Answer:
Step-by-step explanation:
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- The value of the n is 8.
- There are 7 positive integers between 100 and 200 which are divisible by 14.
<u>Step-by-step explanation:</u>
The sum of first n odd positive integer is n^2. The nth odd number is 2n-1.
i.e. 1 + 3 + ........+ (2n-1) = n^2.
1 + 3 +..........+ (2n-1) = 64
n^2 = 64
n = 8.
The positive integers between 100 and 200 which are divisible by 14 are 112, 126, 140, 154, 168, 182, 196. It is obtained by the multiples of 14 between 100 and 200.
100 = 7 * 14 + 2
200 = 14 * 14 + 4. The answer is 14 - 7 = 7
The seven numbers are
14 * 8 = 112
14 * 9 = 126
14 * 10 = 140
14 * 11 = 154
14 * 12 = 168
14 * 13 = 182
14 * 14 = 196
Median:15 1,11,14,15,31,37,47
Mean:22 (1+11+14+15+31+37+47)/7=22
A perpendicular line has an opposite reciprocal slope. This means that the new line will have a slope of -4/3x. Plug in x and y into the equation y=Mx +b where m is the slope (-4/3):
-3=(-3/4)(-3) + b
and isolate b:
b-3=(-3/4)(-3)
b=(-3/4)(-3) +3
b=9/4+3
b=21/4
The final equation is y= -4/3x + 21/4
The y intercept is (21/4).
Lna^b = blna
let y = lne^e
so y = lne^e = e lne
lne = 1
y = e which is a constant (Euler's number) ~= 2.718
For Euler's number estimating methods request in a comment.
