Answer:
Since a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.
Step-by-step explanation:
Let a/b be the rational number in its simplest form. If we divide a/b by 2, we get another rational number a/2b. a/2b < a/b. If we divide a/2b we have a/2b ÷ 2 = a/4b = a/2²b. So, for a given rational number a/b divided by 2, n times, we have our new number c = a/2ⁿb where n ≥ 1
Since
= a/(2^∞)b = a/b × 1/∞ = a/b × 0 = 0, the sequence converges.
Now for each successive division by 2, a/2⁽ⁿ ⁺ ¹⁾b < a/2ⁿb and
a/2⁽ⁿ ⁺ ¹⁾b/a/2ⁿb = 1/2, so the next number is always half the previous number.
So, we cannot find a smallest positive rational number because there would always be a number smaller than that number if it were divided by half.
Answer:
x=3
Step-by-step explanation:
first let's try to get just 3x on one side. to do this we can subtract 2 from both side of the equation.
3x+(2-2)=11-2
3x=9
now we have to isolate the variable we can divide both sides by 3:
3x/3=9/3
x=3
and you get the answer that x is 3
Answer:
8 i think
Step-by-step explanation:
Answer:
The tabulated value is less than the calculated value, therefore we accept the null hypothesis and It show that there is a difference in the mean overall distance of brands.
Step-by-step explanation:
Answer:
14.7 miles per gallon
Step-by-step explanation:
All you have to do is divide the number of miles by the number of gallons to find out how many miles are driven per gallon of gas. Hope I helped!