Answer:
<em>Cathy was born in 1980 and she was 18 years old in 1998</em>
Step-by-step explanation:
<u>Equations</u>
This is a special type of equations where all the unknowns must be integers and limited to a range [0,9] because they are the digits of a number.
Let's say Cathy was born in the year x formed by the ordered digits abcd. A number expressed by its digits can be calculated as
In 1998, Cathy's age was
And it must be equal to the sum of the four digits
Rearranging
We are sure a=1, b=9 because Cathy's age is limited to having been born in the same century and millennium. Thus
Operating
If now we try some values for c we notice there is only one possible valid combination, since c and d must be integers in the range [0,9]
c=8, d=0
Thus, Cathy was born in 1980 and she was 18 years old in 1998. Note that 1+9+8+0=18
The answers to these are:
G. x=4
J. x=-5
Answer:
Step-by-step explanation:
Let's start by finding Sandra's salary this year.
We are given that she saved $3,360 or 8% of her total salary this year.
Let's represent her total salary this year as "x" and set up an equation:
Note that any percentage is equivalent to that number over 100.
Multiply 100 to both sides:
Divide both sides by 8
The question states "this year her salary was $2000 more than in the previous year".
This means that her salary in the previous year is equivalent to:
The most consistent attendance is the one that has less variability (it's more regular). Not necessarily the one with more students. So, the case with less variability is the one with less IQ, sigma or range (all three measure the dispersion of a distribution. IQ is more robust than sigma, and sigma more than the range, although in practice everyone uses sigma).
So, the answer to A) is the third High School: HS P
B) Here one looks at the central measurement: mean, median. This example is not super easy. HS N has the highest mean value, but HS P has the highest median. The median is more robust than the mean, since it is less affected by outliers. So HS P is a good candidate.
Finally, looking at the Low/High values, one can see that the high is the same: some day(s) when all students went and all HS have a maximum number of 180 students. However, the highest low is HS P.
So, I think HS P should also be awarded for the highest rate, since its median
is the highest and the lower number of students is the highest.
Median means 50% of the cases have values less than the median. Mean is an average.
