Answers
The maximum value of the objective functions are 2600, 27 and 1980
Solving the objective function graphicallyGiven that
Max Z = 8x + 16y
Where the constraints are
3x + 6y ≤ 900
x + y ≤ 200
y ≤ 125
x, y ≥ 0
Plotting the constraints 3x + 6y ≤ 900, x + y ≤ 200 and y ≤ 125 on the same graph, the coordinates of the feasible region are:
(x, y) = (100, 100), (75, 125) and (50, 125)
So, we have
Z = 8(100) + 16(100) = 2400
Z = 8(75) + 16(125) = 2600
Z = 8(50) + 16(125) = 2400
Hence, the maximum value is 2600
Solving the objective function graphicallyGiven that
Max Z = 6x + 3y
Where the constraints are
2x + y ≤ 8
3x + 3y ≤ 18
y ≤ 3
x, y ≥ 0
Plotting the constraints 2x + y ≤ 8, 3x + 3y ≤ 18 and y ≤ 3 on the same graph, the coordinates of the feasible region are:
(x, y) = (3, 3), (2.5, 3) and (2, 4)
So, we have
Z = 6(3) + 3(3) = 27
Z = 6(2.5) + 3(3) = 24
Z = 6(2) + 3(4) = 24
Hence, the maximum value is 27
Solving the objective function by simplexGiven the objective function, the constraints and the final simplex tableau
We have the final values to be
Z = 1980
This means that the maximum value is 1980
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Related Questions
Need some help with this khan academy question, thanks.
Answers
The relative frequency of the two frequency table is completed as below
less than 2 years 2 or more years row total
college degree 0.26 0.74 1.00
no coll degree 0.70 0.30 1.00
How to fill the tableThe relative frequency table is filled by comparing the values as below
less than 2 years 2 or more years row total
college degree 5/19 14/19 1.00
no coll degree 16/23 7/23 1.00
The row total
5 + 14 = 19 so we have 5/19 (0.26) and 14/19 (0.74)
16 + 7 = 23 o we have 16/23 (0.70) and 7/23 (0.30)
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Help!!
You flip a coin and roll a dice. The resultant outcome table where H means heads, T means Tails, and the number represents what number was rolled on the dice. The outcome list is as follows: Coin Toss H H H H H H TTTTTT Die Roll 1 2 3 4 5 6 1 2 3 1 2 3 4 5 6 What is the probability that the coin reads heads or tails and the dices number is less than or equal to 6?
Answers
The probability that the coin reads heads or tails and the dices number is less than or equal to 6 is 1/3 or approximately 0.333.
How to calculate the probability that the coin reads heads or tails and the dices number is less than or equal to 6?There are 12 possible outcomes in the table where the coin reads heads or tails and the dice roll is less than or equal to 6. These are:
Coin Toss: H, Die Roll: 1
Coin Toss: H, Die Roll: 2
Coin Toss: H, Die Roll: 3
Coin Toss: H, Die Roll: 4
Coin Toss: H, Die Roll: 5
Coin Toss: H, Die Roll: 6
Coin Toss: T, Die Roll: 1
Coin Toss: T, Die Roll: 2
Coin Toss: T, Die Roll: 3
Coin Toss: T, Die Roll: 4
Coin Toss: T, Die Roll: 5
Coin Toss: T, Die Roll: 6
Out of these 12 outcomes, 6 have the coin reading heads and 6 have the coin reading tails. So, the probability that the coin reads heads or tails and the dice number is less than or equal to 6 is:
P(heads or tails and dice number <= 6) = P(heads and dice number <= 6) + P(tails and dice number <= 6)
= 6/36 + 6/36
= 12/36
= 1/3
Therefore, the probability is 1/3 or approximately 0.333.
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The Hartford offered an annuity that pays 5.5% compounded monthly.
What equal monthly deposit should be made into this annuity in order
to have $100000 in 10 years?
Answers
If an annuity pays 5.5% compounded monthly, then the "equal-monthly-deposit" to have $100000 in 10 years is $627.
