Convert the function from factored form to standard form by multiplying:

Answer: [tex]5027.2\ ft^2[/tex]

Step-by-step explanation:

Given

The radius of the circle is [tex]r=40\ ft[/tex]

The area of the circle is given by [tex]\pi r^2[/tex]

Insert the value of radius and get the area to play

[tex]\Rightarrow \text{Area A=}\pi \times 40^2\\\\\Rightarrow A=3.142\times 1600\Rightarrow A=5027.2\ ft^2[/tex]

Thus, the area to play is [tex]5027.2\ ft^2[/tex]

Problem 1

Answers:

It costs 1.72 dollars to send a letter that is 1.5 ounces

It costs 1.72 dollars   to send a letter that is 2 ounces

In short, both answers are  1.72 dollars

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Explanation:

The piecewise function may seem really ugly and complicated, and I can understand why many don't like them, but they aren't too bad once you get used to it.

A piecewise function is simply a collection of many functions glued together. Instead of listing four different functions, your teacher has combined them all into one super function of sorts.

Here are the rules for this function

As you can see, the definition of F(w) will change depending on what w is.

If the weight is w = 1.5 ounces, then we're on the interval [tex]1 < w \le 2[/tex] since 1.5 is between 1 and 2. So we go for the second definition shown above and we conclude that it will cost $1.72 to send this 1.5 ounce letter.

If you wanted, you could rewrite those four bulleted points into this equivalent form

which is a less mathematical way of stating it. It might also help to make it into a chart, which would help customers better who may not want to deal with math.

A letter that's 2 ounces will cost $1.72 as well since w = 2 makes [tex]1 < w \le 2[/tex] true.

In short, both the 1.5 ounce and 2 ounce letters cost $1.72 each.

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Problem 2

Answer: The graph is shown below (attached image)

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Explanation:

We have what is called a step function, or a staircase function. Either name will work. The graph consists of the horizontal portion of the stairs, but the vertical parts of the stairs are not drawn (or else we wouldn't have a function due to the vertical line test).

Note the placement of the open and closed endpoints. An open endpoint excludes the value in question, while a closed endpoint includes the value.

For instance, we have an open endpoint at (1, 1.72) while there's a closed endpoint at (1, 1.15). Each closed endpoint is directly connected to the "or equal to" portion of the inequality sign, and each open endpoint does not have the "or equal to" portion.

As the graph shows, we basically have the a certain flat cost for the four different regions. This corresponds to the costs given in the piecewise function. Each height is drawn from the list {1.15, 1.72, 2.29, 2.86}

The point labels of A,B,C,D,E,F,G,H are optional. I only put them in there to help identify which endpoints are open or closed. Points on the left side of each segment, or horizontal stair component, are open endpoints. Points on the right side are closed endpoints.

Answer:

Step-by-step explanation:

640

Answer:

200 pounds

Step-by-step explanation:

We can write a proportion to represent the problem. Let's take x as the weight of 5 televisions. If we know that 4 televisions weigh 160 pounds we can write: 4/160. Then, 5 televisions will weigh x pounds which is 5/x. Now, we can set up a proportion: 4/160 = 5/x

Cross multiply to get: 4x = 800

Isolate x: x = 800/4

Solve: x = 200

200 pounds

Answer:

The data provide sufficient evidence to indicate a difference in the mean stopping distances of the two types of automobiles

Step-by-step explanation:

Formulate the null and alternate hypothesis as

H0: u1= u2  against the claim Ha: u1≠ u2

The data given is

y`1=118,    y`2=109     s21=102,   s22=87

The test statistic used is t= y1`- y2`/ Sp√1/n1+ 1/n2

n1= n2= 64

And

Sp² = (n1-1) s12 + (n2-1) s22 / n1+n2-2

Sp² = 63*102+6*87/64+64-2

Sp² = 94.5

Sp= 9.7211

Putting the values in the test statistic

t= 118-108/9.7211√1/64+1/64

t= 5.237

Now finding the value of t at ∝=0.01 for two tailed test

t( 126,0.005)= ±2.6154

At alpha= 0.01  the null hypothesis is rejected.

Now finding the value of t at ∝=0.05 for two tailed test

t( 126,0.025)= ±1.979

Even at alpha= 0.05 the null hypothesis is rejected.

Also at alpha= 0.05 the null hypothesis is rejected because the critical value is  ±1.657

Hence it is concluded that the data provide sufficient evidence to indicate a difference in the mean stopping distances of the two types of automobiles

Answer:

494.16 units²

Step-by-step explanation:

Total surface area of the solid = 4(area of a triangular face) + area of the square base

Area of a triangular face = ½*b*h

b = x = 11.6

h = z = 15.5

Area = ½*11.6*15.5 = 89.9 units²

Area of the four triangular faces = 4(89.9) = 359.6 units²

Area of the square base = s²

s = x = 11.6

Area = 11.6²

Area = 134.56 units²

✔️Total surface area of the solid = 359.6 + 134.56 = 494.16 units²

Answer: 1 is a quadrilateral. I’m very sorry I don’t know the second shape.

Step-by-step explanation: a quadrilateral has 4 sides and two triangles.

9514 1404 393

Answer:

  about 15 or 16 items

Step-by-step explanation:

The break-even point is where revenue is equal to cost.

