Example 3: using the multiplication rule for independent events
a number cube has faces numbered 1 through 6, and a coin has two sides, heads and tails. the number cube will be rolled, and the coin will be flipped. find the probability that the cube
shows a 4 and the coin lands on heads. because the events are independent, we can use the multiplication rules we just learned.
if you toss the coin five times, what is the probability you will see a head on all five tosses?
if you tossed the coin five times and got five heads, would you think that this coin is a fair coin? why or why not?
if you roll the number cube three times, what is the probability that it will show 4 on all three throws?
if you rolled the number cube three times and got a 4 on all three rolls, would you think that this number cube is fair? why or why not?
suppose that the credit card company introduced in exercise 1 states that when a customer is selected at random, the probability that the customer pays his bill in full each month
is 0.35, the probability that the customer makes regular online purchases is 0.83, and these two events are independent. what is the probability that a randomly selected customer pays
his bill in full each month and makes regular online purchases?

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

not sure but it may be b, as i said i'm not sure.

26 is 33.33% of 78

step-by-step explanation:

26 is what percent of 78?

26 is p% of 78

equation: y = p% * x

solving our equation for p

p% = y/x

p% = 26/78

p = 0.3333

convert decimal to percent:

p% = 0.3333 * 100 = 33.33%