15 points please help. Math. Marginal profit function

ANSWER

EXPLANATION

Given:

Desired Outcome:

1. Domain

2. Range

Determine the domain of the function

Note: We want to include only input values that do not require the denominator to be 0 when there is a denominator. As a result, we'll set the numerator to 0 and solve for x.

We'll now remove 4 from the domain. All of the answers are real numbers x > 4 or x < 4. We will also use Union notation to combine the two sets.

That is:

Determine the range of the function

Set x to 4 to find y

We'll also remove 3 from the range. All of the answers are real numbers y > 3 or y < 3. We will also use Union notation to combine the two sets.

That is:

By identifying the first values of each point in the graph, we saw that the domain of the relationship is:

D: {-3, -1, 1, 3, 6}

A relation can be defined by a set of points (x, y), where the values of x are the values in the domain and the values of y are the values in the range.

Here we have the graph of a relation, and we can see the points:

(-3, 3)(-1, -1)(1, 2)(3, 0)(6, -2)

The domain of the graphed relationship will be the set of the first values of each of these points, then we can see that the domain is:

D: {-3, -1, 1, 3, 6}

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Answer:

y = 1/6x + 1

Step-by-step explanation:

Add 2x to both sides of the equation.

12y = 12 + 2x

Divide each term in 12y = 12 + 2x by 12 and simplify.

y = 1 + x/6

Write in y=mx+b form.

y = 1/6x + 1

Given:

Required:

To find the probability that the dart land will be in the shaded region.

Explanation:

Area of the circle is given by the formula:

Where r = radius

Thus the area of the circular region

The area of the square is given by the formula:

Thus the area of the given square

The probability of an event is given by the formula:

The probability that the dart land will be in the shaded region

Thus probability

Final answer:

Thus the probability that the dart land will be in the shaded region is 0.349.

The number that should go in the gap to factorise the given expression is 2

From the question, we are to determine the number that should go in the gap in order to factorise the given expression.

The given expression is

6x + 14

To determine the number that should go in the gap,

First we will factorize the given expression

6x + 14

The greatest common factor (GCF) of 6 and 14 is 2

Thus,

We can factor out 2 as follows

2(3x + 7)

The factored form of the expression is 2(3x + 7)

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Answer:

She worked for 4 hours and made 16 shirts (work below)

Step-by-step explanation:

let h = number of hours worked

and s = number of shirts made :]

28h+2s = 144

4h = s

28h+8h=144

h=4, s=16

:]

To simplify the expression

-0.26v + v - 0.07

we will only add the ones with variable v

0.74v -0.07

The correct option is

0.74v - 0.07

If Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years

The deposited amount = $500

The simple interest = 7.5%

The interest she earned = $225

Then the final amount = The deposited amount + The interest she earned

= 500+225

= $725

The equation of simple interest

A = P(1+rt)

Where A is the final amount

P is the initial amount

r is the interest rate

t is the time period

725 = 500(1+(7.5/100)×t)

(1+0.075t) = 1.45

0.075t = 0.45

t = 0.45/0.075

t = 6 years

Hence, if Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years

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3xy-5x+9y-45

Step-by-step explanation:

Step by Step Solution

STEP1:STEP2:Pulling out like terms

 2.1     Pull out like factors :

   3y - 15  =   3 • (y - 5) 

Equation at the end of step2: (x • (3y - 5)) + 9 • (y - 5) STEP3:Equation at the end of step 3 x • (3y - 5) + 9 • (y - 5) STEP4:Trying to factor a multi variable polynomial

 4.1       Split       3xy-5x+9y-45 

 4.1       Split       3xy-5x+9y-45 

             into two 2-term polynomials

             -5x+3xy   and    +9y-45

             This partition did not result in a factorization. We'll try another one:

             3xy-5x   and    +9y-45

             This partition did not result in a factorization. We'll try another one:

             3xy+9y   and    -5x-45

             This partition did not result in a factorization. We'll try another one:

             3xy-45   and    +9y-5x

             This partition did not result in a factorization. We'll try another one:

             -45+3xy   and    +9y-5x

             This partition did not result in a factorization. We'll try 

The number of horse is 1, goat is 2 and sheep is 3 a man has.

The problem we are dealing with is related to the linear equation which is referred to as the algebraic condition where each term has an exponent of 1 and when this condition is graphed, it continuously comes about in a straight line.

