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andriy [413]
3 years ago
8

Cal is creating a circular garden for his yard. The radius of the garden is 15 feet. He wants to put fencing around the garden t

hat costs $3.54 per foot. How much will the fencing cost? Explain your steps.
Mathematics
1 answer:
notsponge [240]3 years ago
7 0

Answer:

The fence will cost $333.64

Step-by-step explanation:

In order to calculate how much it'll cost to build the fence around his garden we first need to know the length of material he'll need to buy. To do that we must find the length of the circle that surrounds the garden and then multiply by the price of each foot. The length of the circle is given by:

length = 2*pi*r

length = 2*pi*15

length = 30*pi

length = 94.25 feet

The cost of the fence, is:

cost = length*(cost per foot) = 94.25*3.54

cost = 333.64

The fence will cost $333.64

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Find the regression equation, letting the first variable be the
Sonbull [250]

Answer:

y=0.00673(253) +90.190=91.894

And the difference is given by:

r_i =91.894-83=8.894

Step-by-step explanation

We assume that th data is this one:

x: 242-255 -227-251-262-207-140

y: 91- 81 -91 - 92 - 102 - 94 - 91

Find the least-squares line appropriate for this data.  

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i =242+255+227+251+262+207+140=1584

\sum_{i=1}^n y_i =91+ 81 +91 + 92 + 102 + 94 + 91=642

\sum_{i=1}^n x^2_i =242^2 +255 ^2 +227^2 +251^2 +262^2 +207^2 +140^2=369212

\sum_{i=1}^n y^2_i =91^2 + 81 ^2 +91 ^2 + 92 ^2 + 102 ^2 + 94 ^2 + 91^2=59108

\sum_{i=1}^n x_i y_i =242*91 +255*81 +227*91 +251*92 +262*102 +207*94 +140*91=145348

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=369212-\frac{1584^2}{7}=10775.429

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=145348-\frac{1584*642}{7}=72.571

And the slope would be:

m=\frac{72.571}{10775.429}=0.00673

Now we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{1584}{7}=226.286

\bar y= \frac{\sum y_i}{n}=\frac{642}{7}=91.714

And we can find the intercept using this:

b=\bar y -m \bar x=91.714-(0.00673*226.286)=90.190

So the line would be given by:

y=0.00673 x +90.190

The prediction for 253 seconds is:

y=0.00673(253) +90.190=91.894

And the difference is given by:

r_i =91.894-83=8.894

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When 144 is squared, it is equal to 12.
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3 years ago
A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire
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Answer:

If length of the field is 30 ft, then width is 120 ft.

If the  length of the field is 60 ft, then width is 60 ft.

Step-by-step explanation:

Let us assume the length of the rectangular park = L ft

Let us assume the breadth of the rectangular park = B  ft

Now, AREA of the given park =  L x B

⇒ L x B  = 3,600 sq ft   ... (1)

Also, the perimeter of three sides  = 180 ft

⇒ 2 L +  B  = 180  ..... (2)

Now, from (1) and (2), we get:

L x B  = 3,600

2 L +  B  = 180   ⇒ B  = 180 - 2 L

Substitute this in(1) , we get:

L x B  = 3,600   ⇒ L x (180 - 2 L)  = 3600

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⇒ L = 30 or L  = 60

So, if L  = 30  ft , then B = 180 - 2L  =  180 - 60 = 120 ft

So, if L  = 60  ft , then B = 180 - 2L  =  180 - 120 = 60 ft

So, if length of the field is 30 ft, then width is 120 ft.

And if the  length of the field is 60 ft, then width is 60 ft.

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The experimental probability of rolling a 6 is the number of 6s divided by the number of rolls.
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