Answer:
The equations for each situation are
A = 36 + 6t
B = 21 + 9t
After 3 years, Tree A is taller.
Step-by-step explanation:
From the question,
Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and
Tree A grew by 6 inches per year and Tree B grew by 9 inches per year after planting.
For Tree A,
Given a period of t years after planting, the height would have increased by 6t
∴ A = 36 + 6t
For Tree B,
Given a period of t years after planting, the height would have increased by 9t
∴ B = 21 + 9t
To determine, which tree is taller after 3 years,
t = 3
For Tree A
A = 36 + 6t
A = 36 + 6(3)
A = 36 + 18
A = 54 inches
For Tree B
B = 21 + 9t
B = 21 + 9(3)
B = 21 + 27
B = 48 inches
Hence, After 3 years, Tree A is taller.
A furniture manufacturer makes two types of furniture: chairs and sofas. The production of the sofas and chairs requires three operations: carpentry, finishing, and upholstery. Manufacturing a chair requires 3 hours of carpentry, 9 hours of finishing, and 2 hours of upholstery. Manufacturing a sofa requires 2 hours of carpentry, 4 hours of finishing, and 10 hours of upholstery. The factory has allocated at most 66 labor hours for carpentry, 180 labor hours for finishing, and 200 labor hours for upholstery. The prfit per chair is $90 and the profit per sofa is $75. The manufacturer wants to know how many chairs and how many sofas should be produced each day to maximize the profit.
Formulate a linear programming (LP)problem you would use to find a solution.
Answer:
Chair x₁ = 10
Sofa x₂ = 18
z(max) = 2250 $
Step-by-step explanation:
Information:
Operation-Profit Carpentry Finishing Upholstery Profit
hours hours hours $
Chair (x₁) 3 9 2 90
Sofa (x₂) 2 4 10 75
Objective Function z:
z = 90*x₁ + 75*x₂
Constrains:
1.-66 hours of carpentry available
3*x₁ + 2*x₂ ≤ 66
2.- 180 hours of finishing available
9*x₁ + 4*x₂ ≤ 180
3.- 200 hours of upholstery
2*x₁ + 10*x₂ ≤ 200
Model:
z = 90*x₁ + 75*x₂ to maximize
Subject to:
3*x₁ + 2*x₂ ≤ 66
9*x₁ + 4*x₂ ≤ 180
2*x₁ + 10*x₂ ≤ 200
x₁ >= 0 x₂ >= 0
From simplex method solver we get the answer
x₁ = 10 x₂ = 18 z = 2250
The linear programming model is:
Maximize [tex]\mathbf{Z = 90x + 75y}[/tex]Subject to [tex]\mathbf{3x + 2y \le 66}[/tex], [tex]\mathbf{9x + 4y \le 180}[/tex], [tex]\mathbf{2x + 10y \le 200}[/tex], [tex]\mathbf{x,y \ge 0}[/tex]Represent sofa with y and chairs with x.
The given parameters are:
Carpentry:
[tex]\mathbf{Chair =3\ hours}[/tex]
[tex]\mathbf{Sofa =2\ hours}[/tex]
[tex]\mathbf{Available = 66\ hours}[/tex]
So, we have:
[tex]\mathbf{3x + 2y \le 66}[/tex]
Finishing
[tex]\mathbf{Chair =9\ hours}[/tex]
[tex]\mathbf{Sofa =4\ hours}[/tex]
[tex]\mathbf{Available = 180\ hours}[/tex]
So, we have:
[tex]\mathbf{9x + 4y \le 180}[/tex]
Upholstery
[tex]\mathbf{Chair =2\ hours}[/tex]
[tex]\mathbf{Sofa =10\ hours}[/tex]
[tex]\mathbf{Available = 200\ hours}[/tex]
So, we have:
[tex]\mathbf{2x + 10y \le 200}[/tex]
The profit is given as: $90 per chair, and $75 per sofa.
So, the objective function is:
[tex]\mathbf{Z = 90x + 75y}[/tex]
Hence, the linear programming model is:
Maximize [tex]\mathbf{Z = 90x + 75y}[/tex]
Subject to
[tex]\mathbf{3x + 2y \le 66}[/tex]
[tex]\mathbf{9x + 4y \le 180}[/tex]
[tex]\mathbf{2x + 10y \le 200}[/tex]
[tex]\mathbf{x,y \ge 0}[/tex]
Read more about linear programming model at:
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The maximum heart rate is the highest heart rate achieved during maximal exercise. In general, you get the most benefits and reduce the risks when you exercise within your target heart rate zone. Usually this is when your exercise heart rate (pulse) is about 80 percent of your maximum heart rate. The formula M = 0.8 ( 220 − A ) M = 0.8 ( 220 - A ) , gives the recommended maximum heart rate, M M , in beats per minute, for a person who is A A years of age. Determine the age of a person whose target heart rate is 128 beats per minute. The recommended maximum heart rate is 128 beats per minute for a person who is years old.
