Answer:
A) Since all of the students had an opportunity to respond, this is evidence that a majority of all the students supports major changes.
Step-by-step explanation:
Since all the students were given equal opportunity then the response suggest that a major change is required by the students.
Answer: d
Step-by-step explanation: the responses were from voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions
Which expression is the greatest common factor of the two addends in 18x + 30x2?
Step-by-step explanation:
I think common factors are
18 = 1 2 3 6 9 18
30 = 1 2 3 10 15 30
So highest common factor is 3
18x + 30x2
3x (6 + 10x)
Answer:
The answer is 6x
Step-by-step explanation:
Roger Brown works for the sanitation department. He earns a salary of $721.00 biweekly. His boss gave him
a raise that will go into effect at the first of the year. His new annual salary will be $20.995.00. How much
more money will Roger make next year than this year?
Answer:
2249 dollars more
Step-by-step explanation:
52 weeks in one year so divide by 2 and then multiply by 721 and then take that amount and dubtract the new salary 20.995 and subtract the previous annual amount and then boom 2295 more
Final answer:
Roger will make $2,249.00 more money next year than he did this year.
Explanation:
To determine how much more money Roger will make next year compared to this year, we need to find the difference between his new annual salary and his current biweekly salary.
To calculate the annual salary, we can multiply the biweekly salary by the number of biweekly periods in a year. There are 26 biweekly periods in a year (52 weeks / 2). So, Roger's current annual salary is $721.00 x 26 = $18,746.00.
The difference between his new annual salary and his current annual salary is $20,995.00 - $18,746.00 = $2,249.00. Therefore, Roger will make $2,249.00 more money next year than he did this year.
Maria has promised her neighbor to plant spring flowers in his garden. If the area is 250 square feet and she has completed 1/3 of it, how many square feet does she have left to plant flowers
Answer:
She still has 166.67 square feet does she have left to plant flowers
Step-by-step explanation:
The sum of total area planted, and the remaining area left to plant, is 100% = decimal 1.
She has planted 1/3 of the area. So
[tex]\frac{1}{3} + p = 1[/tex]
[tex]p = 1 - \frac{1}{3}[/tex]
[tex]p = \frac{3-1}{3}[/tex]
[tex]p = \frac{2}{3}[/tex]
So she still has to paint two thirds of the area.
The area is of 250 square feet.
2/3 of 250
[tex]250\frac{2}{3} = 166.67[/tex]
She still has 166.67 square feet does she have left to plant flowers
Can someone answer this plz ?
Roberta grows pea plants, some in shade and some in sun. She picks 8 plants of each type at random and records the heights. Shade plant heights (in.) 7 12 12 8 9 8 8 8 Sun plant heights (in.) 19 24 20 23 24 23 23 20
Answer: 2.6
Step-by-step explanation:
Step 1: Calculate the mean of Shade's plant heights.
= 7+12+12+8+9+8+8+8/8
= 72/8
=9
Step 2: Calculate the range of Shade's plant heights. Range is highest minus lowest number. This will be:
12 - 7 = 5
Step 3: Calculate the mean of Sun plant heights.
19+24+20+23+24+23+23+20/8
= 176/8
= 22
Step 4: Find the range of Sun plants height.
= 24 - 19 = 5
Step 5: Find the difference of means
= 22 - 9
= 13
Step 6: Divide the difference of means by the range.
= 13 ÷ 5
= 2.6
The difference in mean and range are 13 and 0 respectively.
We are to find the difference in mean and range of the plant height.
Given the Shade plant heights expressed as 7 12 12 8 9 8 8 8
Mean = 7 + 12+12+ 8+ 9+ 8+ 8+ 8
Mean = 72
Sample size = 8
Mean of shade heights plant = 72/8 = 9Range = Highest value - Lowest value
Range = 21 - 7
Range = 5Given the Sun plant heights expressed as 19 24 20 23 24 23 23 20
Mean = 19+ 24+ 20+ 23+ 24+ 23+ 23+ 20
Mean = 176
Sample size = 8
Mean of shade heights plant = 176/8 = 22Range = Highest value - Lowest value
Range = 24 - 19
Range = 5Evaluate the difference in mean
Difference in mean = 22 - 9
Difference in mean = 13
Evaluate the difference in range
Difference in range = 5 - 5
Difference in range = 0
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What’s the first answer I’m it’s very easy I just need help thanks
Answer:121
Step-by-step explanation:
11 times 11.