In order to calculate the "monthly-deposit" needed to accumulate $100,000 in 10 years at 5.5% compounded monthly, we use the formula for the future value of an annuity:
Which is : FV = P × [(1 + r)ⁿ - 1]/r,
where:
FV is "future-value" = $100000,
P = monthly deposit
r = monthly interest rate (5.5%/12 = 0.00458)
n = number of months (10 years × 12 months per year = 120 months)
Substituting the values,
We get,
⇒ 100000 = P × [(1 + 0.00458)¹²⁰ - 1]/0.00458,
⇒ P = 100000 × 0.00458 / [(1 + 0.00458)¹²⁰ - 1],
⇒ P ≈ $627,
Therefore, an equal monthly deposit is approximately $627.
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you need 18 lb of peeled and cored apples to make applesauce.apples have a yield percentage of 78%, how many pounds of whole apples are needed
Answers
You would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.
Explanation:
To find out how many pounds of whole apples are needed to make 18 lbs of peeled and cored apples with a yield percentage of 78%, we can use the following formula:
Pounds of whole apples needed = (Pounds of peeled and cored apples needed) / Yield percentage
Plugging in the values we have:
Pounds of whole apples needed = 18 lb / 0.78Pounds of whole apples needed = 23.077 lb (rounded to three decimal places)
Therefore, you would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.
A television show conducted an experiment to study what happens
Answers
Answer:
Step-by-step explanation:
[tex]H_o: p = 0.5,H_1:p\neq 0.5[/tex]
[tex]p(\text{buttered side down})=\frac{19}{51}[/tex]
[tex]\pi _o=0.5\\n=51[/tex]
[tex]z=\frac{p-\pi _o}{\sqrt{\frac{\pi _o(1-\pi _o)}{n} } } =\frac{\frac{19}{51}-0.5 }\sqrt{{\frac{0.5(1-0.5)}{51} } }[/tex]
≈ [tex]-1.82[/tex]
a = 0.01 [tex]z_a/z=2.58\\|z| < |z_[ay}}_2|[/tex]
Thus, it cant reject H₀
The toast will land with the buttered side down 50% of the time.
{Hypothesis test}
Lee watches TV for 2 hours per day. During that time, the TV consumes 150 watts per hour. Electricity costs (18 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?
Answers
If the TV consumes 150 watts per hour and electricity costs (18 cents)/(1 kilowatt-hour), it would cost Lee $1.62 to operate his TV for a month of 30 days.
To calculate the cost of operating Lee's TV for a month of 30 days, we need to determine the total amount of electricity used by the TV in that period.
First, we need to calculate the total number of hours Lee watches TV in a month:
2 hours/day x 30 days = 60 hours
Next, we need to calculate the total electricity consumed by the TV:
150 watts/hour x 60 hours = 9,000 watt-hours or 9 kilowatt-hours (kWh)
Now, we can calculate the cost of operating the TV for a month:
9 kWh x $0.18/kWh = $1.62
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If the TV consumes 150 watts per hour and electricity costs (18 cents)/(1 kilowatt-hour), it would cost Lee $1.62 to operate his TV for a month of 30 days.
To calculate the cost of operating Lee's TV for a month of 30 days, we need to determine the total amount of electricity used by the TV in that period.
First, we need to calculate the total number of hours Lee watches TV in a month:
2 hours/day x 30 days = 60 hours
Next, we need to calculate the total electricity consumed by the TV:
150 watts/hour x 60 hours = 9,000 watt-hours or 9 kilowatt-hours (kWh)
Now, we can calculate the cost of operating the TV for a month:
9 kWh x $0.18/kWh = $1.62
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Indirect measurement, pls help, I am stuck on this question.
Answers
The building is 246 feet tall.
What are similar triangles?Two or more triangles will always be referred to as similar if on comparing their corresponding properties, some common relations holds. Some of the relations are relations between their length of sides, relations among their internal angles etc.
