Answer:
The value that represents the 90th percentile of scores is 678.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Find the value that represents the 90th percentile of scores.
This is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.
The value that represents the 90th percentile of scores is 678.
6y - 4(y - 1) +6
6y - 4y -4(-1) + 6
6y - 4y +4 + 6
2y + 10
Answer:
(3, 1)
Step-by-step explanation:
(a) Algebraic solution
(1) y = -⅔x + 3
(2) y = 2x - 5
Set Equation (1) equal to Equation (2)
-⅔x + 3 = 2x - 5
Multiply each side by 3
-2x + 9 = 6x - 15
Add 15 to each side
-2x + 24 = 6x
Add 2x to each side
24 = 8x
Divide each side by 3
(3) x = 3
Substitute (3) into (2)
y = 2×3 - 5 = 6 - 5 = 1
The ordered pair that makes both equations true is (3, 1).
(b) Graphical solution
In the diagram below, the red line is the graph of Equation (1). The blue line is the graph of Equation (2). The point of intersection is at (3, 1).
First, start off by listing a few of the numbers that follow the first three clues to see if you can narrow it down.
7,111,111
7,333,333
7,555,555
etc.
Then, start adding up digits to see if you're getting close.
7+1+1+1+1+1+1 = 13
7+3+3+3+3+3+3 = 25
7+5+5+5+5+5+5 = 37
Since 7,555,555 is too high, we step it down to 7,555,333
7+5+5+5+3+3+3 = 31
7,555,333 will work as an answer, as well as 7,333,555, since it's the same amount when the digits are added together.
