Represent each of these fractions as a decimal by using the long-division algorithm.
(a) $\frac{7}{8}$

(b) $\frac{53}{40}$

Convert the following decimal numbers to their binary equivalents:

a. 64 b. 100 c. 111 d. 145 e. 255

Use the Ratio Test to determine whether each series converges or diverges or state that it provides no information. $\sum_{k=1}^{\infty} \frac{(2 k) !}{5^{k} 3^{k-1}}$

Write down the binary representation of the decimal number 63.25 assuming the IEEE 754 double precision format.

A farmer who has two pieces of lumber of lengths a and b(a<b) decides to build a pen in the shape of a triangle for his chickens. He sends his son out to cut the lumber and the boy, without taking any thought as to the ultimate purpose, makes two cuts, one on each piece, at randomly selected points. He then chooses three of the resulting pieces at random and take them to his father. What are the chances that they can be used to form a triangular pen?

Differentiate the causes of frequent voiding associated with cystitis and with renal insufficiency.

Is it possible for two parents with widow’s peaks to have a child that has a straight hairline? Is it possible for two parents with straight hairlines to have a child with a widow’s peak? (Remember that a widow’s peak hairline is dominant, and a straight hairline is recessive.)

Discuss the following problem. The glycosaminoglycan polysaccharide chains that are linked to specific core proteins to form the proteoglycan components of the extracellular space are highly negatively charged. How do you suppose these negatively charged polysaccharide chains help to establish a hydrated gel-like environment around the cell? How would the properties of these molecules differ if the polysaccharide chains were uncharged?

Use what you know about the vocabulary terms listed on the Study Guide to answer the following questions.

What is the term for minerals containing silicon and oxygen?

Sketch the graph of the function. Show vertical and horizontal asymptotes and x-intercepts.

$$y=\frac{x^2-16}{x^2-6 x+8}$$

Convert each of the following binary numbers into its decimal equivalent.

(a) 101

(b) 10101

(c) 1110101

(d) 1101011011

Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist.

$$f\left(x_1, x_2\right)=x_1^2+x_2^2, \quad x_1+x_2=1$$

Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions. Check the results by squaring each root.

$$x^2=81$$

Solve the inequality.

$$2 ( k - 5 ) < 2 k + 5$$