Math help please?

Question

I have a few questions

1.A person starting with $256 makes eight bets and wins exactly four times. The wins and losses occur in random order. if each wager is for half the moey she has at the time of the bet, how much will she win or lose?

2.How many four-digit positive integers divisible by 7 have the property that, when the first and last digits are interchanged, the result is a (not necessarily four-digit) positive integer divisible by 7?

3. Each day chris is chided for not cleaning up his room, so he picks up approx. 10% of the items on the floor in the morning. (he always rounds off to the nearest whole number if his calculations result in a fraction.) each day, ten new items somehow end up on the floor. If he has a clean flooron Sunday morning, how many items will be on the floor on Saturday night?

4. Each spring 12 meter x 12 meter graden has its length increased by 2 meters but its width decreased by 50cm. What will be the max. attainable area of the garden?

Answer 1

1. A win multiplies her money by 1.5 while a loss multiplies it by 0.5.
So 256x1.5x1.5x1.5
x1.5x0.5x0.5x0.5x0.5 = 81

The order does not matter because multiplication is commutative.

Answer 2

1. Going to make an assumption here: "The winning payoff is equal to the bet, which means they end up with 3/2 of what they had before". From your quest, after a loss they have 1/2 as much. So they end up with 256 * (1/2)^4 * (3/2)^4 = 81. The question was how much did they win or lose, so we say they have 256-81 = 175. They lost $175.
Don't believe the math? Let's try some examples: first 4 wins then 4 losses make: 384, 576, 864, 1296, 648, 324, 162, 81. Try 4 losses, then 4 wins: 128, 64, 32, 16, 24, 36, 54, 81. Mixing up the wins and losses end in the same result.

2. This one is much harder to explain. Since you didn't actually ask for proof's, I'll just give you the answer. You can create 210 positive integers that fit this situation.

3. I know this one, I'm a messy Chris :-)
This one is simple to do with a calculator, or Excel. It is:
=round(prevCell * 0.9,0) + 10
(The ,0 means round to zero decimal places)
Sunday you would have 10, Monday would be 19, Tu: 27, W: 34, Th: 41, F: 47, Saturday you would have 52.

4. First I had to find out that there are 100 centimeters in one meter. That makes 50cm = 0.5m. The initial 12 by 12 size and +2 by -0.5 growth each year is (12+2*year) * (12-0.5*year). Again using this in a spreadsheet for years 0 through ? we maximize at year=9 with an area of (12+2*9)*(12-0.5*9) = 255.

Have fun with these and next time, do your own homework :-)
=mike

Answer 3

I'll just answer #1 for now.
After each win, she has 3/2 times what she had before, and after each loss, 1/2 of it. So she ends up with (3/2)^4 • (1/2)^4 • 256 = $81.

#4 is easy, too. Area is (12+2x)(12 - .5x), which has a max at x=9, Area = 225 m².

Answer 4

ans.4 :
area of garden as variable of years x is:
a(x)=(12+2x)(12-x/2)
=144+18x-x^2
a'(x)=18-2x
therefore maximum at x=9yrs
max. attainable area =225 sqr.meter

ans3
sunday morning: 0
monday morning: 10-1/10(10)=9
tuesday morning: 10+9-1/10(19)=17
wednesday morning: 24
thursday morning: 31
friday morning: 37
saturday morning: 42
saturday night = 52
ans 2
it is solved by c++ program
answer is 11
ans1
if she wins she gets 1.5 of what she bets
if she loses she gets .5
therefore
at the end
she has :256*(1.5)^4*(.5)^4=81$
money is =81

hey mike u don't know either u don't know how to use excel
or
ur excel is wrong because u have given two wrong answers
thanks & good luck

Answer 5

Sorry, I wish I could help you but I can't. Try to find someone to help you before school maybe. Like a fellow classmate, friend, or even a teacher that's not busy if you can.
GOOD LUCK.

Answer 6

DOING LAST MINUTE HW EHHH?