ 3 }}(x-\stackrel{x_1}{5}) \\\\\\ y-7=\cfrac{ 7 }{ 3 }x-\cfrac{ 35 }{ 3 }\implies y=\cfrac{ 7 }{ 3 }x-\cfrac{ 35 }{ 3 }+7\implies {\Large \begin{array}{llll} y=\cfrac{ 7 }{ 3 }x-\cfrac{14}{3} \end{array}}[/tex]

There are 364 positive variables and 5984 non - negative integers.

An integer is zero (0), a positive integer (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). [1] A negative number is the additive reciprocal of the corresponding positive number. [2] In mathematics languages, sets of integers are often represented by a bold Z or blackboard bold . The integers form the smallest group and smallest ring containing the natural numbers. In algebraic number theory, integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, (rational) integers are algebraic integers that are also rational numbers.

Let us take each xi = a₁+1

x₁+x₂+x₃+x₄ = 35

∴a₁+a₂+a₃+a₄ = 31 ,where each ai is non-negative.

Now using the stars and bars method the answer is -

([tex]\left \{ {{31 + 4 - 1} \atop {4 - 1}} \right.[/tex]  = [tex]\left \{ {{34} \atop {3}} \right.[/tex]}

               = [tex]\frac{34!}{3! * (34 - 3)!}[/tex]

               = 5984

A particular solution of this equation corresponds to the placement of 3 addition signs in the 14 spaces between successive ones in a row of 15 ones.

Since, a particular solution of the equation corresponds to the placement of k−1 addition signs in the n−1 spaces between successive ones in a row of n ones, the number of solutions of the equation x₁ + x₂ + x₃ +⋯+xₐ=n in the positive integers is

[tex]\left \{ {{n - 1} \atop {k - 1}} \right.[/tex]}

For instance, placing an addition sign in the fourth, seventh, and twelfth spaces gives

                         1111+111+11111+111

which corresponds to the solution x₁ = 4, x₂ = 3, x₃ = 5, x₄ = 3.

Hence, the number of such solutions is the number of ways we can select which three of the 14 spaces between successive ones in a row of 15 ones will be filled with addition signs, which is

                                    [tex]\left \{ {{14} \atop {3}} \right.[/tex]}

                             = [tex]\frac{14!}{3! * (14 - 3)!}[/tex]

                             = 364

Therefore, there are 364 positive variables and 5984 non - negative integers.

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Answer:

y=5x

Step-by-step explanation:

Because we already know we need atleast 5 quarters to complete a full load (Wash and dry) so we would multiply that number by how many loads were doing (x) and y is the amount we need. For example five loads is y=5x5 and then we can find y which would be y=25

The equation that describes the line that passes through (2, 1) and (0, -5) is: B. y = 3x - 5.

To find the equation of a line, find the value of the slope (m) and the y-intercept (b), and plug in the values into y = mx + b.

Given the points:

(2, 1) and (0, -5)

Slope (m) of the line = change in y / change in x = (-5 - 1) / (0 - 2)

Slope (m) = -6/-2

Slope (m) = 3

The y-intercept (b) = -5 (this is because it is the value of y when x = 0).

To write the equation, substitute m = 3 and b = -5 into y = mx + b:

y = 3x - 5

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Answer:

32

Step-by-step explanation:

Just plug in the numbers for [ d times e ]

The equation is then [ 10 x 3.2 = ? ]

The answer is 32

The value of e⁻ᴿᵗ is 0.8886 for the given the standard deviation of returns averages 28 percent with the options mature in 5 years and the risk-free rate is 2.36 percent.

So, the correct option is option ( C).

Exponential function is characterized by rapid increase (as in size or extent) and an exponential growth rate.

We have given that,

standard deviation of returns averages = 28%

options mature, t = 5 years and

Risk-free rate , R = 2.36 percent.

we have to calculate the value of e−Rt.

Exp(-Rt) = e⁻⁽²·³⁶⁾⁵

use exp(value) function to find the value :

=exp(-5 × 2.36%)

= exp(- 0.118 )

=0.8886

Hence, the the value of e⁻ᴿᵗ is 0.8886.

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Complete question:

I. M. Greedy has been granted options on 500,000 shares. The stock is currently trading at $48 a share and the options are at the money. The standard deviation of returns averages 28 percent. The options mature in 5 years and the risk-free rate is 2.36 percent. What is the value of e-rt?

a) .7087

b) .8476

c) .8886

d) .6087

e) .7952

To make the similar cake for 8 persons , the number of cups of both flour and milk will be needed is [tex]4\frac{2}{3}[/tex] cups .

In the question ,

it is given that ,

number of cups of milk needed  to make the cake is = 1 cup

number of cups of flour needed  to make the cake is = [tex]2\frac{1}{2}[/tex] = 5/2 cups .

So , the total is = cups of milk + flour

= 1 + 5/2 = 7/2

So , for 6 persons , 7/2 cups of milk and flour is needed .

for 1 person 7/12 cups of milk and flour is needed .

and for 8 persons = 8×7/12 cups of milk and flour is needed .  