Answer:
[tex]121[/tex]
Step-by-step explanation:
[tex]11^{2} \\ write \: the \: exponentiation \: as \\ multiplication. \\ \\ 11 \times 11 \\ multiply \\ \\ 121[/tex]
The perimeter of a square is represented by 4x − 16. What is the length of a side of this square?
Answer:
(x-4)
Step-by-step explanation:
Since a square has 4 equal sides, the perimeter of a square is 4 times one of the sides (which is equal to adding all the sides together). So:
Perimeter = 4(a side) = 4x-16
a side = (4x-16)/4 = (x-4)
The length of a side of a square with perimeter 4x - 16 is x - 4.
perimeter of a square is represented as follows:
perimeter = 4lwhere
l = length
Therefore,
4l = 4x - 16
divide both sides by 4
l = x - 4
The length = x - 4
Note a square have all its side equal to each other.
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Determine whether each of the following LTIC systems is i) BIBO stable, ii) asymptotically stable, and iii) marginally stable. Explain why or why not. (a) d 3y dt3 − 3 dy dt − 2y(t) = df dt − f(t) (b) d 3y dt3 − 3 dy dt − 2y(t) = df dt − 2f(t) (c) d 2y dt2 + 3 dy dt + 2y(t) = df dt + f(t) (d) d 2y dt2 + 2 dy dt + 2y(t) = f(t) (e) d 2y dt2 + 2y(t) = f(t)
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Construct a 90% confidence interval of the population proportion using the given information.
X= 175
n= 250
Tbe confidence interval marked the range of values for which the true population mean is estimated to be given a certain level of confidence. Hence, the confidence interval is (0.6523, 0.7477)
Since the sample size is large enough, we use the the Z distributuon :
Confidence interval is defined thus :
Mean ± margin of errorMargin of Error :
[tex] Z = Z* \sqrt{\frac{pq}{n}}[/tex] Mean, p = x/n = 175/250 = 0.7q = 1 - 0.7 = 0.3Zcritical at 90% = Z* = 1.645Hence,
Margin of Error = [tex] 1.645 \sqrt{\frac{0.7\times 0.3 }{250}} = 0.0477[/tex]Lower confidence boundary = 0.7 - 0.0290 = 0.6523
Upper confidence boundary = 0.7 + 0.0290 = 0.7477
Therefore, the confidence interval is (0.6523, 0.7477)
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To construct a 90% confidence interval for the population proportion, calculate the sample proportion, the standard error, and use the confidence interval formula.
Explanation:Step 1:
Calculate the sample proportion, which is X divided by n. In this case, it is 175 divided by 250, which gives us 0.7.
Step 2:
Calculate the standard error, which is the square root of (p*(1-p))/n, where p is the sample proportion. In this case, it is the square root of (0.7*(1-0.7))/250, which is approximately 0.0266.
Step 3:
Construct the confidence interval using the formula p ± z*(standard error), where p is the sample proportion and z is the z-score corresponding to the desired level of confidence. For a 90% confidence interval, the z-score is approximately 1.645. Therefore, the 90% confidence interval is 0.7 ± 1.645*0.0266, which becomes (0.658, 0.742).
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kevin built a deck in his backyard. The length of the deck was 5x+1 units and the width of the deck was 4x-1 units. Write and simplify an expression to repersent the perimeter of kevins deck.
Answer:
Perimeter =
[tex]2(length + width) \\ 2(5x + 1 + 4x - 1) \\ 2(5x + 4x + 1 - 1) \\ 2(9x ) \\ 9 \times 2 \\ = 18[/tex]
Triangle DEF is congruent to TriangleGHJ by the SSS theorem. Which rigid transformation is required to map TriangleDEF onto TriangleGHJ?
Answer:
Rotation
Step-by-step explanation:
Given:
Triangle DEF is congruent to Triangle GHJ by the SSS theorem
To find: transformation required to map Triangle DEF onto Triangle GHJ
Solution:
Two figures are said to be congruent if they overlap each other.
Two polygons are said to be congruent if they have same size and shape.
