A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to separate the regions) are made up of fencing, as shown below. A rectangular area consisting of two separated regions. If the farmer has 162 feet of fencing, what are the dimensions of the region which enclose the maximal areas?

Answer:

  13.636

Step-by-step explanation:

The area can be found using Heron's formula:

  A = √(s(s-a)(s-b)(s-c))

where s=(a+b+c)/2.

For the given triangle, ...

  a=9, b=4, c=12, s=(9+4+12)/2 = 12.5

  A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636

The area of the triangle is about 13.636 square units.

Answer:

24 units\

Step-by-step explanation:

Answer:

It should be D if not Than A

Answer:

it should be D

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

Total Cards = 5

Even Numbers = 3

P(even) = 3/5

In %age:

=> 60%

Answer:

60%

Step-by-step explanation:

The numbers that are even from the list are 2, 4, and 6.

3 numbers are even out of 5 total numbers.

3/5 = 0.6

P(even) = 60%

Step-by-step explanation:

The difference between. Each numbers is 5 so, it's answer is 22 and 27

Answer:

12pi(8-pi), or

183.158 to third decimal place

Step-by-step explanation:

The geometry is indicated in the attached figure.

A. by integration

We will find the volume of the solid by the method of shells, i.e. we will integrate strips parallel to the axis of rotation to form many thin shells, then integrate to get the sum of all these shells.

For each shell, of thickness dy, we integrate strips of length located at y

L(x) = y(x)

and area

L(x)dy

Each strip is at a distance of (4-y) from

for which the volume of each shell equals

dV = 2*pi*(4-y)*L(x)dy = 2*pi*(4-y)*y(x) dy

The total volume of the solid can be obtained by integrating y from 0 to pi

integral( dV ) from 0 to pi

= integral (2*pi*(4-y)*y(x) dy) for y from 0 to pi

= 12*pi(-sin(y)+y*cos(y)-4*cos(y)) for y from 0 to pi

=12(8-pi)*pi

= 183.158

B. Using Pappus theorem

Pappus theorem simplifies the calculation of volume of revolution by multiplying the area of the rotating region by 2pi times the distance between the centroid and the rotation axis.

Here the area of the figure is A=2*6=12, (2 is the area under the sine curve from 0 to pi), or

A = integral (6sin(x))dx, x from 0 to pi

= 6 cos(x), x from 0 to pi

= 6(1- (-1))

= 12

Distance from centroid to axis of rotation = (4-pi/2)

Volume = 2*pi*A*(4-pi/2) = 2*pi*12*(4-pi/2)

= 12pi(8-pi)

=183.158    as before

Answer:

solution,

[tex] \frac{ac}{ef} = \frac{cb}{fd} \\ or \: \: \frac{12}{y} = \frac{15}{5} \\ or \: 15 \times y = 12 \times 5( \: cross \: multiplication) \\ or \: 15y = 60 \\ or \: y = \frac{60}{15} \\ y = 4[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

The value of y is 4

Step-by-step explanation:

What is similarity ?

In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given,

ΔACB~ΔEFD

The proportional sides are equal.

[tex]\frac{AC}{EF}=\frac{CB}{FD}=\frac{AB}{DE} \\\frac{12}{y}=\frac{15}{5} \\y=12*\frac{5}{15}\\\\ y=4[/tex]

To know more about similarity, similar here

https://brainly.com/question/25087910

#SPJ2

Answer:

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

here is where stephen makes the mistake, he uses the 4 in the rooth and the 3 in the power.

so the expression actually is:

∛(16)/e

Answer: 30 folders - 15 folders which she keeps = 15 folders; 15 folders / 3 friends = 5 folders per firend.

Step-by-step explanation:

Answer:

x= (30 -15)/3

Step-by-step explanation:

If we call x the number each friend gets, then the equation is:

Solving this we get:

Each friend gets 5 folders

Answer:

[tex] |w-0.3| \leq 0.0003[/tex]

And solving we got:

[tex] -0.0003 \leq w-0.3 \leq 0.0003[/tex]

[tex]0.3-0.0003 \leq w \leq 0.3+0.0003[/tex]

[tex] 0.2997 \leq w \leq 0.3003[/tex]

Step-by-step explanation:

For this case we can define the following notation:

[tex] W[/tex] represent the width

And we want a maximum error of 0.0003 so we can set up the following equation:

[tex] |w-0.3| \leq 0.0003[/tex]

And solving we got:

[tex] -0.0003 \leq w-0.3 \leq 0.0003[/tex]

[tex]0.3-0.0003 \leq w \leq 0.3+0.0003[/tex]

[tex] 0.2997 \leq w \leq 0.3003[/tex]

Answer:

B. y = 3x + 4

Step-by-step explanation:

Step 1: Find slope-intercept form of 1st equation

2y = 6x + 4

2y/2 = 6x/2 + 4/2

y = 3x + 2

A parallel line has the same slope but different y-intercept:

y = -3x + 3 (No, different slope)

y = 3x + 4 (Yes, same slope, different y-int)

y = x + 3 (No, different slope)

y = -2x - 3 (No, different slope)

y = 1/2x + 3 (No, different slope)

Answer:

Area = 7 square units

Perimeter = 14 units

Step-by-step explanation:

The shape is made up of 7 identical squares and, we are told the side length of each square is 1 unit.

