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Mademuasel [1]
3 years ago
13

A playground is in the shape of a square with each side equal to 109 yards. It has skating rinks in the shape of the quadrants o

f a circle at each corner. If the area of the remaining field is 9055, find the radius of each skating rink. Also, find the cost of cementing the skating rinks at $2.50 per square yards. Use
Mathematics
1 answer:
I am Lyosha [343]3 years ago
6 0

Answer:

radius = 30 yd , cost of cement = $7065

Step-by-step explanation:

First we will find the area of the circular sectors. From that we can find the cost of cement and their radius.

The area of the playground is ...

playground area = (109 yd)^2 = 11,881 yd^2

Then the area of the skating rinks is:

rink area = playground area - remaining field

rink area = 11,881 yd^2 - 9,055 yd^2 = 2,826 yd^2

Then the cost of cement for the rink area is ...

(2826 yd^2)($2.50 yd^2) = $7065

The four quarter-circle skating rinks add to a total area of a full circle. That area is given by ...

A = πr^2

Put the values in the formula:

2826 = 3.14r^2

Divide both sides by 3.14

900 = r^2

By taking square root at both sides we get,

30 = r

The radius of each quadrant is 30 yards....

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The sum of all three numbers is 12. The sum of twice the first number, 4 times the second number, and 5 times the third number i
DaniilM [7]

Answer:

The numbers are 7, 4 and 1

Step-by-step explanation:

Let the numbers =x, y, z.

The sum of all three numbers is 12, x+y+z=12--------i

The sum of twice the first number, 4 times the second number, and 5 times the third number is 35, 2x+4y+5z=35-------ii

The difference between 8 times the first number and the second number is 52, 8x-y=52---------iii

Now, from (i),z =1-x-y--------iv

substitute (iv) in (ii),

2x+4y+5(12-x-y)=35

2x+4y+60-5x-5y=35

collect like terms

-3x-y=-25

that is, 3x-y=25--------v

solving (iii) and (v) simultaneously (add iii and v), we have

11x=77

divide both sides by 11 to obtain x=7

Put x=7 in (v)

3(7)+y=25

21+y=25

implies y=25-21=4

put x=7 and y=4 in (iv)

z=12-7-4=1

Hence, the numbers are 7, 4 and 1.

4 0
2 years ago
3x=15-6y in slope intercept form
sdas [7]

Answer:  y= -1/2x + 5/2

Step-by-step explanation:

3x = 15 -6y

+6y       + 6y

3x +6y =15

-3x           -3x

6y= 15-3x   divide both sides by 6

y= 15/6 - 3/6x

in slope intercept form us y= -3/6x + 15/6  in simplest form is y= -1/2x + 5/2

3 0
3 years ago
Suppose you want to study the relationship between smoking and cancer. You assume that smoking is a cause of cancer. Studies hav
finlep [7]

Answer:

The correct answer is:

In the above example cancer is an independent variable. (b)

Step-by-step explanation:

In order to explain the choice made, let m first explain what independent and  dependent variables are:

Independent variable: An independent variable is a variable that is under the direct control of the experimenter, and can be changed at will. In this example, the number of cigarettes or amount of tobacco smoked is the independent variable because it can be manipulated at will, to determine the outcome of the dependent variable.

Dependent variable: A dependent variable is a variable that the experimenter sets out to study. The independent variable is not under the direct manipulation of the experimenter but has values that come about as a result of the change of the independent variable. In this example, cancer is the dependent variable, because it is the result of the manipulation of the amount of tobacco.

Therefore, it is not true to say that cancer is the independent variable as seen in option b

6 0
2 years ago
⚠️URGENT PLS HELPPPPP<br><br> LINKS WILL BE REPORTED
balu736 [363]
The answer is the last one
6 0
2 years ago
A: 28, 23,30, 25, 27
Serggg [28]

Answer:

8

Step-by-step explanation:

mean of A=28+23+30+25+27/5 = 26.6

average of B=22+19+15+17+20/5 = 18.6

now,

difference= 26.6-18.6

=8,,

6 0
3 years ago
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