A rotation is a transformation that turns a figure about the center of rotation.
Rotation transformation is required to map Triangle DEF onto Triangle GHJ
Answer:
translation
Step-by-step explanation:
Given:
f(x) = x2 - 6x + 13
What is f (4)?
Answer:
5
Step-by-step explanation:
f(x) = x^2 -6x+13
Let x=4
f (4) = 4^2 -6(4) +13
= 16 -24 +13
= 5
The value of f(4) for the function f(x) = x^2 - 6x + 13 is 5.
Explanation:In order to find f(4) for the function f(x) = x2 - 6x + 13, we replace each x in the equation with 4. So, f(4) = (4)2 - 6(4) + 13. Squaring 4 gives us 16, and 6 times 4 gives us 24.
Therefore, our equation is now f(4) = 16 - 24 + 13. Solving for f(4), we subtract 24 from 16 to get -8, and then add 13 to get 5.
Thus, f(4) = 5.
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What is the positive slope of the asymptote of the hyperbola? The positive slope of the asymptote is .
Answer:
2
Step-by-step explanation:
edge
The positive slope of the asymptote of a hyperbola is a straight line with positive slope.
Explanation:The positive slope of the asymptote of a hyperbola is a straight line with positive slope (option b). A positive slope indicates that the line moves up the y-axis as the x-value increases, while a negative slope means that the line moves down the y-axis. The appearance of positive slope differs from negative slope and zero slope in that it moves up the y-axis as the x-value increases, while negative slope moves down the y-axis and zero slope means a horizontal line.
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
D
Step-by-step explanation:
This function resembles that of the absolute value function, never going into the negative y values. Hope this helps!
A fifth grade class sets up 418 chairs for a graduation ceremony. Each row has 22 chairs.
How many rows of chairs does the class set up? Enter your answer in the box.
Answer:
19
Step-by-step explanation: all you have to do is divide 418 by 22, and u can use long division...Final answer:
The class set up 19 full rows of chairs for the graduation ceremony by dividing the total number of chairs, 418, by the number of chairs in each row, 22.
Explanation:
To determine how many rows of chairs the fifth grade class set up for a graduation ceremony, we divide the total number of chairs by the number of chairs in each row. They have set up a total of 418 chairs, and each row contains 22 chairs.
Divide the total number of chairs (418) by the number of chairs per row (22).
Perform the division: 418 ÷ 22 = 19.
The result is that they set up 19 full rows of chairs.
Giving brainliest for CORRECT awnser.
Answer:
11> x
Step-by-step explanation:
-5 > x-16
Add 16 to each side
-5+16 > x-16+16
11> x
the histogram represents the number of gallons of gasoline that driver purchased weekly . how many driver represented by the histogram
Answer:
6
Step-by-step explanation:
I did it
Lindsay Electronics, a small manufacturer of electronic research equipment, has approximately 7 comma 000 items in its inventory and has hired Joan Blasco-Paul to manage its inventory. Joan has determined that 10% of the items in inventory are A items, 35% are B items, and 55% are C items. She would like to set up a system in which all A items are counted monthly (every 20 working days), all B items are counted quarterly (every 60 working days), and all C items are counted semiannually (every 120 working days). How many items need to be counted each day?
Answer:
108
Step-by-step explanation:
As per the given question the solution of items need to be counted each day is provided below:-
Here to reach the items needs to be counted each day first we need to find out the number of items which are as follows:-
[tex]For\ item\ A\ = Inventory\ A\ Percentage \times \ Number\ of\ inventory\ items[/tex]
[tex]= 10\% \times \ 7,000[/tex]
[tex]= 0.1 \times \ 7,000[/tex]
[tex]= \ 700[/tex]
[tex]For\ item\ B\ = Inventory\ B\ Percentage \times \ Number\ of\ inventory\ items[/tex]
[tex]= 35\% \times \ 7,000[/tex]
[tex]= 0.35 \times\ 7,000[/tex]
[tex]= \ 2,450[/tex]
[tex]For\ item\ C\ = Inventory\ C\ Percentage \times \ Number\ of\ inventory\ items[/tex]
[tex]= 55\% \times \ 7,000[/tex]
[tex]= 0.55 \times\ 7,000[/tex]
[tex]= 3,850[/tex]
Now, we will find out the items to be counted each day
[tex]Items\ to\ be\ counted\ each\ day\ = \frac{Item\ A}{Working\ Days\ of\ A} \ + \frac{Item\ B}{Working\ Days\ of\ B} \ + \frac{Item\ C}{Working\ Days\ of\ C}[/tex]
[tex]= \frac{700}{20} \ + \frac{2,450}{60}\ + \frac{3,850}{120}[/tex]
[tex]= \ 35\ + \ 40.83\ + \ 32.08[/tex]
[tex]= \ 107.92[/tex]
or
= 108
So, we have calculated the items to be counted for each day by using the above formula.
