Mrs. Claus makes a
delicious fruitcake that
serves 11 people. There are
14 fruitcakes on the table.
How many people will this
feed?

Answer:

(a) The number of units that will give the maximum profit is 2,000 units.

(b) The maximum possible profit is $274,000.

Step-by-step explanation:

(a) How many units will give the maximum profit?

From the attached photo in the question, we are given;

R(x) = 324x - 0.0495x^2 ………………....................................……….. (1)

C(x) = 8000 + 162x - 0.099x^2 + 0.00003x^3 …………………….. (2)

In economics, profit function, P(x), is obtained as follows:

P(x) = R(x) - C(x) ………………………. (3)

Substituting the equations (1) and (2) for R(x) and C(x) respectively into equation (3) and then simplify, we have:

P = 324x - 0.0495x^2 - (8000 + 162x - 0.099x^2 + 0.00003x^3)

P = 324x - 0.0495x^2 - 8000 - 162x + 0.099x^2 - 0.00003x^3

P = -8000 + 162x + 0.0495x^2 - 0.00003x^3 ………………….. (4)

Taking a derivative of equation (4) with respect to x and equating to 0, we have:

162 + 0.099x - 0.00009x^2 = 0 .................... (5)

Using the almighty formula as follows:

x = (-b +/- (b^2 - 4ac)^0.5) / 2a ………………. (6)

Where, from equation (5);

a = - 0.00009

b = 0.099

c = 162

Substituting the values into equation (6), we have:

x = (-0.099 +/- (0.099^2 - (4 * (- 0.00009) * 162))^0.5) / (2 * - 0.00009)

x = (-0.099 +/- 0.261) / -0.00018

x = (-0.099 + 0.261) / -0.00018, or x = (-0.099 - 0.261) / -0.00018

x = -900, or x = 2000

Since negative number does not have economic value in economics, the number of units that will give the maximum profit is therefore 2,000 units.

(b) What is the maximum possible profit?

From part a, x = 2000

Substituting x = 2000 into equation (4) and then solve, we have:

P(x) = -8000 + (162 * 2000) + (0.0495 * 2000^2) - (0.00003 * 2000^3)

P(x) = 274,000

Therefore, the maximum possible profit is $274,000.

Answer:

ΔEFD and ΔXYZ

Answer: y=-3/4x+2

Step-by-step explanation:

y=mx+b

y=-3/4x+b

-4=-3/4(8) +b

-4=-6+b

b=2

y=-3/4x+b

y=-3/4x+2

Answer:

45%

Step-by-step explanation:

This means x = 2, y = 3 and z = 1

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

Work Shown:

Double everything in the second equation to get 4x-2y+4z=6

Add this result to the first equation

[tex]x+2y-4z = 4\\4x-2y+4z = 6\\5x+0y+0z = 10[/tex]

The first two lines of that expression above shows us adding x+2y-4z=4 to the equation 4x-2y+4z = 6

The x terms add to x+4x = 5x

The y terms add to 2y+(-2y) = 0y

The z terms add to -4z+4z = 0z

The terms on the right hand side add to 4+6 = 10

That's how we end up with the new equation 5x+0y+0z = 10

That becomes 5x = 10 which solves to x = 2 when we divide both sides by 5.

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

Use this x value in the third original equation to find z

3x-8z = -2

3(2)-8z = -2

6-8z = -2

-8z = -2-6

-8z = -8

z = -8/(-8)

z = 1

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

Use the x and z values we found to find y

x+2y-4z = 4

2+2y-4(1) = 4

2+2y-4 = 4

2y-2 = 4

2y = 4+2

2y = 6

y = 6/2

y = 3

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

Overall we get the solutions to be x = 2, y = 3 and z = 1

We can say the solution as an ordered triple is (x,y,z) = (2,3,1)

Answer:

$19.65

Step-by-step explanation:

Adding decimals is the same as simple addition just line up the point in the numbers and add.

Answer:

y = 5/2x - 17/2

Step-by-step explanation:

First, find the slope of the equation by using the slope formula:

m = (y2 - y1) / (x2 - x1)

m = (-6 - 4) / (1 - 5)

m = 10/4

m = 5/2

Next, find the y-int by plugging in one of the two points into the equation we have so far:

y = 5/2x + b

(5, 2)

4 = 5/2(5) + b

4 = 25/2 + b

4 - 25/2 = b

b = -17/2

Now you have your final equation:

y = 5/2x - 17/2

Answer:

[tex]y=\frac{5}{2}x-\frac{17}{2}[/tex]

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Points: (5, 4), (1, -6)

Slope (Calculated): [tex]\frac{5}{2}[/tex]

[tex]y = \frac{5}{2}x+b[/tex]

[tex]-6 = \frac{5}{2}(1)+b[/tex]

[tex]b=-\frac{17}{2}[/tex]

[tex]y=\frac{5}{2}x-\frac{17}{2}[/tex]

Answer:

The sequence of transformations are;

A translation by 1 unit left, followed by a reflection across the x-axis

Step-by-step explanation:

Here, we want to know the transformation sequence

Let us select one point

J(1,4)

to J’(0,-4)

To translate 1 unit right means that we are subtracting the value of 1 from the x-coordinate

That leaves us with (0,4)

To get the change in the y-coordinate value to negative, it means that we have reflected over the x-axis

x-axis reflection turns (x,y) to (x,-y)

So, the sequence of transformations that maps the two is;

A translation by 1 unit left followed by a reflection across the x-axis

Answer:

translation 1 unit left, then 180 degrees

Step-by-step explanation:

J (1,4)

K (6,4)

L (1,1)

Moving it 1 unit left,  x unit - 1

J (0,4)

K (5,4)

L (0,1)

Now, rotate it 180 degrees, (x,y) = (-x,-y)

J' (0,-4)

K' (-5,-4)

L' (0,-1).