==>Find area of the shape by calculating the area of 1 square, then multiply by the number of square used in the construction.

Thus, area of 1 square = s² = 1² = 1 square units.

Area of shape = 7 × 1 square units = 7 square units

==>Find the Perimeter of the shape by adding all the lengths of the boundary formed by the square to make up the shape.

(Check attachment to understand how we got the measurement of the boundary)

The perimeter = 1 + 1 + 1 + ½ + ½ + 1 + 1 + 1½ + ½ + 1 + 1 + 4 = 14 units

Answer:

The equation in point slope form is [tex]y - 47\,in = \left(-3\,\frac{in}{h}\right)\cdot (t-0\,h)[/tex]

Step-by-step explanation:

Since the swimming pool is being drained at a constant rate, the equation of the process must be a first-order polynomial (linear function), where depth of water decrease as time goes by. The form of the expression is:

[tex]y = m \cdot t + b[/tex]

Where:

[tex]t[/tex] - Time, measured in hours.

[tex]b[/tex] - Initial depth of the water in swimming pool (slope), measured in inches.

[tex]m[/tex] - Draining rate, measured in inches per hour.

[tex]y[/tex] - Current depth of the water in swimming pool (x-Intercept), measured in inches.

If [tex]m = -3\,\frac{in}{h}[/tex] and [tex]y (5\,h) = 32\,in[/tex], the initial depth of the water in swimming pool is:

[tex]b = y - m\cdot t[/tex]

[tex]b = 32\,in -\left(-3\,\frac{in}{h} \right)\cdot (5\,h)[/tex]

[tex]b = 47\,in[/tex]

The equation in point slope form is:

[tex]y-y_{o} = m \cdot (t-t_{o})[/tex]

Where [tex]y_{o}[/tex] and [tex]t_{o}[/tex] are initial depth of the water in swimming pool and initial time, respectively. Then, the equation in point slope form is:

[tex]y - 47\,in = \left(-3\,\frac{in}{h}\right)\cdot (t-0\,h)[/tex]

Answer:

[tex] 4x-12= 16 +8x[/tex]

And we can subtract 4x in both sides and we got:

[tex] -12 = 16 +4x[/tex]

Now we can subtract in both sides 16 and we got:

[tex] -28 = 4x[/tex]

And if we divide both sides by 4 we got:

[tex] x = -7[/tex]

And the best solution would be:

-7

Step-by-step explanation:

For this case we assume the following equation:

[tex] 4x-12= 16 +8x[/tex]

And we can subtract 4x in both sides and we got:

[tex] -12 = 16 +4x[/tex]

Now we can subtract in both sides 16 and we got:

[tex] -28 = 4x[/tex]

And if we divide both sides by 4 we got:

[tex] x = -7[/tex]

And the best solution would be:

-7

Answer:

1. Red red blue blue

2. Red blue red blue

Step-by-step explanation:

A 50 percent chance

Answer:

option 1 both statements are true

Step-by-step explanation:

Prove by PMI -- Principle of Mathematical  Induction

1) n³ + 2n

n= 1 , 1³ +2*1 = 1+2 = 3 = 3*1   ---->divisible by 3

n = 2 ; 2³ + 2*2 = 8+4 = 12  = 3*4  ----> is divisible by 3

Assume that It is valid for n = k ;  

[tex]k^{3}+2k[/tex] = 3*m -----(I) , for all m ∈ N

We have to prove for n =k +1 , the statement is true.

n = k+1, [tex](k+1)^{3}+2(k +1) =k^{3}+3k^{2}+3k +1 +2k +2[/tex]

                                           = k³ + 3k² + 3k + 3 + 2k

                                           =  k³ +  2k + 3k² + 3k + 3

                                           = 3m + 3 (k² + k + 1)

                                          = 3(3 + [k² + k + 1] ) is divisible by 3

Therefore, this statement is true

2) [tex]5^{2n}-1\\[/tex]

[tex]n=1 ; 5^{2}-1 = 25 -1 = 24 divisible by 24\\\\n = 2 ; 5^{2*2}-1 = 5^{4}-1 = 625 - 1 = 624 divisible by 24[/tex]

This statement is also true

Answer: Area is 1840units²

Step-by-step explanation:

From the given information,

Firstly, area of a rectangle is given as

A = l × b ie, length multiply by the breadth.

One of the side of the rectangle is known , AD = 16 , now to calculate the other side, we need some calculations.Since FE = 23 and

FD = DE ,,therefore,

DE = 23/2.

