Answers
Related Questions
What is the y-intercept of a line that has a slope of 3 and passes through point (–1, –7)?
Answers
Answer:
the y intercept is -4 (as a point it is (0,-4))
Step-by-step explanation:
Hi there!
We are given a slope (m) of 3 and the point (-1,-7).
We need to find the y intercept of the line that has the slope of 3 and passes through (-1,-7)
One way to find the y intercept is to write the equation of the line in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept).
Since we are given the slope, we can immediately substitute it into the equation
Here it is so far:
y=3x+b
now we need to find b (the y intercept)
since the line passes through the point (-1,-7), we can use it to solve for b
substitute -1 as x and -7 as y into the equation
-7=3(-1)+b
multiply
-7=-3+b
add 3 to both sides
-4=b
so the y intercept is -4 . If you need it as a point, its (0,-4) as the y intercept is the point where the equation passes through the y axis, so the value of x is 0.
Hope this helps! :)
what is 186.4 ounces oz of water in millliiters (mL)
Answers
Answer:
The answer is 5284.35 using the conversion
Answer:
5284.4
Explanation:
Tbh if you have a conversion table then see the conversion for what 1 oz is equal to in mL and do the math like that… •_•
Hope this helps, have a good day!
With the growth of internet service providers, a researcher decides to examine whether there is a correlation between cost of internet service per month and degree of customer satisfaction (higher scores mean high satisfaction). The researcher only includes programs with comparable types of services. Calculate the Pearson's correlation coefficient for the dataset below and interpret what that means.
Answers
Answer:
The correlation is 0.373 . There is a moderate positive linear association between Dollars and Satisfaction.
Step-by-step explanation:
Given the data:
Dollars Satisfaction
70.99 32
76.01 34
67.24 27
69.33 17
67.59 23
74.06 29
76.04 25
72.63 31
68.01 26
67.98 31
Using technology, the Pearson correlation Coefficient calculator ; we can obtain the Pearson correlation Coefficient is 0.3729
Interpretating this value, a correlation Coefficient value of 0.3729 is positive, this means a positive linear relationship exists between the values. Also 0.3729 is closer to 0 than 1 ; this mean that the strength of their relationship is moderate to weak .
Hence, a correlation Coefficient value of 0.3729 means that a weak positive relationship exists between dollar and satisfaction
EXPAND AND SIMPLIFY
Answers
Answer:
5⁴a²
Step-by-step explanation:
(5³a³)÷5a-¹×5-²a²
5³a³÷5a-¹×5-²a²
5³a³÷5¹-²×a-¹+²
5³a³÷5-¹a
5³a³/5-¹a
5³-(-¹)a³-¹
5⁴a²
A park, in the shape of a quadrilateral ABCD has angle B=900 , AB=9m, BC=40m, CD=15m, DA=28m. How much area does it occupy?
Answers
Given:
In quadrilateral ABCD, angle B=90° , AB=9m, BC=40m, CD=15m, DA=28m.
To find:
The area of the quadrilateral ABCD.
Solution:
In quadrilateral ABCD, draw a diagonal AC.
Using Pythagoras theorem in triangle ABC, we get
[tex]AC^2=AB^2+BC^2[/tex]
[tex]AC^2=9^2+40^2[/tex]
[tex]AC^2=81+1600[/tex]
[tex]AC^2=1681[/tex]
Taking square root on both sides, we get
[tex]AC=\sqrt{1681}[/tex]
[tex]AC=41[/tex]
Area of the triangle ABC is:
[tex]A_1=\dfrac{1}{2}\times base\times height[/tex]
[tex]A_1=\dfrac{1}{2}\times BC\times AB[/tex]
[tex]A_1=\dfrac{1}{2}\times 40\times 9[/tex]
[tex]A_1=180[/tex]
So, the area of the triangle ABC is 180 square m.
According to the Heron's formula, the area of a triangle is
[tex]Area=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where,
[tex]s=\dfrac{a+b+c}{2}[/tex]
In triangle ACD,
[tex]s=\dfrac{28+15+41}{2}[/tex]
[tex]s=\dfrac{84}{2}[/tex]
[tex]s=42[/tex]
Using Heron's formula, the area of the triangle ACD, we get
[tex]A_2=\sqrt{42(42-28)(42-15)(42-41)}[/tex]
[tex]A_2=\sqrt{42(14)(27)(1)}[/tex]
[tex]A_2=\sqrt{15876}[/tex]
[tex]A_2=126[/tex]
Now, the area of the quadrilateral is the sum of area of the triangle ABC and triangle ACD.
[tex]A=A_1+A_2[/tex]
[tex]A=180+126[/tex]
[tex]A=306[/tex]
Therefore, the area of the quadrilateral ABCD is 306 square meter.
\A and \B are supplementary angles. If m\A= (3x – 23) and m
\B = (2x – 12), then find the measure of \B.
Answers
2 supplementary angles when added together need to equal 180 degrees.
Add:
3x-23 + 2x-12 = 180
Simplify:
5x -35 = 180
Add 35 to both sides:
5x = 215
Divide both sides by 5:
X = 43
Now replace x with 43 in the equation for angle b:
2(43) -12 = 86-12 = 74 degrees
Angle B = 74 degrees
Nine subtracted from four times a number is -21 what is the number?
Answers
Answer:
-3
Step-by-step explanation:
My knowledge ;D
In the population of young children eligible to participate in a study of whether or not their calcium intake is adequate, 52% are 5 to 10 years of age and 48% are 11 to 13 years of age. For those who are 5 to 10 years of age, 18% have inadequate calcium intake. For those who are 11 to 13 years of age, 57% have inadequate calcium intake.
Required:
a. Use letters to define the events of interest in this exercise.
b. Convert the percents given to probabilities of the events you have defined.
Answers
Answer:
(a) A = 5 to 10 years old
B = 11 to 13 years old
C = adequate calcium intake
I = inadequate calcium intake.
(b) P(A) = 0.52, P(B) = 0.48, P(I|A) = 0.18, P(I|B) = 0.57.
Step-by-step explanation:
Complete question
Please find the attached image
(a) A = 5 to 10 years old
B = 11 to 13 years old
C = adequate calcium intake
I = inadequate calcium intake.
b) P(A) = 0.52, P(B) = 0.48, P(I|A) = 0.18, P(I|B) = 0.57.
In how many ways can a committee of 3 men and 2 women be formed from a group of 9 men and 10 women?
Answers
Answer:
first you have to find the number of ways 3 men can be chosen, then the number of ways 2 women can be chosen, and then you need to multiply these numbers together to get the number of ways because multiplication will show the total arrangements possibilities. use combination since order does not matter.
number ways for 2 out of 10 women total: 10 choose 2= 45
number of ways for 3 out of 9 men total: 9 choose 3= 84
84x45= 3780
3780 total ways
number of ways
After reading the directions to paint, on the paint drum, the information
indicated two coats of paint is required when using the 5 litre paint
and one coat with the 20 litre drum. With both paints 1 litre of paint
covers 9 m2
1.3.1 There are 28 rooms to be painted. Show with calculations which
will be the cheaper paint to buy.
(1
Answers
Step-by-step explanation:
jnx-avkj-uup p.l.z join
Student researchers investigated whether balsa wood is less elastic after it has been immersed in water. They took 60 pieces of balsa wood and randomly assigned half to be immersed in water and the other half not to be. They measured the elasticity by seeing how far (in inches) the piece of wood would project a dime into the air.
Required:
​Does the p-value obtained using the theory-based method (p < 0.0001) agree with that obtained using the randomization/simulation-based method (p < 0.0001)?
Answers
Yes, they are quite similar. the p-value obtained using the theory-based method (p < 0.0001) agree with that obtained using the randomization/simulation - based method (p < 0.0001)
P- value is the probability of obtaining a value of test statistic more extreme in the direction of alternative hypothesis than the observed one. In easy words if p -value < level of significance we reject H0 in favor of H1.
Here:
p-value < 0.0001 => we reject H0.
If the statistical software renders a p value of 0.000 it means that the value is very low, with many "0" before any other digit.
So the interpretation would be that the results are significant, same as in the case of other values below the selected threshold for significance.
Therefore, yes they are quite similar.
Learn more about balsa wood here:
https://brainly.com/question/33256379
#SPJ2
Incomplete Question:
Student researchers investigated whether balsa wood is less elastic after it has been immersed in water. They took 60 pieces of balsa wood and randomly assigned half to be immersed in water and the other half not to be. They measured the elasticity by seeing how far (in inches) the piece of wood would project a dime into the air.
Does the p-value obtained using the theory-based method (p < 0.0001) agree with that obtained using the randomization/simulation-based method (p < 0.0001)?
