6. (10 points) Consider the sum \( \sum_{k=1}^{4}(2 k+1) \). (a) Write out the sum in expanded form. (b) Calculate the value of the sum.

\begin{tabular}{l|l}\( \begin{array}{l}\text { Find the } \\ \text { value of the } \\ \text { expression. }\end{array} \) \\ \( |-10|-|-5| \)\end{tabular}

Four beneficiaries are to divide an estate of \( \$ 189,000 \) in the ratio \( \frac{1}{3}: \frac{1}{4}: \frac{3}{8}: \frac{1}{24} \). How much should each receive? The first beneficiary should receive \( \$ 63,000 \). (Simplify your answer.) The second beneficiary should receive \( \$ 47,250 \). (Simplify your answer.) The third beneficiary should receive \( \$ \) (Simplify your answer.)

Find the value of the expression. \( |-7|+|-8|-|-15| \)

Four beneficiaries are to divide an estate of \( \$ 189,000 \) in the ratio \( \frac{1}{3}: \frac{1}{4}: \frac{3}{8}: \frac{1}{24} \). How much should each receive? The first beneficiary should receive \( \$ 63,000 \). (Simplify your answer.) The second beneficiary should receive \( \$ \) (Simplify your answer.)

Simplify. \( 6 \cdot\{(272-63 \div 7)-[(40 \div 8) \cdot(40 \div 8)-6 \cdot 2]\} \) \( 6 \cdot\{(272-63 \div 7)-[(40 \div 8) \cdot(40 \div 8)-6 \cdot 2]\}=\square \)