Targeted Review Solutions

Use the following scenario for problems 1–2.

A consumer advocacy group investigated whether cereal box color (red, blue, or yellow) affects calories per serving. They sampled 200 US cereal boxes, noting color and calorie count from labels.

Name the type of study and the population.

Observational study
Population: all cereal boxes sold in the United States

Identify the variables and classify them as quantitative or categorical.

Quantitative: calorie count from labels
Categorical: color of the cereal box

Use the following scenario for problems 3–4.

The fuel efficiency (in miles per gallon, mpg) of a specific make and model of car is collected from all owners who purchased the car in the first six months of sales. The average fuel efficiency is 28 mpg with a standard deviation of 3 mpg.

Sketch a normal curve showing the Empirical rule.

Determine the fuel efficiency for cars in the 97.5th percentile.

$z = 1.96 \begin{matrix} (3) (1.96) = \frac{X - 28}{3} (3) \\ 5.88 = X - 28 \\ + 28 + 28 \\ X = 33.88 \end{matrix}$

Cars in the 97.5th percentile will have a fuel efficiency of 33.9 mpg.

Determine the value of x if $\log_{4} x = - 3$ .

$4^{- 3} = x x = \frac{1}{4^{3}}$

$x = \frac{1}{64}$

Solve: ${(\frac{5}{3})}^{x} = {(\frac{27}{125})}^{3 x - 2}$

$\begin{array}{rcl} {(\frac{3}{5})}^{- x} & = & {(\frac{3}{5})}^{3 (3 x - 2)} \\ - x & = & 3 (3 x - 2) \\ - x & = & 9 x - 6 \\ 6 & = & 10 x \\ x & = & \frac{6}{10} \end{array}$

$\begin{array}{rcl} x & = & \frac{3}{5} \end{array}$

Sketch a graph with technology. Label the intercept(s) and turning points.
$f (x) = x^{4} + 3 x^{3} + x^{2} - 3 x - 2$

Sketch a graph with technology. Label the intercept(s).
$y = \frac{1}{2} {(3)}^{x} - 1$

Multiple Choice

Describe the transformation from f(x) to g(x).
$f (x) = {(2)}^{x}, g (x) = \frac{1}{4} {(2)}^{x + 4}$

g(x) is vertically stretched and translated 4 units up
g(x) is vertically stretched and translated 4 units left
g(x) is vertically compressed and translated 4 units up
g(x) is vertically compressed and translated 4 units left

$\begin{matrix} f (x) & g (x) \\ a : & 1 & \frac{1}{4} \\ h : & 0 & 4 \\ k : & 0 & 0 \end{matrix}$

Note

A, B) When a is a fraction between zero and one, the graph is compressed.
A, C) The value of h is zero for both functions, so the graph is not moving up.

Identify the sampling method.A teacher wants to select a student at random to present their project. They write each student’s name on a separate slip of paper, put all the slips into a jar, and draw one name without looking.

Simple random sample
Systematic
Stratified
Cluster

Note

See definitions of sampling methods

Identify the type of study conducted.
A beverage company wants to test whether its new energy drink improves mental performance. They recruit 100 college students and randomly divide them into two groups. Group A receives the new drink, and Group B is given a placebo.

Observation
Experiment
Survey
Cannot be determined

Two groups: an experiment and a control group

Note

See definitions of types of studies

Boyle’s Law states that pressure, p, of a compressed gas is inversely proportional to the volume, v, or $p_{1} v_{1} = p_{2} v_{2} .$ If the volume of gas is 200 cubic inches when a pressure of 25 pounds per square inch exists, what is the pressure for a volume of 125 cubic inches?

$25 lb / {in}^{2}$
$40 lb / {in}^{2}$
$125 lb / {in}^{2}$
$1000 lb / {in}^{2}$

Note

This option is the amount when 125 and 25 are substituted in on the same side of the formula.
This option is the given amount of pressure.
This option is the amount if the volumes were multiplied together and divided by the pressure.

$\begin{array}{rcl} (200) (25) & = & 125 p \\ \frac{(200) {(25)}^{1}}{125_{5}} & = & \frac{125 p}{125} \\ p & = & \frac{200}{5} \\ p & = & 40 \end{array}$

Problem	1	2	3	4	5	6	7	8	9	10	11	12
Origin	L47	L47	L45	L46	L39	L38	L34, L35	L37	L37	L48	L47	L36

L = Lesson in this level, A1 = Algebra 1: Principles of Secondary Mathematics