Kiran surveyed a random sample of students in her school district, and she found these statistics: P(rides bike to school) = 0.14
P(has crossing guard) = 0.48
P(rides bike and crossing guard) = 0.12
Find the probability that a student rides a bike to school, given that the student's school has a crossing guard.

P (rides bike crossing guard) =

Barney & noblet customers can choose to purchase a membership for $25 per year members receive 10% off all store purchases 1. how much would a member pay per year if he bought $50 worth of items each year? 2. write a slope-intercept equation that expresses how much a member pays per year using x to represent his purchases per year 3. how much would a member have to spend per year to pay off his membership fee?

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5 part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points) part b: is the point (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)

Which of the following vectors are orthogonal to (2,1)? check all that apply