Exam 8: Real Numbers and Algebraic Thinking

Solve the problem. Leave the answer in exponential notation. -The expression $2 ^ { 6 } \cdot 64 ^ { t }$ approximates the number of bacteria after t hours. What is the initial number of bacteria, that is, the number when $t = 0$ ?

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation. -"Is a cousin of"

Solve the problem. -The cost of a cab ride in dollars is given by C(x)= 1.80 + 1.10x, where x is the number of miles. What are the charges for a ride of 25 miles?

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and S is the set of irrational numbers, list the set(s)to which the given number belongs. If the number does not belong to any, state none. -9

Find or investigate the function as requested. -If t(n) represents the nth term of a sequence for $\mathrm { n } \in \mathrm { N }$ and $t ( n ) = n ^ { 2 } + 2 n + 5$ , then is 29 a value of the function whose domain is N ?

Solve the equation. -7(2x + 1)+ 9(2x + 1)= 144

Find or investigate the function as requested. -If t(n) represents the nth term of a sequence for $\mathrm { n } \in \mathrm { N }$ and t(n)=4 n+2 , then is 33 a value of the function whose domain is N?

Write an equation relating the variables in the situation described. -The number of words W typed in t minutes if you type 29 words in one minute.

Write an expression in terms of the given variable(s)that represents the indicated quantity. -Mark has half as many stickers as Derek. If Derek has d stickers and Mark m stickers, and Derek gives Mark 10 stickers, how many stickers does each have in terms of d?

Write an expression in terms of the given variable(s)that represents the indicated quantity. -The cost of having an electrician spend h hours at your house if the electrician charges $48 for coming to the house and $x per hour for labor

If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and S is the set of irrational numbers, list the set(s)for which a solution to the given equation exists. If a solution to the given equation does not belong to any set, state none. - $x ^ { 2 } = 3$

Decide if the number is rational or irrational. - $- \sqrt { 170 }$

Solve the problem. -A cab ride costs $1.70 base plus $0.90 a mile. How far can you go for $13.40?

Solve the problem. -A paint mixture contains 46 gallons of base for every gallon of color. In 1786 gallons of paint, how many gallons of color are there?

Solve the problem. -Find the nth term of the following arithmetic sequence: $\pi + 0.5 , \pi + 5.5 , \pi + 10.5 , \ldots$

The sum of any two positive irrational numbers is an irrational number.

Solve the problem. -A house was purchased for $79,000. After 9 years the value of the house was $106,000. Express the house's value V(t)in terms of time t in years.

Write an equation relating the variables in the situation described. -The temperature in Fahrenheit F if five times the temperature in Fahrenheit is equal to the sum of nine times the temperature in degree Celsius C and 160.

The product of any two distinct positive irrational numbers is irrational.

Solve the problem. -Find the nth term of the following arithmetic sequence: $2,2 + \sqrt { 5 } , 2 + 2 \sqrt { 5 } , \ldots$