You have a bag with two coins. one will come up heads 40% of the time, and the other will come up heads 60%. you pick a coin randomly, flip it and get a head. what is the probability it will be heads on the next flip?

13/50

Step-by-step explanation:

First, we need to put all the possible scenarios.

Let's call coin A as the coin that flips head 40% of the time, and coin B the 60% of the time.

Now, 40% in fraction is 40/100 = 4/10 = 2/5 for coin A. This is the probability of the coin A to get head. (Pa)

60% of the time is 60/100 = 6/10 = 3/5. Probability to get head in coin B (Pb)

Now, we don't know which coin is picked, all we know is that the first flipping is head. so, as the coins are picked randomly, we have 1/2 probability to choose either coin A or coin B, so, let's suppose we picked coin A:

Pa = 1/2 * 2/5 = 2/10 * 2/5 = 4/50

If the coin picked is coin B:

Pb = 1/2 * 3/5 = 3/10 * 3/5 = 9/50

So, finally the probability that if we flip the coin a second time, to get a head, no matter which coin was picked, is just the sum of both probabilities so:

P = 4/50 + 9/50 = 13/50

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)