nbined, there are 174 Asians, Africans, Europeans, and Americans in a village. The number of \( A \) eeds the number of Africans and Europeans by 70 . The difference between the number of Europ Americans is 8 . If the number of Africans is doubled, their population exceeds the number of opeans and Americans by 20 . Determine the number of Asians, Africans, Europeans, and Ameri village.

b) \( \frac{x}{3}-\frac{x}{5}+\frac{1}{3}=7 \)

Given complex numbers \( z_{1} \) and \( z_{2} \) \[ z_{1}=5\left(\cos \frac{11 \pi}{4}+i \sin \frac{11 \pi}{4}\right), z_{2}=16\left(\cos \frac{11 \pi}{12}+i \sin \frac{11 \pi}{12}\right) \] Give an exact answer. Express any numbers as integers or simplified fractions. Part 1 of 2 (a) Find \( z_{1} z_{2} \) and write the product in polar form with \( 0 \leq \theta \leq 2 \pi \) The polar form is \( 80\left(\cos \frac{5 \pi}{3}+i\right. \) sin \( \left.\frac{5 \pi}{3}\right) \) Part: \( 1 / 2 \) Part 2 of 2 (b) Find \( \frac{z_{1}}{z_{2}} \) and write the quotient in polar form with \( 0 \leq \theta \leq 2 \pi \)

Solve the system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set \( \left\{\begin{array}{r}2 x-4 y=4 \\ 2 x-4 y=5\end{array}\right. \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is exactly one solution. The solution set is \( \} \). (Simplify your answer. Type an ordered pair, using integers or fractions.) B. There are infinitely many solutions. The solution set is \( \{(x, y) \mid 2 x-4 y=4\} \) or \( \{(x, y) \mid 2 x-4 y=5\} \).

6. Alyssa has saved \( \$ 77 \) from mowing lawns. She spends \( \$ 34 \) on back-to-school shopping. How much of her savings does Alyssa have left? savings \( \rightarrow \) \$77

Rewrite the radical expression as an expression with a rational exponent. \( \sqrt[3]{x^{7}} \) a b d a