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bogdanovich [222]
3 years ago
15

A farmer wants to construct a rectangular pigpen so only 3 sides of the pen will need to be fenced. If the farmer has 400 ft of

fence, whats the maximum area he can enclose?
Mathematics
1 answer:
Fofino [41]3 years ago
3 0

Answer:

The answer is "\bold{100\ ft \times 200\ ft}"

Step-by-step explanation:

A = area of the pigpen 

x = its perpendicular length of the sides of the stone wall

Maximize function:

\to A = x (400-2x)\\\\Where\ \ 0

So, the size of pigpen is = 100 ft by 200 ft that is (perpendicular and parallel to wall), that's why the answer is "\bold{100\ ft \times 200\ ft}"

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15. For each of the following, write the probability as the intersection of two events. Then, indicate whether the two events ar
LuckyWell [14K]

Answer:

Step-by-step explanation:

a. The probability of selecting a 6 from the first draw and a 7 on the second draw when two balls are selected without replacement from a container with 10 balls numbered 1 to 10

Not independent because without replacement

Prob for both = \frac{1}{10} \frac{1}{9} \\=\frac{1}{90}

b. The probability of selecting a 6 on the first draw and a 7 on the second draw when two balls are selected with replacement from a container with 10 balls numbered 1 to 10

Here independent because with replacement makes probability independent.

Prob for both = P(A) *P(B) = \frac{1}{10} *\frac{1}{10} \\=\frac{1}{100}d

c. The probability that two people selected at random in a shopping mall on a very busy Saturday both have a birthday in the month of June. Assume that all 365 birthdays are equally

likely, and ignore the possibility of a February 29 leap-year birthday.

Here independent because one person birthday will not affect the other person birthday

Prob for both = (\frac{30}{365})^2\\ =\frac{25}{5329}

d. The probability that two socks selected at random from a drawer containing 10 black socks and 6 white socks will both be black

Prob for I sock black = 10/16 and II sock black if first sock is black = 9/15

Hence not independent

Prob for both = \frac{10C2}{16C2} \\=\frac{3}{8}

 

 

5 0
4 years ago
∠1, ∠2, and ∠3 form a straight line. If m∠3 is six more than twice m∠1 and m∠2 is 27 less than m∠3, find m∠2.
Anarel [89]

Answer:

m<2 = 57

Step-by-step explanation:

Since they are all in a straight line, the sum of the three angles = 180

Let m ∠3 = x

Thus;

2m<1 = x - 6

m<1 = (x-6)/2

m<2 = x-27

Adding all

x + x-27 + (x-6)/2 = 180

Multiply through by 2

2x + 2x -54 + x -6 = 360

5x -60 = 360

5x = 360 + 60

5x = 420

x = 420/5

x = 84

But m<2 = x -27

m<2 = 84 -27 = 57

5 0
4 years ago
Using the following equation, find the center and radius: x2 −2x + y2 − 6y = 26 (5 points)
Lisa [10]

Answer:

Center: (1,3)

Radius: 6

Step-by-step explanation:

Hi there!

x^2-2x + y^2 - 6y = 26

Typically, the equation of a circle would be in the form (x-h)^2+(y-k)^2=r^2 where (h,k) is the center and r is the radius.

To get the given equation x^2-2x + y^2 - 6y = 26 into this form, we must complete the square for both x and y.

<u>1) Complete the square for x</u>

Let's take a look at this part of the equation:

x^2-2x

To complete the square, we must add to the expression the square of half of 2. That would be 1² = 1:

x^2-2x+1

Great! Now, let's add this to our original equation:

x^2-2x+1+y^2-6y = 26

We cannot randomly add a 1 to just one side, so we must do the same to the right side of the equation:

x^2-2x+1+y^2-6y = 26+1\\x^2-2x+1+y^2-6y = 27

Complete the square:

(x-1)^2+y^2-6y = 27

<u>2) Complete the square for y</u>

Let's take a look at this part of the equation (x-1)^2+y^2-6y = 27:

y^2-6y

To complete the square, we must add to the expression the square of half of 6. That would be 3² = 9:

y^2-6y+9

Great! Now, back to our original equation:

(x-1)^2+y^2-6y+9= 27

Remember to add 9 on the other side as well:

(x-1)^2+y^2-6y+9= 27+9\\(x-1)^2+y^2-6y+9= 36

Complete the square:

(x-1)^2+(y-3)^2= 36

<u>3) Determine the center and the radius</u>

(x-1)^2+(y-3)^2= 36

(x-h)^2+(y-k)^2=r^2

Now, we can see that (1,3) is in the place of (h,k). 36 is also in the place of r², making 6 the radius.

I hope this helps!

3 0
3 years ago
Read 2 more answers
Mike kohl, an employee of spotswood company, has gross earnings for the month of october of $8,000. fica taxes are 7.65% of gros
boyakko [2]
Gross earning = $8,000
FICA tax = 8000*0.0765 = $612
Federal income tax = $1,270
Sate income tax = 8000*0.02 = $160
Voluntary deductions = $20

Total deductions = 612+1270+160+20 = $2,062

Net pay = 8000-2062 = $5,938
3 0
3 years ago
A room in the lower level of a cruise ship has a circular window with a diameter of 30 inches. Find the total area of the window
jeka57 [31]
A≈2827.43 i’m pretty sure
5 0
3 years ago
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