To determine the height of the building, we have;
height of pole = 7 ft
total length of the building's shadow = 167 ft
the length of the shadow of the pole = 4.75 ft
Let the height of the building be represented by h. On comparison, we have;
4.75/ 167 = 7/h
4.75h = 167 x 7
= 1169
h = 1169/ 4.75
= 246.11
The building is 246 ft. tall.
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The claim is that for a smartphone carrier's data speeds at airports, the mean is 18.00 Mbps. The sample size is n= 14 and the test statistic is t= -2.645 .
whats the P-value?
Answers
According to given information the P-value is approximately 0.016.
What is P-value?In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic as extreme as or more extreme than the observed results, under the assumption that the null hypothesis is true.
According to given information:To find the P-value for this hypothesis test, we need to use a t-distribution with degrees of freedom equal to n-1 = 14-1 = 13. Since the test statistic is t = -2.645, we need to find the area under the t-distribution curve to the left of t.
Using a t-table or calculator, we can find that the area to the left of t = -2.645 with 13 degrees of freedom is approximately 0.008. This is the probability of observing a t-value less extreme than -2.645, assuming the null hypothesis is true.
Since this is a two-tailed test (we are testing whether the true mean is less than or greater than 18.00 Mbps), we need to double the one-tailed P-value to get the two-tailed P-value. Therefore, the P-value is approximately 0.016 (i.e., 2 x 0.008).
So, the P-value is approximately 0.016.
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part B write a numerical expression of angle C
Answers
The index of refraction of the second material is 1.27.
We are given that;
Angle= 59°
Randomized Variables 1 = 1.47θ1 = 59°θ2 = 69°
Now,
To find n2, we can rearrange Snell’s law as:
n2 = n1 sin θ1 / sin θ2
Plugging in the given values, we get:
n2 = 1.47 sin 59° / sin 69°
n2 = 1.47 (0.857) / (0.934)
n2 = 1.27 (rounded to two decimal places)
Therefore, by the expression the answer will be 1.27
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7. El área de un terreno de forma rectangular es 4332 m?. Si de ancho mide la tercera parte de su medida de largo, ¿Cuáles son las dimensiones del rectángulo?
Answers
x(x/3) = 4332
Resolviendo para x, obtenemos:
x²/3 = 4332
Multiplicando ambos lados por 3, obtenemos:
x² = 12996
Tomando la raíz cuadrada de ambos lados, obtenemos:
x = 114
Por lo tanto, las dimensiones del rectángulo son 114 m de largo y 38 m de ancho.
Please help asap!!!!!
Answers
Answer:
[tex]f(-1) = -2\\[/tex]
[tex]f(0)=0[/tex]
[tex]f(1)=2[/tex]
Step-by-step explanation:
f(x)=2x
1) f(-1) = 2(-1) = -2
2) f(0) = 2(0) = 0
3) f(1) = 2(1) = 2
How is the product of a complex number and a real number represented on the complex plane?
Consider the product of 2−4i and 3.
Drag a value or phrase into each box to correctly complete the statements
Answers
Answer:
2 root 5
6 root 5
are the same
Step-by-step explanation:
Answer:
[tex]2\sqrt{5} \\6\sqrt{5}[/tex]
are the same
Step-by-step explanation:
MARKING AS BRAINLIST PLS HELP
Answers
Answer:
The angle of C is 118.6
Step-by-step explanation:
Change zero degrees Celsius to Fahrenheit.
Answers
Answer: F=32
Step-by-step explanation:formula: F = Celsius*9/5+32
so plug the zero for Celsius, in this case, 0*9/5+32 = 32
based on an exponential model of the data, what is the predicted value of variable 2 when variable 1=2? round your answer to the nearest whole number.
a. variable 2 ≈ 128
b. variable 2≈ 166
c. variable 2≈ 181
d. variable 2≈ 263
Answers
The predicted value of Variable 2 when Variable 1 = 2 is 82.
How to calculate the value :-
The graph shows that the data has a diminishing exponential trend.
