F(x) factors as
f(x) = x(x+1)(x-3)
so has zeros of x = -1, 0, 3, because these values make the factors be zero.
The appropriate choice is ...
C. -1, 0, and 3
One interpretation of this problem would be:
The prob. that Jamie both makes money in both bonds and stocks is
(1/20)(0.82), approximately. That comes out to 0.041. This is true onlyl if the two given events are completely independent, which is most likely not the case, because simiilar business climates affect both stocks and bonds.
<h3>
Answer:</h3>
- <u>20</u> kg of 20%
- <u>80</u> kg of 60%
<h3>
Step-by-step explanation:</h3>
I like to use a little X diagram to work mixture problems like this. The constituent concentrations are on the left; the desired mix is in the middle, and the right legs of the X show the differences along the diagonal. These are the ratio numbers for the constituents. Reducing the ratio 32:8 gives 4:1, which totals 5 "ratio units". We need a total of 100 kg of alloy, so each "ratio unit" stands for 100 kg/5 = 20 kg of constituent.
That is, we need 80 kg of 60% alloy and 20 kg of 20% alloy for the product.
_____
<em>Using an equation</em>
If you want to write an equation for the amount of contributing alloy, it works best to let a variable represent the quantity of the highest-concentration contributor, the 60% alloy. Using x for the quantity of that (in kg), the amount of copper in the final alloy is ...
... 0.60x + 0.20(100 -x) = 0.52·100
... 0.40x = 32 . . . . . . . . . . .collect terms, subtract 20
... x = 32/0.40 = 80 . . . . . kg of 60% alloy
... (100 -80) = 20 . . . . . . . .kg of 20% alloy
She is incorrect, her statement comes with no solution.
Okay!
Notable things in the problem:
2011 <u>minutes</u> <u>AFTER</u> the beginning of January 1rst.
12:00AM will be our starting time, because that's when January 1rst begins.
It'll be a bit easier to work with if we convert the 2011 minutes into hours.
So take 2011 minutes and divide it by 60 to get the number of hours.
2011 / 60 = 33 hours and 31 minutes
You wouldn't be able to easily get the exact number of minutes from a calculator. You'll need to use long division. The remainder will be the number of minutes. If you want to check you can multiply the number of hours by 60 and add 31 to the product. If it doesn't equal 2011 minutes then something is amiss.
12:00 AM
Since we know this is a 24 hour clock we can subtract 24 from our number of hours. (Just remember that this is the next day)
12:00 AM with 9 hours and 31 minutes left.
9:31 AM a day later is our time!<u />
