Hello I am having a hard time understanding questions 310 An

Hello, I am having a hard time understanding questions 3-10. Any help would be great! Thanks

A traffic signal is green for 20 seconds out of every minute. Find the probability that the signal will be green when you turn the corner and first see it. You can model the signal\'s color intervals by using a number line. Let an interval of 60 represent one cycle of green, yellow, and red. Inside that interval, an interval of 20 represents a green light. You come across the signal at a random point in time, so P(green) = time light is green/total time of cycle = 20/60 = 1/3 1. The traffic signal is green when you first see it. What is the probability that it will turn yellow within 5 seconds? 2. The traffic signal is red when you first see it. What do you need to know to find the probability that it will not turn green for another 15 seconds? The following continuous situations involve functions and conic sections that vou have studied to this point. For each, assume that you pick real numbers a and b at random between 0 and 10. Find the probability of each of the following. 3. The line y = ax intersects the segment joining (0,10) and (5,10). See graph at the right. 4.The circle (x - a)^2 + (y - b)^2 = 1 lies entirely within a square with opposite vertices (0,0) and (10,10). 5. The ellipse x/a^2 + y/b^2 = 1 has a vertical major axis. 6. The hyperbola x/a^2 - y/b^2 = 1 has a horizontal transverse axis. 7. The interval from 4 to 6 is a part of the domain of the function y = squareroot x-a+b. 8. The function y = ab^x a models growth. 9. The function y = 1/x-a + b has a horizontal asymptote. 10. The point (a, b) is in the upper triangle formed by the diagonals of a square whose sides lie on the axes and the lines v = 10 and y = 10.

Solution

(3) segment joining (0,10) and (5,10).

Now, From y = ax

Let take (1,10) --- 10 = a(1)

a = 10

(5,10) --- 10 = a(5)

a = 2

So, a can be anything from 2 to 10.

probabilty = 8/10 = 0.8

(4) (x-a)²+(y-b)² = 1

center = (a,b) radius = 1

Now, square has side = 10

center can be (1,1) to (9,9).

So, a and b can be from 1 to 9.

Hence probabilty = 9/10 = 0.9

Rest you can do like this. make figure and try to figure out that what can be the maximum and minimum value of a and b. then find the probablity.