The selling price of an item is a
function of the cost of
making the item. is it a function or not?

The maximum income is Maximum cost C is $19740

Let Q represent the number of cars rented per day and P the rate.

To form the demand equation;

Q = a - bP

A car rental agency rents 440 cars per day at a rate of ​$40 per day

440 = a - 40b ......1

For each ​$1 increase in​ rate, 10 fewer cars are rented

(440-10) = a - (40+1)b

430 = a - 41b ......2

Subtracting equation 2 from 1

10 = b

From equation 1;

440 = a - 10(40)

a = 440 + 400 = 840

So;

Q = 840 - 10P

Cost C = Q×P = P (840-10P) = 840P - 10P^2

Maximum cost is at dC/dP = 0

dC/dP = 840 - 20P = 0

P = 840/20 = $42

Maximum cost C is

C = P(840-10P) = 42(840-370) = 42 × 470 = $19740

The maximum income is Maximum cost C is $19740

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The number of Kid's Launches that are possible is 128. This is solved using Combination Principle.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant.

Hence,

The number of possible "Sizes" from the specified 4 sizes are ⁴C₁

The number of sorts of bun that is possible from the specified two bun types is:  ²C₁

From the four sides, the number of possible side purchases is:  ⁴C₁

Of the available four drinks, the number of the possible drinks is: ⁴C₁

Now the possible number of all lunches are:

⁴C₁ x  ²C₁ x  ⁴C₁ x  ⁴C₁

= 4 x 2 x 4 x 4

= 128

Hence the number of Kid's Lunches that are possible are 128.

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The volume V generated by rotating the region bounded by the given curves is V = 960π/7.

Given:

the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8.

27y= x³, y=0, x=6

dV = π(8^2-(8-y)^2)dx

y = [tex]x^{3} /27[/tex]

= π*([tex]8^2-(8-(x^3/27)^2)dx[/tex]

= π(64 - 64+16*[tex]x^3/27[/tex]-[tex]x^6/729[/tex])dx

[tex]= \int\limits^6_0 {16x^3/27-x^6/729} \, dx[/tex]

= π(4.[tex]6^6/27 - 6^7/7.729[/tex])

= π(5184/27 - 384/7)

= π(960)/7

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Answer:

[tex]0.4514 = 45.14%[/tex]

Step-by-step explanation:

Use the equation:
[tex]Z=\frac{X-u}{a}[/tex]

Given:

[tex]u=159, o=13,n=60,s=1.68[/tex]

This is the pvalue of Z when [tex]X = 159+1 = 160[/tex]  subtracted by the pvalue of Z when [tex]X = 159-1 = 158[/tex]

[tex]x = 160[/tex]

[tex]Z=\frac{X-u}{o}[/tex]

Central Limit Theorem  applied:

[tex]Z=\frac{X-u}{o}[/tex]

[tex]Z=\frac{160-159}{1.68}[/tex]

[tex]Z=0.6[/tex]

[tex]Z=0.6(\text{P-value}:0.7257)[/tex]

[tex]X=150[/tex]

[tex]Z=\frac{X-u}{o}[/tex]

[tex]Z=\frac{158-159}{1.68}[/tex]

[tex]Z=-0.6[/tex]

[tex]Z=-6(\text{P-value}:0.2743[/tex]

[tex]0.7257-0.2743=0.4514[/tex]

This means that there is a 45.14% probability.

Answer:

4x[tex]\sqrt{6x}[/tex]

Step-by-step explanation:

This can be written:

[tex]\sqrt{(3)(2)(2)(2)(2)xxx}[/tex]  Pull out all the pairs. There are 2 pairs of 2 and 1 pair of x's

(2)(2)x[tex]\sqrt{(3)(2)x}[/tex]  Clean up

4x[tex]\sqrt{6x}[/tex]

Answer: not 100% but i think its A

Step-by-step explanation:

The system of equations given have infinite number of solutions

A system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions. A system of equations can be classified in a similar manner as single equations.

In the equations given;

4x + y = 10 ...eq(i)

16x + 4y = 40 ...eq(ii)

Solving both equations;

The value of x and y is

y = 10 - 4x

This shows that the system has infinite number of solutions.

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Answer:

[tex]x \geqslant 360[/tex]

See the graph. It shows the sketch.

