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tatuchka [14]
3 years ago
5

How many gallons of a 50% antifreeze solution must be mixed with 60 gallons of 30% antifreeze to get a mixture that is 40% antif

reeze? Use the six-step method
Mathematics
1 answer:
Mariulka [41]3 years ago
6 0

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

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nekit [7.7K]

Answer:

2^3*2^4=4^7 is wrong.

Step-by-step explanation:

2^3*2^4=2^7

3 0
2 years ago
Read 2 more answers
Which of these relations on the set {0, 1, 2, 3} are equivalence relations? If not, please give reasons why. (In other words, if
Delicious77 [7]

Answer:

(1)Equivalence Relation

(2)Not Transitive, (0,3) is missing

(3)Equivalence Relation

(4)Not symmetric and Not Transitive, (2,1) is not in the set

Step-by-step explanation:

A set is said to be an equivalence relation if it satisfies the following conditions:

  • Reflexivity: If \forall x \in A, x \rightarrow x
  • Symmetry: \forall x,y \in A, $if x \rightarrow y,$ then y \rightarrow x
  • Transitivity: \forall x,y,z \in A, $if x \rightarrow y,$ and y \rightarrow z, $ then x \rightarrow z

(1) {(0,0), (1,1), (2,2), (3,3)}

(3) {(0,0), (1,1), (1,2), (2,1), (2,2), (3,3)}

The relations in 1 and 3 are Reflexive, Symmetric and Transitive. Therefore (1) and (3) are equivalence relation.

(2) {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)}

In (2), (0,2) and (2,3) are in the set but (0,3) is not in the set.

Therefore, It is not transitive.

As a result, the set (2) is not an equivalence relation.

(4) {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}

(1,2) is in the set but (2,1) is not in the set, therefore it is not symmetric

Also, (2,0) and (0,1) is in the set, but (2,1) is not, rendering the condition for transitivity invalid.

5 0
3 years ago
Alyssa takes part in the triathlon. She cycles 4/5 of the route, runs 7/8 of the route, and swims the rest of the way. She swims
hjlf

Answer:

12 miles

Step-by-step explanation:

Alyssa takes part in the triathlon. She cycles 4/5 of the route, runs 1/8 of the route, and swims the rest of the way. She swims 0.9 miles. Find the total distance of the triathlon route.

Total distance Alyssa cycled and ran =

\frac{4}{5} + \frac{1}{8}

\frac{32 + 5}{40} = \frac{37}{40}

Distance she swam =  1 - 37/40 = 3/40

3/40 of the distance is 0.9

the total distance = 40/3 x 0.9 = 12 miles

3 0
2 years ago
Which expression is equivalent
Tatiana [17]

Given expression is

\sqrt[4]{\frac{16x^{11}y^8}{81x^7y^6}}

Radical is fourth root

first we simplify the terms inside the radical

\frac{x^{11}}{x^7}=x^4

\frac{y^(8)}{y^6}=y^2

So the expression becomes

\sqrt[4]{\frac{16x^4y^2}{81}}

Now we take fourth root

\sqrt[4]{16} = 2

\sqrt[4]{81} = 3

\sqrt[4]{x^4} = x

We cannot simplify fourth root (y^2)

After simplification , expression becomes

\frac{2x\sqrt[4]{y^2}}{3}

Answer is option B


8 0
2 years ago
What is value of x? Please help! Will reward
Andre45 [30]
X = 50
.................
8 0
3 years ago
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