Answer:
160 years
Step-by-step explanation:
The formula for the heart rate is given by :
M=0.8 (220−A) ...(1)
M is the maximum heart rate in beats per minute and A is the age in years
Put M = 128 beats per minute in the above formula.
128=0.8(220-A)
160=220-A
A=220-160
A = 160 years
So, the age of person is 160 years if heart rate is 128 beats per munute
Answer:
B
Step-by-step explanation:
Plz give brainliest
a package of 4 pairs of isulated gloves costs $33.96. what is the unit price of gloves
Answer:
8.49 per pair/pack of gloves
Step-by-step explanation:
i got this by taking 33.96 divided by 4 so i could find out how much for one pair
The US emerged as a world power because of its success in
A. the Korean War
B. World War I
C. World War II
D. the Cold War
Answer:
its c
Step-by-step explanation:
trust and dont vote me out! its not me i sware its cyan he sus!
Answer:
It's C
Step-by-step explanation:
A furniture company is producing three types of furniture. Product A requires 7 board feet of wood and 4 lbs of wicker. Product B requires 5 board feet of wood and 5 lbs of wicker. Product C requires 4 board feet of wood and 3 lbs of wicker. There are 3000 board feet of wood available for product and 1400 lbs of wicker. Product A earns a profit margin of $35 a unit, Product B earns a profit margin of $42 a unit, and Product C earns a profit margin of $20 a unit. Formulate the problem as a linear program.
Step-by-step explanation:
this is a linear programming problem, and we are expected to draw up the linear program for the solution of the problem.
The objective function is
Maximize
35A+42B+20C=P
subject to constraints(board and wicker)
The constraints are
board
7A+5B+4C=3000
wicker
4A+5B+3C=1400
A>0, B>0, C>0
The length of a rectangle is 10 meters more than the width. If 3 meters is added to both the length and the width, the new area will be 299 square meters. Find the length and width of the original rectangle.
HELP HELP HELP HELP
Answer:
L = 20
W = 10
Step-by-step explanation:
L = (w + 10)
NL = (w + 13)
Divide 299 by 13:
299 ÷ 13 = 23
So, 23 x 13 = 299
L = 23
W = 13
Subtract 3 from both to get the original length and width
q(x)= -2x+1
r (x)=x²+2
Find the value of r r(q (2)).
Answer:
r(q(2)) = 11
Step-by-step explanation:
given r(x) = x^2 + 2, and q(x) = -2x + 1.
Here is the equation to the composite function:
r(q(x)) = (-2x+1)^2 + 2 = 4x^2-4x+3 .
Then just substitute the input and solve:
r(q(2)) = 4(2)^2- 4(2) + 3 = 16 - 8 + 3 = 16 - 5 = 11
______________________________
Or if you don't like this, first find the answer to q(2) = -2(2) + 1 = -3
Then substitute this value into the second equation r(x).
r(x) → r(-3) = (-3)^2 + 2 = 9 + 2 = 11
The average cost of a compact car at a certain dealership over the last 10 years has ranged from $15,000 to $24,500. Suppose you were going to plot these points on a coordinate grid. (a) What is a good scale [range] would be good to use for the y-axis to make a nicely sized graph? Explain your reasoning. (b) What is a good interval [step size] would be good to use for the y-axis to make a nicely sized graph? Explain your reasoning. (c) What is a good scale [range] would be good to use for the x-axis to make a nicely sized graph? Explain your reasoning. (d) What is a good interval [step size] would be good to use for the x-axis to make a nicely sized graph? Explain your reasoning. Note: The step size the distance between the marks on the graph, and the range is the maximum and minimum values (ex: -10 to 10).
Answer:
this is what i did i apologize if i’m late and u no longer need the answer or if i’m wrong
Step-by-step explanation:
i need an answer help !
A stack of books is 62 inches high. How high is it in feet and inches?
Answer:
5 feet and .16667 inches
Step-by-step explanation:
if you where to simplify the inches it would be 2 inches because the 6 next to the 1 is greater then five making the 1 a 2
Laura red 312 page book in 13 hours if she read the same number of pages each hour how many pages did she read i
Answer:
24 pg per hour
Step-by-step explanation:
Divide 312 by 13, and the result will be 24. Hope it helps!
