WILL MARK BRANLIEST AND THANK! 10 POINTS, EASY QUESTION!!
1 answer:
Answer: 2±√3 and 1/(2±√3)
This might seem wrong, but you'll understand when you read the explanation.
Step-by-step explanation:
For this problem, you can write 2 equations to find the two numbers. Let's establish x for the first number and y for the second number.
Equation 1:
x+y=4
This equation comes from the problem that says the 2 numbers add up to 4.
Equation 2:
x*y=1
This equation comes from the part that says multiplies to 1.
Even if the problem states that the numbers can be negative, it is tricking us. We know in order for the product of 2 numbers to be positive, it has to be +*+ or -*-. Since the added numbers have to be +4, we know we cannot use -1 and 1 as our answer. What we can do is to use substitution to solve for x and y.
x+y=4 becomes y=4-x
We can substitute this into equation 2.
x(4-x)=1
4x-x²=1
4x-x²-1=0
-x²+4x-1=0
Since this equation is not factorable, we use the quadratic equation, (<em>Please ignore the weird looking A that's in front of the ± sign. I don't know what's wrong with the system, but it's not supposed to be there)</em>
We plug our a, b, c into the equation and get x=2±√3.
Now that we know our x, we can plug it into any of the above equations.
(2±√3)(y)=1
y=1/(2±√3)
Our final 2 numbers are 2±√3 and 1/(2±√3)
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Answer:
So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.
Step-by-step explanation:
1) 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".
2) Solution to the problem
Let X the random variable that represent the scores on the LSAT of a population, and for this case we know the distribution for X is given by:
Where and
We want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.35 of the area on the left and 0.65 of the area on the right it's z=-0.385. On this case P(Z<-0.385)=0.35 and P(Z>-0.385)=0.65
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.