Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP problem:
Maximize contribution = 5X1 + 4X2 + 3X3
Subject to: 1X1 + 7X2 + 4X3 <= 90 (hours on machine 1)
2X1 + 1X2 + 7X3 <= 96 (hours on machine 2)
8X1 + 4X2 + 1X3 <= 90 (hours on machine 3)
X1, X2, X3 >=0
Determine the optimal solution using LP software. the optimal achieved is
X1=
X2=
X3=
Answer:
Step-by-step explanation:
[tex]\text{Maximize p = 5X1 + 4X2 + 3X3 subject to;} \\ \\ 1X1 + 7X2 + 4X3 <= 90[/tex]
[tex]2X1 + 1X2 + 7X3 <= 96[/tex]
[tex]8X1 + 4X2 + 1X3 <= 90[/tex]
[tex]X1 > = 0[/tex]
[tex]X2 >= 0[/tex]
[tex]X3 >=0[/tex]
[tex]\text{USing LP software, The Optimal Solution: Maximum Contribution} = 90.547;}\\ \\ x1 = 7.07692, \\ \\ x2 = 5.62393, \\ \\ x3 = 10.8889[/tex]
Please help me with this :)
If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.
Answer:
A' (-2,-4) B' (-3,-7) C' (-1,-8) D' (1,-6)
Step-by-step explanation:
Just take it one point at a time and move each point down 3 and 4 left. Prime notation just means to put this little sign ' so it indicates that this is the new coordinate. So A was (2,-1) and A' (the new one) is (-2,-4)
Antonio constructs a model of a moon orbiting a planet along an elliptical orbit. The equation StartFraction x squared Over 342.25 EndFraction + StartFraction y squared Over 324 EndFraction = 1, with units in inches, represents the shape of the orbit. If the planet is located at one of the foci, which phrase describes a possible location of the model planet relative to the center?
approximately 0.5 in. below the center
approximately 4.3 in. above the center
approximately 0.5 in. to the left of the center
approximately 4.3 in. to the right of the center
Answer:
D
Step-by-step explanation:
edge
D. approximately 4.3 in. to the right of the center
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the problem; determining, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a teacher may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Learn more about problem-solving here
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#SPJ2
HELP PLS QUICK!MIGHT GIVE BRAINLIST IF TWO PEOPLE ANSWER!
Answer: A=bh to find the area of parallelograms.
Step-by-step explanation:
A trawler caught 2/3 ton of fish on Monday and 1/2 on Tuesday. What was the total amount of fish caught?
Answer:
1 1/6 ton
Step-by-step explanation:
What is the measure of X?
154.3
A. 25.7°
Supplementary Angles: Two angles that
add to equal 180°
B. 180°
C. 64.3°
D. 26.3°
B
оооо
Answer:
A. 25.7°
Step-by-step explanation:
the sum of straight angle is 180°.
so, i subtract 154.3 from 180.
i get 25.7 °
Rewrite the number in Standard form
1.2 x 107
Can someone please help me with this?
132 beads is split into 96 beads and 36 beads. in simplest form , what is the ratio of the split
Answer:
16:6
Step-by-step explanation:
96:36
Highest common factor is 6
divide both sides by 6
16:6
Timothy earned $300 mowing lawns this summer. He budgets
$25 to spend each week. Write an equation to show the
relationship between the number of weeks, w, and the
amount of money Timothy has, r.
NO LINKS PLEASE and make sure it's correct
Answer: The answer is 20 3/16
Step-by-step explanation:.
Its B.
In his free time, Gary spends 11 hours per week on the Internet and 8 hours per week playing video games. If Gary has five hours of free time per day, approximately what percent of his free time is spent on the Internet and playing video games?
Answer:
Around 54% is what I would say.
Step-by-step explanation:
two numbered cubes are rolled then a spinner with 4 different colors on it spun twice then two coins are flipped how many total possible outcomes are their(show you working out)
Answer: 12 possible outcomes in total
Step-by-step explanation:
Please help!!!!!!!!!!!!