From the information, DE = 1/10 of DC. We now find DC the required side for finding the area of the rectangle by simple equation. Since DE = 23/2 , the equation now looks like this to get DC

23/2 = DC/10. Now , solving this

2DC = 23 × 10

2DC = 230

DC = 230/2

= 115.

Now the area of the rectangle will be

A = 16 × 115

= 1840units²

Answer:

The answer is explained below

Step-by-step explanation:

What use are statistics if there is no engineer to use them? In other words, a statistician corrects, improves, reinforces, and supports an engineer in building / designing / developing a new product and / or improving an existing product.

The statistician provides a special kind of vision through which I see the same problem in a completely different vision. So you can see the strengths, weaknesses of my product and the promise of improvements that can be made.

Each class of statistics is essential for a student to see and understand a problem in a whole new way where it is much easier to understand information.

Answer:

BG is always perpendicular to GF. The measure of angle BGF is always 90 degree

Step-by-step explanation:

Answer:

is always perpendicular to . The measure of  is always 90°.

Step-by-step explanation:

Plato Awnser

Answer:

Yes

Step-by-step explanation:

b is as in 1b so. . .

2 + 1 = 3

We can plug in b or as "b"

2b + b = 3b

So yes in whatever case 2b + b's value  will always equal 3b's value

Answer:

yes

Step-by-step explanation:

because you can use any number to put for B and they will have the same value as an example we will use 3 for b so 2b = 6 + b = 9 and 3b = 9

Answer:

It might be 4 * [tex]7^{1/2}[/tex] * [tex]x^{3}[/tex]

Answer:

see below

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

  = 4/3 pi ( 7)^3

  = 1372/3 pi in^3

Using 3.14 for pi

V =1436.0266666 in^3

Using the pi button

1436.75504 in^3

Answer:

B. No; the graph fails the vertical line test.

Step-by-step explanation:

If you hold a pencil up to the graph, the parabola would technically touch the pencil at more than one point. That means it failed the test, and therefore it is not a function.

hope this helped :)

Answer:

30 ways

Step-by-step explanation:

Given the following :

Number of boys in school (n1) = 5

Number of girls in school (n2) = 3

Total number of team members to be selected = 4

Number of boys required in team(r1) = 2

Number of girls required in team(r2) = 2

How many different teams made up of two girls and two boys could be chosen?

= (2 boys from 5) * (2 girls from 3)

Using combination :

5C2 * 3C2

Recall :

nCr = n! ÷ (n-r)! r!

5C2 = 5! ÷ (5-2)! 2!

5C2 = 5! ÷ 3!2!

5C2 = (5*4) / 2 * 1 = 10ways

3C2 = 3! ÷ (3-2)! 2!

3C2 = 3! ÷ 1!2!

3C2 = (3) /  1 = 3ways

3C2 = 3/1 = 3ways

10 * 3 = 30 ways

Answer:

0.9 (9/10)

Step-by-step explanation:

(see picture)

Answer:

P-value =0.062

At a signficance level of 0.05, there is not enough evidence to support the claim that the unemployment rate is less than 5%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the unemployment rate is less than 5%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]

The significance level is 0.05.

The sample has a size n=1500.

The sample proportion is p=0.041.

[tex]p=X/n=61/1500=0.041[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1500}}\\\\\\ \sigma_p=\sqrt{0.000032}=0.0056[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.041-0.05+0.5/1500}{0.0056}=\dfrac{-0.0087}{0.0056}=-1.5401[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.5401)=0.062[/tex]

As the P-value (0.062) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the unemployment rate is less than 5%.

Answer:

Step-by-step explanation:

When you have several evaluations to do, it is often convenient to put the formula into a graphing calculator or spreadsheet.

__

If you must evaluate a polynomial by hand, it is often easier if the expression is written in "Horner form":

  g(x) = (-2x +3)x -5

Then we have ...

  g(-2) = (-2(-2) +3)(-2) -5 = 7(-2) -5 = -19

  g(0) = (-2(0) +3)(0) -5 = -5

  g(3) = (-2(3) +3)(3) -5 = (-3)(3) -5 = -14

Answer:

0

Step-by-step explanation:

√12 can be rewritten as √2²·3 = 2√3

√75 can be rewritten as √5²·3 = 5√3

2/5 * 5 = 2

so

2√3 - 2/5 * 5√3 = 2√3 - 2√3 = 0

Answer:

0

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

The non-even numbers are 1, 3, and 5 on the dice.

3 numbers out of 6.

3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

Total sides of 6-sided die = 6

Numbers not even = 3

Probability of not getting an even = 3/6

=> 1/2

120N

f= mgh

=o. 6x10x20

= 120N

Step-by-step explanation:

given,

mass ( m)=0.6kg

gravity=9.8 m/s^2

by the formula of force,

f= ma

=0.6×9.8

therefore force is 5.88 n.