The maximum profit is achieved when the manufacturer spends $4,000 on development and $4,000 on promotion.
How to calculate the profitThe 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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4. The measures of segment BS and segment PS are both 4.5 feet and m_PBS = 56°.
a. Find the measure of BSP. Item 2 says that “Angle QPS is supplementary to PSR."
b. Is BPS a unique triangle, or can more than one triangle be formed using the given segment
lengths and angle measures? Explain.
What is the area of ADEF?
Answer:
6 sq ft
Step-by-step explanation:
Look at the pattern below. Which fraction would complete the pattern?
1/4, 2/8, ___, 4/12.
answer
A. 3/12
B. 3/14
C. 3/9
D. 3/15
The answer is: A. 3/12
Find the area of the following figure: 11in 10in
Answer:
(no simplification) = 55 + (25[tex]\pi[/tex]/2) in^2
(with simplification) = (110 + 25[tex]\pi[/tex])/2 in^2
(with pi rounded to 3.14) = 94.25 in^2
Step-by-step explanation:
Let's start with the easier shape, the triangle. The formula for area of a triangle is 1/2(base)(height). Since at the far right we have 10 in, we can apply that to the triangle to get the base = 10 inches. The height is given as 11 inches so we can then calculate the area which is 55 in^2.
Then, the circle. We know that area of a whole circle = [tex]\pi r^{2}[/tex]. Since we know that a semicircle is 1/2 of a full circle, we can find the area of the entire circle then divide it by 2.
It gives the diameter as 10, divide that by 2 to get the radius. r=5. Plug 5 into the equation of [tex]\pi r^{2}[/tex] and you get 25[tex]\pi[/tex]. Divide that by 2 to get 25[tex]\pi[/tex]/2.
Add the triangle and the semicircle areas.
(no simplification) = 55 + (25[tex]\pi[/tex]/2) in^2
(with simplification) = (110 + 25[tex]\pi[/tex])/2 in^2
(with pi rounded to 3.14) = 94.25 in^2
Andrew randomly selects a number from 1-15. What is the probability that the number he selects is an even number?
Answer:
7/15
Step-by-step explanation:
Probability= Number of even numbers / Total numbers
There are 7 even numbers between 1 and 15
P = 7/15
Find the Mode:
88, 82, 81, 89, 77, 95
89, 90, 81, 75
Answer:
81 is the mode
Step-by-step explanation:
THe mode is the number ina. Set of data that appears the most. In this case, 81 appears twice while all the other numbers only appeared once. So 81 in this case is the mode.
0.9, 0.99, 0.09, 0.91, from least to greatest
Answer:
0.09, 0.9, 0.91, 0.99
Step-by-step explanation:
Well I'm in 7th grade so I already know this stuff
15 POINTS
Consider the line in the coordinate plane that passes through the point (-7, -3) and the origin. Find the slope of a line perpendicular to the line described.
A) - 1, 3
B) - 3, 7
C) - 7, 3
D) 3, 7
Answer:
C. -7/3Step-by-step explanation:
The slope of the line that passes through points (0, 0) and (-7, -3) is:
m = (y₂ - y₁)/(x₂ - x₁) m = (-3 - 0)/(-7 - 0) = 3/7Perpendicular lines have opposite-reciprocal slopes:
-1 / (3/7) = - 7/3Correct choice is C
what is the measurements of the circle?
Answer:
what is the circle
○ YW 42
Please help
here the question
Rosalina just started a new job. She has $500 in her bank account. Every week, she deposits $40 into her bank account.
A)
Write an expression to represent how much Rosalina has in her account at any given time using x to represent the number of weeks.
I ALREADY SOLVED A BUT I NEED HELP WITH C
B) Rosalina wants to save $700 for the new smart tv write and equation to determine how many weeks (x) it will take for rosalina to have enough money to purchase her new tv
C) using your equation from b will rosalina have enough money for her new tv in four weeks?
also) how would the equation change if rosalina stopped working wasn't able to deposit $40 and had to instead withdraw $40 a week? Which part of your equation would change?
please help!
THANK YOU!!
Answer:
Let M represent the amout at any time.
She saves $40 per week so total amount becomes 40x in any specified week.
where x is the number of weeks.
In the start she has $500 in her bank account so we 'll add this amount into the savings per week. So expression becomes
M = 40x+500
Simply put number of week in place of x and find the total amount.
Step-by-step explanation:
Answer:
for c it is no
Step-by-step explanation:
it is no because she deposits 40 a week, in 4 weeks she deposits 40x4=160, which is nowhere close to the 700 she needs. Even if you count the 500 in her account it is still no since it would total up to 660, not 700
Name:
L153
Mean Absolute Deviation
Find the mean absolute deviation of each set of data. Round your answer to two decimal
places.
1) 61, 87, 46, 79,53, 46
2) 9, 2, 1, 3
Absolute
Absolute
Data Mean Difference
Data Mean
Value
Difference
Value
Answer:
amen
Step-by-step explanation:
amen you shall pass
Factor the expression.
20b + 35 =
(Factor completely.)
Answer:
I think it would be 5(4b+7)
Step-by-step explanation:
I divided both terms by 5.
how do we pass maths
Answer:
1- Create a Distraction Free Study Environment. Mathematics is a subject that requires more concentration than any other.
2- Master the Key Concepts.
3- Understand your Doubts.
