A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 86m long and 64m wide. Find the area of the training field. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.

Step-by-step explanation:

If you agree that increasing age (for elementary school children) causes increasing foot size, and therefore increasing shoe size, then you expect a correlation between age and shoe size. Correlation is symmetric, so shoe size and age are correlated.

To solve this problem, we have to find the net displacement and the net force and the multiply the dot product together and get the work done.

The work done on moving the object is 27ft*lbs

To find the work done on this object, let's find the net force on the object.

Data;

The unit vector of the force is

[tex]\sqrt{4^2 +(-2)^2} =\sqrt{16 + 4} = \sqrt{20}[/tex]

[tex]\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} }[/tex]

The net force acting on the object is

[tex]F = 4(\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} })\\F= (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } )[/tex]

The displacement on the object is 7ft through (0,4) to (5, -1)

The unit vector on displacement is

[tex]\sqrt{5^2 + (-1-4)^2} = \sqrt{25+25} = \sqrt{50}[/tex]

[tex]\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }[/tex]

The net displacement will be

[tex]7(\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }) = \frac{35}{\sqrt{50} }, \frac{-35}{50}[/tex]

The work done will be F.d

[tex]w = f. d \\[/tex]

[tex]w = (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } ) * \frac{35}{\sqrt{50} }, \frac{-35}{50}\\w = 17.71+ 8.854\\w = 26.567 = 27ft*lbs[/tex]

The work done on moving the object is 27ft*lbs

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Answer: the answer is B 27ft

Step-by-step explanation: its cam btw

Answer:

42

Step-by-step explanation:

You turn the percentage into a decimal, 25%=0.25

then you multiply 0.25 to 168

Then you get 42

0.25 x 168 = 42

Hope this helps <3

Answer:

there are 50 orange balls

Step-by-step explanation:

let green balls be x

orange balls be y

green balls = orange balls + 10

x = y+10

orange balls + green balls = 110

x + y = 10

y + 10 + y = 110

2y + 10 = 110

2y = 110 -10

2y = 100

y = 50

thus there 50 orange balls

Answer:

B

Step-by-step explanation:

add 8 to both sides and multiply both y and 8 by 4 to get 4y and 32

The null hypothesis is that the observed difference is due to chance alone in a research.

Your information is incomplete. Therefore, an overview of a hypothesis will be given. A null hypothesis is a hypothesis that states that there is no relationship between two population parameters.

It should be noted that researchers reject or disprove the null hypothesis to set the stage for further experimentation or research that explains the position of interest.

The null hypothesis: H0 is the complement of the alternative hypothesis. Type I error is when we reject the null hypothesis when it is correct.

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Answer: 2,3

Step-by-step explanation: I think this is the right answer. Have a good day!! :)

Answer:

  (d)  944 mm³

Step-by-step explanation:

The volume of a prism is given by the formula ...

  V = Bh

where B is the area of the base, and h is the distance between bases.

__

Here, the base of the prism is a rectangle with a semicircle on top. The circle has a diameter of 9 mm, so a radius of 4.5 mm. The area of the semicircle is ...

  A = 1/2πr² = 1/2π(4.5 mm)² ≈ 31.809 mm²

The area of the rectangle is the product of its length and width.

  A = LW = (9 mm)(6 mm) = 54 mm²

So, the total base area is ...

  31.809 mm² +54 mm² = 85.809 mm²

The prism volume is this area multiplied by the length of the figure:

  V = Bh = (85.809 mm²)(11 mm) ≈ 944 mm³

The volume of the figure is about 944 mm³.

Step-by-step explanation:

[tex]2 {}^{2} \times 2 {}^{3} \times 2 {}^{1} \times 3 {}^{ - 1} {}^{ (- 2)} [/tex]

[tex]2 {}^{6} 3 {}^{2} [/tex]

The cardinal number of the given sets are:

As a general rule, the cardinal number of a set is the number of distinct elements in the set

Using the above definition the cardinal number of the given sets are:

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Answer:

8

Step-by-step explanation:

5 + 3 = 8

Answer:

20.11 °

Step-by-step explanation:

31.1 ° + 35.8 ° + 90m + 44.2 ° = 20.11 °

Step-by-step explanation:

by using the formula of principal

p= I×100/T×R

Answer:

90

Step-by-step explanation:

PRT/100

75×30×2/100

9000/100

=90

Answer:

See below

Step-by-step explanation:

(36 - 2x) * (17-2x) = 700      I think, given the info

4x^2 - 106x + 612 = 700     expanded....

