(A) Graph y = x + b for b = − 5 , − 3 , 0 , 3 and 5 simultaneously in the same coordinate system . Verbally describe the geometric significance of b . (B) Graph y = m x − 1 for m = − 2 , − 1 , 0 , 1 , and 2 simultaneously in the same coordinate system. Verbally describe the geometric significance of m . (C) Using a graphing calculator, explore the graph of y = m x + b for different values of m and b .
(A) Graph y = x + b for b = − 5 , − 3 , 0 , 3 and 5 simultaneously in the same coordinate system . Verbally describe the geometric significance of b . (B) Graph y = m x − 1 for m = − 2 , − 1 , 0 , 1 , and 2 simultaneously in the same coordinate system. Verbally describe the geometric significance of m . (C) Using a graphing calculator, explore the graph of y = m x + b for different values of m and b .
Solution Summary: The author analyzes the equation y=x+b and its significance.
(A) Graph
y
=
x
+
b
for
b
=
−
5
,
−
3
,
0
,
3
and
5
simultaneously in the same coordinate
system. Verbally describe the geometric significance of
b
.
(B) Graph
y
=
m
x
−
1
for
m
=
−
2
,
−
1
,
0
,
1
,
and
2
simultaneously in the same coordinate
system. Verbally describe the geometric significance of
m
.
(C) Using a graphing calculator, explore the graph of
y
=
m
x
+
b
for different values of
m
and
b
.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Q9. If A and B are two events, prove that P(ANB) ≥ 1 − P(Ā) – P(B). [Note: This
is a simplified version of the Bonferroni inequality.]
Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 222 grams of protein and at least 162 grams of fat. If chicken costs 11¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost? (If an answer does not exist, enter DNE.)
Q6. Consider a situation where cars entering an intersection could turn right, turn left,
or go straight. An experiment consists of observing two vehicles moving through
the intersection.
(a) How many sample points are there in the sample space? List them.
(b) Assuming that all sample points are equally likely, what is the probability that
at least one car turns left?
(c) Again assuming equally likely sample points, what is the probability that at
most one vehicle turns right?
Chapter 1 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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