Answer:
E) is correct, 2/3
Step-by-step explanation:
The points that are 20 inches apart from P form a circle that contains Q. We can suppose that P is in the position (0,0) and Q in the position (20,0) (we can rotate and move the circle without making any effect on the probability).
A point in the circle at distance 20 of Q has the form (20 cos(Ф), 20 sen(Ф) ) for certain angle Ф between 0 and 2π. Since it is at distance 20 of Q, we have that (20-20cos(Φ))² + (0-20sen(Φ))² = 20²=400, thus
400 - 800 cos(Φ) + 400cos²(Φ) + 400sen²(Φ) = 800-800cos(Φ) = 400, so
400 = 800cos(Φ)
cos(Φ) = 1/2
By looking at a trigonimetric table, you can find that Φ is either π/3 or 2π-π/3 = 5π/3.
As a result, the angles that will give you a point R at distance from Q greater than 20 are between π/3 and 5π/3, hence , the points that are a distance greater than 20 form a chord of length 20*(5π/3-π/3) = 80π/3. Comparing this with the perimeter of the circle (20*2π = 40π), this gives us a probability of 80π/3 / 40π = 2/3 that the point R is closer to P than it is to Q.
Answer:
99
Step-by-step explanation:
132/4 = 33 33*3=99 99+132+33=264
Answer:
4424
Step-by-step explanation:
the number 614 is in the base ten system that we use every day. the base five system represents each digit in the number represents the number of copies of that power of 5.
check out:
rapidtables.com/convert/number/base-converter.html
The question ask to calculate the expression as the square of a binomial and also find the value of c that makes the expression a perfect square and the best answer would be that the value of C is 49/4 and its perfect square is (7/2)^2. I hope you are satisfied with my answer and feel free to ask for more