An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained. (Please show the calculation process)

To calculate the conditional probability of at most 3 men entering the drugstore given that 10 women entered using Poisson Distribution. The gender doesn't influence the probability, therefore the events are treated as independent. Assumption made is that occurrences are independent and happen at a known average rate.

To compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour, we would apply Poisson Distribution. Poisson Distribution is used to find the probability of a number of events in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event.

However, in this case, the number of men entering is independent of the number of women entering. Therefore, the fact that we know 10 women entered does not affect the probability regarding the number of men. The gender of the individuals entering the drugstore is irrelevant, and we can consider them as independent events. The result is the same if we simply asked: What is the probability that at most 3 people entered the drugstore?

To calculate this, we would use the formula for Poisson Distribution, summing up the probabilities of 0, 1, 2 and 3 events happening. The assumption made here is that the occurrences are independent of each other and occur with a known average rate, λ, which is 10 in this question.

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Answer:

There were 333 seniors in 1990

153 seniors had jobs in 2010.

Step-by-step explanation:

Let the number of high school seniors in 1990 = x

75% of x had jobs in 1990

In 2010 there were 50 more seniors. That is, the number of seniors is x+50.

40% of (x+50) had jobs in 2010.

Total number of jobs in both years = 403.

\[0.75 * x + 0.4 * (x + 50) = 403\]

\[0.75 * x + 0.4 * x  + 20 = 403\]

=> \[1.15 * x  = 403 - 20\]

=> \[1.15 * x  = 383\]

=> \[x  = 383/1.15\]

=> \[x  = 333\]

Number of seniors having job in 2010 = 0.4 * (333 + 50) = 0.4 * 383 = 153.2 = 153(approx)

Answer:

Ans 1. [tex]x= 7[/tex]

Ans 2.a.

[tex]\overline {AC} \cong \overline {JL} \\\textrm{is the additional information required to prove the triangles are congruent by SAS postulate}[/tex]

Ans.2.b.

[tex]\overline {BC} \cong \overline {KL} \\\textrm{is the additional information required to prove the triangles are congruent by the HL theorem}[/tex]

Step-by-step explanation:

Solution:

1.

Vertically opposite angles are equal.

[tex]\therefore (x+16) = (4x-5)\\\therefore (4x-x) = (16+5)\\\therefore (3x) = (21)\\\therefore x = 7[/tex]

2.a.

proof for Δ BAC ≅ ΔKJL by SAS postulate.

InΔ BAC and Δ KJL

BA ≅  KJ               Given

∠ BAC ≅ ∠ KJL   {measure each angle is 90}

[tex]\overline{AC} \cong \overline{JL}\ \textrm{additional information require to prove the tangles are congruent by SAS postulate}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Side-Angle-Side postulate...PROVED}[/tex]

2.b.

proof for Δ BAC ≅ ΔKJL by HL theorem.

InΔ BAC and Δ KJL

BA ≅  KJ               Given

∠ BAC ≅ ∠ KJL   {measure each angle is 90}

[tex]\overline{BC} \cong \overline{KL}\ \textrm{additional information require to prove the tangles are congruent by HL theorem}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Hypotenuse Leg Theorem......PROVED}[/tex]

Answer:

She have $1133.33 in account which pays  5% annual interest and he have $1933.33 in account which pays 10% annual interest

Step-by-step explanation:

Let x be the amount she invested at 5% annual interest

She invested $800 more in 10%

So, she invested x+800 at 10% annual interest

Case 1:

Principal = x

Time = 1 year

Rate of interest = 5%

[tex]Si =\frac{P \times R \times T}{100}[/tex]

[tex]SI=\frac{x \times 5 \times 1}{100}[/tex]

[tex]SI=\frac{5}{100}x[/tex]

Case 2:

Principal = x+800

Time = 1 year

Rate of interest = 10%

[tex]Si =\frac{P \times R \times T}{100}[/tex]

[tex]SI=\frac{(x+800) \times 10 \times 1}{100}[/tex]

[tex]SI=\frac{10}{100}(x+800)[/tex]

Interest = Amount - principal = 880+1.1x-x=880+0.1x

Her total interest for a year is $250

So, [tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]

[tex]\frac{5}{100}x+\frac{10}{100}(x+800)=250[/tex]

[tex]\frac{5}{100}x+\frac{10}{100}x+80=250[/tex]

[tex]\frac{15}{100}x+80=250[/tex]

[tex]\frac{15}{100}x=250-80[/tex]

[tex]x=170 \times \frac{100}{15}[/tex]

[tex]x=1133.33[/tex]

So the amount she invested at 5% annual interest is $1133.33

She invested at 10% annual interest=x+800=1133.33+800=1933.33

Hence she have $1133.33 in account which pays  5% annual interest and he have $1933.33 in account which pays 10% annual interest

The amount she has in the account that an annual interest of 5% is $3400.

