Frank bought 10 pounds of dog food for $17. 50. At this rate how much would he pay for 15 pounds.

The value of a should be 2 for the function to be composite.

What is composite function?

When two functions, f and g, are combined to create a third function, h, the result is such that h(x) = g(f(x)).

Main Body:

A commutative function means that when you insert one function in space of x in the other function, they will equal x. The equation is

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

So, 2([tex]\frac{x+1}{a}[/tex]) - 1 = [tex]\frac{(2x-1)+1}{a}[/tex]

If you multiply both sides by a, you get   2a([tex]\frac{x+1}{a}[/tex]) - a = (2x-1)+1

Simplify it                                                   2a([tex]\frac{x+1}{a}[/tex]) - a = 2x

Add a to both sides                                    2a([tex]\frac{x+1}{a}[/tex])  = 2x +a

The two as on the left cancel out                   2(x+1)=2x+a

Distribute the 2:                                              2x+2=2x+a

Then subtract 2x from both sides                        2 = a

Therefore, a = 2

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Answer:

B. 2

Step-by-step explanation:

Right on Edge

It would require 2257920 blocks to construct the great pyramid.

Given,

Side of  base of pyramid = 756 ft = [tex]\frac{756}{3}[/tex] = 252 yard

height of pyramid = 480 ft = [tex]\frac{480}{3}[/tex] = 160 yard

volume of 1 block which is used to construct pyramid = 1.5 cubic yard

Volume of pyramid can be determined by formula,

[tex]Volume\ of\ pyramid\ =\ \frac{1}{3}*area\ of\ base*height[/tex]

At first,

area of base=side x side = 252x252= 63504 square yard

now,

[tex]Volume\ of\ pyramid\ =\ \frac{1}{3}*area\ of\ base*height\\\\Volume\ of\ pyramid\ = \frac{1}{3}*63504*160\\\\Volume\ of\ pyramid\ = \frac{1}{3}*10160640\\\\Volume\ of\ pyramid\ = 3386880\ cubic\ yard[/tex]

Now, the number of blocks required to construct the pyramid will be,

[tex]Number of blocks =\frac{3386880}{1.5}=2257920[/tex]

Thus, the number of blocks required to construct the great pyramid is 2257920.

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Your question is incomplete, please complete the question

Ordered pairs are in the solution set of the system of linear inequalities are as follows

> Negative one-halfx

y < One-halfx + 1

On a coordinate plane, the 2 straight lines are shown.

The first solid line has a negative slope and goes through (0, 0) and (4, -2).

Everything above the line is shaded. The second dashed line has a positive slope and goes through (-2, 0) and (2, 2).

Hence, everything below the line is shaded.

(5, –2), (3, 1), (–4, 2)

(5, –2), (3, –1), (4, –3)

(5, –2), (3, 1), (4, 2)

(5, –2), (–3, 1), (4, 2)

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Answer:

12-9

Step-by-step explanation:

Answer:

D. Cl₂

Step-by-step explanation:

the inequality that shows the values of x for which the expression is defined √x-2•√x+3 is √x-2≤4 and √x+3≤-9

p ≠ q means that p is not equal to q

p < q means that p is less than q

p > q means that p is greater than q

p ≤ q means that p is less than or equal to q

p ≥ q means that p is greater than or equal to q

Therefore, √x-2≤4 and √x+3≤-9

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The equation of g(x) after the translation up is g(x) = 4x² - 10

The given parameter represents the function f(x) in the question.

This function is given as

f(x) = 4x² - 13

The translation is given as

3 units up.

i.e. a translation up by 3 units

Mathematically, this can be represented as

(x, y) = (x, y + 3)

So, we have

g(x) = f(x) + 3

Substitute the known values in the above equation, so, we have the following representation

g(x) = 4x² - 13 + 3

Evaluate the like terms

g(x) = 4x² - 10

Hence, the equation of g(x) is g(x) = 4x² - 10

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Answer:

469

Step-by-step explanation:

871/13 =67

67 x 7 = 469

Answer:

[tex] \large\bold{ \underline{ \color{aqua} \clubs{} \color{blue}exponential \: \: \: notation. \color{lime} \clubs}}[/tex]

✏ The result of this problem when solving is:

[tex] \red{\boxed{\boxed{\bold{\color{blue}answer \color{black} \rightarrow \color{red} \boxed{ \bold\color{blue} \frac{ {81x}^{28} }{625} }}}}}[/tex]

⭐Step-by-step explanation:

✏ To solve this problem we will do the following:

• This problem is about "Exponential Notation" and "Laws of exponents".