Line A:

1. The points are (4,5) and (2,3)

2. The slope is 1

3. Unit for slope is inch/week

Line B:

1. The points are (4,4) and (2,3)

2. The slope is 1/2

3. Unit for slope is inch/week

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Line A:

1. The points are (4,5) and (2,3) ( write in (x,y) form )

2. slope = (5-3)/(4-2) = 2/2 = 1

( slope= change in y values/  change in x values )

3 . mark the slope as 1 inch/week

Line B:

1. The points are (4,4) and (2,3)

2. slope = (4-3)/(4-2) = 1/2

3 . mark the slope as 1/2  inch/week

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The error interval for x will be 3.65<x<3.75 rounded to 1 decimal place.

It is defined as the representation of a set of values that satisfy a relation or a function. It can be represented as open brackets and close brackets the close brackets mean the value at the close bracket is also included, and the open bracket means the value at the open bracket does not include.

It is given that, the number is 3.7.

We have to find the error interval for x rounded to 1 decimal place for the number 3.7.

Thus, the error interval for x will be 3.65<x<3.75 rounded to 1 decimal place.

When a number has been rounded or truncated, error intervals are the upper bounds of accuracy. They represent the range of values that a number might have had before being rounded or truncated.

This is so that we may round the range of 3.65 to 3.75 to one decimal place, and as 3.74 or less is considered to be below 3.75, rounding to one decimal place gives us 3.7.

Thus, the error interval for x will be 3.65<x<3.75 rounded to 1 decimal place.

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The graph of y=1.4log (x) is black, graph of y=1.2ln(x) is green, graph of y=log(2.25-x) is blue, graph of y=log(0.75-x) is red.

A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.

To determine the color of each function, plot the graph of each function,

The graph of y=1.4log (x) is black.

The graph of y=1.2ln(x) is green.

The graph of y=log(2.25-x) is blue.

The graph of y=log(0.75-x) is red.

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Answer:

7a-7b

Step-by-step explanation:

we distribute the 7 by multiplying it to each term

7(a)-7(b)

7a-7b

Hopes this helps please mark brainliest

Answer:

7a - 7b

Step-by-step explanation:

Given expression,

→ 7(a - b)

Let's simplify the expression,

→ 7(a - b)

→ (7 × a) - (7 × b)

→ 7a - 7b

Hence, the answer is 7a - 7b.

From the position of the metals on the electrochemical series, there would be no reaction of the solution with iron and copper.

We know that a reaction is said to have occurred between a metal and a solution if the metal is able to displace the cation that is in the solution. This displacement would in turn have a lot to do with the position of the metals in the electrochemical series.

Given that iron and copper are all less than aluminum which is the cation in the solution in the electrochemical series then it would not be possible for these metals to displace it in solution thus there would be no reaction.

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Answer:

E $80

Step-by-step explanation:

This would be like paying for 9 lessons

9 x 40 is 360

The first lesson costs twice as much, so it costs 80.

Answer:

x = 55

x = 13

Step-by-step explanation:

Use the distributive property to solve.

0.5(x+9)=32

0.5x + 4.5 = 32

0.5x = 27.5

x = 55

Solve by dividing first

0.5(x+9)=32

x + 9 = 32/0.5

x + 9 = 64

x = 55

Use the distributive property to solve.

2(x+12)=50

2x + 24 = 50

2x = 26

x = 13

Solve by dividing first

2(x+12)=50

x + 12 = 50/2

x  + 12 = 25

x = 13

The number of pupils altogether that said cola was their favorite is 26.

From the question:

The total number in pupils in the class = 60

Number of  Boys in the  classroom =32

Number of Girls in the classroom=Total number of pupils - Number of  Boys in the  classroom

Number of Girls in the classroom= 60-32

                                                       = 28

Number of Boys that like Cola only= 12

Number of Boys that like water best = 4

Number of Girls that like water best = 9

 The number of pupils altogether that said Milk was their favorite =21

The number of pupils altogether that said Water was their favorite =  9 boys+  4girls

The number of pupils altogether that said Water was their favorite =13

Thus,

The number of pupils altogether that said cola was their favorite =Total number of pupils  -The number of pupils altogether that said Water was their favorite -  The number of pupils altogether that said Milk was their favorite

= 60 - 21 - 13

=26

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Step-by-step explanation:

For Part A:

Refer to the photo for an explanation on how to graph z=x+y+24 and how to set up the first integral. I will not explain how to do the other five but I have placed them beneath....