A. No, they are different.
B. Yes, they are quite similar.
This is a 30-60-90 triangle. What is the measure of x? rationalize the denominator.
Answers
Answer:
[tex] x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]
Step-by-step explanation:
Since, given is a 30°-60°-90° triangle.
[tex] \therefore \sqrt 7 = \frac{\sqrt3}{2} \times x[/tex]
[tex] \therefore 2\sqrt 7 = \sqrt3 \times x[/tex]
[tex] \therefore x=\frac{2\sqrt 7}{\sqrt 3}[/tex]
[tex] \therefore x=\frac{2\sqrt 7(\sqrt 3)}{\sqrt 3(\sqrt 3)}[/tex]
[tex] \huge \therefore x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]
NEED HELP ASAP!!! Giving brainliest!!!!!!!
Answers
C.(f-g)(x) = 4x^3 +5x²-7x-1
Step-by-step explanation:
Given information :
[tex]f(x) = 4 {x}^{3} + 5 {x}^{2} - 3x - 6 \\ g(x) = 4x - 5[/tex]
Find :
[tex](f - g)(x) = \\ (4 {x}^{3} + 5 {x}^{2} - 3x - 6) \\ - 4x -5[/tex]
Open bracket and Simplify
[tex]4 {x}^{3} + 5 {x}^{2} - 3x - 6 - 4x + 5 \\ 4 {x}^{3} + 5 {x}^{2} - 7x - 1[/tex]
Help please which option
Answers
Answer:
Step-by-step explanation:
-1<x<3. I hope it helpful!
a. Chéo hóa ma trận A .
b. Từ kết quả câu a, hãy tính 10 A .
Answers
100 POINTSSS! ASAP ANSWEERR PLS
The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price of two products, A and B, over time.
The price f(x), in dollars, of product A after x years is represented by the function below:
f(x) = 0.69(1.03)x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer.
Part B: The table below shows the price f(t), in dollars, of product B after t years:
t (number of years) 1 2 3 4
f(t) (price in dollars) 10,100 10,201 10,303.01 10,406.04
Which product recorded a greater percentage change in price over the previous year? Justify your answer.
Answers
PART A
Given:
f(x) = 0.69(1.03)x
To find:
If the price of the product is increasing or decreasing and by what percentage
Steps:
we know the formula to find the price of Product A per year, so
f(1) = 0.69 * 1.03 * 1
Price = $0.7107
f(2) = 0.69 * 1.03 * 2
Price = $1.4214
Here the Price of Product after 2 years is greater than the price of Product after one year. So the price of the product A is increasing.
Now to find percentage increase,
Percentage increase = [tex]\frac{FV-SV}{SV}*100[/tex] (FV = final value, SV = starting value)
Percentage increase = [tex]\frac{1.4214 - 0.7107}{0.7107}*100[/tex]
Percentage increase = [tex]\frac{0.7107}{0.7107}*100[/tex]
Percentage increase = 100 %
Therefore, the percentage increase of Product A is 100%
PART B
Given:
Price of product B in 1st year = $10,100
Price of product B in 2nd year = $10,201
Price of product B in 3rd year = $10,303.01
Price of product B in 4th year = $10,406.04
To find:
Which product recorded a greater percentage change over the previous year
Steps:
We need to find the percentage change of Product B and Product A of each year. We know that the percentage change of product A is 100 % for each year, so we only need to calculate for product B
PC of product B from 1st to 2nd year = [tex]\frac{10,201-10,100}{10,100}*100[/tex]
= [tex]\frac{101}{10,100}*100[/tex]
= 0.01 * 100
= 1 %
PC of product B from 2nd to 3rd year = [tex]\frac{10,303.01-10,201}{10,201} *100[/tex]
= 1%
PC of product B from 3rd to 4th year [tex]=\frac{10,406.04-10,303.01}{10,303.01}*100[/tex]
≈ 1%
So, percentage change of product B is 1% per year
Therefore, Product A has greater percentage change
Happy to help :)
If u need more help, feel free to ask
Answer:
A) The price of product A is increasing by 3% per year.
(B) The product A recorded a greater percentage change in price over the previous year.
Step-by-step explanation:
(A)
The function representing the price, in dollars, of product A after x years is:
FA(x)=0.69*(1.03)x
The function FA(x)can be written as:
FA(x)=0.69*1+(0.03)x
The function FA(x) is similar to the exponential growth function, y=a(1+r)x .
