Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the lifetime for a TV of a population, and for this case we know the distribution for X is given by:
Where 
and 
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability like this:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
1/2 (Base x height) = area
1/2 (4*x)=10
2x=10
X=5
The height is 5 units
Answer:
D
Step-by-step explanation:
First, find the coordinates of pointD if A(2,-6), B(10,2) and point D divides line segment AB in the ratio of 5:3.
If point D divides the segment AB in the ratio m:n, then
So
Point C has the x-coordinate the same as point A and the y-coordinate the same as point D.
Thus, C(2,-1)
f(x) is a quadratic equation with the x-side squared and a is positive which means that the graph of the function is a parabola facing up. The range of f(x) is given by {y|y ≥ k}, where k is the y-coordinate of the vertex.
, written in vertex form is
, where (h, k) = (-1, -11)
Therefore, range ={y|y ≥ -11}
Answer: 14.73
Step-by-step explanation:
The given triangle is a right angle triangle.
EF^2 + DF^2 = ED^2
The hypotenuse is |ED| while the two shorter legs are |EF| and |DF|.
We can then apply the Pythagoras Theorem to find the length of EF.
(EF)^2 + (DF)^2 = (ED)^2
(EF)^2 + (12)^2 = (19)^2
(EF)^2 + 144 = 361
(EF)^2 = 361 - 144
(EF)^2 = 217
EF = 14.73
