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…
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:
- B. 8
- H. 7
- B. 6.8
- C. 2
- 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.