(16) Two numbers have an absolute value of 4 . Which of the two numbers is farther from 1 on the number line?

Cabinet \( X \) costs \( \$ 30 \), requires \( 12 \mathrm{sq} \mathrm{ft} \mathrm{of} \mathrm{floor} \mathrm{space} \),and holds 36 cu ft of files. Cabinet \( Y \) costs \( \$ 50 \), requires 6 sq ft of floor space, and holds 30 cu ft . To get maximum storage, how many of each should be purchased with a budget limit of \( \$ 450 \) and floor space of 96 sq ft? The manager should buy \( \square \) of cabinet \( X \) and \( \square \) of cabinet \( Y \). (If two possibilities provide maximum storage, use the option that involves buying at least one of cabinet \( X \) and at least one of cabinet \( Y \).)

1. Fill in the Blank 16 points A sequence is defined by \( f(1)=8 \) and \( f(n)=3 f(n-1) \), for each whole number where \( n>1 \).

Rationalize the denominator: \( \frac{15}{\sqrt{75}} \) \( A=\square \)

Find the value of the determinant. \[ \left|\begin{array}{rrr}9 & 6 & 10 \\ -1 & -1 & 7 \\ -4 & -2 & 1\end{array}\right| \] The determinant value is

7) Simplify the logarithm so that no argument contains a product, quotient or a powe \( \ln \left(e x^{3}\right)= \) a) \( 1-3 \ln x \) b) \( 01+3 \ln x \) c) \( 03-\ln x \) d) \( 3+\ln x \)