We can utilize the trendline tool in a spreadsheet program like Excel to discover the equation of the exponential function that matches the data. Using the trendline feature, we obtain the following equation:
Variable number 2 = 120.28 * 0.8555Variable number one
We can now use this equation to estimate the value of Variable 2 when Variable 1 = 2:
82 Variable 2 = 120.28 * 0.85552
When Variable 1 = 2, the anticipated value of Variable 2 is 82, rounded to the closest whole number.
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The predicted value of Variable 2 when Variable 1 = 2 is 82.
How to calculate the value :-
The graph shows that the data has a diminishing exponential trend.
We can utilize the trendline tool in a spreadsheet program like Excel to discover the equation of the exponential function that matches the data. Using the trendline feature, we obtain the following equation:
Variable number 2 = 120.28 * 0.8555Variable number one
We can now use this equation to estimate the value of Variable 2 when Variable 1 = 2:
82 Variable 2 = 120.28 * 0.85552
When Variable 1 = 2, the anticipated value of Variable 2 is 82, rounded to the closest whole number.
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7
An acceleration of 2.5 miles per hour per second
mi/hr
S
feet per hour per second
is closest to which of the following values, in
(1 mile = 5,280 feet)
A) 13,200
B) 2,112
C) 220
D)
1/2,112
Answers
The converted acceleration in feet per hour per second is 13200 feet per hour per second
Converting the acceleration from miles per hour per second to feet per hour per secondFrom the question, we have the following parameters that can be used in our computation:
Acceleration = 2.5 miles per hour per second
From the question, we have
(1 mile = 5,280 feet)
Substitute the known values in the above equation, so, we have the following representation
Acceleration = 2.5 * 5,280 feet per hour per second
Evaluate the products
So, we have
Acceleration = 13200 feet per hour per second
Hence, the acceleration = 13200 feet per hour per second
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The length of a rectangle is 4 meters less than 3 times the width. The perimeter is 24 meters. Find the width
Answers
Answer:
Step-by-step explanation: length of a rectangle is 4 meters less than 3 times the width so we can write L = 3W-4
The formula for the perimeter of a rectangle: P = 2L+2W
Now plug the numbers: P = 2(3W-4)2W
24 = 6W - 8 +2W
24 = 8W - 8
32 = 8W
W = 4
The diagram shows a field. 66 m 140 m 102 m Work out the area of the field.
Answers
The area of the field, given that it is a trapezium, would be 7, 986 m ² .
How to find the area ?The field is in the shape of a trapezium which means that the area of the field can be found by the formula :
= ( a + b ) / 2 x height
Side a = 102 m
Side b = 140 m
height = 66 m
The area of the field is therefore:
= ( 102 + 140 ) / 2 x 66
= 121 x 66
= 7, 986 m ²
In conclusion, the area of the field is 7, 986 m ².
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what is the inverse of f(x)=(4x-9)^1/2
Answers
The inverse of f(x) = [tex](4x-9)^{1/2[/tex] when the variables of x and y are switched is [tex]F(x)^{-1}[/tex] = [tex]\frac{x^{2}+9 }{4}[/tex]
What is an Inverse of a Function?Inverse of a function is a function which can be reversed into another function. It is also a function that undoes the action of the another function.
How to determine this
When f(x) = (4x-9)^1/2
To determine the inverse, [tex]f(x)^{-1}[/tex]= y
y = (4x-9)^1/2
y = [tex]\sqrt{4x-9}[/tex]
By squaring both sides
y^2 = 4x - 9
By swapping the variables
x^2 = 4y - 9
Subtracting 9 from both sides
x^2 +9 = 4y
divide through by 4
[tex]\frac{x^{2}+9 }{4}[/tex] = 4y/4
y = [tex]\frac{x^{2}+9 }{4}[/tex]
Therefore [tex]F(x)^{-1}[/tex] = [tex]\frac{x^{2}+9 }{4}[/tex]
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2. Why was the Constitutional Convention held?
lengte
A. Each state's government was too weak.
B. Americans wanted to win independence from England.
C. The national government was too weak.
D. The states wanted to form the first American government.
Anyone pls
Answers
2.1. Consider the following pattern. 2.1.1 complete the table. (match-sticks were used to make each shape) (6marks) Shape No. of match-sticks Rule 1 4 2 7 3 10 4 13 6 241 10 40 43 21 82
Answers
Number of matchsticks = 3n + 1, where n is the shape number.
Using this rule, we can complete the table as follows:
Shape | No. of match-sticks
--- | ---
1 | 4
2 | 7
3 | 10
4 | 13
5 | 16
6 | 19
7 | 22
8 | 25
Therefore, the completed table is:
Shape | No. of match-sticks
--- | ---
1 | 4
2 | 7
3 | 10
4 | 13
5 | 16
6 | 19
7 | 22
8 | 25
There are only red counters, blue counters and green counters in a bag.
number of red counters: number of blue counters: number of green
counters = 1:3:7
A counter is going to be taken at random from the bag.
Complete the table below to show each of the probabilities that the counter will be red or blue or green.
(2 marks)
Answers
Answer:
Color Probability
Red 1/11
Blue 3/11
Green 7/11
Step-by-step explanation:
The total number of counters in the bag is 1+3+7=11. The probability of selecting a red counter is 1/11, because there is only one red counter in the bag. The probability of selecting a blue counter is 3/11, because there are three blue counters in the bag. Similarly, the probability of selecting a green counter is 7/11, because there are seven green counters in the bag.
320.041 - 47.96 multiple it for me
Answers
Answer:
320.041 - 47.96 = 272.081
Step-by-step explanation:
I need more information on what you want me to do.
Do you want me to:
Multiply 320.041 by 47.96?
Subtract 47.96 from 320.041?
Multiply the difference between 320.041 and 47.96 by 47.96?
Multiplying 320.041 by 47.96 gives 152,399.6896.
Subtracting 47.96 from 320.041 gives 272.08.
Multiplying the difference between 320.041 and 47.96 by 47.96 gives 13049.0048.
Talisa plans a 36-foot deep pond. While digging, she hits rock 30 feet down. How can Talisa modify the radius to maintain the original volume of the pond?
Talisa should make the radius ___ ft
Answers
The radius of the pond should be modified to 19.72ft to be able to maintain the original volume of the pond.
How to modify the radius to maintain the original volume?The original shape of the pond is the shape of a cylinder and the formula tye can be used to calculate the volume of a cylinder = πr²h
The volume of the original pond is calculated as follows;
π = 3.14
Radius = 18 ft
height = 36ft
Vol = 3.14×18×18×36
= 36,624.96ft³
The radius of the modified pond is calculated as follows; Volume = 36,624.96ft³
height = 30ft
radius = ?
That is;
36,624.96 = 3.14×r²× 30
r² = 36,624.96/94.2
= 388.8
r = √388.8
= 19.72 ft
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What questions please help me thanks
Answers
1. The monthly payment for Loan A is roughly $516.40.
2. The total interest for Loan A is roughly $1590.4
How do we calculate the monthly payment and total interest?We've been given the formula: PMT = (P(r/n)) / [1 - (1 + r/n)^-nt] to calculate the monthly payment loan.
If we should insert the figures given to the formula, it should be
PMT = (17000(0.059/12)) / [1 - (1 + 0.059/12)^(-12*3)]
PMT = 516.40
To calculate total interest for loan A, we use the formula (PMT x n x t) - P.
If we insert the figure provided, it should be;
(598.87 x 12 x 3) - 17000
= $1590.4
The above answer is in response to the question below as seen in the picture;
Suppose that you decide to borrow $17,000 for a new car. Installment loan A: 3 years at 5.9%. Use PMT = (p(r/n))/ [1 - (1 + r/n)^-nt]
Find the monthly payment and the total interest for loan A. The monthly payment for Loan A is $..............
