Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
Chapter 11.4, Problem 28E
(a)
To determine
To explain: The outcome of the thumbtack landing point up and the thumbtack landing point down are equally likely.
(b)
To determine
To list: The sample points in the sample space of this experiment.
(c)
To determine
To explain: The probability that both thumbtacks land point up (uu) is the same as the probability that both thumbtacks land point down (dd).
(d)
To determine
To explain: The possibility to compute the theoretical probability of a thumbtack landing point up and the theoretical probability of a thumbtack landing point down.
(e)
To determine
The empirical probability of thumbtack landing point up when dropped and the empirical probability of a thumbtack landing point down when dropped a box of thumbtacks.
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 4x4) 5,
a = -1
lim f(x)
X--1
=
lim
x+4x
X--1
lim
X-1
4
x+4x
5
))"
5
))
by the power law
by the sum law
lim (x) + lim
X--1
4
4x
X-1
-(0,00+(
Find f(-1).
f(-1)=243
lim (x) +
-1 +4
35
4 ([
)
lim (x4)
5
x-1
Thus, by the definition of continuity, f is continuous at a = -1.
by the multiple constant law
by the direct substitution property
4 Use Cramer's rule to solve for x and t in the Lorentz-Einstein equations of special relativity:x^(')=\gamma (x-vt)t^(')=\gamma (t-v(x)/(c^(2)))where \gamma ^(2)(1-(v^(2))/(c^(2)))=1.
Pls help on both
Chapter 11 Solutions
A Survey of Mathematics with Applications plus MyLab Math Student Access Card -- Access Code Card Package (10th Edition)