We happly the following formula:

[tex] \: \: \boxed{\boxed{\color{blue} \bold{ {( \frac{a}{b})}^{n} \color{black}= \color{blue}\frac{ {a}^{n} }{ {b}^{n}} \: \: \: b\color{black}\:\:\ne{ \color{blue}0}}}}[/tex]

• Now we solve:

[tex] \bold{ {( \frac{ {3x}^{7} }{5})}^{4} = \sf{ \frac{ {81x}^{(7)(4)} }{ {5}^{4} }}} \\ \\ \\ \color{red}\boxed{\boxed{\color{blue}\bold{ \color{black}= \color{blue}\frac{ {81x}^{28} }{625} }}}[/tex]

[tex]\bold \color{lime} \spades{\colorbox{aqua}{ \color{blue}john200817 \: from \: brainly.com} \spades}[/tex]

[tex] \color{blue}\boxed{\color{aqua}\boxed{\color{aquamarine}\boxed{\color{turquoise}\boxed {\bold{ \color{yellow}\bigstar{} \color{cyan}\dag{} \color{lime}\clubs{} \: \color{deepskyblue}i \: \: \: \color{lawngreen}h \color{orange}o \color{red}p \color{blue}e \: \: \: \color{springgreen}m \purple{y} \: \: \: \color{deepskyblue}a \color{lawngreen}n \color{orange}s \color{red}w \color{blue}e \color{springgreen}r \: \: \: \purple{w} \color{deepskyblue}i \color{lawngreen}ll \: \: \: \color{orange}s \color{red}e \color{blue}r \color{springgreen}v \purple{e} \: \: \: \color{deepskyblue}y \color{lawngreen}o \color{orange}u \color{red}. \color{lime}\clubs{} \color{cyan}\dag{} \color{yellow} \bigstar}}}}}[/tex]

The types of symmetry that this geometric figure has include the following:

In Mathematics, rotational symmetry is sometimes referred to as radial symmetry and it can be defined as the property that a geometric figure (shape) has when it looks the same as the original figure, after some rotation on its own axis by an angle between 0° and 360°.

In Geometry, a point symmetry can be defined as a type of symmetry in which a geometrical figure (shape) is divided into two (2) equal and symmetrical parts by a central point.

In this context, we can reasonably and logically deduce that this geometrical figure (shape) has both a point symmetry and rotational symmetry.

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By using the SAS congruence rule, we can prove that AC = BD

What is SAS congruence Rule?

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

What is CPCT?

When we study the congruent triangle, we come across the term CPCT. Corresponding Parts of Congruent Triangles are abbreviated as CPCT. Congruent triangles have equal corresponding parts, as is well known. We frequently use the abbreviation cpct in short terms rather than the complete form while discussing triangle topics and answering inquiries.

In the given figure, we have:

ABCD is a quadrilateral, where AB=DC and ∠DAB=∠CDA

Construction: Joining the two diagonal AC and BD;

Now,

In △ABD and △BAC;

⇒AB=DC                       [ Given ]

⇒  ∠DAB=∠CDA          [ Given ]

⇒  AB=BA            [ Common side ]

∴  △ABD≅△BAC         [ SAS Congruence rule ]

So,

AC = BD, by CPCT;

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The number of video games bought is 6, when $20 is in your account

information given in the question

equation of the video games bought is represented by y=80-10x

x = number of video games

y = total amount in savings account

You have $20 in your account after buying video games

The given information is represented as

money left in bank after buying the video game = 80 - 10x

20 = 80 - 10x

10x = 80 - 20

10x = 60

x = 6

Since x is the number of video games then 6 video games was bought

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She has a 0.0755 chance of accurately answering three questions at most.

Given data;

A student is completing a multiple-choice exam that consists of 7 questions and 4 possible answers. Suppose the student guesses the right response with a probability of 0.75 while not knowing the topic.

The terms are expanded using the binomial theorem.

7 questions total.

The probability of doing it right is 0.75.

The chance of getting it wrong is 1 - 0.75 = 0.25

The likelihood that she will accurately respond to no more than three questions is indicated as;

[tex]P = ^nCr p^rq^n^-^r[/tex]

[tex]P = ^nCo (0.75)^r(0.25)^n^-^r[/tex]

Here, r ranges from (0, 1, 2, 3)

[tex]P = ^7Co (0.75)^o(0.25)^7+^7C1 (0.75)^1(0.25)^6+^7C2 (0.75)^2(0.25)^5+^7C3(0.75)^3(0.25)^4[/tex]

[tex]P = (0.25)^7+7(0.75)^1(0.25)^6+21(0.75)^2(0.25)^5+35(0.75)^3(0.25)^4[/tex]

P = 0.0755

Therefore, the probability that she will answer at most 3 questions correctly is 0.0755.

