The profit from the expenditure of x thousand dollars on advertising is given by P(x)=930+15x-4x^2.
Find the marginal profit when the expenditure is x = 7.

Answer:

[tex]y=3/2[/tex]

Step-by-step explanation:

[tex]f(t)=\frac{3t^{1/3}}{(64t^2 +4)^{1/6}} \\ \\ =\frac{3}{(64+4t^{-2})^{1/6}} \\ \\ \\ \lim_{t \to \infty} f(t)=\frac{3}{64^{1/6}}=3/2 \\ \\ \\ \lim_{t \to -\infty} f(t)=\frac{3}{64^{1/6}}=3/2 \\ \\ \therefore y=3/2[/tex]

The amount donated by the person follows a geometric progression, which is given by an exponential function.

First part:

Second part;

An exponential function is one in which the input variable is an index of a constant

A constant rate relationship is one in which at all points of the function, the ratio of the output to input stays the same or is a constant.

The given parameters are;

The Pennies a person plans to donate to the library on each day of the month, is given by the following table;

Day. Amount Donated

1. 1

2 2

3 4

4 8

First part

Required;

If the relationship between the day and the amount donated is a constant rate relationship

Solution;

Given that we have;

1/1 = 2/2 ≠ 4/3 ≠ 8/4, the relationship between the day of the month and the amount donated is not a constant rate relationship

Second part;

The shape of the graph of Day to the Amount Donated

Solution;

The sequence of the day has a constant difference of one day, which is given by the equation;

U = 1 × n

Where;

U = The day of the month

n = The number of days

The sequence for the amount donated is given by the exponential function;

S = a•r^n

Where;

a = The first term = 1

r = The common ratio = 2

U = The number of days

The graph of Amount Donated to the Days is therefore the graph of an exponential function, please see the attached graph of Amount Donated to the Day of the month

The possible questions obtained from a similar question are;

First part; If the amount donated and the days have a constant rate relationship

Second part; The shape of the graph of the Amount Donated to the Day of the month

Learn more about exponential functions here:

https://brainly.com/question/1528738

#SPJ1

The slope of the linear equation that passes through the points (9,1) and (10,−1) is -2.

For a linear equation that goes through two points (x₁, y₁) and (x₂, y₂), the slope is given by the formula:

slope = (y₂ - y₁)/(x₂ - x₁)

In this case, we know that our line goes through the points (9,1) and (10, −1), so we can use these two values in the equation for the line, we will get:

slope = (-1 - 1)/(10 - 9) = -2/1 = -2

So the slope of the linear equation is -2.

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

By definition, a one-to-one function is a function that maps distinct elements of its domain to distinct elements of its codomain.

Graph 1

From this graph, we see that for distinct elements of x, we have the same value of y. For example:So this function is NO a one-to-one function.

• f(2) = f(-2) = 4.

T

Graph 2

From this graph, we see that for distinct elements of x, we have the same value of y. For example:is function is NO a one-to-one function

• f(2) = f(4) = 4.

Th.

Graph 3

From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.

Graph 4

From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.

Graph 5

From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.

Graph 6

From this graph, we see that for distinct elements of x, we have the same value of y.This function is NO a one-to-one function.

• Graph 1: No

• Graph 2: No

• Graph 3: Yes

• Graph 4: Yes

• Graph 5: Yes

• Graph 6: No

High school = 1446 students

Middle school = 1/6 as many as Highschool

Multiply 1/6 by the number of students enrolled at the high school.

m = 1/6 (1446) = 241

It is a multiplicative question

The area is the entire amount of space occupied by a flat (2-D) surface or shape of an object.

The area of the face is 17 in²/17 inches2.

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area.

Draw a square on a piece of paper using a pencil. A 2-D figure, that is.

The term "Area" refers to the area that a shape occupies on paper.

By squaring the side's length, the area of each face may be calculated.

To determine the overall surface area of the cube, multiply the area of each face by the number of faces.

For big square,

a = 4 in

a*a = 4 * 4 inches

[tex]a^{2}[/tex] = 16 in²

For another small square,

a = 1 in

[tex]a^{2}[/tex] = 1*1 = 1 in²

In total,

[tex]a^{2}[/tex] = 16 + 1 = 17 in²

Therefore, the area of the face is 17 in²

To learn more about the area of the face, refer

https://brainly.com/question/2348798

#SPJ13

The total number of lefties present in the class are 125.

For the given question;

The total students in the class are 50.

There are 10 out of 50 on an average students be left-handed.

Let the percentage of left handed be 'x'.

Then, x% of 50 = 10

x = 10×100 / 50

x = 20%.

Now the average number of left-handed students are 25.

The total students will be.

Let 'y' be the total number of students.

Then, 25 is the 20% of y.

20% of y = 25.

y = 25 ×100 / 20

y = 125

Thus, the total number of lefties present in the class are 125.