helphelphelphelphelphelphelphelphelphelphelp
The X-intercept (-250, 0)
The Y-intercept (0, 100)
These are the Y and X intercepts because this the first time the line intercepts. I hope I explained it well...
Have a good day!
Blake has only nickels and dimes. He has twice as many nickels as
dimes. The total value of his coins is 40 cents.
Answer:
Blake has 2 dimes and 4 nickels
Step-by-step explanation:
2 dimes = 20 cents
4 nickels = 20 cents
20 + 20 = 40 cents
2 × 2 = 4 dimes
Final answer:
Explanation of the relationship between the number of nickels and dimes in a coin collection yielding a total value of 40 cents.
Explanation:
Problem Statement:
Blake has only nickels and dimes. He has twice as many nickels as dimes. The total value of his coins is 40 cents.
Solution:
Let the number of dimes be 'x', so the number of nickels is '2x'.
Value of dimes = 10x cents, value of nickels = 5(2x) = 10x cents.
Given total value is 40 cents, so 10x + 10x = 40.
Solving the equation, x = 2. Therefore, Blake has 2 dimes and 4 nickels.
A pair of sunglasses is priced at $42.95. They are put on sale at 27% off the original price. Shane estimates the discounted price of the sunglasses to be around $36. Is this a reasonable estimate?
Answer:
no,
Step-by-step explanation:
1/4 of 40 is 10
40-10=30
It depends. The actual price would be $31.35. So it is not really reasonable since it is closer to the original price than it is to the discounted one... Just use your best judgement...
In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample is $105. The population standard deviation is known to be $16. Calculate the value of the test statistic that you would use to test the hypothesis that the average room price is significantly different from $108.50. (Round your answer to two decimals.)
Answer:
9.76
Step-by-step explanation:
I am very smart
Mark bought a brand new car for $35,000 in 2008. If the car depreciates in value approximately 8% each year, write an exponential function to model the situation. Then, find the value of the car in 2015. Is this considered growth or decay?
Answer:
[tex]V(t) = 35000(0.92)^{t}[/tex]
Decay function
The value of the car in 2015 is $19,525.
Step-by-step explanation:
A exponential value function has the following format:
[tex]V(t) = V(0)(1+r)^{t}[/tex]
In which V(t) is the value after t years, V(0) is the initial value and 1+r is the yearly variation rate.
If 1+r>1, the function is a growth function.
If 1-r<1, the function is a decay function.
Mark bought a brand new car for $35,000 in 2008.
This means that [tex]V(0) = 35,000[/tex]
If the car depreciates in value approximately 8% each year
Depreciates, then r is negative. So [tex]r = -0.08[/tex]
Then
[tex]V(t) = V(0)(1+r)^{t}[/tex]
[tex]V(t) = 35000(1-0.08)^{t}[/tex]
[tex]V(t) = 35000(0.92)^{t}[/tex]
0.92 < 1, so decay function.
Then, find the value of the car in 2015.
2015 is 2015-2008 = 7 years after 2008. So this is V(7).
[tex]V(t) = 35000(0.92)^{t}[/tex]
[tex]V(7) = 35000(0.92)^{7}[/tex]
[tex]V(7) = 19525[/tex]
The value of the car in 2015 is $19,525.
What is the sum of a regular octagon?
A.) 540
B.) 360
C.) 1080
D.) 900
Answer:
The answer is C.
Step-by-step explanation:
(n-2) * 180
(8-2) * 180
(6) * 180
1080
A circle with a diameter of 10 cm and a central angle of 30° is shown. What is the length, to the nearest tenth, of the arc formed by the 30° angle?
