I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal
Answer:
a = -1
Step-by-step explanation:
The line of symmetry for the parabola given by ...
y = ax² +bx +c
is
x = -b/(2a)
Using the given values, we have ...
-2 = -(-4)/(2a)
Multiplying by -a/2, we get ...
a = (4/2)(-1/2) = -1
The value of "a" is -1.
Answer:
It's 2
Step-by-step explanation:
I don't know what to write
Volume of a cube = Side^3
Volume = 5.1^3
A number cubed is that number times itself 3 times:
5.1 x 5.1 x 5.1 = 132.651 cubic inches.
The answer is 132.651
Answer: Either 2, 5, or 8
This means the number 426 is divisible by 6. So are 456 and 486
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Explanation:
A number is divisible by 6 if both of the following are true
- The number is divisible by 2
- The number is divisible by 3
This is simply because 6 = 2*3. So if 6 is a factor of a number, then 2 and 3 must be factors.
- To have 2 be a factor, the units digit must be in the set {0,2,4,6,8} which is the case here (the units digit is 6 in this case). Therefore we know the number is a multiple of 2 regardless of what the other digits are.
- To have 3 be a factor, the digits must add up to a multiple of 3. Through trial and error, we see that 0 doesn't work because 4+0+6 = 10 which is <u>not</u> a multiple of 3. Same goes for 4+1+6 = 11, but 4+2+6 = 12 is a multiple of 3.
Therefore, 426 is a multiple of 6
Increment that middle digit 2 by 3 and we jump from 426 to 456. Those three digits add to a multiple of 3 as well (4+5+6 = 15). Following that line of logic, we go from 456 to 486 as the last possible three digit number that has these conditions of having 4 first and 6 last, and the number is a multiple of 6.
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In short,
The numbers 426 and 456 and 486 are all multiples of 6 since they are multiples of 2 and 3 at the same time.
So we could replace that middle digit with either 2, 5 or 8.