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Please answer this question quickly
FOR 35 POINTS
I WILL GIVE BRAINLIEST
Answers
Answer: 0
Step-by-step explanation:
[tex]log_{3} log_{5} log_{2} 32[/tex]
Let's evaluate
[tex]log_{2}32[/tex] this is the same as
[tex]2^{x}=32[/tex] 2*2*2*2*2=32
or
you can think of it as 2 to the what power is 32
so x=5
now substitute that in for [tex]log_{2}32[/tex]
[tex]log_{3} log_{5} 5[/tex]
Now evaluate [tex]log_{5}5[/tex]
5 to the what power is 5
=1
substitute into [tex]log_{3} log_{5} 5[/tex]
[tex]log_{3} 1[/tex]
3 to the what power is 1
=0
Anything to the 0 power is 1 (it's a rule)
3x+2=8 what is the value of x
Answers
Answer:
x = 2
Step-by-step explanation:
3x + 2 = 8
Subtracting both sides by 2 we get,
=> 3x + 2 - 2= 8 - 2
=> 3x = 6
=> x = 6/3
=> x = 2
3x + 2 - 2 = 8 - 2
3x = 6
3x/3 = 6/3
x = 2
How do you write 9.6522 as a percentage
Answers
To convert a decimal number to a percentage, you need to multiply it by 100.
So, to write 9.6522 as a percentage, you need to multiply it by 100, which gives you:
9.6522 x 100 = 965.22%
Therefore, 9.6522 written as a percentage is 965.22%.
60. What is the slope of a line that passes through the point (-1, 1) and is parallel to a line that passes through
(3, 6) and (1,-2)?
Answers
The equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
What is slope?The slope of a line is a measure of its steepness, and is calculated as the change in the y-coordinate divided by the change in the x-coordinate.
In this case, the line passing through the points (3, 6) and (1, -2) has a slope of [tex]$\frac{6 - (-2)}{3 - 1} = \frac{8}{2} = 4$[/tex].
Therefore, the line that passes through the point (-1, 1) and is parallel to the given line has the same slope of 4.
To find the equation of the line passing through (-1, 1) and having a slope of 4, we need to use the point-slope formula.
The point-slope formula is given by: [tex]$y - y_1 = m(x - x_1)$[/tex] where [tex]$(x_1, y_1)$[/tex] is a point on the line, and m is the slope of the line. In this case, [tex]$(x_1, y_1)$[/tex] is (-1, 1) and m is 4, so the equation of the line is:
[tex]$y - 1 = 4(x - (-1))$[/tex]
[tex]$y - 1 = 4x + 4$[/tex]
[tex]$y = 4x + 5$[/tex]
Therefore, the equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
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The equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
What is slope?The slope of a line is a measure of its steepness, and is calculated as the change in the y-coordinate divided by the change in the x-coordinate.
In this case, the line passing through the points (3, 6) and (1, -2) has a slope of [tex]$\frac{6 - (-2)}{3 - 1} = \frac{8}{2} = 4$[/tex].
Therefore, the line that passes through the point (-1, 1) and is parallel to the given line has the same slope of 4.
To find the equation of the line passing through (-1, 1) and having a slope of 4, we need to use the point-slope formula.
The point-slope formula is given by: [tex]$y - y_1 = m(x - x_1)$[/tex] where [tex]$(x_1, y_1)$[/tex] is a point on the line, and m is the slope of the line. In this case, [tex]$(x_1, y_1)$[/tex] is (-1, 1) and m is 4, so the equation of the line is:
[tex]$y - 1 = 4(x - (-1))$[/tex]
[tex]$y - 1 = 4x + 4$[/tex]
[tex]$y = 4x + 5$[/tex]
Therefore, the equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].
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Determine the function is positive, negative, increasing, or decreasing. Then describe the end behavior of the function.
Answers
The function is positive and increasing.
Given is an exponential function y = √4x,
So, since all the value of the function will be above x-axis therefore, the function is positive.
Now,
Differentiating the function,
y' = d(√4x)/dx
y' = 1/2 × [tex]4x^{-1/2[/tex]
y' = 1/2√4x
y' = 1/4√x
Since, y' > 0, therefore, the function is increasing.
Now,
For functions with exponential growth, we have the following end behavior.
The end behavior on the left (as x → -∞), it has a horizontal asymptote at y = 0,
The end behavior on the right (as x → ∞), y→ ∞.
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