Answer:
x =
Step-by-step explanation:
Given
-
=
← factor denominator
-
=
[ x ≠ 0, x ≠ - 1 as these would make the terms undefined ]
Multiply through by x(x + 1)
4x² - 5(x + 1) = 4
4x² - 5x - 4 = 4 ( subtract 4 from both sides )
4x² - 5x - 9 = 0 ← in standard form
(x + 1)(4x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
4x - 9 = 0 ⇒ 4x = 9 ⇒ x =
However, x ≠ - 1 for reason given above, then
solution is x =
Answer:
Step-by-step explanation:
Answer:
1) FALSE
2) FALSE
3) TRUE
4) TRUE
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".
Part 1
The mean and standard deviation of a normally distributed random variable which has been standardized are one and zero, respectively.
The mean and the deviation for the normal standard distribution are:
So then that's FALSE.
Part 2
Using the standard normal curve, the z−score representing the 10th percentile is 1.28.
We are looking for a value a, that satisfy this:
(a)
(b)
We can find a z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.10 and P(Z>-1.28)=0.90
So that's FALSE.
Part 3
Let z1 be a z−score that is unknown but identifiable by position and area. If the symmetrical area between −z1 and +z1 is 0.9544, the value of z1 is 2.0
If we find this probability:
So on this case we can approximate to 0.9544. And that's TRUE.
Part 4
Using the standard normal curve, the z−score representing the 75th percentile is 0.67.
We are looking for a value a, that satisfy this:
(a)
(b)
We can find a z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.67. On this case P(Z<0.67)=0.75 and P(Z>0.67)=0.25
So that's TRUE.