= 14/3

= [tex]4\frac{2}{3}[/tex] cups .

Therefore , the number of cups of milk and flour needed is  [tex]4\frac{2}{3}[/tex] cups .

The given question is incomplete , the complete question is

A recipe calls for 1 cup of milk for every [tex]2\frac{1}{2}[/tex] cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 persons ?

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Answer:

The answer is 65 degrees fahrenheit.

Step-by-step explanation:

Coverage Error results from the exclusion of certain groups of subjects from a population frame. The answer for the given statement is Coverage Error.

Coverage errors come from failure to cover sufficiently all components of the population being studied. Incomplete sampling frames usually result in coverage errors. Coverage errors happen because of the divergences between the target population and the frame.

Coverage error also may happen when not all members of the population of interest have an equal chance of being selected for the survey. For example, if we use e-mail lists or phone lists to build the sample and not all potential respondents are on those e-mail or phone lists.

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Answer:

Subtract 58388383 - 776463783

The number of bluebirds is 18.

The following equations can be determined from the question:

10 = c - r equation 1

b = 3r equation 2

Where:

Substitute for c in the first equation :

10 = 16 - r

r = 16 - 10

r = 6

Substitute for r in the second equation:

b = 6 x 3

b = 18

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The remaining credit after 63 minutes of calls is $19.92.

From the information illustrated, the remaining credit after 36 minutes of calls is $24.24, and the remaining credit after 55 minutes of calls is $21.20.

The rate will be:

= (24.24 - 21.20) / (55 - 36)

= 3.04 / 19

= 0.16

The remaining credit after 63 minutes of calls will be:

= $21.20 - ((63 - 55) × $0.16)

= $21.20 - $1.28

= $19.92

The credit is $19.92.

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His bottom line was a gain from selling and 3% commission is $257.50.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

The cost price of 200 shares of BUI is (19.50×200) = $3900.

The selling price of 200 shares of BUI is (20.75×200) = $4150.

The net gain is (4150 - 3900) = $250 and with 3% commission it is,

= (103/100)×250.

= $257.50.

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To find the distance between two cities on the map, we can use the formula provided in the question:

d = 250n

where d is the actual distance between the cities in miles, and n is the number of inches on the map. Since we are given that the actual distance between the two cities is 1,125 miles, we can substitute this value for d in the formula above to find the number of inches on the map:

1,125 = 250n

Solving for n, we get:

n = 1,125 / 250 = 4.5 inches

This means that the distance between the two cities on the map should be 4.5 inches, so the correct answer is (D) 4.5 inches.

Answer: 210

Step-by-step explanation:

Answer: 210cm

Step-by-step explanation:

This is a parallelogram, the sides opposite of each other are congruent. So we can just add up all the sides 50+50+55+55=210cm.

Answer:

5x³ - x - 3

Step-by-step explanation:

(f - g)(x) =

f(x) - g(x) =

5x³-2 - (x+1) =  ==> plug in known values

5x³-2 - x - 1 =   ==> simplify

5x³ - x - 2 - 1 = 5x³ - x - 3

f(x) = 5x³ - 2

g(x) = x + 1

Therefore, (f - g)(x) = (5x³ - 2) - (x + 1) = 5x³ - x - 3

So, (f - g)(x) = 5x³ - x - 3.

Check the picture below.

Answer:

∠ U = 12°

Step-by-step explanation:

the inscribed angle RST is half the measure of its intercepted arc RT , then

arc RT = 2 × ∠ RST = 2 × 30° = 60°

the secant- tangent angle U is equal to half the difference of its intercepted arcs, that is

∠ U = [tex]\frac{1}{2}[/tex] ( RS - RT ) = [tex]\frac{1}{2}[/tex] × (84 - 60)° = [tex]\frac{1}{2}[/tex] × 24° = 12°

The value of the formula will be;

⇒ S = 180 (n - 2)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.''

Now,

Since, The algebraic expression is,

''The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.''

Hence, We can formulate the expression as;

⇒ S = 180 (n - 2)

Thus, The value of the formula is,

⇒ S = 180 (n - 2)

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On solving the provided question, we got to know that he can bake 200/57 loaves or 3 29/57 loafs.

Mathematically speaking, fractions are represented by integers that indicate a portion of a whole. In the same way that a whole can be any quantity, value, or object, a fraction can be a portion or subset of any quantity of a whole. As an example, let's try to comprehend this idea. The pizza in the picture below is cut into 8 equally sized pieces. The chosen slice of pizza might now be expressed as 1/8 if we wanted to. This indicates that we are talking about one of eight equally sized sections. It denotes a ratio of 1/8. Reading options include: One-eighth, or

1 by 8

13 1/3 divided by 3 4/5

Let's first convert these mixed numbers to incorrect fractions.

13  1/3 =  13(3) + 1 = 39 + 1 = 40/3

3 4/5 = 3(5) + 4= 19/5

Now that we have divided 40/3 by 19/5, we can just switch the operation to multiplication and flip the second fraction because we know how to divide fractions.

40/3 x 5/19 = 200/57

he can bake 200/57 loaves or 3 29/57 loafs.

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