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maria [59]
3 years ago
15

The width of a rectangle is 75% the length of the rectangle. the perimeter of the rectangle is 42 inches. a circle is drawn that

contains all four vertices of this rectangle. if the area of the circle is xπ square inches, then what is the value of x ?

Mathematics
1 answer:
matrenka [14]3 years ago
4 0

Answer:

  x = 56.25

Step-by-step explanation:

The sides of the rectangle are in the ratio 3:4, so those together with the diagonal of the rectangle make a 3-4-5 right triangle. The sum of these adjacent-side ratio units is 3+4 = 7, so the perimeter in ratio units is 2×7 = 14. The actual perimeter is 42 inches, so each ratio unit must stand for ...

  (42 in)/(14 units) = 3 in/unit

The diagonal of the rectangle is the diameter of the circle. Its length is 5 units, or ...

  (5 units)×(3 in/unit) = 15 inches.

Then the radius is half the diameter, or 7.5 inches.

The area of a circle is given by ...

  A = πr² = π(7.5 in)² = 56.25π in²

The value of x is 56.25.

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melamori03 [73]

The probability that more than 5 students will pass their exam is 0.0188416.

<h3>How to find the probability?</h3>

The probability that a student passes their examination = 40% = 0.4

The probability that more than 5 students pass their statistics exam = Probability that 6 students pass their exam + Probability that 7 students pass their exam

The probability that 6 students pass their exam =

7C_{6} (0.4)^{6} (0.6)^{1}\\=7(0.4)^6(0.6)\\=0.0172032

The probability that 7 students pass their exam =

7C_{7} (0.4)^{7} (0.6)^{0}\\=(0.4)^7\\=0.0016384

The probability that more than 5 students pass their statistics exam = 0.0172032 + 0.0016384

= 0.0188416

Therefore, we have found the probability that more than 5 students will pass their exam to be 0.0188416.

Learn more about probability here: brainly.com/question/24756209

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4 0
1 year ago
Three-fifths of the students in a room are girls. One-third of the girls have blond hair. One-half of the boys have brown hair.
yan [13]

Answer:

a. Of all the students, \frac{1}{5} are girls with blond hair.

b. Of all the students, \frac{1}{5} are boys without brown hair.

Step-by-step explanation:

a. You know that \frac{3}{5} of the students are girls (This means that \frac{2}{5} of the studes are boys) and \frac{1}{3} of these girls have blond hair.

Then, \frac{1}{3} of \frac{3}{5} is:

(\frac{3}{5})(\frac{1}{3})=\frac{1}{5}

Therefore, of all the students, \frac{1}{5} are girls with blond hair.

b. You know that \frac{1}{2} of the boys have brown hair.

Then, \frac{1}{2} of \frac{2}{5} is:

(\frac{2}{5})(\frac{1}{2})=\frac{1}{5}

Of all the students, \frac{1}{5} are boys without brown hair.

8 0
2 years ago
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2 {x}^{3}  + 2 {x}^{2}  - 40x =

2x( {x}^{2}  + x - 20) =

2x(x  - 4)(x + 5)

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The correct answer is (( a )) .

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8 0
2 years ago
Read 2 more answers
Annie, Brianna &amp; Carly are selling fruit boxes to raise money for their soccer team. All together the girls have sold 105 bo
GaryK [48]

Step-by-step explanation:

Annie = x

Brianna = y

Carly = z

Now,

x + y + z = 105 ...(1)

Carly has sold ten more than three times Brianna's sales.

z = 10 + 3y ...(2)

Brianna sold five more than Annie.

y = 5 + x ...(3)

Now,

z = 10 + 3y

z = 10 + 3(5 + x)

z = 10 + 15 + 3x

z = 25 + 3x

Now,

x + y + z = 105

x + (5 + x) + 25 + 3x = 105

5x + 30 = 105

5x = 105 - 30

5x = 75

5x/5 = 75/5

x = 15

So,

y = 5 + x

y = 5 + 15

y = 20

Now,

z = 25 + 3x

z = 25 + 3(15)

z = 25 + 45

z = 70

Thus,

Annie Sold 15 boxes

Brianna Sold 20 boxes

Carly Sold 70 boxes

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2 years ago
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timofeeve [1]

Answer:

The answer is 2/5 or 5.25

Step-by-step explanation:

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5 0
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