  150x = 7x +2200

  143x = 2200 . . . . . . . subtract 7x

  x ≈ 15.38 . . . . . . . . . . divide by 143 (multiply by the inverse of 143)

__

When 15 items are sold, revenue doesn't quite cover costs. Costs still exceed revenue by 55. When 16 items are sold, revenue exceeds costs by 95. (I would call this the break-even point, because I prefer a slight profit over a slight loss.)

Answer:

B. cos 46°

Step-by-step explanation:

I calculated it logically

Answer:

b. cos 46

Step-by-step explanation:

There are three angles to choose from since there are three angles in a triangle. Of these, the 90° angle can't be used (90° angles don't work with trigonometric ratios), and neither can the 44° (we're told to use a different one from this), so we're left with the unmarked angle on the bottom right. Since the angles in a triangle add to 180, and the other two angles total 134 (90+44=134), we can say this angle is 46°.

Since cos46 is our only option that involves this angle (and since cos46=x/9), this is the option which could be used to find x.

Answer:

24

Step-by-step explanation:

sorry if incorrect

Answer:

b. The fitted regression line is approximately Y = 82.42(runtime)

Step-by-step explanation:

The regression line is Y=  aX + b

here b= 82.42   a = -3.31

Hence the regression equation is

Y= 82.42- 3.31 X

where x is the runtime and the slope  is given by b.

Option  a is correct because from the above equation we see that for every additional minute it takes to run the 1500 m the estimated oxygen consumption rate decreases by 3.31.

Option b is incorrect because the runtime is not given by Y it is given by X.

Option C is correct  as  

Y= 82.42-3.31*10

Y= 82.42-33.1

Y= 49.32  almost 50

Option d is also correct that the equation line shows a relationship between oxygen consumption and the run time.

Option e is also correct because the slope is given by b and b= 82.42

Answer:

x = 50°

x = 70°

Step-by-step explanation:

A right angle is indicated by a small box.

The angles shown are right angles = 90° each. Therefore:

✔️x + 40° = 90°

Subtract 40° from each side

x = 90° - 40°

x = 50°

✔️x + 20° = 90°

Subtract 20° from each side

x = 90° - 20°

x = 70°

the answer is that you get the same outcome

Answer:

Step-by-step explanation:

d

Answers:

1. 24 cans/lb x 15,000 lb/trailer = 360,000 cans/trailer

2. Answer will depend on your price per can or per pound. For example, if price is 60 cents per pound: $0.60/lb x 15,000 lb = $9,000

3. 15,000 lbs/trailer / 30 lbs/collector = 500 can collectors/trailer

4. 15,000 lbs/trailer / 800 lbs/bale = 18 complete bales (and 3/4 of another bale)/trailer

5. 24 cans/lb x 800 lb/bale = 19,200 cans / bale

6. 100 bales/boxcar x 800 lbs/bale = 80,000 lb. cans / boxcar

7. 100 bales/boxcar x 19,200 cans/bale = 1,920,000 cans / boxcar

8. Answer will depend on your price per can or per pound. For example, if price is 60 cents per pound: $0.60/lb x 80,000 lb/boxcar = $48,000/boxcar

Pick the right one.

Answer:

A. 16

Step-by-step explanation:

Answer:

I believe the answer is A

Answer:

A is your answer I think

Step-by-step explanation:

maybe wait for someone else to answer as well haha

Answer:

2/5 times 30 equals 12.

Answer:Step-by-step explanation:

Answer:

3.5 or 3[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

First, subtract. 347.50 - 225.00 = 122.50

Then, divide. 122.50 ÷ 35 = 3.5

Next, you can turn the decimal into a fraction 3[tex]\frac{1}{2}[/tex]

Lastly, have a wonderful day! :)

Answer:

The statement "[tex]\angle BAF[/tex] and [tex]\angle EAB[/tex] are complimentary" is false.

Step-by-step explanation:

Complimentary angles are defined by angles that add up to [tex]90^{\circ}[/tex]. Angles BAF and EAB represent one side of a line, which is [tex]180^{\circ}[/tex]. Therefore, they are actually supplementary and not complimentary. Thus, the statement "[tex]\angle BAF[/tex] and [tex]\angle EAB[/tex] are complimentary" is false.

Answer:

Answer:

(SEE ATTACHED PICTURE)

Step-by-step explanation:

You put a circle above the number used in the inequality.

The circle is closed if the inequality is greater than or equal to, or less than or equal to. This indicates that the number is included.

The circle is open if the inequality is greater than, or less than. This indicates that the number is not included.

The arrow goes to the left if it is less than, and to the right if it is greater than.

So, for your problem, an open circle goes about the number 4 and points left.

Answer:

17x+44+51 = 180

x=5

Step-by-step explanation:

The angles in a triangle add to 180, so set up the equation by adding the measures of each angle on one side and putting 180 on the other side, then solve:

17x+44+51 = 180

17x+95=180

17x=85

x=85/17=5

Hope this helps :)

Answer:

hi

Step-by-step explanation:

you should eat more sushi because it will help you digest food better! just letting you know to help you and make you feel healthy!

xoxo

let h= 3, k=-2

radius (r) = 11 ,then

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

(x-3)^2 + ( y+2)^2 = 11^2

x^2 -6x +9 + y^2 +4y +4 = 121

x^2 + y^2 - 6x +4y -108 = 0 is the required eq

Answer:

Step-by-step explanation:

we know ∠K is 90° by Thales theorem

then

180 = 90 + 4x-1 + 4x -5

96 = 8x

12 = x

x = 12

∠JLk = 4(12)-1

∠JLk = 47°