9514 1404 393
Answer:
2.6 cm
Step-by-step explanation:
The full circle is 360°, so an arc of 30° will have 30/360 = 1/12 of the measure of the circumference of the circle.
arc length = πd/12 = π(10/12) ≈ 2.6 cm
Solve the inequality |4x+2|<26
Answer:
-7<x<6
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variables
Mark me brainliest please!
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 55% salt and Solution B is 80% salt. She wants to obtain 130 ounces of a mixture that is 75% salt. How many ounces of each solution should she use?
Answer:
26 ounces of 55% solution104 ounces of 80% solutionStep-by-step explanation:
Let x represent the quantity of 80% solution. Then 130-x is the amount of 55% solution. The total amount of salt in the mix is ...
0.80x +0.55(130 -x) = 0.75·130
0.25x = 0.20·130 . . . . . . . subtract 0.55(130)
x = 0.20/0.25(130) = 104
130-x = 26
She should use 26 ounces of 55% solution and 104 ounces of 80% solution.
Final answer:
The scientist would need to use 26 ounces of Solution A and 104 ounces of Solution B to create 130 ounces of a 75% salt mixture.
Explanation:
To solve the problem of mixing two salt solutions of different concentrations to achieve a specific final concentration, we can set up a system of equations based on the amounts of salt and total solution. We know that Solution A is 55% salt and Solution B is 80% salt, and we want 130 ounces of a 75% salt mixture.
Let x be the amount of Solution A and y be the amount of Solution B. The first equation is based on the total amount of solution, and it is:
x + y = 130 ... (1)
The second equation is based on the amount of salt in the final mixture:
0.55x + 0.80y = 0.75(130) ... (2)
From equation (1), we can express y as y = 130 - x. Substitute this into equation (2) and solve for x:
0.55x + 0.80(130 - x) = 97.5
0.55x + 104 - 0.80x = 97.5
-0.25x = -6.5
x = 26 ounces (Solution A)
Substitute x back into equation (1) to find y:
x + y = 130
26 + y = 130
y = 104 ounces (Solution B)
So, to obtain 130 ounces of a 75% salt mixture, the scientist would use 26 ounces of Solution A and 104 ounces of Solution B.
In ΔFGH, f = 37 cm, ∠F=28° and ∠G=124°. Find the length of g, to the nearest 10th of a centimeter.
Answer:
65.3 cm
Step-by-step explanation:
The law of sines can be used for this.
g/sin(G) = f/sin(F)
g = (37 cm)sin(124°)/sin(28°) ≈ 65.3 cm . . . . multiply by sin(G)
The length of g is about 65.3 cm.
When working properly, a machine that is used to makes chips for calculators does not produce more than 4% defective chips. Whenever the machine produces more than 4% defective chips, it needs an adjustment. To check if the machine is working properly, the quality control department at the company often takes samples of chips and inspects them to determine if they are good or defective. One such random sample of 200 chips taken recently from the production line contained 12 defective chips. Find the p-value to test the hypothesis whether or not the machine needs an adjustment. What would your conclusion be if the significance level is 2.5%
Answer:
The proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.
Step-by-step explanation:
In this case we need to test whether the proportion of defective chips produced by the machine is more than 4%.
The hypothesis can be defined as follows:
H₀: The proportion of defective chips produced by the machine is not more than 4%, i.e. p ≤ 0.04.
Hₐ: The proportion of defective chips produced by the machine is more than 4%, i.e. p > 0.04.
The information provided is:
X = 12
n = 200
α = 0.025
The sample proportion of defective chips is:
[tex]\hat p=\frac{X}{n}\\\\=\frac{12}{200}\\\\=0.06[/tex]
Compute the test statistic as follows:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}\\\\=\frac{0.06-0.04}{\sqrt{\frac{0.04(1-0.04)}{200}}}\\\\=1.44[/tex]
The test statistic value is 1.44.
Decision rule:
We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.
Compute the p-value of the test:
[tex]p-value=P(Z>1.44)\\=1-P(Z<1.44)\\=1-0.92507\\=0.07493\\\approx 0.075[/tex]
The p-value of the test is 0.075.
p-value = 0.075 > α = 0.025
The null hypothesis was failed to be rejected at 2.5% level of significance.
Thus, it can be concluded that the proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.
To test the hypothesis whether or not the machine needs an adjustment, we can use a one-sample proportion test. Calculate the sample proportion, the standard error of the proportion, and the test statistic. Find the p-value and compare it to the significance level to make a conclusion.
Explanation:To test the hypothesis whether or not the machine needs an adjustment, we can use a hypothesis test. The null hypothesis (H0) is that the machine is working properly and the alternative hypothesis (Ha) is that the machine needs an adjustment. We can use a one-sample proportion test since we are testing the proportion of defective chips.
Calculate the sample proportion, which is the number of defective chips divided by the sample size: p-hat = 12/200 = 0.06.Calculate the standard error of the proportion: SE = sqrt((p-hat * (1 - p-hat)) / n) = sqrt((0.06 * 0.94) / 200) = 0.0212.Calculate the test statistic, which is the difference between the sample proportion and the hypothesized proportion divided by the standard error: z = (p-hat - p) / SE = (0.06 - 0.04) / 0.0212 = 0.9434.Find the p-value associated with the test statistic using a standard normal distribution table or a calculator. In this case, the p-value is the probability of observing a test statistic as extreme as 0.9434 or more extreme if the null hypothesis is true.If the p-value is less than the significance level (2.5%), we reject the null hypothesis and conclude that the machine needs an adjustment. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the machine needs an adjustment.
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A farmer owns a 100 acre farm and plans to plant at most three crops. The seed for crops A,B, and C costs $40, $20, and $30 per acre, respectively. A maximum of $3200 can be spent on seed. Crops A,B, and C require 1,2, and 1 workdays per acre, respectively, and there are maximum of 160 workdays available. If the farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C, how many acres of each crop should be planted to maximize profit
The 0 acres of crop A, 60 acres of crop B, and 40 acres of crop c each crop should be planted to maximize profit $26,000.
Given that,
A farmer owns a 100-acre farm and plans to plant at most three crops. The seed for crops A, B, and C costs $40, $20, and $30 per acre, respectively.
A maximum of $3200 can be spent on the seed. Crops A, B, and C require 1,2, and 1 workday per acre, respectively, and there are a maximum of 160 workdays available.
If the farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C,
We have to find,
How many acres of each crop should be planted to maximize profit?
According to the question,
The farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C,
[tex]\rm P = 100A + 300B + 200C[/tex]
The seed for crops A, B, and C costs $40, $20, and $30 per acre, respectively.
And A maximum of $3200 can be spent on the seed.
[tex]\rm 40A + 20B + 30C \leq 3200[/tex]
Then, Sum of seed for crops costs = area of the farm
[tex]\rm A + B + C \leq 100[/tex]
Crops A, B, and C require 1,2, and 1 workday per acre, respectively, and there are a maximum of 160 workdays available.
[tex]\rm A + 2B + C = 160[/tex]
Solving all the equations,
From equation 3,
[tex]\rm A = 100-B-C[/tex]
Substitute the value of A in equation 4,
[tex]\rm 100 - B - C+ 2B + C = 160\\\\100 + B = 160 \\\\B = 160 - 100\\\\B = 60[/tex]
Put B = 60 in the equation,
[tex]\rm A = 100-B-C\\\\A = 100-60-C\\\\A = 40-C[/tex]
Substitute the value of A in equation 2,
[tex]\rm 40(40-C) + 20\times 60 + 30C = 3200\\\\1600 - 40C + 1200 + 30C = 3200\\\\-10C + 2800 = 3200\\\\-10C = 3200-2800\\\\-10C = 400\\\\C = \dfrac{400}{-10}\\\\C = -40[/tex]
The area can not be negative then the value of C is +40.
And the value of A is,
[tex]A + B + C = 100\\\\A = 100 - 60 -40\\\\A = 100-100\\\\A = 0[/tex]
Then, Maximize profit is,
[tex]\rm P = 100A + 300B + 200C\\\\\rm P = 100(0) + 300(60) + 200(40)\\\\P =0+18000+8000\\\\P = 26000[/tex]
Hence, The 0 acres of crop A, 60 acres of crop B, and 40 acres of crop c each crop should be planted to maximize profit $26,000.
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