<u><em>Answer:</em></u>
Total fair of the two trips was $32.7
<u><em>Explanation:</em></u>
<u>We are given that the expression that taxi fair is:</u>
2.85 + 2.7M where M represents the number of miles
<u>1- For Thursday:</u>
Number of miles covered = M = 6 miles
<u>Substitute with M=6 in the given equation to get the fair on Thursday as follows:</u>
Fair on Thursday = 2.85 + 2.7(6) = $19.05
<u>2- For Friday:</u>
Number of miles covered = M = 4 miles
<u>Substitute with M=4 in the given equation to get the fair on Friday as follows:</u>
Fair on Friday = 2.85 + 2.7(4) = $13.65
<u>3- The total fair:</u>
Total fair = fair on Thursday + fair on Friday
Total fair = 19.05 + 13.65 = $32.7
Hope this helps :)
Answer:
- 12 gallons 84%
- 8 gallons 4%
Step-by-step explanation:
I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.
Here, that means the ratio of 84% solution to 4% solution is ...
48 : 32 = 12 : 8
Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)
Mary must use ...
- 12 gallons of 84% acid solution
- 8 gallons of 4% acid solution
You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.
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<em>Check</em>
12 × 84% + 8 × 4% = 10.40 = 20 × 52%
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<em>Usual Solution</em>
A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...
0.84x + 0.04(20 -x) = 0.52(20)
0.80x + 0.8 = 10.4 . . . . simplify
0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8
x = 9.6/0.8 = 12 . . . . gallons of 84% acid
20-x = 8 . . . . . . . . . . gallons of 4% acid
Answer:
I've attached a graph with this, that's your answer
A postulate (or sometimes called as an axiom) is something assumed rather than proven. A theorem is something that is proven. To make a theorem, we first start with undefined terms. Such as line, point, and plane. Then next comes the postulates. Then the definitions. And in some theorems, a previously proven theorem is sometimes used in order to prove the new theorem.