answer:We can use the formula for the nth term of an arithmetic sequence, which is a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, d is the common difference, and n is the number of terms. We are given that the fifth term is 5, the sixth term is 9, and the seventh term is 13. So, we have the equations a_1 + 4d = 5, a_1 + 5d = 9, and a_1 + 6d = 13. Subtracting the first equation from the second equation gives d = 4, and subtracting the second equation from the third equation gives d = 4 again. So, the common difference is 4. Substituting d = 4 into the first equation gives a_1 + 4(4) = 5, which simplifies to a_1 + 16 = 5, and subtracting 16 from both sides gives a_1 = -11. The sum of the first four terms is a_1 + a_2 + a_3 + a_4, which is -11 + (-11 + 4) + (-11 + 2(4)) + (-11 + 3(4)), which simplifies to -11 + (-7) + (-3) + 1, which is boxed{-20}. The answer is: -20

answer:A 10% discount means that Rose pays 100% - 10% = 90% of the original price. 90% of 10 is 0.9 * 10 = 9. So Rose paid 9 after the discount. 9 The answer is: 9

answer:Consider the equation x^n + x^{n-1} + dots + x + 1 = 0. If we subtract 1 from both sides and factor, we get (x-1)(x^{n-1} + x^{n-2} + dots + 1) = 0. So one root is x=1. For the second factor, note that if we substitute x=1 into this factor, we get n. So if n is odd, the second factor is equal to 1, and there are no other real roots. If n is even, the second factor is a sum of positive terms, so it is always positive and there are no real roots. Therefore, the largest possible number of real roots for this polynomial is boxed{1}. The answer is: 1

answer:It takes 3 minutes per smoothie to transform the ice cubes into smoothies, so for 5 smoothies, it will take 5 * 3 = 15 minutes. In addition to the time to make the smoothies, it takes 40 minutes to freeze the ice cubes, so the total time required is 15 + 40 = 55 minutes. 55 The answer is: 55