Here r is the growth rate.
Thus, it can be said that the price of product A is increasing by 3% per year.
(B)
Consider the data of product B for the year 3 and 4.
The price of product B for year 3 and 4 are 10,303.01 and 10,406.04.
Compute the percent price change from year 3 to 4 as follows:
10406.04-10303.01/10303.01*100
which is 0.999%
~1%
The price of product B is increasing by 1% per year.
Thus, the product A recorded a greater percentage change in price over the previous year.
Jerome's game score changed by
-20 points because of penalties that
were worth -5 points each. How
many times was Jerome penalized?
Answers
is 20 ÷ 5 the question? if so he was penalized 4 times. 5 × 4 is 20
In the coming year, a vehicle manufacturer has decided to manufacture 150 vehicles per day. The function v = 150d represents the company’s production for the coming year, v, with respect to the number of days, d.
The rate of change of the function representing the number of vehicles manufactured for the coming year is , and its graph is a . So, the function is a function.
Answers
Given:
v = 150d
v represents company's production for the coming year
d represents the number of days
150 is the daily production
The rate of change of the function representing the number of vehicles manufactured for the coming year is CONSTANT (150) , and its graph is a STRAIGHT LINE . So, the function is a LINEAR function.
I hope this helps!
Answer:
v = 150d
v represents company's production for the coming year
d represents the number of days
150 is the daily production
A cyclist travels 3 miles in 15 minutes and then a further 7 miles in 25 minutes without stopping.
Calculate the cyclist's average speed in mph.
Answers
Answer:
15 mph
Step-by-step explanation
i used a calculator but correct me if im wrong pls
-1/13-10/39 in lowest terms
Answers
Step-by-step explanation:
the answer is already as simplified as it could be
Carly withdraws $18 from her bank account. Which number line represents this amount?
Answers
Solve the equation by using the quadratic formula.
3 x squared minus 1 = 7 x
Answers
Answer:
b. [tex]\frac{7+\sqrt{61} }{6} ,\frac{7-\sqrt{61} }{6}[/tex]
Step-by-step explanation:
[tex]3x^{2} -1=7x[/tex]
Quadratic equations are suppose to be written as: [tex]ax^2+bx+c=0[/tex]
so the new quadratic equation for this problem will be: [tex]3x^{2} -1-7x=0[/tex]
Now rearrange the terms: [tex]3x^{2} -7x-1=0[/tex]
Then use the Quadratic Formula to Solve for the Quadratic Equation
Quadratic Formula = [tex]x=\frac{-b±}{} \frac{\sqrt{b^2-4ac} }{2a}[/tex]
Note: Ignore the A in the quadratic formula
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
[tex]3x^{2} -7x-1=0[/tex]
a = 3
b = -7
c = -1
[tex]x=-(-7)±\frac{\sqrt{(-7)^2-4(3)(-1)} }{2(3)}[/tex]
Evaluate The Exponent
[tex]x=\frac{7±\sqrt{(49)-4(3)(-1)} }{2(3)}[/tex]
Multiply The Numbers
[tex]x=\frac{7±\sqrt{49+12} }{2(3)}[/tex]
Add The Numbers
[tex]x=\frac{7±\sqrt{61} }{2(3)}[/tex]
Multiply The Numbers
[tex]x=\frac{7±\sqrt{61} }{6}[/tex]
Calculate the total number of pizzas that must be bought for a birthday party if
each pizza is cut into 8 slices and each 26 children invited would be given 3
slices.
Answers
Answer:
10
Step-by-step explanation:
26×3=78
78÷8=9.75
round up to 10 since you can't buy .75 of a pizza
The Molokai Nut Company (MNC) makes four different products from macadamia nuts grown in the Hawaiian Islands: chocolate-coated whole nuts (Whole), chocolate-coated nut clusters (Cluster), chocolate-coated nut crunch bars (Crunch), and plain roasted nuts (Roasted). The company is barely able to keep up with the increasing demand for these products. However, increasing raw material prices and foreign competition are forcing MNC to watch its margins to ensure it is operating in the most efficient manner possible. To meet marketing demands for the coming week, MNC needs to produce at least 1,000 pounds of the Whole product, between 400 and 500 pounds of the Cluster product, no more than 150 pounds of the Crunch product, and no more than 200 pounds of the Roasted product. Each pound of the Whole, Cluster, Crunch, and Roasted product contains, respectively, 60%, 40%, 20%, and 100% macadamia nuts with the remaining weight made up of chocolate coating. The company has 1,100 pounds of nuts and 800 pounds of chocolate available for use in the next week. The various products are made using four different machines that hull the nuts, roast the nuts, coat the nuts in chocolate (if needed), and package the products. The following table summarizes the time required by each product on each machine. Each machine has 60 hours of time available in the coming week.
