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2 years ago

Find the area of the yellow region.

Mathematics

1 answer:

Digiron [165]2 years ago

3 0

Answer:

A = 3.9 in²

Step-by-step explanation:

To find the area of the shaded region, you need to find the (1) area of the entire square, then (2) find the area of the 1/2 circles, then (3) subtract them and divide by 2. Because the 1/2 circles are identical, you can combine them and just use the circle area equation.

Area of the Square:

A = l x w

A = 6 in x 6 in

A = 36 in²

Area of Combined 1/2 Circles:

A = πr²

r = 6 in / 2

r = 3 in

A = π(3)²

A = 9π -----> 28.3 in²

Area of Shaded Region:

A = (Area Square - Area Circle) / 2

A = (36 in² - 28.3 in²) / 2

A = 7.7 in² / 2

A = 3.9 in²

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lisabon 2012 [21]

Answer:

(a) The value of x is 0.30.

(b) The probability that a reported case of rabies is not a raccoon is 0.45.

Step-by-step explanation:

Denote the events as follows:

R = reported case of rabies is a raccoon

F = reported case of rabies is a fox

B = reported case of rabies is a bat

O = reported case of rabies is a some other animal.

The data provided is:

P (R) = 0.55

P (F) = 0.11

P (B) = 0.04

P (O) = x.

(a)

A property of a probability distribution is that the sum of all individual properties is 1.

That is, $\sum P(X)=1$

Compute the value of x as follows:

$\sum P(X)=1\\P(R)+P(F)+P(B)+P(O)=1\\0.55+0.11+0.04+x=1\\0.70+x=1\\x=1-0.70\\x=0.30$

Thus, the value of x is 0.30.

(b)

The probability of the complement of an event is the probability of its not happening.

$P(A^{c})=1-P(A)$

Compute the probability that a reported case of rabies is not a raccoon as follows:

$P(R^{c})=1-P(R)\\=1-0.55\\=0.45$

Thus, the probability that a reported case of rabies is not a raccoon is 0.45.

(c)

Compute the probability that a reported case of rabies is either a bat or a fox as follows:

$P(B\cup F)=P(B)+P(F)\\=0.11+0.04\\=0.15$

Thus, the probability that a reported case of rabies is either a bat or a fox is 0.15.

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3 years ago

A ball rolls over the edge of a platform with only a horizontal velocity. The height of the platform is 1.6 m and the horizontal

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Answer:

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Step-by-step explanation:

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$1.6 = 9.8t^2/2$

$t^2 = 2*1.6/9.8 = 0.327$

$t = \sqrt{0.327} = 0.571s$

This is also the time it takes for the ball to fly horizontally, assume constant horizontal speed, we can calculate the speed it takes to travel across 20m in 0.571s

v = 20 / 0.571 = 35 m/s

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