You can roll a total of 6 by rolling (1, 5), (2, 4), (3, 3), (4, 2), or (5, 1). There are 36 total possible rolls that can be obtained, so you roll a total of 6 with probability 5/36.
You can roll a total of 11 by rolling (5, 6) or (6, 5), hence with probability 2/36 = 1/18.
Any of the other remaining 29 outcomes occurs with probability 29/36.
The expected value of your winnings is
$18*5/36 + $72*1/18 - $9*29/36 = -$0.75
so the answer is E.
7
5
25
28
9.
Find the distance between the two points. Round to the nearest tenth if necessary.
(–2, –6), (3, 9)
15.8
250
3.2
20
Answer:
1.
option B is correct
2.
Option A is correct.
Step-by-step explanation:
Using distance formula:
1.
Given the points:
(8, 8) and (12, 11)
then;
Therefore, the distance between the two points is, 5 units.
2.
Given the points:
(-2, -6) and (3, 9)
then;
Therefore, the distance between the two points is, 15.8 units
a = b − 2
What is the solution to the set of equations in the form (a, b)?
(−2, −2)
(−3, −1)
(−9, −7)
(−5, −3)
The solution to the set of equations in the form (a, b) is (-5, -3).
Hence, 4th option is the right choice.
A system of equations, also known as an equation system or a set of simultaneous equations, is a finite collection of equations for which common solutions are found.
We are given two equations in a and b and are asked to find the solution to them. The equations are:
a - 3b = 4 . . . . . . . . . . . . . . (1)
a = b - 2 . . . . . . . . . . . . . . (2)
We substitute the value of a = b - 2 from (2) in (1) to get,
(b - 2) -3b = 4
or, b - 2 - 3b = 4.
or, b -2 - 3b + 2 = 4 + 2 (adding 2 two both sides of the equation)
or, -2b = 6 (simplifying)
or, -2b/(-2) = 6/(-2) (dividing both sides by -2)
or, b = -3 (simplifying)
Now, we substitute this value of b = -3, in (2) to get
a = (-3) - 2
or, a = -5.
∴ (a, b) = (-5, -3)
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