A 33 gram sample has k value of .1124
(Actually I think the problem SHOULD be worded: A 33 gram sample has k value of -.1124/days)
See attached graphic:
Half-Life = ln (.5) / k
Half-Life = -.693147 / -.1124/days
Half-Life =
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6.1667882562
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days
Source:
http://www.1728.org/halflif2.htm
First, subtract 700 from both sides and you are left with .15m≤50
Then divide both sides by .15 and you are left with m ≤ 333.33. Thus, the limo can only travel 333.33 miles.
The number is 66.
Solution:
Let the number be x.
To find the number x using given conditions.
Start with the last condition.
It is less than 7 times 8 + 23 = 7 × 8 + 23 = 79
So, the number is less than 79 which implies x < 79.
Using condition (4),
It is greater than 5 times 4 = 5 × 4 = 20
So, the number is greater than 79 which implies x > 20.
Combining condition (4) and (7), we get 20 < x < 79.
Using condition (3) and (5),
The number is a multiple of 11 and 6.
The number which is multiplied by both 11 and 6 is 66, 132, ...
But here x lies between 20 < x < 79.
So x = 66.
66 is not odd number and the sum of the digits is divisible by 2.
Therefore condition (1) and (2) also satisfied.
Hence the number is 66.
Y=4x+1
Let y=0
0=4x+1
4x=-1
x=-1/4
Let x=0
Y=4*0+1
Y=0+1
Y=1
Therefore, the ordered pair is (-1/4, 1)
Looking at the graph, we know that A. 3 boxes are filled every 4 min and D. 0.75 boxes are filled per minute are the correct answers.
Hope this helps~