The amount she has in the account that an annual interest of 10% is  $4,200.

x - y = $800 equation 1

0.1x + 0.05y = $250 equation 2

Where:

Multiply equation 1 by 0.1

0.1x - 0.1y = 80 equation 3

Subtract equation 3 from equation 2

0.05y = 170

Divide both sides by 0.05

y = $3,400

Substitute for y in equation 1

x - 3400 = 800

x = 3400 + 800

x = $4,200

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Answer:

d. 29ft

Step-by-step explanation:

Using pythagoras theorem which states that

a^2 + b^2 = c^2

where a and b are the opposite and adjacent sides of a right angled triangle and c is the hypotenuse side

From the attached image, Let the length of the rope be x

[tex]x^{2} = 8^{2}+ 28^{2} \\[/tex]

[tex]x^{2} = 64 + 784[/tex]

[tex]x^{2} = 848[/tex]

[tex]x =\sqrt{848}[/tex]

[tex]x = 29.12[/tex]

x≈29

There are 4 people in Molly's group.

Step-by-step explanation:

Let,

x be the number of people.

Individual ticket price = $42

Price after discount = $30

Discount per ticket = $3

Discount for x people = 3x

According to given statement;

42-3x=30  

Subtracting 42 from both sides

[tex]42-42-3x=30-42\\-3x=-12\\[/tex]

Dividing both sides by -3

[tex]\frac{-3x}{-3}=\frac{-12}{-3}\\x=4[/tex]

There are 4 people in Molly's group.

Keywords: Subtraction, division

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Answer:

A. 20%

Step-by-step explanation:

These events are independent, because if David eats a healthy breakfast cannot influence on would be rain or not.

"And" for probabilities  of independent events means "x" (times).

80% = 0.8

25% = 0.25

0.8*0.25 = 0.2 = 20%

Answer:

x = 1

y = -4

Step-by-step explanation:

We will multiply the 2nd equation by 4 first:

4 * [-x + y = -5]

-4x + 4y = -20

Now we will add this equation with 1st equation given. Shown below:

4x + 3y = -8

-4x + 4y = -20

---------------------

7y = -28

Now, we can solve for y easily:

7y = -28

y = -28/7

y = -4

Now, we take this value of y and put it in 1st original equation and solve for x:

4x + 3y = -8

4x + 3(-4) = -8

4x - 12 = -8

4x = -8 + 12

4x = 4

x = 4/4

x = 1

So, this is the only solution to this problem ( 1 intersection point at x = 1 and y = -4)

Answer:

x=4

Step-by-step explanation:

EF is half of the top and bottom lines comined so you would make an equation:

5x+8/2=2x+6

5x+8=4x+12

x=4

Answer: 2432 visitors

Step-by-step explanation:

An employee of a museum surveyed a random sample of 350 visitors that came to the museum. Of the visitors that were surveyed, 266 stopped at the gift shop.

Since 266 out of 350 stopped at the gist shop, we find the fraction or decimal of people who stopped at the gift shop. This will give 266/350 = 19/25 or 0.76.

If 3200 visitors come to the museum, the expected number of people to stop at the gift shop are:

= 0.76 × 3200

= 2432

2432 visitors are expected to stop at the gift shop out of 3200 visitors.

Final answer:

There are 371 students who have taken a course in either calculus or discrete mathematics, 157 students have taken calculus but not discrete mathematics, and 24 students have taken discrete mathematics but not calculus.

Explanation:

To determine how many students have taken a course in either calculus or discrete mathematics, we use the principle of inclusion and exclusion. The formula for two sets A (calculus students) and B (discrete mathematics students) is: |A∪B| = |A| + |B| - |A∩B|.

A. Using the provided numbers: |A∪B| = 347 (calculus students) + 214 (discrete mathematics students) - 190 (students in both) = 371 students have taken a course in either calculus or discrete mathematics.

B. The number of students who have taken calculus but not discrete mathematics is found by subtracting the number of students who have taken both from the total number of calculus students: 347 - 190 = 157 students.

C. Similarly, the number of students who have taken discrete mathematics but not calculus is found by subtracting the number of students who have taken both from the total number of discrete mathematics students: 214 - 190 = 24 students.

Answer:

Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.

If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.

Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.

Answer:

b. Exactly two outcomes are possible on each trial.

Step-by-step explanation:

The correct answer is option B: Exactly two outcomes are possible on each trial.

We can define the binomial probability in any binomial experiment, as the probability of getting exactly x successes for n repeated trials, that can have 2 possible outcomes.

The binomial probability distribution is applicable when an experiment has exactly two outcomes. These trials are independent and the probabilities of the outcomes remain the same for each trial, referred to as Bernoulli trials. Using this distribution, we can calculate mean and standard deviation for the function.

The characteristic of an experiment where the binomial probability distribution is applicable is when exactly two outcomes are possible on each trial, referred to as 'success' and 'failure.' These are termed as Bernoulli trials for which binomial distribution is observed. In this situation, 'p' denotes the probability of a success on one trial, while 'q' represents the failure likelihood. The trials are independent, which means the outcome of one trial does not affect the results of subsequent trials. Moreover, the probabilities of the outcomes remain constant for every trial. The random variable X signifies the number of successes in these 'n' independent trials. The mean and standard deviation can be calculated using the formulas µ = np and √npq, respectively.

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Answer:

Their intercepts are unique.

Explanation:

[tex]\displaystyle x^3 - 24x^2 + 192x - 508 = (x - 8)^3 + 4[/tex]

This graph's x-intercept is located at approximately [6,41259894, 0], and the y-intercept located at [0, −508].

[tex]\displaystyle g(x) = x^3[/tex]

The parent graph here, has both an x-intercept and y-intercept located at the origin.

I am joyous to assist you anytime.

The plot is missing. I have written the stem-leaf plot below.

Answer:

(a) 35 participants

(b) 22 participants traveled more than 14 km.

Step-by-step explanation:

Given:

(a)

The stem-leaf plot is given as:

12| 3  3  6 7 9 9

13| 1 1 4 5 5

14| 0 0 2 3 3 8 8 9

15| 2 2 2 2 2 3 5 5 7

16| 4 5 5 9 9

17| 3 5

The total number of numbers on the leaf side gives the total number of participants.

So, the number of participants is equal to the total number of elements on the leaf part. The total number of elements on the leaf part is 35.

Therefore, the total number of participants is 35.

(b)

Given:

12| 3  3   6 7 9 9

13| 1 1 4 5 5

14| 0 0 2 3 3 8 8 9

15| 2 2 2 2 2 3 5 5 7

16| 4 5 5 9 9

17| 3 5

One element of the stem part and one part of leaf part is represented as:

12 | 3 means 12.3 km

So, the number of walkers traveling more than 14.0 km is the list of all numbers greater than 14.0 km. Let us write all the numbers which are greater than 14.0 km. The numbers are:

14 | 2 3 3 8 8 9 = 6 participants

15 | 2 2 2 2 2 3 5 5 7 = 9 participants

16 | 4 5 5 9 9 = 5 participants

17 | 3 5 = 2 participants

Therefore, the total number is the sum of all the above which is equal to:

= 6 + 9 + 5 + 2 = 22 participants

Answer:

Step-by-step explanation:

She uses all the food to feed the dogs in 6 days. She feeds the with an equal amount of food in 6 days. This means that whatever amount of food she buys, the least amount she would feed the dogs with is 1/6 of that amount.

There are 31 cups of dog food. This means that the amount she would feed them with each day is

1/6 × 31 = 5.1 cups

So the least amount is 5 cups

Therefore,

The number of cups she feeds her dogs with would be between 5 and 6 cups.

Ground: y = 0

- 16t² + 128t + 50 = 0

Apply quadratic equation.

t = 0, 8 (rounded to the nearest second)

8 seconds

The time it will take for the object to hit the ground is approximately 4 seconds (rounded to the nearest second).

The given function a(t) = -16t^2 + 128t + 50 represents the approximate altitude, in feet, of an object released from the top of a building t seconds after it is released. To find the time it will take for the object to hit the ground, we need to find the value of t when the altitude is 0.

Setting a(t) = 0, we get:

-16t^2 + 128t + 50 = 0

Using the quadratic formula, we can solve for t.

t = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values a = -16, b = 128, and c = 50, we get t = 0.54 s or t = 3.79 s. Since the object is already at a height of 0 at t = 0 (the time of release), the time it will take for the object to hit the ground is approximately 4 seconds (rounded to the nearest second).

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Answer:

0.7 is the probability that a randomly selected person either has high blood pressure or is a runner or both.

Step-by-step explanation:

We are given the following information in the question:

Probability that a randomly selected person has high blood pressure = 0.4

[tex]P(H) = 0.4[/tex]

Probability that a randomly selected person is a runner = 0.4

[tex]P(R) = 0.4[/tex]

Probability that a randomly selected person has high blood pressure and is a runner = 0.1

[tex]P(H \cap R) = 0.1[/tex]

If the events of selecting a person with high blood pressure and person who is a runner are independent then we can write:

[tex]P(H \cup R) = P(H) + P(R)-P(H\cap R)[/tex]

Probability that a randomly selected person either has high blood pressure or is a runner or both =

[tex]P(H \cup R) = P(H) + P(R)-P(H\cap R)\\P(H \cup R) = 0.4 + 0.4 -0.1 = 0.7[/tex]

0.7 is the probability that a randomly selected person either has high blood pressure or is a runner or both.

Final answer:

The probability that a randomly selected person either has high blood pressure or is a runner or both is 0.7.

Explanation:

To find the probability that a randomly selected person either has high blood pressure or is a runner or both, we use the formula for the probability of either event A or event B occurring, which is:

P(A or B) = P(A) + P(B) - P(A and B).

Given:

P(H) = probability of high blood pressure = 0.4

P(R) = probability of being a runner = 0.4

P(H and R) = probability of both high blood pressure and being a runner = 0.1

Using the formula, we plug in the given probabilities:

P(H or R) = 0.4 + 0.4 - 0.1 = 0.7.

So, the probability that a randomly selected person either has high blood pressure, is a runner, or both events occur is 0.7.

Answer:

$25 each ticket!

Step-by-step explanation:

6*4=24

124-24=100

100/4=25

Answer: P = 0.156

Step-by-step explanation:

Initially in the jar, we have 9 red and 13 blue marbles, so we have a total of 22 marbles in the jar.

If we want to take a red ball for the jar, the probability of getting one is equal to the number of red balls divided by the total number of balls, so:

P1 = 9/22 .

Now, suppose you already took one red ball, we want to take the second one; the probability is calculated in the same way, but now we already took a red ball, so we have 8 red balls and 21 balls in total; so:

P2 = 8/21

Now the probability of both events to happen is equal to the product of their probabilities:

P = P1*P2 = (9/22)*(8/21) = 0.1558

Now we want to round it to the nearest thousandth.

The thousandth is the second number after the decimal point, and the number that comes after is an 8, so we need to round it up; then we get:

P = 0.156, or 15.6% in percentage form.

Answer:

21.10 m

Step-by-step explanation:

Given:

Height of the temple above ground is, [tex]H=24\ m[/tex]

Total number of steps is, [tex]N=91[/tex]

Let us assume that each step is of same height, then the height of each step is given as:

[tex]\textrm{Each step height}=\frac{Total\ Height}{Total\ steps}=\frac{H}{N}=\frac{24}{91}\ m[/tex]

Now, height corresponding to 1 step = [tex]\frac{24}{91}\ m[/tex]

∴ Height corresponding to 80 steps = [tex]\frac{24}{91}\times 80=\frac{24\times 80}{91}=21.10\ m[/tex]

So, I would be at a height of 21.10 m above the ground at the [tex]80^{th}[/tex] step.

Answer:

x − 1

x + 2

Step-by-step explanation:

f(x) = 2x³ + 5x² − x − 6

Plug in the zero of each binomial.  If that zero is also a zero of f(x), then the binomial is a factor of f(x).

f(1) = 0

f(-1) = -2

f(2) = 28

f(-2) = 0

The correct options are option A and option D that is the factors of given binomial expressions are x  - 1 and x + 2.

What is binomial factor ?

Binomial factors are polynomial factors that have exactly two terms. Factoring a polynomial is the first step to finding its roots.

The given binomial expression is equal to :

2x³ + 5x² - x - 6

We know that factor theorem states that if [tex]x_{1}[/tex] , [tex]x_{2}[/tex], --- --- --- --- , [tex]x_{n}[/tex] are roots of a function , them (x - [tex]x_{1}[/tex]) , (x - [tex]x_{2}[/tex]) , --- --- --- --- , ( x - [tex]x_{n}[/tex]) are the factors of given binomial expression.

In the given question :

f(x) = 2x³ + 5x² - x - 6

If we put x = 1 , then we get f(x) = 0 . This implies the binomial factor will be (x - 1).

So ,

(ax² + bx + c ) ( x - 1) = 2x³ + 5x² - x - 6

ax³ + (b-a) x² + (c - b) x - c = 2x³ + 5x² - x - 6

If we compare both sides we get :

a  = 2 , b - a  = 5 , c - b  = 1 and c = 6

So , b = 7

We know that general form is given by :

ax² + bx + c

or

2x² + 7x + 6

Then :

Δ = 7² - 4 × 2 × 6 = 1

and other roots of solutions are :

x1 = [tex]\frac{-7 + \sqrt{1} }{4}[/tex] = [tex]\frac{-3}{2}[/tex]

x2 = [tex]\frac{-7 - \sqrt{1} }{4}[/tex] = -2

So , the other factors will be x + [tex]\frac{3}{2}[/tex] and x + 2.

Therefore , the correct options are option A and option D that is the factors of given binomial expressions are x  - 1 and x + 2.

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Answer:

The mean and standard deviation of Y are, 94 and 0.28 respectively.

Step-by-step explanation:

Let the random variable , 'Test grades on the last statistics exam' be X.

Then according to the question,

E(X) = 78 ------------(1)

and

[tex]\sigma_{X}[/tex] = 0.14------------(2)

Now, according to the question,

Y = 2(X - 31)

⇒E(Y) = 2(E(X) - 31)

          = [tex]2 \times (78 - 31)[/tex]

          = 94  ----------------(4)

and

V(Y) = 4V(X)

⇒[tex]\sigma_{Y} = 2 \times \sigma_{X}[/tex]

⇒[tex]\sigma_{Y} = 2 \times 0.14[/tex] = 0.28

So, the mean and standard deviation of Y are, 94 and 0.28 respectively.

Answer:

1 : -1

2:2

3:-5

4: 1/2

5: -3

6: -3/2

7: 1/2

8: -1/2

9: 1

10: 1/3

Step-by-step explanation:

well all u have to do is do rise over run, rise/run. find 2 points and go up according to how much it goes up and go left or right based on the graph. AND sometimes the slope will be negative like number 1.

Answer:

Step-by-step explanation:

Phil is going to store to buy a hat and a coat.

Let $x represent the cost of the cos of the hat. The coat cost 3 times as much as the hat. It means that the cost of the coat will be 3×x = $3x

His mom tells him that he cannot spend more than $120. Assuming he spends exactly $120. It means that

3x + x = 120

4x = 120

x = 120/ 4 = 30

The hat costs $30

The coat costs 30×3 = $90

The most he can spend on a coat is $90 since he cannot spend more than $120

Answer:

Sample 2

Step-by-step explanation:

Correlation  is a technique that show strongly pairs of variables.

For example height and width .There are several different correlation techniques .Correlation is determined by dividing  product of two variables. standard deviation.Standard deviation is a dispersion of  data. Co relation between two variable could be positive or negative or both.

Correlation between two sample is computed. if test statistic is larger in sample 1 then sample 2 will have the larger value of correlation coefficient.

He has a 26% of getting a strike, which means he has a 74% chance of not getting a strike ( 100% - 26% = 74%).

Multiply the chance of not getting a strike by the number of attempts:

0.74 x 0.74 x 0.74 x 0.74 x 0.74 = 0.22

The answer is B) 0.22

The probability of making a free throw is 77%, the probability of not making one would be 23% ( 100% - 77% = 23%).

Add the probability of making the first one ( 0.77) by the probability of making the second one multiplied by the probability of missing the second one ( 0.77x 0.23)

0.77 + (0.77 x 0.23)

0.77 + 0.18 = 0.95

The answer is D) 95%

Final answer:

To find the probability that Keyshawn doesn't get a strike until after his first five attempts, we need to find the probability of him not getting a strike on each individual attempt. The probability that Keyshawn doesn't get a strike until after his first five attempts is 0.19. To find the probability that Coram makes his first free throw within his first two shots, we need to find the probability of him making a free throw on the first or the second shot. The probability that Coram makes his first free throw within his first two shots is 95%.

Explanation:

To find the probability that Keyshawn doesn't get a strike until after his first five attempts, we need to find the probability of him not getting a strike on each individual attempt. Since each attempt is independent, we can multiply the probabilities together.

The probability of him not getting a strike on each attempt is 1 - 0.26 (the probability of getting a strike). So the probability of not getting a strike on the first five attempts is (1 - 0.26) * (1 - 0.26) * (1 - 0.26) * (1 - 0.26) * (1 - 0.26).

Calculating this expression, we get:

(0.74) * (0.74) * (0.74) * (0.74) * (0.74) = 0.192.

So the probability that Keyshawn doesn't get a strike until after his first five attempts is approximately 0.192.

Therefore, the correct answer is A) 0.19.

To find the probability that Coram makes his first free throw within his first two shots, we need to find the probability of him making a free throw on the first or the second shot. These events are mutually exclusive, so we can add the probabilities together.

The probability of him making a free throw on the first shot is 0.77, and the probability of him missing the first shot and making a free throw on the second shot is (1 - 0.77) * 0.77. So the total probability is 0.77 + (1 - 0.77) * 0.77.

Calculating this expression, we get:

0.77 + 0.23 * 0.77 = 0.77 + 0.1771 = 0.9471.

So the probability that Coram makes his first free throw within his first two shots is approximately 0.9471.

Therefore, the correct answer is D) 95%.

The speed is 66.33 miles per hour

Step-by-step explanation:

Given

Total distance = 325 miles

They still have 126 miles to go. In order to find the distance they have covered, we will subtract the remaining miles from the total

So,

[tex]Distance\ covered=325-126=199\ miles[/tex]

the car has been driving for 3 hours

So,

t= 3 hours

d = 199 miles

[tex]Speed=\frac{d}{t}\\=\frac{199}{3}\\=66.33\ miles\ per\ hour[/tex]

The speed is 66.33 miles per hour

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Answer:

Area = 2500 square feet is the largest area enclosed

Step-by-step explanation:

A rectangular piece of land borders a wall. The land is to be enclosed and to be into divided 3 equal plots with 200 feet of fencing

Let x be the length of each box and y be the width of the box

Perimeter of the box= 3(length ) + 4(width)

[tex]200=3x+4y[/tex]

solve for y

[tex]200=3x+4y[/tex]

[tex]200-3x=4y[/tex]

divide both sides by 4

[tex]y=50-\frac{3x}{4}[/tex]

Area of the rectangle = length times width

[tex]Area = 3x \cdot y[/tex]

[tex]Area = 3x \cdot (50-\frac{3x}{4})[/tex]

[tex]A=150x-\frac{9x^2}{4}[/tex]

Now take derivative

[tex]A'=150-\frac{9x}{2}[/tex]

Set it =0 and solve for x

[tex]0=150-\frac{9x}{2}[/tex]

[tex]150=\frac{9x}{2}[/tex]

multiply both sides by 2/9

[tex]x=\frac{100}{3}[/tex]

[tex]A''=-\frac{9}{2}[/tex]

For any value of x, second derivative is negative

So maximum at x= 100/3

 [tex]A=150x-\frac{9x^2}{4}[/tex] , replace the value of x

[tex]A=150(\frac{100}{3})-\frac{9(\frac{100}{3})^2}{4})[/tex]

Area = 2500 square feet is the largest area enclosed

Final answer:

To find the largest enclosed area with 200 feet of fencing divided into 3 plots, solve the equation 2l + 4w = 200 and substitute the value of l into the area formula.

Explanation:

To find the largest area that can be enclosed with 200 feet of fencing and divided into 3 equal plots, we can first find the length of each side of the rectangular piece of land. Let's assume the length of the land is 'l' and the width is 'w'.

Since the land is divided into 3 equal plots, each plot will have a length of l/3 and a width of w.

From the information given, we can form the equation 2l + 4w = 200 (each length side is counted twice and each width side is counted once). We can solve this equation for l and substitute it back into the area formula (A = l * w) to find the largest possible area.