Question

1. (l136) find the median, mean, mode, and range of the data. number of miles biked each day 12.1 10 11.5 9.8 14.4 10.5 8 10.2 13.3 9.2 10.5 11.3 12.9 11.8 a) median = 2.8; mean = 2.9; mode = 10.5; range = 6.4 b) median = 2.8; mean = 9.8; mode = 12; range = 6 c) median = 10.9; mean = 9.8; mode = 10.5; range = 6.4 d) median = 10.9; mean = 11.1; mode = 10.5; range = 6.4 e) none of the above 9. (l133) solve the absolute - value equation: |4x| = 20 a) x = 5, x = - 5 b) x = - 27, x = 9 c) x = 27, x = - 9 d) x = 8, x = 7 e) none of the above 10. (l133) solve the absolute - value equation: |(1/3)x - 3| = 6 a) x = 5, x = - 5 b) x = - 27, x = 9 c) x = 27, x = - 9 d) x = 8, x = 7 e) none of the above

Explanation:

8.

Step1: Arrange data in ascending order

$8,9.2,9.8,10,10.2,10.5,10.5,11.3,11.5,11.8,12.1,12.9,13.3,14.4$

Step2: Calculate the median

There are $n = 14$ data - points. The median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. $\frac{14}{2}=7$ and $\frac{14}{2}+1 = 8$. So, median$=\frac{10.5 + 11.3}{2}=10.9$.

Step3: Calculate the mean

Mean$\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{8 + 9.2+9.8+10+10.2+10.5+10.5+11.3+11.5+11.8+12.1+12.9+13.3+14.4}{14}=\frac{155.5}{14}\approx11.1$.

Step4: Find the mode

The mode is the number that appears most frequently. Here, $10.5$ appears twice and other numbers appear only once, so mode = $10.5$.

Step5: Calculate the range

Range = maximum value - minimum value. Maximum value is $14.4$ and minimum value is $8$, so range$=14.4 - 8=6.4$.

Step1: Recall the absolute - value property

If $|a|=b$ ($b\geq0$), then $a = b$ or $a=-b$. For the equation $|4x| = 20$, we have $4x=20$ or $4x=-20$.

Step2: Solve for $x$ in $4x = 20$

Dividing both sides by $4$, we get $x = 5$.

Step3: Solve for $x$ in $4x=-20$

Dividing both sides by $4$, we get $x=-5$.

Step1: Recall the absolute - value property

If $|\frac{1}{3}x - 3|=6$, then $\frac{1}{3}x-3 = 6$ or $\frac{1}{3}x-3=-6$.

Step2: Solve for $x$ in $\frac{1}{3}x-3 = 6$

Add $3$ to both sides: $\frac{1}{3}x=6 + 3=9$. Then multiply both sides by $3$ to get $x = 27$.

Step3: Solve for $x$ in $\frac{1}{3}x-3=-6$

Add $3$ to both sides: $\frac{1}{3}x=-6 + 3=-3$. Then multiply both sides by $3$ to get $x=-9$.

Answer:

d) median = 10.9; mean = 11.1; mode = 10.5; range = 6.4

9.