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The maximum profit is achieved when the manufacturer spends $4,000 on development and $4,000 on promotion.

The profit is given by

(150 - 50) * (320y/(y+2) + 160x/(x+4)) - x - y

= 100 * (320y/(y+2) + 160x/(x+4)) - x - y

= 32000y/(y+2) + 16000x/(x+4) - x - y

We want to maximize this function subject to the constraint that x + y = 8.

We can do this by using Lagrange multipliers. The Lagrangian is given by

L = 32000y/(y+2) + 16000x/(x+4) - x - y + lambda(x + y - 8)

Setting the partial derivatives of L with respect to x, y, and lambda equal to zero, we get the following equations:

32000/(y+2) - 1 - lambda = 0

16000/(x+4) - 1 - lambda = 0

x + y - 8 = 0

Solving these equations, we get x = 4, y = 4, and lambda = 0.

Therefore, the maximum profit is achieved when the manufacturer spends $4,000 on development and $4,000 on promotion.

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Answer:

7<x<31

Step-by-step explanation:

The third side of any triangle must be more than the difference between the other two sides.

x>19-12

x>7 (or) 7<x

The third side of any triangle must be less than the sum of the other two sides.

x<19+12

x<31 (or) 31>x

Put them together.

7<x<31 (or) 31>x>7

7<x<31 are the possible values of x.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that  side lengths of a triangle are 12, 19, and x units.

We need to find the value of x.

We know that the third side of any triangle must be more than the difference between the other two sides.

x is greater than difference of nineteen and twelve

x>19-12

x>7 (or) 7<x

The third side of any triangle must be less than the sum of the other two sides.

x<19+12

x<31 (or) 31>x

From this we get the interval as

7<x<31 (or) 31>x>7

Hence, 7<x<31 are the possible values of x.

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Answer:

x has to be greater than or equal to 10 (x ≥ 10)

Step-by-step explanation:

x + 3 ≥ 13

x ≥ 13 - 3

x ≥ 10

Answer:

A=hbb/2 hope this helps :)

Step-by-step explanation:

Answer:

The first Transition is a reflection over the line M

The second transition is a 180 degree rotation.

Step-by-step explanation:

Answer:

A, B, and D

Step-by-step explanation:

A variable could be represented as a letter.

Coefficient is the number multiplying a variable.

Product means multiplication.

Therefore the expressions that represent the product of a variable and a coefficient are:

11c, ½t, and j*4

Answer:

$15

Step-by-step explanation:

Step-by-step explanation:

180 - 120 = 60

32 + 60 = 92

180 - 92 = 88

Answer:

The sequence is Geometric sequence

Answer:

12cm squared

Step-by-step explanation:

Since the area of a triangle is BxH/2, the area will be 24/2. That equals 12cm squared.

Answer:

I this 500$

Step-by-step explanation:

Answer:

-15x-4

Step-by-step explanation:

-21x + 6x-4

-15x-4

Answer:

$440

Step-by-step explanation:

40 x 11 = your answer 440

Answer:

angle 1= 120 and angle 2 and 3 = 30

Step-by-step explanation:

Answer:

answer is below

Step-by-step explanation:

angle1=120°

[tex]angle2=angle3=\frac{180-120}{2} =30[/tex]°

Answer:

Step-by-step explanation:

You have all correct choices.

We can use the given values and work out the equation:

The function for this situation is:

Answer:

2(2)^t

Step-by-step explanation:

PLATO

Answer:

I think it's false

Step-by-step explanation

Answer: [tex]30^{\circ}[/tex]

Step-by-step explanation:

Given

[tex]\sin 60=\dfrac{\sqrt{3}}{2}[/tex]

For

[tex]\cos \theta =\dfrac{\sqrt{3}}{2}[/tex]

It indicates [tex]\theta[/tex] lies in I st quadrant. The value of cosine [tex]30^{\circ}[/tex] is equal to  [tex]\dfrac{\sqrt{3}}{2}[/tex]

Therefore, [tex]\theta[/tex] must be [tex]30^{\circ}[/tex]

Answer:

1st option

Step-by-step explanation:

You have to take the radius and times it by 1 which gives you 8 in.