To know more about the percentage, here

https://brainly.com/question/24877689

#SPJ13

Answer:

x (y + 1)

Step-by-step explanation:

Simplify the following:

x y + x

Factor x out of x y + x:

Answer: x (y + 1)

Answer:

b

Step-by-step explanation:

the square root of 9 is 3 because 3*3=9

3+6=9

there are 4 properties we can use to prove if it is a parallelogram, in which 3 of them involve seeing if the sides are parallel or congruent, however for those we must know the value for the angles or sides, the other property is to prove that the diagonals bisect each other.

To prove the diagonals bisect each other is to see if the point of crossing divides into equal parts.

in this case since the division of the points gives the same values for both diagonals we can say that ABCD because the diagonals bisect each other.

Answer:

64 is the area!

- love bri <3

The graph shown have roots of x = -2 and x = 5

We could solve for x in each of the quadratic equations or we could plot the graphs of each of the quadratic equation.Then we pick the one with the roots of -2 and 5.

Plotting the graphs:

The roots of quadratic functionis the value of x when y is equal to zero.

From the graph attached above, f(x) = x² + 3x – 10 representing the blue parabola has roots of (-5, 0) and (2, 0).

This means the roots are -5 and 2.

Hence, the function in the graph is f(x) = x² + 3x – 10

The equation of the parabola having focus (1,1) and directix y = -1 is

y = x²/4 - x/2 + 1/4

The focus of the parabola (h , k + p) = (1,1)

The directrix of the parabola is y = -1

From, the focus

           k + p = 1

           k = 1 - p

The formula of directrix is

              y = k - p                                                    (1)

Substituting the value of directrix and k

              -1 = 1 -p -p

              -1-1 = -2p

               -2 = -2p

               p = 1

Substituting the value p in equation (1)

                k = 0

Now, we have got the vertex of the parabola (h ,k) is (1,0)

The equation of the parabola is

    (x-h)² = 4p (y - k)

     (x - 1)² = 4 (1) (y - 0)

     ( x -1 )² = 4(y )

     x² - 2x + 1 = 4y

     x²/4 - 2x/4 + 1/4 = y

    y = x²/4 - x/2 + 1/4

which is the equation of the parabola.

Learn more about Equation of Parabola in

https://brainly.com/question/21685473

#SPJ9

Answer:

Measure of angle B = 39

Step-by-step explanation:

(7x-20) + (2x-7) = 180 (combime like terms)

9x - 27 = 180 (move 27 to the other side)

9x = 207 (divide both sides by 9)

x = 23

2x - 7 (subsititute x with 23)

2 (23) - 7

46 - 7

39

measure of angle b = 39

The students were able to identify 16 of the pieces out of 80 which is 20 % in the percentage form.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.

The students were able to identify 16 of the pieces out of 80.

We have to determine the percentage of the classical pieces the students identify.

As per the given information, the required solution would be as:

⇒ (16/80) × 100

⇒ (0.20) × 100

⇒ 20 %

Therefore, the percentage of the classical pieces the students identify would be 20 %.

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ1

This is a Permutations of 4 people in a line

The answer is 24

[tex]d(f-4)=2(1-f)\\\\frac{d(f-4)}{d} =\frac{2(1-f)}{d} \\f-4=\frac{2(1-f)}{d} \\f=\frac{2(1-f)}{d} +4[/tex]

Attached is the solution

Answer:

Step-by-step explanation:

d= 2(1-f) / f-4

d = 2 - 2f / f-4

d = 1/2 - 2f - f

d = 1/2 - f

0=1/2-f-d

f = 1/2 - d

An equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex is y = 4x² - 80x + 404.

             y = a(x - h)² + k  where (h, k) is the vertex.

Given:

f(x) = 4x²

Vertex =  (10,4)

a = 4

The value of a in the vertex form of the equation is taken to be 4 since the coefficients of x² must match for the parabola to have the same shape as the given parabola.

The equation can be written as,

y = a(x - h)² + k  where (h, k) is the vertex.

Replacing the value of the vertex, we get

y = 4(x - 10)² + 4

y = 4(x² - 20x + 100) + 4

y = 4x² - 80x + 400 + 4

y = 4x² - 80x + 404

To learn more about vertex form of parabola visit:

https://brainly.com/question/20333425

#SPJ9

The probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go is 0.3240

Probability:

The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.

The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes.

Given,

Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita reports that 48% of its customers order their food to go.

Here we need to find the probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go.

