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ters established the following price – demand function:
p(x) = 10 – 0,001x, where p(x) is the wholesale price in dollars at which x thousand computers can be sold.
Total cost (in dollars) of producing x items is given by C(x) = 7000 + 2x.
A) Find the revenue function and state its domain.
B) Find the marginal revenue function. Find R´(4000) and R´(6000). Interpret the results.
C) Evaluate the approximate revenue and exact revenue of producing 101-th notebook.
D) Find the profit function
E) Find the marginal profit function.
F) Evaluate the approximate profit and exact profit of producing 101-th notebook.
G) Find P´(5000) and P´(7000). Interpret the results.

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Your answer should be written in slope-intercept form.
P(0, 0), x = −4y − 18

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units.
Chemical Equation: Write a generic chemical equation for the dehydration of cobalt (II) chloride ∙ x hydrate (include the state symbols of the reactant and two products). [T2]
Mass of Reactants and Products:
a) Calculate the initial mass of the hydrated cobalt (II) chloride. [T1]
b) Calculate the final mass of the anhydrous cobalt (II) chloride remaining in the cruiio8icible. [T1]
c) Calculate the mass of water given off by the sample of hydrated cobalt (II) chloride. [T1]
Moles of Products:
a) Calculate the moles of anhydrous cobalt (II) chloride remaining in the crucible. [T1]
b) Calculate the moles of water released from the hydrate. {T1]
4. Mole Ratio
a) Create an experimental mole ratio between the b) and a). [T1]
5. Formula of Hydrate: State the chemical formula you have determined for this hydrate.
Round the formula to the closest whole number value for x. [T1]
Discussion/Conclusion Questions: [T6]
Based on the chemical formula of the hydrate, calculate the percentage composition (percent by mass) of the hydrated cobalt (II) chloride. Remember to determine the percentage of each element (Co, Cl, H, and O). [T2]
A possible source of systematic error in this experiment is insufficient heating. Suppose that the hydrate was not completely converted to the anhydrous form. Describe how this would affect: the calculated percent by mass of water and the experimental molecular formula (i.e. would x be higher, lower or the same).
Suppose a student spilled some of the hydrated cobalt (II) chloride. Describe how this would affect the calculated percent by mass of water (would it be higher, lower or the same) and the experimental chemical formula of the hydrate. [T2]

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= 4, y = 15, and dy/dt = 1.
x2 + y2 = 241
dx/dt= ??

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5.3. Given: x ∈ Q and y ∈ Q. Prove that 3x − 5y ∈ Q. You may use without proof: the ...

ference, and product of integers
is an integer.
4. Given: x ∈ R. Prove:
9x
2 + 5 > 12x.
At the idea stage, reduce the given inequality by setting it to 0. Then, it
should be helpful to complete the square.

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ow do you substitute to get your answer. How do you make X the subject of the formula

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rued when you go from making 1 chai tea latte a day to 40 chai tea lattes a day. (Hint: relationship between marginal cost and total cost)
2. Suppose that C(x) = -0.01x + 5 represents the daily cost of heating the doughnut shop, in dollars per day, where x is time in days and x = 0 corresponds to January 1, 2020. Find the total cost of heating the shop for the first two weeks of January, and find the average cost to heat the shop each day for the first two weeks of January.

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producer's surplus if the equilibrium price of a unit
$
99
.A retailer anticipates selling
7600
units of its product at a uniform rate over the next year. Each time the retailer places an order for
x
units, it is charged a flat fee of
$
100
. Carrying costs are
$
38
per unit per year. How many times should the retailer reorder each year and what should be the lot size to minimize inventory costs? What is the minimum inventory cost?
For a particular commodity, the demand function is
q
=
1
4
(
400
−
p
2
)
.
a
.
Find
ε
when
p
=
8
.A hotel rents
240
rooms at a rate of
$
60
per day. For each
$
1
increase in the rate, three fewer rooms are rented. Find the room rate that maximizes daily revenue.

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estimated he consumed 12, 000 kcal/day.
Given that the formation of one ATP molecule from ADP and inorganic phosphate, requires 7.3 kcal/mole and that aerobic respiration is only 34% efficient, how many ATP molecules did Michael Phelps produce each day?
Reminder: There are 6.022 x 10^23 molecules/mole.

