Question

sults on the bar exam of law school graduates
the table above summarizes the results of 200 law school graduates who took the bar exam. if one of the surveyed graduates who passed the bar exam is chosen at random for an interview, what is the probability that the person chosen did not take the review course?
a) $\frac{18}{25}$
b) $\frac{7}{25}$
c) $\frac{25}{200}$
d) $\frac{7}{200}$
e) $\frac{7}{93}$
8.) the scatter plot below compares the math and science scores of twelve students in one classroom. based on the trend shown in the line - of - best fit, which is closest to the expected grade of a student that scores an 78 in math?
a) 78
b) 80
c) 81
d) 84
e) 87
9.) determine the equation from the table of values.
a) $y = 2x+8$
b) $y=\frac{1}{2}x - 8$
c) $y=-\frac{1}{2}+8$
d) $y = 2x+7$
e) $y=\frac{1}{2}x + 8$

$x$	$y$
-2	7
0	8
2	9
4	10
6	11

Explanation:

7.

Step1: Calculate number of passed students

The number of students who passed the bar - exam is \(18 + 7=25\).

Step2: Calculate number of passed students who didn't take review course

The number of students who passed and didn't take the review course is \(7\).

Step3: Calculate the probability

The probability \(P\) that a randomly - chosen passed student did not take the review course is \(P=\frac{7}{25}\) (using the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\) for conditional probability).

Step1: Locate the math score on the x - axis

Locate \(x = 78\) on the x - axis (math scores) of the scatter - plot.

Step2: Find the corresponding y - value on the line of best fit

Draw a vertical line from \(x = 78\) to the line of best fit and then a horizontal line to the y - axis (science scores). The value on the y - axis is closest to \(80\).

Step1: Recall the slope - intercept form of a line

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Find the y - intercept

When \(x = 0\), \(y = 8\), so \(b = 8\).

Step3: Calculate the slope

Using two points \((x_1,y_1)=(0,8)\) and \((x_2,y_2)=(2,9)\), the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{9 - 8}{2-0}=\frac{1}{2}\).

Step4: Write the equation

The equation of the line is \(y=\frac{1}{2}x + 8\).

Answer:

B. \(\frac{7}{25}\)

8.