A farmer wants to plant soy beans and corn. He wants to plant at least 2 acres of soy beans. He has only $1200 to spend and each acre of soy beans costs $200 to plant and each acre of corn costs $100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of soy beans and 2 hours to plant an acre of corn. The farmer profits $500 per acre of soy beans and $300 per acre of corn. If the farmer wants to maximize his profit, how many acres of each should he plant?

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Answer:

  4 acres of each

Step-by-step explanation:

Let s and c represent the number of acres of soybeans and corn, respectively. The problem statement gives rise to several constraints. There is also an objective function to maximize. The linear programming problem can be described by ...

  maximize 500s +300c subject to ...

  s ≥ 2

  200s +100s ≤ 1200 . . . . cost to plant

  s + 2c ≤ 12 . . . . . . . . . . . . hours to plant

__

The attached graph shows the objective function is maximized at (s, c) = (4, 4).

The farmer should plant 4 acres each of soybeans and corn.

__

For the solution here, the constraint that s ≥ 2 is irrelevant. If the graph included it, the vertices of the feasible solution space would be (2,5), (4, 4), (6, 0) and (2, 0). The solution that maximizes profit is (4, 4).

lf 9/28 of the students at Williards High school participate in after school sports activities, what fraction of the students do not participate in after school activities

find the area of the figure

A quiz has 5 questions with answers that are either true or false. How many different combinations of answers are
possible?
Ο 10
Ο 16
Ο Ο Ο
25
Ο 32

What is the
average rate of change between:
x = 1 and x = 2?
x = 2 and x = 3?
X = 3 and x = 4?

Sketch and Write the Equation

Equation=
Ordered Pair = (-3, 5)
Slope=
y-intercept= - 5

A man made a loss of 4% on an article he had sold for Tzs 240 more he had made a profit of 8%. Find the cost price​

plzzz i’ll give brainliest

Researchers asked 250 families whether or not they were homeowners and how many cars they had. Their responses are summarized in the following table.
No car or one car Two or more cars
Homeowner
25
90
Not a homeowner
45
90
(a) what percentage of the families are homeowners?
(b) What percentage of the familles have two or more cars?
х
S
?
(b) 1%
Explanation
Check
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Please help me please

Identify the missing measures

Use linear regression to find a
function that fits the following
points.
(0,5), (2,-13)

The amount of time (in minutes per day) spent on social media for a sample of 10 teens has a mean of 186.7 and a sample standard deviation of 19.99. An independent sample of 8 older adults has a mean of 93.5 minutes with a sample standard deviation of 32.01. Assume that the time spent on social media is approximately normally distributed for each group. a) Determine the value of the test statistic to test H subscript 0 colon space mu subscript t e e n end subscript equals mu subscript o l d e r end subscript against H subscript A colon space mu subscript t e e n end subscript not equal to mu subscript o l d e r end subscript. b) Determine the p-value or critical value for this test at alpha equals 0.05. c) What is your conclusion about whether the two age groups spend the same average amount of time on social media

Which iwo operations are needed to write the expression that represents four times the difference of a number and
three"?
multiplication and subtraction
division and subtraction
multiplication and addition
O division and addition




J

Im on a girls basketball team , 3 are in sixth grade , 5 are in seventh grade , and 6 are in eighth grade . so which is the ratio of seventh graders to eighth graders on the team ?

The angles shown below are supplementary:
What is the value of x?
BRAINLIEST
PLEASE HELP
SHOW WORK

Find the total surface area of a sphere radius being 7cm

Given the system of equations, what is the solution?

x + 2y = 7
x - 2y = -1

A.) {(-4, 6)}
B.) {(-8, -12}
C.) {(3,2)}

The height , in feet, windowsills in a high-rise building is represented by this sequence: 3,15,27,39,...

Need answers ASAP please

HELP WHAT COLOR DO I PICJ!!

100 Points!!!!! PLEASE HELP. Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.

Sarah can use the expression 5(2j + 3 + j) to represent the amount of money they can earn.

Part 1: Writing Expressions

1. Write an expression that looks like Sarah’s expression: 5(2j + 3 + j). Replace the coefficients so that your expression is not equivalent. You may use any number that you choose to replace the coefficients. Be sure to leave the variables the same. For example, 8(3j + 7 + 3j) looks like Sarah’s expression but is not equivalent.

2. Translate the new algebraic expression you created in Question 1 to a verbal expression.

Part 2: Writing Equivalent Expressions

3. You will now use mathematical properties to create two expressions that are equivalent to the expression you created in Question 1. Make sure you show all steps in your work.

a. Use either the commutative property or combine like terms to create an equivalent expression.

b. Use the distributive property to create an equivalent expression.

4. Pick a number from 1 to 10. Use that number to verify your three expressions (the original, the one from 3a, and the one from 3b) are equivalent by substituting it into each expression. Show all your work for complete credit.

Part 3: Finish the Story

5. Write a few sentences to end Sarah’s story. How many shark teeth did she find? How many shark teeth did John find? How much money did they earn?

Step-by-step explanation:

Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.

Sarah can use the expression 5(2j + 3 + j) to represent the amount of money they can earn.

Part 1: Writing Expressions

Q1. Write an expression that looks like Sarah’s expression: 5(2j + 3 + j). Replace the coefficients so that your expression is not equivalent. You may use any number that you choose to replace the coefficients. Be sure to leave the variables the same. For example, 8(3j + 7 + 3j) looks like Sarah’s expression but is not equivalent.

25(10j + 18 + 5j)

Your expression is good.

Q2. Translate the new algebraic expression you created in Question 1 to a verbal expression.

Skuttle offered to pay his sister Izzy $25 for every four-leaf clover she finds in the woods. Izzy finds 18 clovers but decides to get Roxy’s help. Izzy finds clovers twice as fast as Roxy but they will overall make more money together.

Your verbal expression is good. It reflects your chosen equation.

Use your knowledge of the mathematical properties to create two equivalent algebraic expressions for the algebraic expression you created in Question 1. Explain how you arrived at the equivalent expressions by showing all your steps and stating which properties you used.

Using commutative property of addition, the expression in question 1 can be rewritten as follows:



Using distributive property of multiplication over addition, the expression in question 1 can also be rewritten as follows:



Q 4. Use substitution to prove your algebraic expressions are equivalent. You may substitute any number for the variables you choose. Show all your work for complete credit.


Part 3: Finish the Story

Q5. Write a few sentences to end Sarah’s story. How many shark teeth did she find? How many shark teeth did John find? How much money did they earn?

Which of the following should not be used as justification in a formal proof?
Postulates
Theorems
Axioms
Venn diagrams

if a=1 and b=2 what is the value of a²+b²?​

If you can help me with these 4 questions I'll give brainliest :))​

Plz help me well mark brainliest if correct!!.....

Shamus owes his parents $162. He pays them 60% of the $45 he earns as a soccer referee each week. How many weeks will it take Shamus to pay back all of the money he owes his parents?

A right triangle has a leg of 12 cm and a hypotenuse of 19 cm.

What is the length of the other leg?

Round to the nearest tenth.
-----------------------------------------
7.0 cm

14.7 cm

22.5 cm

217.0 cm

) A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 200 items, 28 are defective. a) Find the 95% confidence interval for the proportion of defectives from this production line b) Interpret the results (the interval) you got

A bag contains 12 colored marbles. Dan drew a single marble from the bag 25 times, replacing the marble each time. He recorded drawing a red marble 9 times, a yellow marble 6 times, a blue marble 4 times, and a green marble 6 times. Based on these results, what is a reasonable conclusion about the makeup of the marbles in the bag?
Select one:

more red marbles than blue marbles

no white marbles

an equal number of yellow and blue marbles

more green marbles than red marbles

The pie chart shows the results of a survey on
students' favourite subjects.
a What fraction of the students chose Science?
b 60 students chose Maths.
i How many students chose Languages?
ii How many students chose Other?
jii How many students took part in the survey?
Favourite subjects
380 1200
O Mathis
Languages
Science
Art
DOther
90° 42
sh
o
a