Hence, the triangle JKL is transformed into triangle J'K'L' when a triangle JKL translates 1 unit to the left and then rotate 180 degrees about the origin.

Answer:

324352

Step-by-step explanation:

Answer:

The 5 is in the tenths place.

Step-by-step explanation:

:)

Answer:

131.6

Step-by-step explanation:

Since the 5 in 131.572 is underlined, we need to round the number to the nearest tenth. When rounding numbers, we need to look at the digit next to the rounded digit. The digit after 5 is 7.

If the digit after that is 1-4, we round down the 5. If the digit after that is 5-9, we round up the 5. Since 7 is between 5 and 9, we round the digit 5 to 6.

Thus, the rounded number would be: 131.6

Answer:

Volume of right circular cone is 388.43 in³

Step-by-step explanation:

Height of circular cone = 16.8 in

Radius of circular cone = 4.7 in

We need to find Volume of right circular cone

The formula used for calculating volume of a right circular cone is: [tex]Volume=\pi r^2\frac{h}{3}[/tex]

Putting values and finding volume

[tex]Volume=\pi r^2\frac{h}{3}\\Volume=3.14\times (4.7)^2 \times \frac{16.8}{3}\\Volume=3.14\times 22.09 \times 5.6\\Volume= 388.43 \:in^3[/tex]

So, Volume of right circular cone is 388.43 in³

Answer:

The answer is: Use a calculator.

Step-by-step explanation

With the calculator you are able to do ANY problem.

Answer: There is no solution.

Step-by-step explanation:

Simplify both sides of the equation

subtract 3x from both sides

add 6 to both sides

0=10

The answer is - there are no solutions

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Probably C but I sure wouldn't bet the farm on it. It looks like C is about 1.5 times the size of X

Answer:

radius = 4units

diameter = 8units

Step-by-step explanation:

The radius is the distance from the midpoint of a circle to any point on the side of the circle. In this case, the radius is, 4units. The diameter is twice the radius and is 8 units.

Answer:

What should Alison do for her first step ? She should learn to intersect the bisector of the intersector of mn such that mn should be the intersection of mn to nm so that no 2 intersections should intersect each other's bisector of mn to intersect of mn.

Step-by-step explanation:

Answer:

I should add that Alison is a very smart girl if she wants to construct such a perpendiculiar bisector of MN--. I am realy gratefull for such a kind and wise little smart girl.

Step-by-step explanation:

Answer:

what

Step-by-step explanation:

Answer:

-6[tex]\sqrt{7}[/tex] /434

Step-by-step explanation:

Answer:

$5

Step-by-step explanation:

We can solve this using a system of linear equations. The equations are written like this:

3v + 9d = 75

5v + 10d = 100 (25 more than Dawn's total is 100)

V represents video games and d represents DVDs.

Let's isolate a variable, I'm going to isolate v in the first equation:

3v = -9d + 75

v = -3d + 25

Now that we isolated v we can plug it in to the second equation:

5(-3d + 25) + 10d = 100

-15d + 125 + 10d = 100

-5d + 125 = 100

-5d = -25

d = 5

Therefore, each DVD cost $5.

Check:

3v + 9(5) = 75

3v + 45 = 75

3v = 30

v = 10

5(10) + 10(5) = 100

50 + 50 = 100

100 = 100

I hope this helps!!

- Kay :)

Answer:

2/3+1/5=10/15+3/15=13/15

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

Radioactive dating becouse they look how long the fossils were there

Answer:

3:2

Step-by-step explanation:

can also be written as 3/2 as a fraction!

Answer:

Blue paint to red paint - 3:2

Red paint to blue paint 2:3

Step-by-step explanation:

For every 3 cups of blue paint there is 2 cups of red paint

For every 2 cups of red paint there is 3 cups of blue paint

Fraction Mode: 3/2 or 2/3

Answer:

2. A

3. H

4. D

5. C

6. G

7. E

8. F

Answer:

it is an answer if you are using a coordinate plane

Step-by-step explanation:

Answer:

The value of x = 4

so

Step-by-step explanation:

We know that an angle bisector bisects the angle into two equivalent angles.

When BD bisects angle ABC, it forms two equivalent angles which are:

such as

m∠ABD = m∠CBD

as

m ∠ABD = 6x-8

m∠CBD = 3x+4

so the equation becomes

m∠ABD = m∠CBD

6x-8 = 3x+4

6x - 3x = 4 + 8

3x = 12

Divide both sides by 3

x = 4

Thus, the value of x = 4

so