Solve x2 + 8x = 33 by completing the square. Which is the solution set of the equation?
1 answer:
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Answer:
And then we can conclude that the middle 75% values of her lap times are from a=126.835 to b=132.585
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 times of a population, and for this case we know the distribution for X is given by:
Where and
Since we want the middle 75% values then on tha tails we need 1-0.75 =0.25 or 25% of the data and since the distribution is symmetric we need 12.5 % of the values on each tail.
For this part we want to find a value a and b, such that we satisfy this condition:
(a)
(b)
We can use the z score formula in order to find the value a and b given by:
As we can see on the figure attached the z value that satisfy the condition (b) with 0.125 of the area on the left and 0.875 of the area on the right it's z=-1.15. On this case P(Z<-1.15)=0.125 and P(z>-1.15)=0.875
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 12.5% of data from the top 87.5% is 126.835.
As we can see on the figure attached the z value that satisfy the condition (b) with 0.875 of the area on the left and 0.125 of the area on the right it's z=1.15. On this case P(Z<1.15)=0.875 and P(Z>1.15)=0.125
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
And then we can conclude that the middle 75% values of her lap times are from a=126.835 to b=132.585
Check the picture below.
segments AC and BC are equal, that means that ABC is an isosceles triangle, with twin sides. Now the twin sides make twin angles on the opposite side, namely the angles at A and B are twins.
if the angles at A and B are twins, and CD is ⟂ to AB, there's only one possibility that can happen, and is if CD is an angle bisector at C.
an angle bisector like CD with twin angles on each side, will cut AB in two equal halves, therefore, if AB = 4, then AD = 2 and DB = 2.
segments AC and BC are equal, that means that ABC is an isosceles triangle, with twin sides. Now the twin sides make twin angles on the opposite side, namely the angles at A and B are twins.
if the angles at A and B are twins, and CD is ⟂ to AB, there's only one possibility that can happen, and is if CD is an angle bisector at C.
an angle bisector like CD with twin angles on each side, will cut AB in two equal halves, therefore, if AB = 4, then AD = 2 and DB = 2.
ANSWER
EXPLANATION
Given information
The sum of the two numbers is 76
The larger number is 16 more than 2 times the smaller number
Let the two numbers be x and y
x ----> Larger number
y ----> smaller number
To find the value of x and y, follow the steps the below
Step 1: Write the algebraic expressions for the statement given
The sum of the two numbers is 72
Mathematically, this can be expressed as
Also, the larger number is 16 more than twice