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KiRa [710]
2 years ago
7

A chemical company makes two brands of antifreeze. The first brand is 45% pure antifreeze, and the second brand is 95% pure anti

freeze. In order to obtain 90 gallons of a mixture that contains 60% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Mathematics
1 answer:
Lesechka [4]2 years ago
5 0

Let x = amount of 45% antifreezeLet y = amount of 70% antifreeze     EQUATION 1:   x + y = 150    (total of 150 gallons mixed)     EQUATION 2:  .45x + .75y = .55(x + y) Simplify and solve the system of equations     Multiply second equation by 100 on both sides to remove the decimals           45x + 75y = 55(x + y)     Combine like terms           45x + 75y = 55x + 55y           45x - 55x + 75y - 55y = 0             -10x + 20y = 0       Now we have the following system of equations:              x  +    y = 150        -10x + 20y =     0     Multiply the first equation by -10 to get opposite coefficients for x;  add the equations to eliminate x           10x + 10y = 1500         -10x + 20y =       0        ------------------------------                    30y = 1500      Solve for y            30y = 1500                y = 50      Since the total mixed gallons is 150, x = 150 - 50 = 100 So we need 100 gallons of the 45% antifreeze and 50 gallons of the 70% antifreeze

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Step-by-step explanation:

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Explanation:

The process of blocking in statistics is where we group up people in blocks, and each block is determined by a characteristic of some sort. In this case, we're grouping people up by pain resistance level. Those very resistant to pain will be in one group, while those who easily feel pain will be in another block, and so on. It might be effective to have a pain scale and sort people by that.

Blocking is done so that we eliminate unwanted variability. We are testing the effectiveness of the itching cream, so all we care about is if the itch reduces or not. We aren't worried about the levels of pain. However, it says that "Previous studies have shown the effects of treatment may vary based on a subject's pain resistance". So we group up the people by pain tolerance to help eliminate the variability of pain tolerance levels.

This is why choice C is the final answer.

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Extra info:

  • Choice A is false because a person's name doesn't have anything to do with if the treatment works or not.
  • Choice B is false because we weren't given any info to indicate it being true. It may be true, but we simply don't have enough info to confirm it.
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