[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,\int\limits^{z-y-24}_0 {} \, 1dxdydz \\\\[/tex]

Where limits are, [tex]0\leq x\leq z-y-24\\0\leq y\leq z-24\\0\leq z\leq 24[/tex]

[tex]\int\limits^{-24}_0 {} \,\int\limits^{y+24}_0 {} \,\int\limits^{z-y-24}_0 {} \, 1dxdzdy\\\\[/tex]

Where limits are, [tex]0\leq x\leq z-y-24\\0\leq z\leq y+24\\0\leq y\leq -24[/tex]

[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,\int\limits^{z-x-24}_0 {} \, 1dydxdz\\\\[/tex]

Where limits are,[tex]0\leq y\leq z-x-24\\0\leq x\leq z-24\\0\leq z\leq 24[/tex]

[tex]\int\limits^{-24}_0 {} \,\int\limits^{x+24}_0 {} \,\int\limits^{z-x-24}_0 {} \, 1dydzdx\\\\[/tex]

Where limits are, [tex]0\leq y\leq z-x-24\\0\leq z\leq x+24\\0\leq x\leq -24[/tex]

[tex]\int\limits^{-24}_0 {} \,\int\limits^{-y-24}_0 {} \,\int\limits^{x+y+24}_0 {} \, 1dzdxdy\\\\[/tex]

Where limits are, [tex]0\leq z\leq x+y+24\\0\leq x\leq -y-24\\0\leq y\leq -24[/tex]

[tex]\int\limits^{-24}_0 {} \,\int\limits^{-x-24}_0 {} \,\int\limits^{x+y+24}_0 {} \, 1dzdydx[/tex]

Where Limits are, [tex]0\leq z\leq x+y+24\\0\leq y\leq -x-24\\0\leq x\leq -24[/tex]

For Part B:

All the above limits equal the same volume. So I will just solve for one of the limits.

Evaluate, [tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,\int\limits^{z-y-24}_0 {} \, 1dxdydz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \, (x]^{z-y-24} _0){} dydz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \, [(z-y-24)-0]{} dydz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,\int\limits^{z-24}_0 {} \,z-y-24{} dydz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,[0-\frac{y^{2} }{2} -0]{} dz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,\frac{y^{2} }{2} ]^{z-24} _{0} {} dz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,[(\frac{(z-24)^{2}}{2})-0] {} dz \\\\[/tex]

[tex]\int\limits^{24}_0 {} \,[\frac{z^2}{2}-288] {} dz \\\\[/tex]

[tex][\frac{z^3}{6}-288z]^{24} _{0} {} \\\\[/tex]

[tex][(\frac{24^3}{6}-288(24))-0] {}[/tex]

[tex](4608-6912)=-2304\\[/tex]

Answer: -2304

The evaluation of the fraction (5/6 + 2/3) - (3/4 + 1/12) in its simplest form is 2/3

A fraction is a number which consists of a numerator and a denominator.

A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.

(5/6 + 2/3) - (3/4 + 1/12)

= (5+4)/ 6 - (9+1) / 12

= 9/6 - 10/12

= 3/2 - 5/6

= (9-5) / 6

= 4/6

= 2/3

Consequently, the answer to the given fraction in its simplest form is 2/3

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Answer:

Step-by-step explanation:

well, you have to determine what the variables are first. this question cannot be answered unless the variables are defined. If x=3 then it is 3(3) +5 which is 9 + 5. Then you add the numbers together which equals 14.

Answer:

8

Step-by-step explanation:

Multiply the two radicals and then square it.

As per the concept of matrix multiplication, the value AB is [tex]\begin{bmatrix}11 &15 &-17 \\ -1&-4 &-4 \\ 17&15 &-22 \end{bmatrix}[/tex]

Matrix multiplication:

Matrix multiplication states that "The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix."

Given,

Here we have the matrix A and B.

And we have to perform the multiplication operation on it.

The value of matrix A is written as,

[tex]\begin{bmatrix} -4& 1 &-4 \\3 & 3 & 1 \\2 & 5 & 5\end{bmatrix}[/tex]

And the value of the matrix B is written as,

[tex]\begin{bmatrix} -4& -5 &4 \\3 & 3 & -5 \\2 & 2 & -1\end{bmatrix}[/tex]

Now, we have to multiply these two matrix, then we get the following,

[tex]\begin{bmatrix} -4& 1 &-4 \\3 & 3 & 1 \\2 & 5 & 5\end{bmatrix}\times\begin{bmatrix} -4& -5 &4 \\3 & 3 & -5 \\2 & 2 & -1\end{bmatrix}[/tex]

And the multiplication of the matrix is written as,

[tex]\begin{bmatrix} -4\times-4+1\times3-4\times2& -4\times-4+1\times3-4\times2 &-4\times4+1\times-5-4\times-1 \\3\times-4+3\times3+1\times2 & 3\times-5+3\times3+1\times2 & 3\times4+3\times-5+1\times-1 \\2\times-4+5\times3+5\times2 & 2\times-5+5\times3+5\times2 & 2\times4+5\times-5+5\times-1\end{bmatrix}[/tex]

When we simplify this one then we get the value of AB is,

[tex]\begin{bmatrix}11 &15 &-17 \\ -1&-4 &-4 \\ 17&15 &-22 \end{bmatrix}[/tex]

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Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is each student in Ms. Lee's class is either a junior or a senior. Ms. Lee took some students from her class on a field trip. Of the 18 juniors in her class, 5/6 went on the trip, and 17 seniors from her class also went on the trip.

[A] - Juniors that did not went are -

18 - (5/6 x 18)

18 - 15

3

[B] - Juniors that went are -

(5/6 x 18)

15

[C] - Not enough information

Therefore -

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The required place values in the chart are as Hundred: 9, Tens: 5, Ones: 0, Tenths: 0, Hundredths: 4, and Thousandths: 8. The number in standard form is 950.048.

The number is given in the question as:

(9 × 100) + (5 × 10) + (4 × 1/100) + (8 × 1/1000)

900 + 50 + 4/100 + 8/1000

1040 + 1/25 + 1/125

118756/125

950.048

As per the requierd place values in the chart are:

Hundred: 9

Tens: 5

Ones: 0

Tenths: 0

Hundredths: 4

Thousandths: 8

Now, the number in standard form is 950.048.

Thus, the required place values in the chart are as Hundred: 9, Tens: 5, Ones: 0, Tenths: 0, Hundredths: 4, and Thousandths: 8. The number in standard form is 950.048.

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Answer: -11

(absolute value) (15 - 6) x -1 = 11 x -1 = -11

Answer:

6 on edge

Step-by-step explanation:

Answer:  19/21

Step-by-step explanation:  Find the least common denominator of the two which is 21 the first fraction since 3 X 7=21

For the first fraction since 3X7=21, 1/3=1X7=7/3X7=7/21

For the second fraction since 7X3=21, 4/7=4X3/7X3=12/21

Add the two like fractions 7/21+12/21=7+12/21=19/21

The answer is 1/3+4/7=19/21

The function notations that could represent the variable, w, are:

f(v) = 2v - 1

f(v) = 1 - 8v

For example, if we are given the function notation as f(b) = b, where a and b are the variables, it means that:

In the same vein, if v is an independent variable and w is a dependent variable, it means that:

w which is the dependent variable is equivalent to f(v)

The value of f(v) is dependent on the value of v.

The function notation can therefore be:

f(v) = 2v - 1

f(v) = 1 - 8v

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The quadratic function of the graph is f(x) = [tex]-3(x+3)^2+8[/tex]

The coordinates of the vertex of the graph = (-3, 8)

The coordinates of the point on the parabola = (0, -19)

The quadratic function of the form

f(x) = [tex]a(x-h)^2+k[/tex]

Where (h, k) is the coordinates of the vertex of parabola

y = [tex]a(x-(-3))^2+8[/tex]

y = [tex]a(x+3)^2+8[/tex]

The coordinates of the point = (0, -19)

-19 = [tex]a(0+3)^2+8[/tex]

Take the square of the number

-19 = a × 9 +8

Multiply the terms

-19 = 9a + 8

9a = -19 - 8

Subtract the terms

9a = -27

a = -27 / 9

Divide the terms

a = -3

Hence, the quadratic function of the graph is f(x) = [tex]-3(x+3)^2+8[/tex]

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