notes for math Flashcards
|x|=a, then x=
a or -a
|x|<a></a>
-a
|x|>a, then
x>a or x
when a linear inequality is expressed in slope intercept form and the inequality is < or <= then the region is… th opposite is true
below the line
a number or expression under a radical is referred to as a
radicand
if the denominator is a binomial, use the … of the denominator to rationalize
conjugate
the exterior angle of a triangle will be equal to the
sum of the other two (non-adjacent) angles of the triangle
the perpendicular bisector of a chord passes through the
center of a circle
congruent chords have congruent .. and vice versa
arcs
arcs between parallel chords are
congruent
arc length in radians:
s=theta*r
arc length in degrees
s= theta/180 pir
area of a sector in radians
A=1/2rs
area of a sector in degrees
A=theta/360 pir^2
sinx= (in terms of cos)
cos(90° -x)
cosx= (in terms of sin)
sin(90°-x)
number of elements in a group=
total number of elements x proportion of elements in a group
confidence intervals describe the …. of the sampling method in terms of an interval
accuracy
the smaller the confidence interval at a given confidence level, the more
accurate the sampling method
confidence interval=
sample statistic +- margin of error
margins of error reflect the confidence level: the higher the confidence level, the
smaller the margin of error
the greater the standard deviation, the greater the
margin of error
if event a and b are mutually exclussive (the fulfillment of one event excludes the possibility of the other), then the probability is
P(A or B)= P(A) + P(B)
for any two independent events a and b, the prob is
P(A and B)= P(A) * P(B)
dependent event prob
P(A and B)= P(A) * P(B|A)
amount of work completed=
rate of work * time word
worker A completes … of the ob per hour and worker B completes …. of the job per hour; total time to complete =
1/x; 1/y; 1/ (1/x + 1/y)
percent change=
amount of change/original amount * 100%
concentration of A=
amount of substance A/ amount of substance B
to get the decimal/percent of a multiple of 1/10, 1/5, 1/4, 1/3, 1/2, or 3/4, take the fraction with the corresponding denominator, convert to a decimal, and
multiply by the numerator of the desired fraction get its decimal equivalent
area of a parallelogram:
A=bh
if you have two racios, a:b and b:c, you can derive a:c by finding a
common multiple of the b terms
linear model: y=
kx +x0
exponential equation:
y= a(1 + r)^x
when you have a group of evenly spaced terms, the mean and median will be
identical
you can find the mean of a group of evenly spaced terms by taking the
mean of the highest and lowest terms
… total cards in a deck
52
(ab)^c =
a^c * b^c
alternate interior angles and alternate exterior angles are
equal
ratio of 45-45-90 is
x:x:xroot2
ratio of 30-60-90 is
x: xroot3: 2x
right square pyramid volume
1/3 * l * w * h
right cone volume
1/3 (pir^2)h
sphere volume
4/3 * pi * r^3
i^2
-1
i^3
-i
i^4
1
sin^2x + cos^2x=
1
pythagorean triplets:
7-24-25; 5-12-13; 3-4-5
correlations do not prove
causation
questions about breaking even involve
systems of equations
when comparing two data sets for consistency, consider both the
data center (mean/median)P and the spread(standard deviation/range)
the inverse of raising a quantity to the 5/2 power is raising t to the
2/5 power
