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Mazyrski [523]
2 years ago
8

Richard has two circular sprinklers to water his rectangular backyard as shown.

Mathematics
1 answer:
makvit [3.9K]2 years ago
8 0

Answer:

109.88 ft² (nearest hundredth)

Step-by-step explanation:

<u>Formulae</u>

  • Area of a rectangle = width × length
  • Area of a circle = πr²

To find the area of the lawn that is not watered, subtract the area of the 2 circles from the area of the rectangle.

From inspection of the diagram

  • width of rectangle = 2r
  • length of rectangle = 4r
  • area = 512 ft²

Substituting the values into the area of a rectangle formula, and solving for r:

⇒ 512 = 2r × 4r

⇒ 512 = 8r²

⇒ r² = 64

⇒ r = ±8

As distance is positive, r = 8 ft

Area of one circle = π8² = 64π  ft²

Therefore,

Area not watered = area of rectangle - 2 × area of circle

                             = 512 - 2(64π)

                             = 109.88 ft² (nearest hundredth)

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Answer:

slope of the line is 0

Step-by-step explanation:

given points are:

(-3 , 2)=(x1 , y1)

(4 , 2)=(x2 , y2)

slope =y2 - y1/x2 - x1

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2 years ago
How do you solve the equation:
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Copy and paste the answer on quizlet
5 0
3 years ago
Please help me with the following math question:
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Answer:

$86.03

Step-by-step explanation:

30% off = 70% of total price. Add .06 to 1 for 6% sales tax.

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6 0
2 years ago
There are 10 employees in a particular division of a company. Their salaries have a mean of 570,000, a median of $55,000,and a s
harkovskaia [24]

Answer:

a) $160,000

b) $55,000

c) $332264.804

Step-by-step explanation:

We are given that there are 10 employees in a particular division of a company and their salaries have a mean of $70,000, a median of $55,000, and a standard deviation of $20,000.

And also the largest number on the list is $100,000 but By accident, this number is changed to $1,000,000.

a) Value of mean after the change in value is given by;

     Original Mean = $70,000

       \frac{\sum X}{n} = $70,000  ⇒ \sum X = 70,000 * 10 = $700,000

   New \sum X after change = $700,000 - $100,000 + $1,000,000 = $1600000

  Therefore, New mean = \frac{1600000}{10} = $160,000 .

b) Median will not get affected as median is the middle most value in the data set and since $1,000,000 is considered to be an outlier so median remain unchanged at $55,000 .

c) Original Variance = 20000^{2} i.e.  20000^{2} = \frac{\sum x^{2} - n*xbar }{n -1}

    Original \sum x^{2} = (20000^{2} * (10-1)) + (10 * 70,000) = $3,600,700,000

    New \sum x^{2} = $3,600,700,000 - 100,000^{2} + 1,000,000^{2} = 9.936007 * 10^{11}  

    New Variance = \frac{new\sum x^{2} - n*new xbar }{n -1} = \frac{9.936007 *10^{11}  - 10*160000 }{10 -1} = 1.103999 * 10^{11}    Therefore, standard deviation after change = \sqrt{1.103999 * 10^{11} } = $332264.804 .

7 0
3 years ago
A swimming pool at a park measures 9.75 meters by 7.2 meters the area of the playground is one and half times that of the swimmi
ElenaW [278]
9.75 x 7.2 = 70.2
Swimming Pool Area: 70.2
The Park Area: 70.2 x 1.5 = 105.3
Total Area of both Swimming Pool & Park area: 70.2 + 105.3 = 175.5
Final Answer: 175.5
8 0
3 years ago
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