Answer:
a) 5 cm b) 12in c) 7yd
I think it's so simple. Anyways
This is your answer. If I'm right so,
Please mark me as brainliest. thanks!!!
Answer:
5 cm, 12in, 3.5 yrds
Step-by-step explanation:
to find the radius you divide the diamenter by 2.
On Triangle ABC, Angle A measures 30 degrees, Angle B measures 90 degrees, and Angle C measures 60 degrees. List the sides of Triangle ABC in order from shortest to longest.
Answer:
A=30 B=90 C=60
Step-by-step explanation:
A=30 C=60 B=90
8 ^4 * 8^3
(YOU CANT GET A FRACTION!)
Answer:
8^(7), which is 2097152
Step-by-step explanation:
8^(4) × 8^(3)
= 8^(4+3)
= 8^(7)
= 2097152
Answer:
The answer is 2097152.
Step-by-step explanation:
1) Use the product rule: x^a x^b = x^ a + b.
[tex] {8}^{7} [/tex]
2) Simplify.
[tex]2097152[/tex]
Thus, the answer will be 2097152.
Graph the inequality n > 1.8
Answer:
Open circle going right. <-- graphed
Step-by-step explanation:
1billion is the correct answerStep-by-step explanation:
Part 1: Identify key features and graph a parabola from standard form.
Answer the following questions to determine the key features of the parabola based on the
equation shown, and then graph it.
12(x + 3) = (y - 2)^2
a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation.
(1 point)
b) What is the vertex of the parabola? (1 point)
c) What is the focus of the parabola? (2 points)
d) What is the directrix of the parabola? (2 points)
e) Sketch a graph of the parabola and label the vertex, focus, directrix, and axis of symmetry. (4 point
Answer:
a) The axis of symmetry is the line, y = 2
b) The vertex of a parabola is (-3, 2)
c) The focus of the parabola is (0, 2)
d) The directrix of a parabola is, x = -6
e) Please find attached the graph of the parabola
Step-by-step explanation:
a) The function for the parabola can be expressed as follows;
12·(x + 3) = (y - 2)²
The general form of the equation of the parabola is x = a·(y - k)² + h
The axis of symmetry is the line, y = k
By comparison, with the given equation of the parabola, we have;
12·(x + 3) = (y - 2)²
x = (1/12)·(y - 2)² - 3
Therefore;
a = (1/12), k = 2, h = -3
The axis of symmetry is y = k
∴ The axis of symmetry is the line, y = 2
b) The vertex of a parabola = (h, k)
∴ The vertex of a parabola = (-3, 2)
c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]
Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)
The focus of the parabola = (0, 2)
d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]
[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]
The directrix of a parabola is, x = -6
e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel
The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6
It is given that the parabola equation is [tex]\rm 12(x+3)=(y-2)^2[/tex]
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We know the standard form of a parabola is:
[tex]\rm x= a(y-k)^2+h[/tex] .........(1)
We have the equation of parabola:
[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)
a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.
By comparing the equation (1) and (2), we get:
Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.
b) Vertex of the parabola = (h,k): (-3, 2)
c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],
[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]
∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]
The focus of the parabola is (0, 2)
d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]
[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]
The directrix of a is x = -6
e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry
Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6
Know more about the parabola here:
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write an equation of the line that passes through the given point and has the given slope (6,4) slope -3/4
Answer:
Its slope is
m = -1/(1/2) = -2
y = -2x + b
Get b from the given point.
-4 = -2(6) + b
b = 8
y = -2x + 8
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given slope (m) = -3/4
and x1 = 6
and y1 = 4
Solve for b (y2) using x2 = 0.
m = -3/4 = (y2-y1)/(x2-x1)
-3/4 = (4-y1)/(6-0)
-3/4 = (4-y1)/6
-(3/4)*6 = 4 - y1
-18/4 = 4 - y1
y1 = b = 16/4 + 18/4 = 34/4 = 8 1/2
therefore the correct answer should be:
Equation of the line:
y = -3/4x + 8 1/2
Over the years, parking has become an issue during spring at MSU as more people bring cars to campus. The waiting time to find a parking spot at Wells Hall parking lot is normally distributed with an average of 9.60 minutes and a standard deviation of 2.60 minutes during peak hours (10 am - 5 pm).
1) What proportion of waiting times are between 8 and 10.8 minutes? Enter your answer to 4 decimal places.
2) What proportion of waiting times are less than 6.8 minutes? Enter your answer to 4 decimal places.
3) You reach Wells Hall parking lot and your class starts in 12 minutes. What is the chance that you are late to class, that is waiting time is at least 12 minutes?
4) Based on your unpleasant experiences in the past you know that your waiting time is in the top 4%. What is the cutoff for the top 4% of waiting times?
5) What is the waiting time for the 30th percentile?
Answer:
1) 0.4096 = 40.96% of waiting times are between 8 and 10.8 minutes.
2) 0.1401 = 14.01% of waiting times are less than 6.8 minutes.
3) 0.1788 = 17.88% probability that you are late.
4) The cutoff for the top 4% of waiting times is of 14.15 minutes.
5) The waiting time for the 30th percentile is of 8.235 minutes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Average of 9.60 minutes and a standard deviation of 2.60 minutes during peak hours.
This means that [tex]\mu = 9.6, \sigma = 2.6[/tex]
1) What proportion of waiting times are between 8 and 10.8 minutes?
This is the pvalue of Z when X = 10.8 subtracted by the pvalue of Z when X = 8. So
X = 10.8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10.8 - 9.6}{2.6}[/tex]
[tex]Z = 0.46[/tex]
[tex]Z = 0.46[/tex] has a pvalue of 0.6772
X = 8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 9.6}{2.6}[/tex]
[tex]Z = -0.62[/tex]
[tex]Z = -0.62[/tex] has a pvalue of 0.2676
0.6772 - 0.2676 = 0.4096
0.4096 = 40.96% of waiting times are between 8 and 10.8 minutes.
2) What proportion of waiting times are less than 6.8 minutes?
This is the pvalue of Z when X = 6.8.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6.8 - 9.6}{2.6}[/tex]
[tex]Z = -1.08[/tex]
[tex]Z = -1.08[/tex] has a pvalue of 0.1401
0.1401 = 14.01% of waiting times are less than 6.8 minutes.
3) You reach Wells Hall parking lot and your class starts in 12 minutes. What is the chance that you are late to class, that is waiting time is at least 12 minutes?
This is 1 subtracted by the pvalue of Z when X = 12. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12 - 9.6}{2.6}[/tex]
[tex]Z = 0.92[/tex]
[tex]Z = 0.92[/tex] has a pvalue of 0.8212
1 - 0.8212 = 0.1788
0.1788 = 17.88% probability that you are late.
4) Based on your unpleasant experiences in the past you know that your waiting time is in the top 4%. What is the cutoff for the top 4% of waiting times?
The cutoff for the top 4% of times is the 100 - 4 = 96th percentile, which is X when Z has a pvalue of 0.96. so X when Z = 1.75.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.75 = \frac{X - 9.6}{2.6}[/tex]
[tex]X - 9.6 = 1.75*2.6[/tex]
[tex]X = 14.15[/tex]
The cutoff for the top 4% of waiting times is of 14.15 minutes.
5) What is the waiting time for the 30th percentile?
This is X when Z has a pvalue of 0.3. So X when Z = -0.525.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.525 = \frac{X - 9.6}{2.6}[/tex]
[tex]X - 9.6 = -0.525*2.6[/tex]
[tex]X = 8.235[/tex]
The waiting time for the 30th percentile is of 8.235 minutes.
If you don’t know I don’t answer (NO LINKS ) please helllllppppp
Answer:
Step-by-step explanation:
1. 6.96 in
2. 2.6 in
3. 8.1 in
4. 5.6 m
5. 1.89 cm
6. 6 in
PLEASE ANSWER QUICK
The sum of the data values divided by the number of data values is a measure of ______ and is called the _____
FIRST BLANK'S OPTIONS = CENTER/SPREAD
SECOND BLANK'S OPTIONS = MEAN/MEAN ABSOLUTE DEVIATION/MEDIAN/RANGE
Answer:
Center... Mean
Step-by-step explanation:
The mean of a data set is the sum of the values divided by the number of values. The median of a data set is the middle value when the values are written in numerical order.
Can someone help me please?
Answer:
uh i dont know lol im new how do i use this thing bahahaha
Step-by-step explanation:
Jenny and Buddy collected 376 plastic bottles for recycling.
They recycled 131 bottles on Monday and 114 bottles on Tuesday.
How many bottles do they have left to recycle?
Complete the equations to solve. Enter your answers in the boxes.
Let
m
=
the number of bottles left to recycle after Monday.
Answer:
151
Step-by-step explanation:
114+131= 272 376-272=104
3x^2 -12x +11=0
How to complete the square
Answer:
Tiger shows you, step by step, how to solve YOUR Quadratic Equations 3x^2-x-11=0 by Completing the Square, Quadratic formula or, ...
I will mark you brainalist
Answer:
1.25 since all prices are sam e
Step-by-step explanation:
If PQRS is a rhombus, find m
Answer:
m<PQR = 82°
Step-by-step explanation:
In a Rhombus, the diagonals bisect its angles. This means that they divide each the four angles into two equal parts.
Therefore:
(4x - 27)° = (2x + 7)°
Solve for x
4x - 27 = 2x + 7
Collect like terms
4x - 2x = 27 + 7
2x = 34
Divide both sides by 2
2x/2 = 34/2
x = 17
✔️m<PQR = (4x - 27) + (2x + 7)
Plug in the value of x
m<PQR = (4*17 - 27) + (2*17 + 7)
m<PQR = 41 + 41
m<PQR = 82°
An insurance office buys paper by the ream, 500 sheets, for use in the copier, fax, and printer. Each ream lasts an average of 4 days, with standard deviation 1 day. The distribution is normal, independent of previous reams. a. Find the probability that the next ream out- lasts the present one by more than 2 days. b. How many reams must be purchased if they are to last at least 60 days with probability at least 80%
Answer:
a) the probability that the next ream out- lasts the present one by more than 2 days is 0.0787
b) the number of reams that must be purchased is 19
Step-by-step explanation:
Given the data in the question;
Lets X₁ and X₂ be the two random variables that represents the first and second ream lasts
given that both random variables follow normal distribution with mean 4 and standard deviation 1.
a)
Find the probability that the next ream out- lasts the present one by more than 2 days.
P( X₂ - X₁ > 2 ) = P( [(X₂ - X₁ - E(X₂ - X₁)) / √(V(X₂ - X₁)] > [ (2-E(X₂ - X₁))/√(V(X₂ - X₁) ]
= 1 - P( Z ≤ [2-(μ₂ - μ₁)] / [√( V(X₂) + V(X₁) ) ] )
= 1 - P( Z ≤ [2-(4 - 4)] / [√( 1 + 1 )] )
= 1 - P = ( Z ≤ 2 / √2 )
= 1 - p( Z ≤ 1.4142 )
from excel; p( Z ≤ 1.41 ) = 0.9213
P( X₂ - X₁ > 2 ) = 1 - 0.9213
P( X₂ - X₁ > 2 ) = 0.0787
Therefore, the probability that the next ream out- lasts the present one by more than 2 days is 0.0787
b)
How many reams must be purchased if they are to last at least 60 days with probability at least 80%
total value is 4n
standard deviation is nσ
so
P(nX ≥ 60 ) = 0.80
P( nX-nμ /nσ ≥ 60-nμ/nσ) = 0.80
P( Z ≥ 60-4n/n) = 0.80
1 - P( Z ≥ 60-4n/n) = 0.80
P( Z < z ) = 0.20
now since z = 60-4n/n
from standard normal table
critical value of z corresponding to cumulative area of 0.20 is -0.841
so
z = - 0.841
60-4n/n = -0.841
60 - 4n = -0.841n
60 = -0.841n + 4n
60 = 3.159n
n = 60 / 3.159
n = 18.99 ≈ 19
Therefore, the number of reams that must be purchased is 19
What is the measure of z?
Answer:
Please edit the question I can't see it completely