Answer:
mean = 1 power failure
variance = 1 (power failure)²
Step-by-step explanation:
Since the mean is computed as
mean = E(x) = ∑ x * p(x) for all x
then for the random variable x=power failures , we have
mean = ∑ x * p(x) = 0 * 0.4 + 1* 0.3 + 2*0.2 + 3* 0.1 = 1 power failure
since the variance can be calculated through
variance = ∑[x-E(x)]² * p(x) for all x
but easily in this way
variance = E(x²) - [E(x)]² , then
E(x²) = ∑ x² * p(x) = 0² * 0.4 + 1²* 0.3 + 2²*0.2 + 3²* 0.1 = 2 power failure²
then
variance = 2 power failure² - (1 power failure)² = 1 power failure²
therefore
mean = 1 power failure
variance = 1 power failure²
Answer:
C or 3rd option
Step-by-step explanation:
1/3 - 2/5
15/15 - 6/15
9/15
B is not correct
2/5 - 1/3
this will be a negative answer
Answer:
D and E
Step-by-step explanation:
27 and 50 are greater than 20. The scale factor is more than 1, so the answer(s) have to be more than 1.
Answer:
a) one solution
b) no solution
Step-by-step explanation:
Systems of equations can be described as having one solution, no solution or infinite solutions:
One solution: 'x' and 'y' are equal to only one value
No solution: 'x' and 'y' can not be solved with the given equations
Infinite solutions: values for 'x' and 'y' include all real numbers
In order to evaluate the systems, putting them in the same format is your first step:
a) - y = -5x - 6 or y - 5x = 6
y - 5x = -6
Since both equations have the same expression 'y - 5x', but there are equal to opposite values, this system would have no solution, as this would not be possible to calculate.
b) y + 3x = -1
y = 3x -1 or y - 3x = -1
Solving for 'y' by adding the equations and eliminating 'x', gives us:
2y = -2 or y = -1
Using y = -1 to plug back into an equation and solve for 'x': -1 + 3x = -1 or x = 0. Since 'x' and 'y' can be solved for a value, the system has just one solution.
Answer:
C
Step-by-step explanation:
Notice that there is a little triangle formed by the lines on the right side of the diagram.
Let's find the angle measures of the triangle. One of them has a supplementary angle of 96 degrees, which means that the actual interior angle is 180 - 96 = 84 degrees.
Another angle has a supplementary angle of 137, which means that the actual interior angle of the triangle is 180 - 137 = 43 degrees.
Finally, we have the expression 2x - 23, which is an exterior angle. By definition, this exterior angle is equal to the sum of the interior angles of the triangle that do not include its supplementary angle. In other words:
2x - 23 = 84 + 43
Now we just solve for x:
2x - 23 = 84 + 43 = 127
2x = 127 + 23 = 150
x = 150/2 = 75 degrees
The answer is 75 degrees, or C.