Answer:
24
Step-by-step explanation:
16,1,0,1,16 input x and output y -2,-1,0,1,2
Answer:
what is the question?
Step-by-step explanation:
help ASAP plz and Thankyou
Answer: B
Step-by-step explanation:
¿Cuál es la desigualdad de 3 x - 4> 4-4-3 x
What is 5 8/100
as a decimal?
O
A. 5.008
0
B. 5.08
O
C. 5.8
0 D. 58
Answer:
5.08
Step-by-step explanation:
5 8/100
Since there are 2 zero's in 100, we need two numbers in the top
Replace 8 with 08 which is the same number
5 08/100
Now write as a decimal
5.08
Answer:
B. 5.08
Step-by-step explanation:
[tex]5\frac{8}{100} = \frac{508}{100}[/tex] 508 ÷ 100 = 5.08I hope this helps!
identify the first term of the algebraic expression. Indicate whether the term is a variable or a constant term.
5y + 8b
Answer:
Someone text me on sc queenalyssa_05
Step-by-step explanation:
Answer:5
Step-by-step explanation:
Solve 27* 9
I will give 100 points!!!!!!
27* 9 = 243 there your welcome and bless you
I mark as brainliest
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
:)
A giant garter snake is at least 64 inches long. If 1 inch is equal to
2.5 cm, how long is the Giant garter snake in cm?
Answer:
The snake would equal 160cm.
Step-by-step explanation:
Correct me if im wrong plz
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Answer:
3(x-2)+6=6x-9
[tex]3x - 6 +6 =6 x - 9 \\ 3x - 6x = - 9 \\ - 3x = - 9 \\ x = - 9 \div - 3 = 3[/tex]
Approximately how many litres is 70 fluid ounces?
Use the conversion 20 fluid ounces = 1 pint and 134
pints = 1 litre
Question 1 Part A: How many beads did Jiao send out? *
Wooden Beads
Oak
4,525
Maple
6,950
Ash
3,720
Ebony
2,475
Bayong
1,250
Answer:
Jiao sent out 18,920 beads.
Step-by-step explanation:
All I did was add.
</3 hope this helps.
Jean's bedroom is 13 feet by 11 feet. She has chosen a carpet which costs $29.65 per square yard. This includes installation.
Determine her cost to carpet her room.
Answer:
The answer is 4239.95
Step-by-step explanation:
First, you would have to do 13x11.
Which will come out to be 143.
Then do 143 times 29.65 to get your answer.
The answer is 4239.95.
Jean's cost to carpet her room is $470.33.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
First, we have to convert the dimensions of the room from feet to yards:
Length in yards = 13 feet / 3 feet per yard = 4.33 yards
Width in yards = 11 feet / 3 feet per yard = 3.67 yards
The area of the room is:
Area = length x width
Area = 4.33 yards x 3.67 yards
Area = 15.86 square yards
The cost per square yard is $29.65, so the total cost is:
Total cost = area x cost per square yard
Total cost = 15.86 square yards x $29.65/square yard = $470.33
Therefore, Jean's cost to carpet her room is $470.33.
Learn more about the area of the rectangle here:
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What is the probability that you will get heads no more than once out of 3 flips? P(0 successes) + P(1 success)=
Answer:
The answer is .5
Step-by-step explanation:
Answer:
The correct answer is 0.5
Step-by-step explanation:
You have to do 0.125 (0 successes) plus 0.375 (1 success). This is equal to 1/2
This is correct on edge.
find the domain of 5x-2
55 points and Brainliest!
Answer:
Um
Step-by-step explanation:
HELP!!!!!!!! I LOVE YOU AND ILL EVEN GIVE BRAIN
Consider a 25 factorial design. (a) How many factors and levels are considered in this factorial experiment
Answer:
Step-by-step explanation:
From the information given;
We are to take a look at a 2⁵ factorial design.
The factorial design consists of carrying out the design of equipment by testing it by modifying not the parameters one by one but by modifying several simultaneous parameters.
An experiment is termed to be a 2⁵ factorial experiment if in the experiment 5 factors are studied consecutively with each at two-level.
Thus, there are five factors and 2 levels in the experiment.
2. How far does light travel in water in 5.0 X
102 seconds, if the speed of light in water is 3
108 m/s?
What is the domain of the function in this table?
X | Y
1 | 2
2 | 4
3 | 3
4 | 2
CHIOCES:
A. (1, 2), (2, 4), (3, 3), 4,2)
B. {1,2,3,4}
C. (1,2)
D. {2,3,4}
PLEASE HELP URGENT
Answer: B. {1, 2, 3, 4}
Step-by-step explanation:
The domain is the set of input values (in other words, x values)