Y=gradient x + zeroth term
Y=2x+5
Notation. x y means x is less than or equal to y. x y means x is greater than or equal to y. x < y means x is less than y. x > y means x is greater than y. The last two inequalities are called strict inequalities. Our focus will be on the nonstrict inequalities. Algebra of Inequalities Suppose x + 3 < 8. Addition works like for equations: x + 6 < 11 (added 3 to each side). Subtraction works like for equations: x + 2 < 7 (subtracted 4 from each side). Multiplication and division by positive numbers work like for equations: 2x + 12 < 22 =) x + 6 < 11 (each side is divided by 2 or multiplied by 1 2 ). 59 60 4. LINEAR PROGRAMMING Multiplication and division by negative numbers changes the direction of the inequality sign: 2x + 12 < 22 =) x 6 > 11 (each side is divided by -2 or multiplied by 1 2 ). Example. For 3x 4y and 24 there are 3 possibilities: 3x 4y = 24 3x 4y < 24 3x 4y > 24 4y = 3x + 24 4y < 3x + 24 4y > 3x + 24 y = 3 4x 6 y > 3 4x 6 y < 3 4x 6 The three solution sets above are disjoint (do not intersect or overlap), and their graphs fill up the plane. We are familiar with the graph of the linear equation. The graph of one inequality is all the points on one side of the line, the graph of the other all the points on the other side of the line. To determine which side for an inequality, choose a test point not on the line (such as (0, 0) if the line does not pass through the origin). Substitute this point into the linear inequality. For a true statement, the solution region is the side of the line that the test point is on; for a false statement, it is the other side.
Answer:
<em>On time: 0.67</em>
<em>Late: 0.33</em>
Step-by-step explanation:
<u>Probabilities</u>
One approach to estimating the probability of occurrence of an event is to record the number of times that event happens (e) and compare it with the total number of trials (n).
The probability can be estimated with the formula:
And the probability that the event doesn't occur is
Q = 1 - P
Paulo arrives on time to school e=53 times out of n=79 times. The probability that he arrives on time is:
P = 0.67
And the probability he arrives late is:
Q = 1 - 0.67 = 0.33
Answer: 48/25
Step-by-step explanation:
Answer:
No, it is not possible to obtain zero by adding two vectors of unequal magnitudes.
Explanation:
The Sum of two vectors can only be zero if they are equal in magnitude and opposite in direction. So no two vectors of unequal magnitude cannot be added to give a null vector. Three vectors of equal magnitude and making an angle 120 degrees with each other gives a zero resultant.
