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s him about the same time to assemble. He figures he has time to make at most 18 pieces of furniture by this Saturday. The materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit.
Using the information in the problem, write the constraints. Let x represent number of bookcases, and y represent number of TV stands.

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2.I am trying to figure out the optimal radius that will give the lowest surface area of a cylinder. I ...

have done the calculus which reveals that the surface area is at a minimum when height is double the radius. I am now trying to find an equation for the relationship between the amount of wasted surface area as a percentage of the minimum surface area and the ratio between height and radius.
If I were to plot it on a graph, the y axis would be the percentage of excess materials needed as a percentage of the minimum possible surface area, and the x axis would be height divided by radius. Since the surface area is minimized when height=2(radius), I know that when x=2, y=0.
The website https://www.datagenetics.com/blog/august12014/index.html explains what I am trying to do quite well and shows the graph below. I am trying to find the equation for this graph, but am unsure how to go about it.

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3.Find the constant of proportionality. z is directly proportional to the sum of x and y. If x = 5 and ...

and
y = 2,
then
z = 56.

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lly a math problem I gotta solve, and I have no idea how to do it cause of lack of my math skills. I am hoping someone can help me with this or I'm screwed.
Co basically I've got this table in excel, where X (row) is a width and Y is a height (column) of a wooden sauna cabin, the X;Y is the price for a sauna with said dimensions. I need to find a relationship between the size of the sauna and the price And formulate ani equation. I can't seem to find it, the price seems to grow non linearly, I can't seem to find any coeficient. Again, I suck at math, maybe solution is simple, but I just don't see it. Can anyone help me please?
Table Is at this link https://ibb.co/fGrxSvf . Thanks for any help!

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tion of X is given as follows:
X 3 4 6
p(X) 0.3 0.4 0.3
Find mean and variance of distributions X, Y.

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ard free energy G° by 18 kJ/mole, with A* having the higher G°.
Use the table below to find how many more molecules will be in state A* compared with state A at equilibrium.
If an enzyme lowered the activation energy of the reaction by 11.7 kJ/mole, how would the ratio of A to A* change?
Table: RELATIONSHIP BETWEEN THE STANDARD FREE- ENERGY CHANGE, ∆G°, AND THE EQUILIBRIUM CONSTANT
Hint: ∆G° represents the free-energy difference under standard conditions (where all components are present at a concentration of 1 mole/litter). From this table, we see that if there is a favourable free-energy change of –17.8 kJ/mole for the transition Y→ X, there will be 1000 times more molecules of X than of Y at equilibrium (K = 1000).

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

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n, y = 0.2x2 – 0.4x – 0.6, where x and y are measured in metres.
a) Find the x intercepts
b) Find the vertex.
c) What is the minimum height of the hammock?

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By 5 Table 1st Row 1st Column x 2nd Column 1 3rd Column 2 4st Column 3 5st Column 4 2nd Row 1st Column y 2nd Column 1.86 3rd Column 3.75 4st Column 6.12 5st Column 11.3 EndTable
Select the correct choice below and fill in the answer boxes to complete your choice.
x: 1,2,3,4
y:1.86,3.75,6.12,11.3
(Type integers or decimals rounded to the nearest hundredth as needed.)
f=_()square root of x
f=_+(_) ln x
f(x)=_
1+(_)e suqare root -(_)x

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seen an equation of a circle this is moved in both the x and y direction be converted to a polar equation.
For example, I know that the equation of a circle x^(2)+(y-2)^(2)=4 is r=4sin(theta) when converted to polar. Same thing for a translation with the x variable. However, I have never seen, nor do I know how to do, a conversion of a circle with both translations. For example, converting this equation of a circle to a polar equation: (x+3)^(2)+(y-4)^(2)=4. I have no idea how to do such a thing and cannot find any examples of such.
Hope you can shed some light on this, Thanks.

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11.(1,5) , (2,10) and (3, 19) are points on the curve y = ax^2 + bx + c. Found a, ...

-1 and c = 4.
So quadratic function is y = 2x^2 - x + 4.
Next question is: suppose that the 3rd point is written as (3, t). Find all values for t that will change the quadratic function y =ax^2 + bx + c into a linear function.

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l unemployment rate dropped to about 4%.
Find the average decline/year in unemployment rate from 2010 to 2018.
Let x be the year since 2010 and y be the unemployment rate. Write an equation for unemployment rate versus year.
Use your equation to estimate the unemployment rate in 2020.

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ned online. Using technology, with x representing the ratings and y representing price, we find that the regression equation has a slope of 130 and a y-intercept of negative 363. Complete parts (a) and (b) below.
a. What is the equation of the regression line? Select the correct choice below and fill in the answer boxes to complete your choice.

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14.Given the points on a line below : x (2,4) y (10,16) (i) Find the values of m and c (ii) ...

hat is the equation of the line passing through the points ?
(iii) Using the equation of the line. For a y value of 28, what is the x value?

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15.2. If the mean of the numbers 9, 10, 11, 12, and x is 12, what is the value ...

s of a sports drink contains 130 milligrams of sodium, what is the total number of milligrams of sodium in 20 ounces of the sports drink?
5. If (k, 3) is a point on the line whose equation is 4x + y = -9, what is the value of k?
9. A flagpole casts a shadow 200 feet long. At the same time, a boy standing nearby who is 5 feet tall casts a shadow 20 feet long. Find the number of feet in the height of the flagpole.
22. What is the greatest value of c for which the roots of the equation x^2 + 4x + c = 0 are real?
24. Find the two acute angles in the right triangle whose sides have the given lengths. Express your answers using degree measure rounded to two decimal places.
7, 24 and 25
A._________________ (smaller value)
B._________________ (larger value)

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16. 1. What is the greatest value of c for which the roots of the equation x^2 + 4x + ...

2. Find the two acute angles in the right triangle whose sides have the given lengths. Express your answers using degree measure rounded to two decimal places.
A._______________________ (Smaller Value)
B. _______________________ (Larger Value)
3. A flagpole casts a shadow 200 feet long. At the same time, a boy standing nearby who is 5 feet tall casts a shadow 20 feet long. Find the number of feet in the height of the flagpole.
4. If (k, 3) is a point on the line whose equation is 4x + y = -9, what is the value of k?
5. If 8 ounces of a sports drink contains 130 milligrams of sodium, what is the total number of milligrams of sodium in 20 ounces of the sports drink?
6. If the mean of the numbers 9, 10, 11, 12, and x is 12, what is the value of x?

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ups need one hour in Machine 1; whereas glasses need one hour. The company has exactly ten hours available in Machine 1. Use the method of substitution to find the maximum values of X and Y and the maximum value for the objective function. Show all the steps in the method.

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

mathematicsalgebra Physics