Let us consider this as,

Binomial Problem with

n = 5 and

By converting the percentage into decimal value,

=> 48/100 = 0.48

p(to go) = 0.48

Then the value is,

P(x=3) = 5C3(0.52)^3*(0.48)2

P(x=3) = 0.3240

To know more about Probability here.

https://brainly.com/question/11234923

#SPJ1

The value of x is 52.5981

The given equation is:

In(x + 2) = 4

Taking log on the right hand side of the equation, we get

x + 2 = [tex]e^{4}[/tex]

The value of [tex]e^{4}[/tex] is 54.59815

⇒ x + 2 = 54.59815

Subtract 2 on both the sides of the equation

⇒ x = 54.59815 - 2

⇒ x = 52.59815

Rounding 52.59815 to 4 places, we get

⇒ x = 52.5981

Know more about Solving for x: -https://brainly.com/question/11502789

#SPJ9

Answer:

favorable opinion of Sanders than Hillary Clinton

(38%). Calculate the 90% confidence interval for for Hillary

4m

The mean difference in game scores over the six​ games is 4.

The ratio of the overall sum of data to the total number of data sets is known as the mean. Mean is often computed by adding up all the data and dividing it by the total number of data.

Given that a basketball team played six games. In those​ games, the team won by 8 ​points, lost by 6​, won by 9​, won by 10​, lost by 4​, and won by 7.

The data's mean difference will be determined as follows:

Mean = ( 8 - 6 + 9 + 10 - 4 + 7 ) / 6

Mean = 4

Therefore, the mean difference in game scores over the six​ games is 4.

To know more about mean difference visit:

https://brainly.com/question/18204878

#SPJ9

From the graph, the y-intercept is the point (0,40). We can calculate the slope of the line, given two points, using the following formula

In our case,

Therefore, the slope-intercept form of the equation of the line is

The answer is y=-20x+40

Answer:

45 degrees

Step-by-step explanation:

The triangle is a 45, 45, 90 meaning that both angles other than the 90 are the same.

Another way to solve is you know that a triangle's angles = 180

Take the 180 and subtract 90 for the right angle

and then subtract 45 for the labeled angle and your answer is 45

Answer:

  13,551,737

Step-by-step explanation:

You want the sum of the first 13 terms of the geometric sequence with first term 17, and successive terms 51, 153, ....

The common ratio is found by dividing a sequence term by the one before it:

  r = 51/17 = 3

The common ratio is 3.

The index of the 13th term of the sequence is n = 13.

The sum of n terms of a geometric sequence with first term a1 and common ratio r is ...

  Sn = a1·(r^n -1)/(r -1)

For a1 = 17, r = 3, and n = 13, the sum is ...

  [tex]S_{13}=17\cdot\dfrac{3^{13}-1}{3-1}=17\cdot\dfrac{1594322}{2}=\boxed{13,\!551,\!737}[/tex]

The last digits of multiplying 5s and 2s with at least one of each will be zero (0)

From the question, we are to determine what the last digit of the product could be

From the given information,

We are multiplying as many 5s and 2s as we want but we must have at least one of each

Since we must have at least one of each of 5 and 2, we will always have a 5 × 2

But, 5 × 2 = 10

NOTE: 10 multiplied by any number will always result in a number with a last digit of zero (0)

Example

2 × 5 × 2 × 2 × 2 × 2 = 160

5 × 2 × 5 × 5 × 5 × 5 = 6250

Thus, the last the digit of the product will be 0

Learn more on Multiplying numbers here: https://brainly.com/question/28169514

#SPJ1

Answer:

1:3

Step-by-step explanation:

circles:total

2:4+2

=2:6

=1:3

Reason

There are 2 circles and 4+2 = 6 shapes total.

The ratio of circles to total shapes is 2:6 which reduces to 1:3

The order is important since 3:1 is different from 1:3.

The types of funding sources that are available to businesses include:

A business can use a particular type of fund that meets its goals.

A reason why companies van use a mix of different funding is to improve a company's financial strength.

Providing resources to finance a need, a program, or a project is the act of funding. While usually in monetary form, this can also refer to an organization or company's time or effort.

Having adequate funding enables your firm to seize any possibilities that present themselves, such as investing in new goods and services that can advance your company. Working capital can act as a safety net when your company requires additional funding.

Although there are many diverse reasons why businesses want financing, there are certain frequent ones. Business grants and loans may be used for working capital, equipment purchases, staff expansion, or even the refinancing of existing debt to lower monthly payments.

Learn more about funding on:

https://brainly.com/question/25887038

#SPJ1

The mathematical question that can be asked in a situation when Dina goes to a carnival and some rides have a height requirement is how many extra centimeters of height Diana has? The information required to solve this question is the required height for the ride and the height of Diana.

According to the question,

We need to ask a mathematical question. Let's solve a mathematical question in the given situation by taking one example.

If the required height to ride is 150 cm and the height of Diana is 165 cm, how many extra centimeters of height Diana has than the required height?

Solution:

Required height = 150 cm

Dian's height = 165 cm

Extra height = Diana's height - required height of the ride

Extra height = 165 cm - 150 cm

Extra height = 15 cm

Hence, in this supposed situation, Diana's height is 15 cm extra than the required height of the ride.

To know more about mathematical question here

https://brainly.com/question/12083755

#SPJ1