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1. Rectangle has integer sides and area=96

(a) How many possible perimeters?

(b) Greatest perim? Least? L=? W=?

Answers

(a) 6

(b) Greatest perim:194; Least:40

Solution: 96 has 6 pairs of factors ---

1,96:2,48;3,32;4,24;6,16;8,12

Each pair has a different sum so there are 6 possible perimeters.

The greatest and least possible occur in the extreme cases, i.e., when the factors are farthest and closest apart. This is generally true.

Note: If integer condition is removed there would be no greatest perimeter and the least would be 16√6, a square!

2. Data:4,6;mean:5

(a) Avg diff from mean= ((4-5)+(6-5))/2=?

(b) v=((4-5)^2+(6-5)^2)/2=?

(c) √v=?

(d)Repeat for 3,7

Obs,Conj?

Common name for √v?

Answers

(a) 0

Note: This is always true -- the avg difference or deviation from the mean is zero! This is why we square the differences to measure deviation!

(b) v=1

Note: The avg of the squared "deviations" from the mean is called the variance.

(c) √v=1

Note: The square root of the variance is called the standard deviation!

(d) For 3,7 ---

Mean is still 5

v=(4+4)/2=4

√v=2, the stand dev.

√v gives a measure of how dispersed the data is from the mean...