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lve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit.
Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point.
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
Let f be a twice-differentiable function such that f′(2)=0 . The second derivative of f is given by f′′(x)=x2e2−x−1 for 0≤x≤6 .
(a) On what open intervals contained in 0
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point O such that O is fixed and A moves to A′ . A′ lies in the first quadrant. In simplest terms the x -coordinate of A′ is a−b√c . What is a+b+c?

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sx, where x represents the number of new customers per month in thousands. How many new customers are needed to maximize profit given that the number of customers that can be supported is between 1000 and 5000? Hint: x is in radian mode

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13. Value: 1 equation image indicator a. (x - 2)2(x - 3)2 b. (x2+ 4)(x2+ 9) c. (x - 2)(x + ...

2)(x - 3)(x + 3)
d. (x2 - 4)(x2+ 9)
Value: 1
The table below shows the cost of purchasing a standard stapler at five office supply stores, A through E. If the median cost of purchasing a standard stapler for these stores was $17.99, which of the following could NOT have been the cost of the stapler for Store A?
staplergraph.jpg
a. $19.95
b. $18.95
c. $16.95
d. $19.25
Value: 1
If equation image indicator then x =
a. 7
b. 1/5
c. 5
d. 1/7
Value: 1
A six−sided die, with sides numbered 1,2, 3,4,5, and 6, is tossed. What is the probability of tossing a number less than three?
a. 1/3
b. 0
c. 1/2
d. 1/4
Value: 1
If 6m + 4 = 8m, then 4m =
a. 6
b. 2
c. 8
d. 4
Value: 1
In the xy-plane, what is the y-intercept of the graph of the equation equation image indicator?
a. 2
b. 4
c. 16
d. There is no y-intercept.
Value: 1
Which of the following equations has both 2 and −4 as solutions?
a. x2 + 6x + 8 = 0
b. x2 - 2x - 8 = 0
c. x2 + 2x - 8 = 0
d. x2 - 2x + 8 = 0
Value: 1
The perimeter of a square is 20 ft. If you increase the length of the square by 2 feet and decrease the width by 1 foot, what is the area, in square feet, of the new figure?
a. 22
b. 28
c. 35
d. 40
Value: 1
(3x-2y4)-3 =
a. equation image indicator
b. equation image indicator
c. equation image indicator
d. equation image indicator
Value: 1
A softball is tossed into the air upward from a first floor balcony. The distance of the ball above the ground at any time is given by the function, distance function.png, where h(t) is the height of the softball above the ground (in feet) and t is the time (in seconds). What was the maximum height, in feet, of the softball above the ground after it was thrown?
a. 28
b. 30
c. 32
d. 34
Value: 1
A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance. If the total paid, for all 100 people, was $1300, how many students attended the museum opening?
a. 20
b. 50
c. 70
d. 80
Value: 1
The ratio of Sam's age to Hank's age is 5 to 3. If the sum of their ages is 24, how old is Hank?
a. 21
b. 15
c. 19
d. 9
Value: 1
In the xy−coordinate plane shown below, point P has coordinates (8, −6). Which of the following is an equation of the line that contains points O and P?
O and P graph.jpg
a. equation image indicator
b. equation image indicator
c. equation image indicator
d. equation image indicator
Value: 1
The variables x and y are inversely proportional, and y = 2 when x = 3. What is the value of y when x = 9?
a. 54
b. 6
c. 2/3
d. 3/2
Value: 1
A farmer has 1235 trees to be planted on a rectangular parcel of land. If there are 24 trees planted in each row and each row must be complete before it is planted, how many trees will be left over after planting?
a. 21
b. 11
c. 0
d. 55

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14.Let's say that I have a data set of every time a certain person has coughed since the beginning of ...

his year. I'm looking for a formula that will tell me the probability that a person will cough x number of times in a given week.
I started with the Poisson Distribution, but Poisson doesn't seem to take into account standard deviation. To calculate the probability with Poisson, only the mean, expected value, and test value are needed, meaning the variance/standard deviation of the data could vary widely, and you'd still get the same probability distribution. For example, if someone coughed exactly 5 times everyday, you'd get the same probability distribution if this person alternated coughing 0 times one day, 10 times the next, 0 times the next day, 10 times the next, and so on.
Does my question make sense? Thanks for your help.

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics