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3 years ago

A farmer plans to enclose two adjacent rectangular pens against a barn wall (see figure).

Mathematics

1 answer:

Licemer1 [7]3 years ago

3 0

Answer: Let's assume that the pig pens need to be fenced in the way shown in the diagram above.

Then, the perimeter is given by

160

−

The area of a rectangle is given by

, however here we have two rectangles put together, so the total area will be given by

(

−

)

−

Now, let's differentiate this function, with respect to y, to find any critical points on the graph.

(

)

−

Setting to 0:

−

Hence, the dimensions that will give the maximum area are

feet.

A graphical check of the initial function shows that the vertex is at

(

1066

)

, which represents one of the dimensions that will give the maximum area and the maximum area, respectively.

Hopefully this helps!

Step-by-step explanation: hope this helps

You might be interested in

Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls. Find the probability that (a)

UNO [17]

Answer:

a) P=0.226

b) P=0.6

c) P=0.0008

d) P=0.74

Step-by-step explanation:

We know that the seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls. Therefore, we have 46 balls.

a) We calculate the probability that are 3 red, 2 blue, and 2 green balls.

We calculate the number of possible combinations:

$C_7^{46}=\frac{46!}{7!(46-7)!}=53524680$

We calculate the number of favorable combinations:

$C_3^{12}\cdot C_2^{16}\cdot C_2^{18}=660\cdot 120\cdot 153=12117600$

Therefore, the probability is

$P=\frac{12117600}{53524680}\\\\P=0.226$

b) We calculate the probability that are at least 2 red balls.

We calculate the probability withdrawn of 1 or none of the red balls.

We calculate the number of possible combinations:

$C_7^{46}=\frac{46!}{7!(46-7)!}=53524680$

We calculate the number of favorable combinations: for 1 red balls

$C_1^{12}\cdot C_7^{34}=12\cdot 1344904=16138848$

Therefore, the probability is

$P_1=\frac{16138848}{53524680}\\\\P_1=0.3$

We calculate the number of favorable combinations: for none red balls

$C_7^{34}=5379616$

Therefore, the probability is

$P_0=\frac{5379616}{53524680}\\\\P_0=0.1$

Therefore, the the probability that are at least 2 red balls is

$P=1-P_1-P_0\\\\P=1-0.3-0.1\\\\P=0.6$

c) We calculate the probability that are all withdrawn balls are the same color.

We calculate the number of possible combinations:

$C_7^{46}=\frac{46!}{7!(46-7)!}=53524680$

We calculate the number of favorable combinations:

$C_7^{12}+C_7^{16}+C_7^{18}=792+11440+31824=44056$

Therefore, the probability is

$P=\frac{44056}{53524680}\\\\P=0.0008$

d) We calculate the probability that are either exactly 3 red balls or exactly 3 blue balls are withdrawn.

Let X, event that exactly 3 red balls selected.

$P(X)=\frac{C_3^{12}\cdot C_4^{34}}{53524680}=0.57\\$

Let Y, event that exactly 3 blue balls selected.

$P(Y)=\frac{C_3^{16}\cdot C_4^{30}}{53524680}=0.29\\$

We have

$P(X\cap Y)=\frac{18\cdot C_3^{12} C_3^{16}}{53524680}=0.12$

Therefore, we get

$P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)\\\\P(X\cup Y)=0.57+0.29-0.12\\\\P(X\cup Y)=0.74$

8 0

3 years ago

Profit is the amount of money that remains after all expenses of a project have been paid. The year has just ended, and Ajax C

lilavasa [31]

Answer:

the Profit earned by the company is $280,489

Step-by-step explanation:

Total Cost of 5 projects awarded = $7,435,000

Cost of Project 1 = $1,245,000

Cost of Project 2 = $985,689

Cost of Project 3 = $1,723,000

Cost of Project 4 = $2,567,054

Cost of Project 5 = $633,768

We need to find the profit earned by the company.

First we need to find Total cost spent on all 5 projects.

It can be found by adding cost spent on all projects.

Total cost spent on all 5 projects = Cost of Project 1 + Cost of Project 2 + Cost of Project 3 + Cost of Project 4 + Cost of Project 5

Total cost spent on all 5 projects = $1,245,000+ $985,689 + $1,723,000+ $2,567,054 + $633,768

Total cost spent on all 5 projects = $7,154,511

Now we can calculate profit earned using formula:

Profit earned = Total Cost of 5 projects awarded - Total cost spent on all 5 projects

Profit earned = $7,435,000 - $7,154,511

Profit earned = $1,280,489

So, the Profit earned by the company is $280,489

6 0

3 years ago

If ON is a midsegment of KLM, find LM. A.2 B.3 C.4 D.5

Aleksandr-060686 [28]

NO is 2 times LM

2(x+1) = 4x

2x + 2 = 4x

2 = 2x

1 = x

Plug that in for 4x

4(1)

4

4 0

3 years ago

Read 2 more answers

2/5+1/3= What is the answer

Alex Ar [27]

Answer:

11/15 OR 0.73

Step-by-step explanation:

2/5 ---> 6/15

1/3 ---> 5/15

6/15 + 5/15 = 11/15

2/5 ---> 0.4

1/3 ---> 0.33

0.4 + 0.33 = 0.73

4 0

3 years ago

Read 2 more answers

In a number with at least two digits, the last number was removed. The resulting number was n smaller than ghe previous one.

BartSMP [9]

Answer:

The largest possible value of n is 11.

(A) is correct option.

Step-by-step explanation:

Given that,

The number with at least two digits,the last number was removed. The resulting number was n smaller than the previous one.

We need to find the largest possible value of n

Using given data,

The smallest number of two digit is 10.

Now, we removed last digit then we get 1 which is equal to 10 divided 10.

So, n = 10

But the largest number of two digit is 99.

We removed last digit then we get 9 which is equal to 99 divided 11.

So, n = 11

Hence, The largest possible value of n is 11.

(A) is correct option.

5 0

3 years ago