Machine Minutes Required per Pound
Whole Cluster Crunch Roasted
Hulling 1 1 1 1
Roasting 2 1.5 1 1.75
Coating 1 0.7 0.2 0
Packaging 2.5 1.6 1.25 1
The selling price and variable cost associated with each pound of product is summarized in the following table:
Per Pound Revenue and Costs
Whole Cluster Crunch Roasted
Selling Price $5.00 $4.00 $3.20 $4.50
Variable Cost $3.15 $2.60 $2.16 $3.10
Required:
a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem, and solve it using Solver.
c. What is the optimal solution?
Answers
Answer:
Profit = Selling price - Variable cost
Formulas:
F2 =SUMPRODUCT(B2:E2,$B$16:$E$16) copy to F2:F12, F14
Optimal solution: The company should produce the following quantities (in pounds) of the four varieties of nuts.
Whole = 1000
Cluster = 500
Crunch = 80
Roasted = 200
Total profit = $ 2913.20
Step-by-step explanation:
PLEASE HELP URGENT Give evidence and proof no links
1/What is the correct written expression for the variable expression: (3 - x)/7 *
the difference of 3 and x divided by 7
3 divided by the difference of 7 and x
the sum of 3 and x divided by 7
the difference of 3 divided by 7 and x
2.Johnny is 5 less than 3 times the age of Elizabeth. If Elizabeth is e years old, which expression shows Johnny's age? *
3e - 5
3e + 5
5 - 3e
5 + 3e
3.What is the value of 4a - 7b - 8, when a = 7 and b = 3? *
1
15
-1
-45
4.Jose has g video games. Tony has 8 fewer games than Jose. What variable expressions represents the total number of video games Jose and Tony have? *
g + 8
2g + 8
g - 8
g + (g - 8)
5. Which written expression represents the variable expression 1/2 (8 - y) *
One half of eight less than a number y
A number y less than half of eight
One half the difference between eight and a number y
the difference of one half of eight and a number y
Answers
A1/ the difference of 3 and x divided by 7
A2/ 3e - 5
A3/ -1
A4/ g + (g - 8)
A5/ One half the difference between eight and a number y
I'm not sure, but I hope it helps :)
Suppose that 48% of high school students would admit to lying at least once to a teacher during the past year and that 25% of students are male and would admit to lying at least once to a teacher during the past year.20 Assume that 50% of the students are male. What is the probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year? Be sure to show your work and indicate all the rules that you use to find your answer.
Answers
Answer:
0.73 = 73% probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year.
Step-by-step explanation:
I am going to treat these events as Venn probabilities, considering that:
Event A: Lying to the teacher.
Event B: Male
48% of high school students would admit to lying at least once to a teacher during the past year and that 25% of students are male and would admit to lying at least once to a teacher during the past year
This means that [tex]P(A) = 0.48, P(A \cap B) = 0.25[/tex]
Assume that 50% of the students are male.
This means that [tex]P(B) = 0.5[/tex]
What is the probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year?
This is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Considering the values we were given:
[tex]P(A \cup B) = 0.48 + 0.5 - 0.25 = 0.73[/tex]
0.73 = 73% probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year.
3. What shape is a prism?
Answers
Answer:rectangular
Step-by-step explanation:
Answer:
TRIANGULAR
Step-by-step explanation:
A prism is a triangular-shaped piece of glass. The white light that reaches the prism contains all of the colors of the visible spectrum even though you can’t see them. As the white light passes through the edge or boundary of the prism, the light waves refract. Each of the different wavelengths contained in the white light refracts differently and results in a different color. The white light is broken up by the prism into all the colors of rainbow. The longest wavelength bends (refracts) the least and is red. The shortest wavelength bends the most and is violet.
28
Here are two rectangles.
Р
e
B
D
S
R
QR = 20 cm
BC = PQ
The perimeter of ABCD is 52 cm
The area of PQRS is 90 cm?
Find the length of AB.
Answers
9514 1404 393
Answer:
21.5 cm
Step-by-step explanation:
Consider rectangle PQRS. Its area is ...
