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:
15 dimes and 10 nickels
Step-by-step explanation:
15 dimes because 15 multiplied by 10 cents is $1.50
10 nickels because 10 multiplied by 5 cents is $0.50
15 x 0.10 = 1.50 10 x 0.50 = 0.50
0.50 + 1.50 = 2.00
Answer:
-2
Step-by-step explanation:
The average rate of change on an interval is ...
average rate of change = (amount of change)/(width of interval)
= (-3 -1)/(1 -(-1)) = -4/2 = -2
The average rate of change between (-1, 1) and (1, -3) is -2.
A. She needs 16 quarter cups of milk.
B. Equation: 4 cups multiplied by 4(four quarter cups per cup) = 16 quarter cups
Hope this helps!!
Answer:
21
Step-by-step explanation:
Let x be the amount of ticket for each game
Given
The expression 8x + 62 represents the total cost of the football game
The total coat for the.game will be
8(7)+62
= 56+62
= 118
If 9x + 34 represents the total cost of the baseball game. The total coat will be;
9(7)+34
= 63+34
=97
To know how much more football game costs, we will take the difference in their cost.
Difference = 118-97
Difference= 21
Hence football game costs 21 more than baseball
