How much water should we add to 5 gallons of 18% acid solution to dilute it to a concentration of 10%?
We should add
gallons of water to dilute the concetration.

4 gallons of water is needed to dilute to a concentration of 10%.

Step-by-step explanation:

It is given that,

The 5 gallons of water contains 18% of acid solution.

Now, we are asked to find the gallons of water needed to dilute it to a concentration of 10% acid solution.

We obtain the equation by stating that the amount of acid 10% in the water must dilute up to 18%.

For this, x amount of water should be added.

Therefore, the equation is framed as,

⇒ 0.1 (x+5) = 5 (0.18)

⇒ 0.1x + 0.5 = 0.9

⇒ 0.1x = 0.9 - 0.5

⇒ x = 0.4 / 0.1

⇒ x = 4

∴ 4 gallons of water is needed to dilute to a concentration of 10%.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.