Answer:
750 grams of 60% alloy
Step-by-step explanation:
Define x = amount of 60% alloy and y = amount of 20% alloy
Equating the amounts of gold:
0.6x+0.2y = 1000(0.5)
Since there must be 1000 grams total:
x+y = 1000
Writing the 2 resulting equations together:
0.6x + 0.2y = 500
x + y = 1000
Multiply the first equation by 5:
3x + y = 2500
x + y = 1000
Subtracting the 2nd equation from the 1st:
2x = 1500
x = 750
Answer: 750 grams of 60% alloy
Answer:
0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
N(489,6)
This means that 
What is the probability that the box will contain less than the advertised weight of 466 g?
This is the p-value of Z when X = 466. So



has a p-value of 0.000064
0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.
The greatest common factor is...
5a
I got this by...
10: 1,2,5,10
15: 1,3,5,15
25: 1,5,25
The GCF is 5 for the numbers.
For the a's, it's...
a: a
a^3: a×a×a
a^6: a×a×a×a×a×a
The GFC is a.
Then multiple 5 and a, and you get...
5a
The GFC is...
5a
Hope this helps!
I don't know what the "six-step method" is, but I do know how to solve the problem:
Let x = number of gallons of 50% solution
amount of antifreeze in 50% solution = 0.50x
amount of antifreeze in 10% solution = 0.10(80) = 8
amount of 40% solution = 0.40(x+80) = 0.40x + 32
Then, 0.50x + 8 = 0.40x + 32
0.10x = 24
x = 240 gal