Now w consider x to be the number of sheep, y to be the  number of  goats, and z to be the number of horses the man owns.

the actual equation for the total number of animals he owns  is :

x+ y+ z

according to the first condition:

that all sheep bar three, means

y+ z=3

similarly, for the other condition, it will be

x+ z=4   and x+ y=5

Now we adding the three  equations:

y + z +x +z +x +y=5+4 +3

2(x+y+z)=12

x+y+z=6........equation(1)

As x + y = 5

Put this in equation in (1), we get

x+y+z = 6

5 + z = 6

z = 1

x + z = 4

x + y + z = 6

y + 4 = 6

y = 2

Now we know

x + y + z = 6

x + 1 + 1 = 6

x = 4

So simplifying the other equation  we get, that the number of horse is 1, goat is 2, and sheep is 4.

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The price will increase if number of students increase

By multiplying the  number of students with cost

Number of students varies in this example

The expression shown for trip amount is c = 10+13x.

The cost for 10 students is 140

The cost for 17 students is 231

Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.

1). The price will increase if number of students increase.

2). By multiplying the  number of students with cost.

3). Number of students varies in this example.

4). Let the number of students

Then total amount(c) of the trip is given by

c = 10+13x  ------ equation (1)

5). Put x = 10 in equation (1)

c = 10+13(10)

c = 140

6).  Put x = 17 in equation (1)

c = 10+13(17)

c = 231

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Answer:

15.9 hours.

Step-by-step explanation:

speed = distance / time.

230 = 3647 / time.

time = 3647 / 230.

time = 15.9 hours.

Answer:

Five times the quantity x plus four equals x minus y.

Step-by-step explanation:

Probably the most confusing part is that parenthesis are pronounced "the quantity"

Let n represent the number of nights

Cost to travel to Bali:

The cost of flight is constant so we simply add it to the cost of hostel per night times the number of nights

Cost to travel to Paris:

Answer:

7,002

Step-by-step explanation:

The product is the answer of a multiplication problem. You just have to multiply the numbers by using the techniques to solve it. Hope this helps!

The final amount after 3 years compounded semi-annually is $3709.20

To solve this problem, we simply need to use compound interest formula which is given as

[tex]A = p(1 + \frac{r}{n})^n^t[/tex]

where

Lets substitute the values into the formula and solve

[tex]A = p(1 + \frac{r}{n})^n^t\\A = 3000(1 + \frac{0.072}{2})^2^*^3\\ A = 3709.20[/tex]

The amount accrued 3 years from now is $3709.20

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A sequence is a series that follows the sum general rule. The sum of the given sequence  ∑(n=1 to 4) [tex]u_{n}[/tex] is {u₁ + u₂ + u₃ + u₄ + u₅}.

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

As per the given series,  ∑(n=1 to 4) [tex]u_{n}[/tex]

The sign ∑ is used to sum the terms of the series in the given interval.

Given that n = 1 to 4

Substiute n = 1 into  [tex]u_{n}[/tex] ⇒ u₁

Substiute n = 2 into  [tex]u_{n}[/tex] ⇒ u₂

Substiute n = 3 into  [tex]u_{n}[/tex] ⇒ u₃

Substiute n = 4 into  [tex]u_{n}[/tex] ⇒ u₄

So, the sum is {u₁ + u₂ + u₃ + u₄ + u₅}.

Hence "A sequence is a series that follows the sum general rule. The sum of the given sequence  ∑(n=1 to 4)".

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Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.

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 a hospital parking lot charges 3.50$ for the first hour and 1.75$ for each additional hour.

The modelled equation representing the above scenerio is -

y = 3.5 + 1.75x

where (x) represents the number of hours for which the car is parked.

Maximum amount with Jose = $19.25

Therefore -

3.5 + 1.75x ≤ 19.25

1.75x ≤ 15.75

x ≤ 9 hours       [Maximum time]

Minimum amount with Jose = $12.25

3.5 + 1.75x ≥ 12.25

1.75x ≥ 8.75

x ≥ 5 hours               [Minimum time]

Therefore, Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.

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Problem

At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain?

Solution

For this case we can set up the following notation

x= number of cheeseburgers

y= small fries

4x +5y= 2310

3x + 2y= 1330

From the first equation we can solve for x and we got:

x= 577.5 - 5/4 y

And now we can replace this into the second equation and we got:

3(577.5 -5/4 y) +2y= 1330

And we can solve for y:

1732.5 - 15/4 y + 2y = 1330

-7/4 y = -402.5

y= 230 cal

And solving now for x we have:

x= 577.5 - 5/4 (230) = 577.5 - 287.5 = 290 cal

Answer:

A - $4060

B - 32 copies

Step-by-step explanation:

A -

P = 1900 + 90c

P = 1900 + 90(24)

P = 1900 + 2160

P = 4060

Total if Ann sold 24 copies: $4060

B -

1900 + 90c = 4780

90c = 4780 - 1900

90c = 2880

c = 32

Total copies: 32

Simplify the equation 4x+9y = -9 in slope-intercept form of equation.

