A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

You have 36 out of the total of 400 raffle tickets sold so you have a (\( \frac{36}{400} \)) x 100 = \( \frac{36 \times 100}{400} \) = \( \frac{3600}{400} \) = 9% chance to win the raffle.

To subtract these radicals together their radicands must be the same:

4\( \sqrt{75} \) - 7\( \sqrt{3} \)
4\( \sqrt{25 \times 3} \) - 7\( \sqrt{3} \)
4\( \sqrt{5^2 \times 3} \) - 7\( \sqrt{3} \)
(4)(5)\( \sqrt{3} \) - 7\( \sqrt{3} \)
20\( \sqrt{3} \) - 7\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them:

The equation for this sequence is:

a_n = a_n-1 + 7

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 7
a₆ = 29 + 7
a₆ = 36