A = LW
90 cm² = PQ×QR = PQ×(20 cm)
(90 cm²)/(20 cm) = PQ = 4.5 cm . . . . . . BC has this value, too
__
Consider the perimeter of ABCD. It is given by ...
P = 2(L +W)
52 cm = 2(AB +BC) . . . . substitute known value for P
26 cm = AB +4.5 cm . . . . use known value for BC, divide by 2
21.5 cm = AB
Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows:
Category Product 1 Product 2 Product 3
Profit/unit $30 $50 $20
Machine 1 time/unit 0.5 2.0 0.75
Machine 2 time/unit 1.0 1.0 0.5
Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 100 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 20% of the units produced.
How many units of each product should be produced to maximize the total profit contribution?
Product # of units
1
2
3
What is the projected weekly profit associated with your solution?
Profit = $
How many hours of production time will be scheduled on each machine? If required, round your answers to two decimal places.
Machine Hours Schedule:
Machine 1 Hours
Machine 2 Hours
What is the value of an additional hour of labor? If required, round your answers to two decimal places.
$
Assume that labor capacity can be increased to 120 hours. Develop the optimal product mix, assuming that the extra hours are made available.
Product # of units
1
2
3
Profit = $
Would you be interested in using the additional 20 hours available for this resource?
Answers
Answer:
z (max) = 1250 $
x₁ = 25 x₂ = 0 x₃ = 25
Step-by-step explanation:
Profit $ mach. 1 mach. 2
Product 1 ( x₁ ) 30 0.5 1
Product 2 ( x₂ ) 50 2 1
Product 3 ( x₃ ) 20 0.75 0.5
Machinne 1 require 2 operators
Machine 2 require 1 operator
Amaximum of 100 hours of labor available
Then Objective Function:
z = 30*x₁ + 50*x₂ + 20*x₃ to maximize
Constraints:
1.-Machine 1 hours available 40
In machine 1 L-H we will need
0.5*x₁ + 2*x₂ + 0.75*x₃ ≤ 40
2.-Machine 2 hours available 40
1*x₁ + 1*x₂ + 0.5*x₃ ≤ 40
3.-Labor-hours available 100
Machine 1 2*( 0.5*x₁ + 2*x₂ + 0.75*x₃ )
Machine 2 x₁ + x₂ + 0.5*x₃
Total labor-hours :
2*x₁ + 5*x₂ + 2*x₃ ≤ 100
4.- Production requirement:
x₁ ≤ 0.5 *( x₁ + x₂ + x₃ ) or 0.5*x₁ - 0.5*x₂ - 0.5*x₃ ≤ 0
5.-Production requirement:
x₃ ≥ 0,2 * ( x₁ + x₂ + x₃ ) or -0.2*x₁ - 0.2*x₂ + 0.8*x₃ ≥ 0
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
The model is:
z = 30*x₁ + 50*x₂ + 20*x₃ to maximize
Subject to:
0.5*x₁ + 2*x₂ + 0.75*x₃ ≤ 40
1*x₁ + 1*x₂ + 0.5*x₃ ≤ 40
2*x₁ + 5*x₂ + 2*x₃ ≤ 100
0.5*x₁ - 0.5*x₂ - 0.5*x₃ ≤ 0
-0.2*x₁ - 0.2*x₂ + 0.8*x₃ ≥ 0
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
After 6 iterations with the help of the on-line solver AtomZmaths we find
z (max) = 1250 $
x₁ = 25 x₂ = 0 x₃ = 25
she sells 6adult tickets and 5 children tickets on the first day totaling $112.50 and on the second day she sells 8adult tickets and 4 childrens tickets totaling $130. write an equation for each day and use the elimination method
Answers
Answer:
Cost of adult ticket = $12.5
Cost of child ticket = $7.5
Step-by-step explanation:
Given:
Cost of 6 adult ticket and 5 child ticket = $112.5
Cost of 8 adult ticket and 4 child ticket = $130
Find:
Equation and solution
Computation:
Assume;
Cost of adult ticket = a
Cost of child ticket = b
So,
6a + 5b = 112.5....eq1
8a + 4b = 130 ......eq2
Eq2 x 1.25
10a + 5b = 162.5 .....eq3
eq3 - eq1
4a = 50
Cost of adult ticket = $12.5
8a + 4b = 130
8(12.5) + 4b = 130
Cost of child ticket = $7.5