Answer:

3/2

Step-by-step explanation:

Step-by-step explanation:

[tex]x + \frac{1}{2} = 2 \\ x = 2 - \frac{1}{2} \\ x = \frac{3}{2} [/tex]

Answer:0.03

Step-by-step explanation:

Answer:

0.03

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

you would do 3+3+3 because there are 3 colors

And i just got it right on my quiz.

There will be 9 branches in the tree diagram of the situation.

In probability theory, tree diagrams can be used to represent probability spaces. A tree diagram can represent a set of independent events or conditional probabilities. Each node in the graph represents an event and is associated with the probability of that event.

Given,

A spinner of three sections colored green, purple and pink.

Number of outcomes = 3

spinner is spun twice,

then number of outcomes = 3 × 3 = 9

Number of branches in tree = 9

Hence, 9 branches will be there in probability tree diagram.

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Answer: 22.9

Step-by-step explanation: Perimeter of a triangle is the sum of all side lengths, in this case, 4, 5, and 13.9, and the sum is 22.9. Hope this helps, and have a great day!

Answer:

22.9 i think

Step-by-step explanation:

Answer:

The number of days and total miles run one.

Step-by-step explanation:

A proportional relationship is y/x being the same everytime. The first table doesnt fit with that. The second graph isnt a straight line. The third table isnt coreect either. Lastly the forth table workng.

Sorry if im incorrect

Answer:

m∠A = 48.81°

Step-by-step explanation:

Given triangle is a right triangle and we have to measure ∠A.

Since, opposite side and adjacent sides of angle A has been given

So we will apply tangent rule to get the measure of angle A.

tan(∠A) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

tan(∠A) = [tex]\frac{8}{7}[/tex]

∠A = [tex]\text{tan}^{-1}(\frac{8}{7})[/tex]

∠A = 48.814

  ≈ 48.81°

Answer: 360

Step-by-step explanation:

Well if you take 640miles and divide it by 16 gallons you get 40mpg so if you get 40mpg times that by 9 and you get 360miles

Answer:

13

Step-by-step explanation:

It is a quadratic equation meaning it has 2 factors and since one of it has root -5, the first factor is (n + 5),

So, we have (n + 5)(n + a) = n^2 + an + 5n + 5a

Thus, by comparison,

n^2 + (5 + a)n + 5a = n^2 - 8n - 65 = 0

5 + a = -8

5a = -65

a = -13

Thus, the other factor is (n -13) and root is 13

Answer:

D. 160

Step-by-step explanation:

This question can be solved by proportions, using a rule of three.

In this question:

For each 3 white carnations, 5 yellows are needed, which leaves us with 8 total carnations. So for 60 white, the total is:

3 white - 8 total

60 white - x total

So

[tex]3x = 60*8[/tex]

Dividing both sides by 3

[tex]x = 20*8 = 160[/tex]

The correct answer is given by option D.

Answer:

a.

Mean:70.2

Median:60

Mode:85

b.

The mode best supports her claim as it is the highest of the three.

c.

Her claim is misleading as it doesn't reflect the fact that her scores are declining and that she tends to actually do worse than 85 (most of her scores are below 85)

Step-by-step explanation:

a.

The mean is the sum of all the terms, divide by the amount of terms:

(85+85+60+62+59)/5=351/5=70.2

The median is the middle-most number in the set 85,85,60,62,59: 60

The mode is the most common number in the set 85,85,60,62,59: 85

b.

The mode best supports her claim as it is the highest of the three.

c.

Her claim is misleading as it doesn't reflect the fact that her scores are declining and that she tends to actually do worse than 85 (most of her scores are below 85)

Step-by-step explanation:

The diagram resembles a right angled triangle,

So, By Pythagoras theorem,

(11)²=(4)²+x²

= 121=16+x²

= 121-16=x²

= 105=x²

= root105 =x