Why is obstruction of the common bile duct so serious? Consider in your answer the multiple functions of the pancreas and the way in which digestive enzymes are processed.

You have an equally likely chance of choosing any number 1 through 30. Find the probability of the given event.

A multiple of 5 is chosen.

Sketch the graph of a function f near a point a. Draw a secant line that passes through (a, f(a)) and a neighboring point (x, f(x)) with x<a. Use arrows to show how the secant lines approach the tangent line as x approaches a.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)

$$\ln z(z-1)^{2}, \ z>1$$

Multiple Choice Which is a counterexample to the conjecture, "If a quadrilateral is equiangular, then it is equilateral"?
A A rectangle that is not a rhombus B A rhombus that is not rectangular C Any square D Any parallelogram

Solve. Use the five-step problem-solving approach.

An envelope is $4 \mathrm{~cm}$ longer than it is wide. The area is $96 \mathrm{~cm}^2$. Find the length and the width.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)

$$\ln \sqrt[3]{\frac{x}{y}}$$

Multiple Choice Which expression does NOT have a value of $-3$ ?

(A) $-2-1$ (B) $10-13$ (C) $5-(-8)$ (D) $-4-(-1)$

Determine whether the statement is true or false. Explain your answer. In a mixing problem, we expect the concentration of the dissolved substance within the tank to approach a finite limit over time.

Let R be the relation defined below. Find each of the following. (a) R(3)

A= {l, 2 , 3, 4 , 6} = B ; a R b if and only if a is a multiple of b.

The greatest amount of phenotypic variation is seen in (a) polygenic traits (b) single-allele traits $(c)$ multiple-allele traits (d) sex-linked traits.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)

$$\log_{5}5x^{2}$$

Four resistors are connected in a circuit as shown in the figure. What value of $R_1$, expressed as a multiple of $R_0$, will make the equivalent resistance for the circuit equal to $R_0$ ?

In this exercise, use the Binomial Theorem to find a polynomial expansion for the given function. Then use a graphing utility and an approach similar to the one in the previous exercises to verify the expansion.

$$f_1(x)=(x+2)^6$$