841,620. 841.620. 841-620. 026,148
Answer:
3:7
Step-by-step explanation:
So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or <em>20%</em> is alcohol. So let's just say that x=alcohol and y=water, this means that:
where c is the total amount in the glass. This means that: 
Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that:
and that:
.
So if we're going to add the two glasses, we simply add the two sides, and get:
. Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get:
Now we can add like terms to get the equation:
. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.
Hope this helps you If you need any more help let me know in the comments
Answer:
Step-by-step explanation:
the formula for the circumference of a circle is 2rπ
the formula for the area of a circle is (r^2)π
the formula for the diameter of a circle is 2r
π=3.14
---------------------------------------------------------------
1. diameter =2r. since diameter=24, r=12
2. circumference=2rπ. since circumference = 314. 314=2rπ r=49.9746
3. circumference=2rπ area=(r^2)π
since r=7, circumference=14π=43.98229 since r=7, area is 49π=153.9380
4. Since the diameter is 20 the radius is 10. so just insert it into the formulas as before: circumference=20π=62.8318 and area=100π=314.15926
5. the formula for the diameter is 2r=d 2(18)=d, 36=d
6. 2rπ=circumference = 2(5)π=10π=31.415926
Hope that helps :)