So slope of line is -4/9 and int

Answers in bold

[tex]\begin{array}{|c|c|} \cline{1-2}k & P(X = k)\\\cline{1-2}0 & \boldsymbol{0}\\\cline{1-2}1 & \boldsymbol{0}\\\cline{1-2}2 & \boldsymbol{0.04}\\\cline{1-2}3 & \boldsymbol{0.18}\\\cline{1-2}4 & \boldsymbol{0.41}\\\cline{1-2}5 & \boldsymbol{0.37}\\\cline{1-2}\end{array}[/tex]

Note: The P(x) values for k = 0 and k = 1 are not actually zero, but they are small enough that they round to 0 when rounding to two decimal places.

=======================================================

Explanation:

I used a spreadsheet to compute the values in bold.

The specific command is called BINOMDIST

The template is BINOMDIST(k,n,p,0)

Let me know if you have any questions about how to use that function in a spreadsheet.

Also, I used the function called ROUND to round each value to 2 decimal places.

Example calculation

=ROUND(BINOMDIST(4,5,0.82,0),2)

This calculates the result of 0.41 and it corresponds to the value k = 4

Don't forget about the equal sign up front when computing these commands in the spreadsheet. Otherwise, it'll stay as text form.

-------------------

If you want to use a TI83 or TI84 calculator, then press the button labeled "2nd". Then press the button labeled "VARS". Scroll down until you reach "binompdf".

The template is binompdf(n,p,k)

So for example, type in binompdf(5,0.82,4) to get the P(X) value for k = 4

If you aren't able to access a spreadsheet or a TI83/84 calculator, then search out "binomial distribution calculator" and there are plenty of free ones to pick from.

In my opinion, a spreadsheet is the best option since the given data is already in tabular form. Also, many real world situations and careers use spreadsheets everyday.

Answer: 36

One die has a total outcome of 6 elements (1, 2, 3, 4, 5, 6). Now, if we roll two dice, each time you roll a number on the first die, there are another 6 possible outcomes for the second die.

Therefore, the number of elements in the sample space would be:

There would be 36 elements in the sample space.

The equation is

Therefore x<-2. The number line representation is

Step 1:

Question 1.1

Arrive time = 7:30

Departure time = 17:00

h (9:30) > 7

Garage B is cheaper

Question 1.2

Arrive time = 8:23

Departure time = 10:53

The time spent by issac and his friends is between 2 < h < 4

Since h = 2:30

Answer R11.00

Question 1.3

Karabo uses Garage B

Time spent is 4 < h < 6

The money was invested for 8.60 years

Given:

Amount in the savings account = $2750

Amount invested = $2000

rate = 4.36% = 0.0436

To find:

the time it took to invest the money to obtain the amount in the account

The investment was done using simple interest. So to get the time, we will apply simple interest formula

2.

The reason for 2 is 'the angles are vertical'.

3. In the diagram below, we can identify the alternate interior angles more easily

Therefore, Therefore, the statements of the third step are

Finally, the corresponding angles of triangles GRA and TRE are all congruent; thus, the two triangles are congruent because of the AA similarity criterion. The answer is AA similarity criterion. The length of the sides is not involved in the demonstration.

Answer:

7 hours

Step-by-step explanation:

25x + 25 = 200.

25x = 175

175/25 = 7.

Answer:

25 + 35h = 200

and

h = 5

(5 hours)

Step-by-step explanation:

you have 200.

costs:

35 per hour

and

25 fee

h will represent the total hours spent renting a boat

25 + 35h = 200

now we will do inverse operations

subtract 25 from both sides

35h = 175

now divide both sides by 35

h = 5

Problem

Solution

For this case we can find the remain angle with this operation:

180 -39-90= 51º

And then we can use the sines law and we can do this:

And solving for x we got:

x= 14*sin(39)/sin (90) = 14*sin 39= 8.81

Solution

- The probability of him getting 1 queston correctly given tahat there is only one correct option out of 4 optins,

- Since here are questions, it implies that there are multiplye trials the student has.