At at least one die come up a 3?We can do this two ways:) The straightforward way is as follows. To get at least one 3, would be consistent with the following three mutually exclusive outcomes:the 1st die is a 3 and the 2nd is not: prob = (1/6)x(5/6)=5/36the 1st die is not a 3 and the 2nd is: prob = (5/6)x((1/6)=5/36both the 1st and 2nd come up 3: prob = (1/6)x(1/6)=1/36sum of the above three cases is prob for at least one 3, p = 11/36ii) A faster way is as follows: prob at least one 3 = 1 - (prob no 3's)The probability to get no 3's is (5/6)x(5/6) = 25/36.So the probability to get at least one 3 is, p = 1 - (25/36) = 11/362) What is the probability that a card drawn at random from an ordinary 52 deck of playing cards is a queen or a heart?There are 4 queens and 13 hearts, so the probability to draw a queen is4/52 and the probability to draw a heart is 13/52. But the probability to draw a queen or a heart is NOT the sum 4/52 + 13/52. This is because drawing a queen and drawing a heart are not mutually exclusive outcomes - the queen of hearts can meet both criteria! The number of cards which meet the criteria of being either a queen or a heart is only 16 - the 4 queens and the 12 remaining hearts which are not a queen. So the probability to draw a queen or a heart is 16/52 = 4/13.3) Five coins are tossed. What is the probability that the number of heads exceeds the number of tails?We can divide
Answer:
Step-by-step explanation:
Y=-2x+2.....(1)
Y=-2x-2.....(2)
Subtracting (1) from (2)
Y - Y = -2x - (-2x) -2 - 2
O = -2x + 2x - 4
O = 0 - 4
Hence it as no solution the the two variables tend to zero
To solve this problem you must apply the proccedure shown below:
1. The formula for calculate the perimeter of a rectangle is:
Where 
is the length and 
is the width.
2. The length is 
more than the width, therefore:
3. Substitute values into the formula for calculate the perimeter and solve for the width:
3. Then, the length is:
The answer is: The length is 
and the width is 
Using the Pythagorean theorem:
12^2 + x^2 = 15^2
144 + x^2 = 225
x^2 = 225 - 144
x^2 = 81
x = sqrt(81)
x = 9
