Everything Flashcards
How would you form a box and whisker chart with this data set?
{2, 4, 4, 5, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9}
The box is formed by the bounds Q1 and Q3. M (median) lies within the box. The whiskers extend to the least and greatest values of the set. M = Q2 and divides the set. Q1 and Q3 are the medians of the remaining halves.
Q1=6, Q3=8.5, Q2/M=7
List the prime numbers from 0 to 107
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107}
What is the interquartile range?
Typically related to boxplot problems, it is the range between Q3 and Q1.
(ie Q3-Q1)
What is the range of a set?
The greatest value of the set minus the least value of the set.
ie {1, 5, 8, 10, 11} -> R=11-1 = 10
What is the mode of a set?
The mode of the set is the most common number.
ie. {2, 3, 3, 3, 3, 7, 8, 9, 10, 24, 53, 13,} -> the mode is 3
What is the mean (arithmetic) of a set?
Often times identical to the median it is the sum of all of the number in the set divided by the number of terms in the set.
ie. {1, 2, 3, 4, 5} -> M = (1+2+3+4+5)/5 = 15/5 = 3
What is the median of a set?
The middle most term or the average of the center two for an even set.
ie. {1, 2, 3, 4, 5, 6} m = 3.5
What are the sides of a 30-60-90 triangle?
What are the sides of a 45-45-90 triangle?
What is the formula for the sum of an arithmetic sequence?
Sn = (n/2)[2a + (n-1)d]
n = # of terms, a = first term in sequence, d = difference between terms
What is the formula for the sum of a geometric sequence?
Sn = a[(rn-1)/(r-1)]
a = starting term in sequence, r = common ratio, n = number of terms.
What is the general formula for a permutation?
nPk = n!/(n-k)!
n = total set, k = subset
What is the general formula for a combination?
nCk = n!/[k!(n-k)!]
n = total set, k = subset
What is the general groups formula (for overlapping sets)?
T = G1 + G2 - B + N
What is the circumference of a circle?
C = 2πr = πD
What is the area of a circle?
A = πr2
What is the sum of the internal angles of the pentagon in degrees?
n = # of sides d = degrees
d = (n-2)(180o)
d = (3)(180o) = 540o)
What is the area of the parallelogram?
Same as rectangle A = lw = lh = 8(20) = 160
What is the area of the trapazoid?
A = 1/2(b1 + b2)h , b1 = 10, b2 = 18
A = 105
What is the least common multiple between 22 and 6?
LCM > smallest number that x and y are both factors of
LCM = 66
What is the greatest common factor between 66 and 99?
GFC > greatest shared factor between x and y
GCF = 33
How many numbers are in a an ordered list of integers from 1,2,3,4……n
where n = the number of terms in the list?
n = greatest value - least value +1
5,6,7 …. 20
n = 20-5 +1
What is the value of the angle C
c = x+y
If r = 10 what is the arc length ABC
Length of Arc= (central angle/360)C
(portion of total circumferance that central angle includes)
ABC = 50/360(10π)
If r = 10 what is the area of the sector defined by arc ABC
Asector = Awhole (central angle/360)
Asector = π(100)(50/360)
What is the volume and area of a regular cylinder?
V = πr2h
A = 2(πr2) +2πrh
How many positive factors does 6600 have
Prime factorize the number. Add one to each exponent. Multiply the exponents together A) (2^3)(5^2)(3^1)(11^1) -> (4)(3)(2)(2) =48
How many positive odd factors does 4500 have?
Prime factorize the number. Add one to each exponent. Multiply the exponents together but disregard the factor of 2 A) (5^3)(3^2)-> (4)(3) =12 positive odd factors
What is the quadratic formula?
B - B is bigger
List the Pythagorean triples
3, 4, 5 (and multiples) 6, 8, 10 9, 12, 15 5, 12, 13 8, 15, 17 7, 24, 25
