By buying two shirts, Alex will save $33 x \( \frac{40}{100} \) = \( \frac{$33 x 40}{100} \) = \( \frac{$1320}{100} \) = $13.20 on the second shirt.

So, his total cost will be
$33.00 + ($33.00 - $13.20)
$33.00 + $19.80
$52.80

52% of the water consumption is industrial use and 31% is personal use so (52% - 31%) = 21% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{21}{100} \) x 20,000 gallons = 4,200 gallons.

The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 5}{3 x 5} \) + \( \frac{8 x 3}{5 x 3} \)

\( \frac{15}{15} \) + \( \frac{24}{15} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{15 + 24}{15} \) = \( \frac{39}{15} \) = 2\(\frac{3}{5}\)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{4}{4}} \)
\( \frac{\sqrt{4}}{\sqrt{4}} \)
\( \frac{\sqrt{2^2}}{\sqrt{2^2}} \)
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