The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%

If the tiger has consumed 30 pounds of food in 5 days that's \( \frac{30}{5} \) = 6 pounds of food per day. The tiger needs to consume 54 - 30 = 24 more pounds of food to reach 54 pounds total. At 6 pounds of food per day that's \( \frac{24}{6} \) = 4 more days.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

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

\( \frac{2 x 2}{6 x 2} \) + \( \frac{7 x 1}{12 x 1} \)

\( \frac{4}{12} \) + \( \frac{7}{12} \)

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

\( \frac{4 + 7}{12} \) = \( \frac{11}{12} \) = \(\frac{11}{12}\)

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.