Targeted Review Solutions

Name the type of data distribution (left-/right-skewed, symmetric) when the mean is 6.78, the median is 5.5, and the mode is 1.

$median < mean$

right-skewed

The area for a standard normal distribution is 0.59 with a mean of 87 and a standard deviation of 6.2.

$\begin{matrix} \begin{array}{rcl} 0.59 & \approx & 0.5910 \\ z & = & 0.23 \end{array} \end{matrix} \begin{matrix} \begin{array}{rcl} (6.2) 0.23 & = & \frac{X - 87}{6.2} (6.2) \\ 1.426 & = & X - 87 \\ X & = & 88.426 \end{array} \end{matrix}$

$\begin{matrix} \begin{array}{rcl} 88.4 \end{array} \end{matrix}$

For problems 3–4:

A t-shirt distributor is trying to figure out which college’s merchandise is most popular with its customers. The distributor divided stores into regions. Then, stores in three regions were selected to record the college logo on every t-shirt sold for one week.

Name the population and the sample.

Population: all t-shirts sold
Sample: every t-shirt with a college logo

Name the type of sampling method used.

The population is divided into regions (or clusters), and certain clusters are selected based on the previously defined parameters.

Cluster

Determine the roots, their multiplicities, and the degree.
$h (x) = x {(x - 3)}^{2} (x + 1) (x - 5)$

$x = 0, x - 3 = 0, x + 1 = 0, x - 5 = 0$

$x = - 1, 0, 3 (multiplicity 2), degree : 5$

For problems 6–8, use the functions: $f (x) = - \frac{1}{2} (x - 6) + 10, g (x) = x^{2} - 9$

$f (x) + g (x)$

$(- \frac{1}{2} (x - 6) + 10) + (x^{2} - 9) - \frac{1}{2} x + 3 + 10 + x^{2} - 9$

$x^{2} - \frac{1}{2} x + 4$

$(f + g) (6)$

$\begin{array}{rcl} (f + g) (6) & = & x^{2} - \frac{1}{2} x + 4 \\ = & {(6)}^{2} - \frac{1}{2} (6) + 4 \\ = & 36 - 3 + 4 \end{array}$

$(f \circ g) (x)$

$\begin{array}{rcl} (f \circ g) (x) & = & f [g (x)] \\ = & - \frac{1}{2} ((x^{2} - 9) - 6) + 10 \\ = & - \frac{1}{2} (x^{2} - 15) + 10 \\ = & - \frac{1}{2} x^{2} - \frac{15}{2} + \frac{20}{2} \end{array}$

$\begin{array}{rcl} (f \circ g) (x) & = & - \frac{1}{2} x^{2} + \frac{5}{2} \end{array}$

Multiple Choice

A research team is studying the effectiveness of a new teaching method in elementary schools. They identify all elementary schools in a large school district, randomly select 8 schools (clusters). Then they implement the new teaching method and collect data from all students in those selected schools.

simple random
systematic
stratified
cluster

Note

Review the definitions for each sampling method.

Solve: $- 3 \log_{2} (3 x + 1) = - 12$

$\frac{7}{3}$
$\frac{17}{3}$
5
no solution

$\begin{array}{rcl} \log_{2} (3 x + 1) & = & 4 \\ 2^{4} & = & 3 x + 1 \\ 16 & = & 3 x + 1 \\ 15 & = & 3 x \\ x & = & 5 \end{array}$

Note

This option is the result when you multiply 2 and 4 rather than raising 2 to the 4th power.
This option is the result if you add one to both sides rather than subtracting one from both sides.

Select the expression equivalent to: $\log (\frac{a b}{h^{c}})$

$\log a + \log b - c \log h$
$\log a + \log b - h \log c$
$\log (a + b) - c \log h$
$b \log a - c \log h$

$\begin{array}{rcl} \log (\frac{a b}{h^{c}}) & = & \log (a b) - \log h^{c} \\ = & \log a + \log b - c \log h \end{array}$

Note

B) The last term switched the exponent and argument.

C, D) The product rule is not used correctly.

Select all measures of center.

mean
median
mode
range

Note

See definition for measures of center.

Problem	1	2	3	4	5	6	7	8	9	10	11	12
Origin	L45	L46	L47	L48	L34	L31	L31	L32	L48	L40	L42	L45

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