4- Apply Maths to Real World Problems.
5- Practice, Practice and Practice even more.
A retail shop is replacing their flooring with laminate wood. The floor plan is shown below. Determine the total square feet of laminate wood needed to complete the the job.
Answer:
1075 ft
Step-by-step explanation:
25*35 = 875
8*25 = 200
875+200 = 1075
Please help... I’ll give Brainliest ❤️
Answer:
triangle B is the reflection of triangle A across the x-axis
Identify the graph of the equation (x+3)2+(y+1)2=9
The resulting graph is a circle with center at (-3,-1) and radius 3.
The graph of the equation (x+3)²+(y+1)²=9
is a circle with center at (-3,-1) and radius 3. The equation of a circle with center (a,b) and radius r is given by the equation (x-a)² + (y-b)² = r². By comparing the given equation with the standard equation of a circle, we can easily see that the center of the circle is (-3,-1) and the radius is 3. To graph a circle, we need to first plot the center of the circle, which is (-3,-1) in this case. Next, we need to mark the radius of the circle, which is 3 units. We can do this by measuring 3 units from the center in any direction and marking the point. Since the radius of the circle is the same in all directions, we can repeat this process for other directions to get points on the circumference of the circle. We can use a compass to make this process easier. After plotting a sufficient number of points, we can draw a smooth curve passing through all the points to obtain the graph of the circle.
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Rewrite 7^-2 using a positive exponent an evaluate the result.
Enter the correct answer in the box.
Simplify the expression x^5•x^7
Answer:
x^12
Step-by-step explanation:
when multiplying with exponents, keep base and add exponents
when dividing with exponents, keep base and subtract exponents
A car costs 12,000. During a sale, it will cost 10,920. By what percent was the price reduced?
Answer:
(12000 - 10920) / 12000 = 0.09
Step-by-step explanation:
Mathematics challenge
Get the equation of the line containing PQ using the point-slope formula:
y - (-2) = 3/2 (x - (-6))
Solve for y to get it in slope-intercept form:
y = 3/2 x + 7
so the y-intercept is (0, 7).
The line containing QR is then
y - 7 = -3/4 (x - 0)
or
y = -3/4 x + 7
The point R is on the x-axis, so its y-coordinate is 0. Plug in y = 0 and solve for x to get the other coordinate:
0 = -3/4 x + 7
3/4 x = 7
x = 4/3×7 = 28/3
So the point R has coordinates (28/3, 0).
Answer:
Point R is on the x-axis, so its y-coordinate is 0. Plug in y = 0 and solve for x to get the other coordinate:
0 = -3/4 x + 7
Take off the zero...
3/4 x = 7
Answer
x = 4/3×7 = 28/3
And there it is
Point R has the coordinates (28/3, 0).
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
7 x - 9 + 11 x - 9 = 180
Step-by-step explanation:
For the equation: 7 x - 9 + 11 x - 9 = 180
Value of X is 11
7x - 9 + 11x - 9 = 180
combine values
18x - 18 = 180
18x = 198
18x/18 = 198/18
x = 11
Angle Measures is
7 (11) - 9 = 77-9 = 68 degrees
11 (11) - 9 = 112 degrees
What is the value of g in the relative frequency table?
Round the answer to the nearest percent.
25%
33%
63%
68%
Answer:
g = 33%
Step-by-step explanation:
The values in the ends of the rows are found by adding together.
For the first row, we would add the value in cell AC to the value in AD to get the value in the corresponding column called "Total". This means we add 20% +g to get 53%;
Subtract 20% from each side
g = 53% - 20%
combine like terms !-3r - 5 + 2r - 3r - 2s
HELP ASAP
pls help!!
Bryant earns $15 in commission for every $150 worth of shoes that he sells. Which equation can be used to find the total commission, C, Bryant will earn if the cost, s, of the shoes he sells is known?
a) c= 1/15s
b) c=1/10s
c) 10s
d) c=15s
Will someone please please help me
Answer:
Step-by-step explanation:
12 + 5 = 17
square root of 9 = 3
5 x 4 = 20
AABC is isosceles.
MZA = 48° and mZB = 4x + 4.
A
B
x= [?]
What's the slop of the line with the two points 3,2 and 7,9
1. A number cube is rolled 24 times and lands on 2 four times and on 6 three times.
a. Find the experimental probability of landing on a 2.
b. Find the experimental probability of not landing on a 6.
c. Compare the experimental probability you found in part a to its theoretical probability.
d. Compare the experimental probability you found in part b to its theoretical probability
Step-by-step explanation:
(A) you takeway 24 by 2 and add 6=28
Jaheem had $15, but he spent $12 at the
bookstore. Which of the following represents the
amount Jaheem spent?
A. 0.08 or 8%
B. 0.8 or 8%
C. 0.08 or 80%
D. 0.8 or 80%
 Consider the line segment LP with endpoint at L (-3, -5) and P (9, 7) and midpoint M.
What is the x—coordinate of N, the point that partitions segment MP in a 1 : 1 ratio?
A. 4
B. -4
C. -6
D. 6
Answer:
D. 6Step-by-step explanation:
M is midpoint of LP and N is midpoint of MP
Use midpoint formula:
x = (x₁ + x₂)/2Find x-coordinate of M:
x = (-3 + 9)/2 = 3Find x-coordinate of N:
x = (3 + 9)/2 = 6Correct choice is D