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Answer: 20 cars and then send the rest of showrooms iin New York

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

All students have to take at least one math class and one language class. Twenty students take calculus, and thirty students take statistics.

When we want to estimate a population parameter then we use hypothesis test.

What is hypothesis test?

In hypothesis testing, an analyst examines a statistical sample with the aim of demonstrating the plausibility of the null hypothesis.

By measuring and reviewing a representative sample of the population under study, statistical analysts test a hypothesis. All analysts use a random population sample to test the null hypothesis and the alternative hypothesis.

Main body:

As the researchers want to understand the difference between to states they need to do a hypothesis test.

Hence a hypothesis test is done.

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If Ariana is buying a car for $15,812and  will repay the rest with 24 equal monthly payments. Her payment each month will  be:  $450.50.

Using this formula to find the monthly payment

Monthly payment = Cost of car - Amount paid in cash / Number of repayment month

Let plug in the formula

Monthly payment = ($15,812 - $5,000)/24

Monthly payment = $10,812 /24

Monthly payment = $450.50

Therefore the correct option is B.

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The three  numbers are -5, -15, and -10 .

Equations of straight lines and equations of degree less than 1 are called "linear equations". The linear equation formula can be written as Y = mx + b. where m is the slope of the line, b is the y-intercept, and x and y are the variables. Slope indicates the direction and slope of the line. This is because (0,y) is the point where the line intersects the y-axis.

b=3a

c=b+5

b-2c=5

b-2(b+5)=5

b-2b-10=5

-b=15

b=-15

c=-15+5

c=-10

-15=3a

a=-5

The numbers are -5, -15, and -10

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Answer: x = 4

Step-by-step explanation:

Let's first look at the equation!

5x-2(2x-1)=6

First thing you do is the -2(2x-1) to break the ( )

So, -2*2x = -4x and -2*-1 = 2

So now we have 5x-4x+2=6

Then you see that there are 2 like terms?

Like terms: the terms that contain the same variable which is raised to the same power.

You can do 5x-4x = 1x!

Now we have 1x+2=

Now we do -2 to get rid of the 2!

We will get 1x=4

Now we divide!

1x divided by 1 giving you x!

and 4 divided by 1 giving you

x = 4!

Step-by-step explanation:

obviously, your scanning did all kinds of strange things with the brackets.

so, I ignore them and we focus only on the numbers.

the domain is the interval or set of all valid x-values (the first number in an ordered pair).

the range is the interval or set of all valid y-values (the second number in an ordered pair).

so,

A and E are correct.

The probability of typing four letters with no repeated letters is 0.785.

Probability is the possibility of happening an event.

Given that, the four letters are typed.

Note that there are a total of 26 letters.

Therefore, the probability of typing four letters with no letters repeated is:

(26/26) × (25/26) × (24/26) × (23/26)

= 358800/456976

= 0.785

Hence, the probability of typing four letters with no repeated letters is 0.785.

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The best line of fit which models the given data can be obtained using a linear regression calculator is y = 12.63x + 274.21

Using a linear regression calculator or excel, the linear regression model obtained by fitting the data is :

y = 12.63x + 274.21

y = Predicted variable

x = predictor variable

Slope = 12.63

Intercept = 274.21

Therefore, the best line of fit is y = 12.63x + 274.21

what is the best fit?

A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

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A polynomial is described as a mathematical expression that contains one or more algebraic in which a constant is multiplied by one or more variables that give rise to a non-negative integral power such as ax² + bx + c.

By considering a polynomial with two terms. Methods and polynomials can be used with these methods.

        2x³ - 5x² = x²(2x - 5)

         x³ - 27  then this be factored as

         x³ - 27 = (x - 3)(x² + 3x + 3²).

         x³ + 27 = (x + 3)(x² - 3x + 3²).

           x² - 16  =  (x + 4)(x - 4)

where perfect-square trinomial and factoring by grouping require more than two terms.

Therefore, the polynomial that has two terms in the factoring methods the Common Factor, the Difference of cubes, the sum of cubes, and the difference of squares can only be considered.

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1. M represents slope.

2. (-1-1)/(-2+4) = -2/2 = -1  

3. Take any of the two given y's and their corresponding x's.

I'll take (3,12) and (4,13)

Plug into y2-y1/x2-x1

13-12/4-3 = 1/1 or 1 over 1

4. 4-0/1-0 = 4/1

Don't worry about the points; keep growing and learning!

Step-by-step explanation:

m = (y2-y1)/(x2-x1)

m= (-5-7)/(6--2)

m = -12/8

m = -3/2

y-b = m(x-a)

y-7 = -3/2(x--2)

y-7 = -3x/2 - 3

y = -3x/2 + 4 <-- Equation of line