So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=
so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
Answer:
Option A) any numerical value in an interval or collection of intervals
Step-by-step explanation:
Continuous Random Variable:
- A continuous random variable can take any value within an interval.
- Thus, it can take infinite values since there are infinite numbers in an interval.
- A continuous variable is a variable whose value is obtained by measuring.
- Examples: height of students in class
, weight of students in class, time it takes to get to school, distance traveled between classes.
- Thus, the correct meaning of continuous random variable is explained by Option A)
Option A) any numerical value in an interval or collection of intervals
Answer:
0.371954
Step-by-step explanation:
Formula- for an approximate result, divide the volume value by 29.574.
2x - 6y = 12
so we pick any number for x and then solve for y
lets say x = 0
2(0) - 6y = 12
-6y = 12
y = -12/6
y = -2....so when x = 0, y = -2....(0,-2) <== one point
lets say x = 1
2(1) - 6x = 12
2 - 6x = 12
-6x = 12 - 2
-6x = 10
x = -10/6
x = - 5/3...so when x = 1, y = -5/3....(1,-5/3) <== another point
Lets say x = 2
2(2) - 6y = 12
4 - 6y = 12
-6y = 12 - 4
-6y = 8
y = -8/6
y = - 4/3....so when x = 2, y = -4/3.....(2,-4/3) <== another point
lets say x = 3
2(3) - 6y = 12
6 - 6y = 12
-6y = 12 - 6
-6y = 6
y = -6/6
y = -1....so when x = 3, y = -1.....(3,-1) <== another point
now there is 4 points.
Answer:
Step-by-step explanation:
Number of the bags = between 8 and 15 and
-
1/2 of bags contain money
- 1/6 of bags contain candy
- 1/3 of bags contain a toy
As per above the number is divisible by 2, 3 and 6. LCM of the three numbers is 6.
<u>
The number between 8 and 15 and divisible by 6:</u>
So the number of bags is 12