5. what is the determinant of $\begin{bmatrix...
5. what is the determinant of $\begin{bmatrix}3&-2\\4&0end{bmatrix}$?\na -8 b 8 c 12 d 20\nuse the table for the next two questions 6 & 7\n|number of cars|\n|10|7|6|9|7|3|5|6|8|4|\n|8|2|7|5|7|9|11|5|7|10|\n6. what is the median of the data?\nf 6.8 g 6 h 7 j 7.5\n7. what is the mean of the data?\na 6.5 b 6.8 c 7 d 7.2\nuse the graph for 8 & 9\n8. $lim_{x\rightarrow2}f(x)$\na 0 b 1 c 2 d 3\n9. $lim_{x\rightarrow3^{+}}f(x)$\nf 3 g 2 h 1 j 0
Answer
# Answer:
5. B. 8
6. H. 7
7. B. 6.8
8. C. 2
9. F. 3
# Explanation:
## Step1: Calculate determinant
For a \(2\times2\) matrix \(\begin{bmatrix}a&b\\c&d\end{bmatrix}\), the determinant is \(ad - bc\). Here \(a = 3\), \(b=- 2\), \(c = 4\), \(d = 0\), so \(3\times0-(-2)\times4=0 + 8=8\).
## Step2: Find median
Arrange the data \(2,3,4,5,5,5,6,6,7,7,7,7,7,8,8,9,9,10,10,11\) in ascending - order. There are \(n = 20\) data points. The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{20}{2}=10\) and \(\frac{20}{2}+1 = 11\). The 10th and 11th values are both 7, so the median is 7.
## Step3: Calculate mean
The sum of the data \(2 + 3+4+5\times3+6\times2+7\times5+8\times2+9\times2+10\times2+11=136\). There are \(n = 20\) data points. The mean \(\bar{x}=\frac{136}{20}=6.8\).
## Step4: Find \(\lim_{x\rightarrow2}f(x)\)
From the graph, as \(x\) approaches 2 from both sides, the function value approaches 2.
## Step5: Find \(\lim_{x\rightarrow3^{+}}f(x)\)
From the graph, as \(x\) approaches 3 from the right - hand side, the function value approaches 3.