The table is:0 1 2 3
x1 0 0.08 0.06 0.04 0.00
1 0.05 0.18 0.05 0.03
2 0.05 0.04 0.10 0.06
3 0.00 0.03 0.04 0.07
4 0.00 0.01 0.05 0.06
Expected difference =
+(0.08*(0-0)) +(0.06*(0-1)) +(0.04*(0-2)) +(0.00*(0-3)) +(0.05*(1-0)) +(0.18*(1-1)) +(0.05*(1-2)) +(0.03*(1-3)) +(0.05*(2-0)) +(0.04*(2-1)) +(0.10*(2-2)) +(0.06*(2-3)) +(0.00*(3-0)) +(0.03*(3-1)) +(0.04*(3-2)) +(0.07*(3-3)) +(0.00*(4-0)) +(0.01*(4-1)) +(0.05*(4-2)) +(0.06*(4-3))
= 0.17
Answer:
24.2 centimeters
Step-by-step explanation:
for height = f(time)
let x be the value of the height at 28hours
solving linearly
(28 - 15)/(32 - 15) = (x - 19)/(12.2 - 19)
solving we have
13/17 = (x - 19)/6.8
0.7647 = (x - 19)/6.8
cross multiplying,
x - 19 = 5.2
x = 5.2 + 19 = 24.2centimetres
Quick answer
Any irrational number. I can't think of any exception to this statement.
sqrt(5) is irrational. 1/2 * sqrt(5) is still irrational.
-sqrt(5) is irrational. -1/2 * sqrt(5) is still irrational
2 + sqrt(5) is irrational. Multiplying this by 1/2 is still irrational.
1/2(2 + sqrt(5) = 1 + 1/2 * sqrt(5) ) is irrational.
Conclusion
There are no exceptions to this. All irrational numbers produce irrationals when multiplied by 1/2
