In the case of factoring the difference between two squares, the answer is: yes, the answer will always have two sets of expressions in parentheses. This is because in factoring you are breaking down a more complicated expression into simpler parts that, when multiplied...
1. Take the sentence: All work and no play makes Jack a dull
boy. Store each word in a separate variable, then print out the
sentence on one line using print.
#! /usr/bin/env python3
# ex1 - words
# All work and no play makes Jack a dull boy.
word1 = "All"
word2 = "work"
word3 = "and"
word4 = "no"
Chapter 2 of How to Think Like a Computer Scientist begins actually exploring Python and its features.
The chapter discusses variables, expressions, and statements. It starts out discussing data types and using the type() function to determine the type of some literals, like strings, integers, and floats. It also discusses using different kind of string delimiters.
First, recall the following identities:
sec t = 1 / cos t
tan t = sin t / cos t
sin2 t + cos2 t = 1 (pythagorean identity)
- cos2 t - cos2 t
f'(x) = (4/3)x-1/3 - (5/3)x2/3
you can factor out (1/3)x-1/3 out of each term and get:
f'(x) = (1/3)x-1/3(4 - 5x)
then, rewrite the x with the negative exponent as the denominator of a fraction:
f'(x) = (4-5x) / (3x1/3)
In preparation for offering Python as a subject I'm planning on reviewing and refreshing my basic Python programming skills using the online text "How to Think Like a Computer Scientist", located at:
As I progress through the chapters I plan on writing a brief summary and reflection on the topics covered...
You didn't provide us with a value of μ or σ, so I'll just leave it as μ and σ in the answer:
1. Since x is less than μ we have a negative z score. The z score which corresponds to a probability of 0.4525 between x and μ is -1.67 (you can find this using...
Just a quick note to add to Ryan's excellent solution:
I created Venn diagram for this problem, which can be viewed here:
By the time I finished that, Ryan had already posted his solution, which is briefer than mine was...
D'oh!, of course zeroth, make sure you copy down the problem right :-)
First, Combine like terms:
y = (x * .4175) + x = 1.4175 * x
y = 1.4175 * x
solve for x (get x by itself):
Multiply both sides...
To calculate a percent you simply divide the amount you're given by the amount which is the whole or base, then multiply by 100 and put a percent sign at the end. So in your case you would do the following:
675/900 = 0.75
0.75 x 100 = 75...
Assuming you meant:
x/(+2) = (x/3) - 3
or, a little prettier:
--- = --- - 3
Assuming you're using 'x' to mean multiplication (rather than using it as a variable), and assuming you're using '_' to mean a blank to fill in, your question of:
can be reduced to:
2 x _ = 10 + 2
You'll need to tell us what corollary 4.4 says in your textbook (as well as the original theorem that it is a corollary to) for anyone to be able to answer this question. Theorems and their corollary don't follow a universal numbering scheme.
Once you've told...
The probability that he makes fewer than 2 incorrect decisions is the same as the probability that he makes 0 or 1 incorrect decision:
P(fewer than 2 incorrect) = P(0 incorrect) + P(1 incorrect)
The binomial probability that he makes x incorrect decisions out of...
9c - 4x = 7
9c - 4x -9c = 7 - 9c (subtract 9c from both sides to get the x term by itself on the left)
-4x = 7 - 9c (simplify, -9c eliminated from left side of equation)
-4x 7 - 9c
----- = -------- (divide both sides...
Combine like terms
5x + 3x => 8x
Eliminate common factors
10 5 x 2 5 x 2 5
--- = ------- = -------- = ---
6 3 x 2 ...
Because radiation, conduction, and convection are three ways of transferring energy in the form of heat from one system to another?
More context would be helpful.
1. The Symmetric Property (http://www.mathwords.com/s/symmetric_property.htm)
2. The Transitive Property (http://www.mathwords.com/t/transitive_property.htm)
3. false. However, assuming you meant to write:
x + 7 = 5; x + 7 - 7 = 5 - 7; x = -2
Then the property...
Assuming you mean:
324/5 - 32-4/5
(which makes some sense, since 32 has a "nice" 5th root of 2)
this is equal to:
(321/5)4 - (321/5)-4 (exponent multiplication)
= (5√32)4 - (5√32)-4...