A circle with area \blue{25\pi}25πstart color #6495ed, 25, pi, end color #6495ed has a sector with a central angle of \purple{\dfrac{9}{10}\pi} 10 9 πstart color #9d38bd, start fraction, 9, divided by, 10, end fraction, pi, end color #9d38bd radians .

Step-by-step explanation:

Given that

The area of circle is 25π square unit

Area = 25π square unit

The area of a circle can be calculated using

Area = πr²

Where r is radius of the circle

Then, let find the radius of the circle

Area = πr²

25π = πr²

Divided Both side by π

25π / π = πr² / π

25 = r²

Take square root of both sides

√25 = √r²

5 = r

Then, the radius of the circle is 5 unit

Then, given that the angle subtended by the sector is 9π/10 rad

θ = 9π/10 rad

Then, we want to find the area of the sector

Area of a sector is calculated using

Area of sector = (θ / 360) × πr²

Area of sector = θ × πr² / 360

The formula is in degree let convert to radian

360° = 2π rad.

Then,

Area of sector = θ × πr² / 2π rad

Then,

Area of sector = θ × r² / 2

Area of sector = ½ θ•r²

Then, Area of the sector is

A = ½ θ•r²

A = ½ × (9π / 10) × 5²

A = (9π × 5²) / (2 × 10)

A = 225π / 20

A = 45π / 4

A = 11.25π Square unit

A = 35.34 square unit

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

you ignore the remainder, therefore the answer is y = x+2

step-by-step explanation:

you have to divide the denominator by the numerator. you can use synthetic division or long division.

[-5] .     1 .     7 .     11

x + 2 + 1/x+5