Answer:

I do not know. sorry I couldn't help

Answer:

x = 125º

Step-by-step explanation:

Angles in a triangle add to 180º so:

180 - 42 - 83 = 180 - 125 = 55º

Angles on a straight line also add to 180º so to find x:

180 - 55 = 125º

x = 125º

Hope this helps.

The exterior angle theorem states that one exterior angle of a triangle will always be equal to the sum of the two opposite interior angles.

x is an exterior angle of the triangle.

We are given two interior angles in the triangle. These are opposite of x.

According to the exterior angle theorem, we can solve for x by adding these two angles:

x = 125

Answer:

(x-2)^2-2

Step-by-step explanation:

x^2-4x+2

take the x out

x(x-4) + 2

(x-2)^2-2

because (x-2)^2 is

x^2-4x+4

its like completing the square

Answer:

(x-2)² -2

Step-by-step explanation:

Consider that (a+b)² = a²+2ab+b²

To find the form (x-A)²+B compare  x²-4x+2 with a²+2ab+b²

x² - 4x +2

a² + 2 a b+ b², so a= x and b = (-2)

x²+ 2· x ·(-2)+ (-2)² -  2  = (x-2)² -2 is in the form (x-A)²+B

Check our answer:

(x-2)² -2= (x²-2·2x+4)-2 = x²-4x +2 ✅

Answer:

People with MERS may experience a fever, cough, or shortness of breath. They may also experience chess pain, fatigue, chills, loss of appetite, body aches, diarrhea, nausea, vomiting, congestion, sneezing, headaches, or a sore throat.

Step-by-step explanation:

A population about which we want to get some information is called the sample.

This is a portion of a population that is known to contain several parts of the population. The information that is gotten from the sample would be used to draw conclusion about the entire information.

Therefore from the definition above the answer to the question is the population sample.

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Answer:

Looking at the question, we are given two points and we need to determine the line that passes through both of these points.  The first step to solving this problem is to find the slope.

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]slope=\frac{8-2}{2-(-1)}[/tex]

[tex]slope=\frac{6}{2+1}[/tex]

[tex]slope=\frac{6}{3}[/tex]

[tex]slope=2[/tex]

Now that we found the slope, we can move onto the next part which is to use the point-slope formula to determine our correct straight line.

[tex](y-y_1)=m(x-x_1)[/tex]

[tex](y-2)=2(x-(-1))[/tex]

[tex]y-2=2(x+1)[/tex]

[tex]y-2=2x + 2[/tex]

[tex]y- 2 + 2=2x + 2 + 2[/tex]

[tex]y=2x + 4[/tex]

Therefore, our straight line that passes through the two points that were provided in the problem is [tex]y=2x + 4[/tex].

Hope this helps!  Let me know if you have any questions

Answer:

A fruit seller buys some oranges and by selling 40% of them he realizes the cost price of all the oranges. As the oranges being to grow over-ripe, he reduces the price and sells 80% of the remaining oranges at half the previous rate of profit.

Step-by-step explanation:

Answer:

68

Explanation:

Sets of equations:

1) a + b = 10

2) a - b = 6

Make 'a' the subject:

1) a = 10 - b --- equation 1

2) a = 6 + b --- equation 2

Solve them by substituting:

⇒ 10 - b = 6 + b

⇒ -b - b = 6 - 10

⇒ -2b = -4

⇒ b = 2

Find value of 'a', a = 10 - b, a = 10 - 2 = 8

Then find (a²+b²), by inserting a = 8, b = 2,

⇒ ((8)²+(2)²) = 64 + 4 = 68

Step-by-step explanation:

given,

a+b=10.............( eqn 1)

a-b=6................(eqn 2)

adding eqn1 and eqn2

a+b=10

a-b=6

______

2a=16

a=16/2

a=8

putting the value of a in eqn 1

a+b=10

8+b=10

b=10-8

b=2

now,

(a²+b²)= 64+4=68

Answer:

5×5=25

8×5÷2=20

25+20= 45

area of a composite 45

Step-by-step explanation:

x = capacity of Marshfield

y = capacity of Browden

x + y = 210,355

x = y + 4,465

so, using the second equation in the first

(y + 4,465) + y = 210,355

2y + 4,465 = 210,355

2y = 205,890

y = 102,945 (Browden)

x = y + 4,465 = 102,945 + 4,465 = 107,410 (Marshfield)

Answer:

Step-by-step explanation: