Problem Cipher Decision Engine Instructions

In a random sample of 150 persons having their lunch at the University cafeteria it was observed that 30 people preferred vegetable dishes. Find a 95% confidence interval for the proportion who liked vegetables.

Congruence Modulo n

3 = 4 mod 7
20 = 5 (mod 2)

Conjugates

3/2+sqrt(6)
5/(7-sqrt(3))
5/sqrt(3)

Consecutive Integer Word Problems

the product of two consecutive integers is 72, what are the numbers?
the sum of two consecutive numbers is 27, what are the numbers?

Cooking Conversions

2 tablespoons
3 tsp.
5ml.

Coupon Comparison

15% or 30 dollars of 100
20 dollars or 15% off 80

Cross Product A × B

8i-j+3k x 5i+j-9k
6i-3j+6k * 8i+2j-9k
(8i-2j+13k)(3i+5j-k)

Cubes

cube side = 3
cube volume equal to 10
cube surface area is 6

Cubic Equation

2x^3 - 4x^2 - 22x + 24

Date Information

4/15/1978
10/30/2001

Decimal Degree Value to Degrees, Minutes, Seconds Conversions

29degrees,50 minutes, 4 seconds
50 degrees4‘24‘‘

Decimal-Binary-Octal-Hexadecimal-Base Change Conversions

110010101
1000101
256 to binary
convert 280 to octal
38 to octal
457 to hexadecimal
93 convert to hex
10 to base 5
convert 40 to base 6

Demoivres Theorem

2cis60^3
4-7i

Derangements - Subfactorials

!5
6 derangements
8 subfactorial

Dewey Decimal System Classification

Dewey Decimal for 005
157 Dewey Decimal System

Distance between two 3-dimensional points

(1,2,3)(4,5,6)
distance between (2,4,6)(3,5,7)
(-1,2,-3)and(4,6,8)
distance between (3,4,5),(5,6,7)

Distance Rate and Time Calculator

rate=5 and time=6
distance=4,time=3
rate=4.65 and distance=8

Effective Annual Yield Rate

4.56% daily
5.67 percent quarterly
2.45 pct compounded monthly

Elapsed Time

Difference between 11:15 a.m. and 6:00 p.m.
12:30 p.m. and 2:00 p.m.

Ellipses

9x^2+4y^2=36

Equation of a Plane

(2,4,6)(1,3,5)(9,8,4)

Equation of Exchange

M=20,V=10,Q=30
V=50,P=70,Q=80

Equilateral Triangle

equilateral triangle side=6
equilateral triangle with side equal to 4

Eulers Formula for Planar Geometry

5 vertices and 4 faces
6 faces,12 edges
e=20,v=12

Eulers Totient (φ)

phi(5)
totient of 10

Exchange Rates

USD to EUR
MXN TO CAD

Expand Master and Build Polynomial Equations

(2a^2b^3c^4 - 6x^3y^4z^5)^5
(2a^2b^3c^4 - 6x^3y^4z^5 + 7l^7m^8n^9)^5
(2x + 3y)(5a + 6b)
6a(3a^2b^2 - 7x^4y^5)
polynomial zeros of 1,3,5

Expanded and Word Notation and Standard Notation

9256 in word notation
4598 expanded notation
twentyfive million
eighty six thousand, four hundred thirty two
100(5) + 20(4) + 6
9 x 1000 + 8 x 100 + 7 x 10
987654321 as words

Factor Pairs and Prime Factorization and Divisibility and Digit Sum

prime factorization of 100
factor pairs of 50
factor 110
divisibility for 60
multiples of 200
digit sum for 987654321
prime power decomposition for 100

Factorials

6!
9 factorial
5!6!4!

Factoring Polynomials-Rational Expressions-Determining Roots-Descarte’s Rule of Signs

factor x^3 - 27y^9
simplify 3w^3x^9 - 81y^9z^12
x^4-3x^3-40x^2=0
Factor 8x^3+22x^2-6x/4x-1
descartes 4x^7+3x^6+x^5+2x^4-x^3+9x^2+x+1

Fibonacci Sequence

50 fibonacci numbers
fibonacci number 80

Fisher Transformation and Fisher Inverse

fisher transformation for 0.75
fisher inverse of -0.5

Fractions and Mixed Numbers

1/5+6/7
3/4-1/2
8/9*5/6
2/3/5/7
1&5/8
4 and 3/7
1/2 and 5/9
2/9 of 3
reciprocal of 9/4
195/6/4
Simplify 15/20
1/2?3/4

Functions-Derivatives-Integrals

given that f(x) = x^3 - x^2 + 2x, what is f(-3)?
c=cost of filling up gas tank g= gallons given the equation c(g)=3.03(g) find c(2)

Gamma Constant γ

gamma
gamma constant

Gas Mileage Calculator

What is the mileage driving 300 miles on 50 gallons?
40 gallons of gas driving for 800 miles

Geometric Distribution

n=5,p=0.3

Grade Point Average (GPA)

ABCDF
C,B,D,C,A,F
grade point average ABCCDFA
gpa A,B,C,D,F
g.p.a. BCDFA

Greatest Common Factor and Least Common Multiple

GCF of 25 and 30
GREATEST COMMON FACTOR 60,75
least common multiple of 50 AND 80
lcm 50,70
l.c.m. 80 and 95
g.c.f 50,100
GCF of 15 and 20 and 30
are 3 and 5 twin prime
are 20 and 29 coprime
lcd of 20 and 25

Heat Index

93% relative humidity and 85 temperature calculate heat index

Hexagons

Hexagon area = 100
hexagon side = 6
hexagon perimeter = 96

Imaginary Numbers

i^50
4i^-32
3i*7i
4i^2*8i^3*7i^5
9i^4*3i^5/6i^2*8i^9

Inclusive Number Word Problems

sum of inclusive numbers 10 to 50
What is the average of all numbers from 30 to 80
Sum of inclusive numbers from 60 to 90
How many integers are there from 20 to 90

Interval Notation and Set Builder Notation

x<5
x<=5
q>5
z>=5
a<0 or a>5
2 <= x <= 20
-4x<0
9j>36
|x|<3
x<7 and x>-4
{x | -1 >x >-10}
2 through 7 inclusive
x<5 or >-5
{x|x<1}
2 is less than or equal to x is less than or equal to 8
natural numbers greater than 4
whole numbers less than 10
integers less than or equal to 27
x<>5
{x|x<>0}
w not equal to 8
[2,infinity]

Lagrange Four Square Theorem (Bachet Conjecture)

lagrange for 454
bachet conjecture for 300

Letter Arrangements in a Word

word arrangments of ANIMAL
word arrangements for calculus

Lever Systems Formula

f1=10,f2=20,x=5

Line Equation-Slope-Distance-Midpoint-Y intercept

(1,4)(2,6)
(-4,5) and (7,-3)
(3,2);m=4
m=4,b=-3

Linear Congruence

3x = 7 mod 4
5y = 8 modulo 3

Linear Conversions

5 inches
6in.
4 yards
3ft.
7 fur.
8 meters
9 km
5 foot 6 inches

Liquid Conversions

5 ounces
4 pint
3 quarts
7 gallons
5 ml
9 liters
7 oz.
3 qt

Literal Equations

V = lwh
2a=3b/4c
2z + 9q = 3b + 4c - 9d
2a+3b=4c+5d solve for c
x/b = a
3x*2y=10 solve for y
x
2(x+a) = 4b

Littles Law

WIP=3000,TH=6
WIP=3000 and CT=5
TH=5,CT=100

Logarithms

log 1000
log(85)
log of 200
logarithm of 500
5^3=125
log4(8)
log2(8x^4/5)
log2(8x^4)

Lotto Drawing Probability

lotto pick 5 out of 28
pick 7 of 40 lotto

Map Scale

The scale on a map is 1 cm = 10 miles. Find the length on the map of 300 miles

Markup Markdown Calculator

John pays a wholesaler $50 for a slab of concrete, and then sells it to a real estate developer for $75. What is the markup rate?
25.28+35%
250 increased by 20%

Military Phonetic Alphabet

alpha zulu yankee

Missing Average

Given 2 scores of 75, 85, what should be score number 3 in order to attain an average score of 72?

Modular Exponentiation and Successive Squaring

11^13 mod 53
2^8633 modulo 8633

Modulus Calculator

120 mod 7
65MOD3
145 MODULUS 8
190 % 6
7 mod 3+5 mod 8 - 32 mod 5

Monomials

(6xy^3)^4
14t/14

Morse Code Translator

math1 to morse code
problem to morse
convert mammal to morse
translate giraffe to morse code
-- .- - ....

Mortgage Calculator

What is the monthly payment on a mortgage of $75,000 with an 8% interest rate that runs for 20 years
50000 loan at 9.5% for 30 years

Multifactorials

16!!!
30!(4)

Multiple Fractions (Addition or Ordering)

1/2+3/4+5/8
1/2,5/8,3/4

Natural Logarithms and Eulers Constant (e)

e^5
e^13.24
Ln 50
LN(80)
natural log 45
3^5x=27
4e^6x=100
e^2q=48

Normal Distribution

P(Z>1.5)
P(Z<2.15)
The amount of Jens monthly phone bill is normally distributed with a mean of $73 and a standard deviation of $12. What percentage of her phone bills are between $37 and $109?

Number Line Midpoint

midpoint 2,5
midpoint of 2 and 6
mpt 3,5

Number Property

30 as a unique number
45 as a composite number
numerical properties of 100
properties of 35
tell me about 72

Odds Probability

3:2 odds
7 to 5
7 to 5 odds against

Opposite Numbers

opposite of 20
opposite number of 5

Order of Operations

92 + 35*(12 - 6)/6

Ordered and Unordered Partitions

10 partitions of 5
18 ordered partitions of 6
50 unordered partitions of 10

Ordered Pairs and Polar and Cartesian Coordinates and Quadrants and Equivalent Coordinates

(1,4)
(2,3) to polar
(5,30) to Cartesian

Ordering Numbers

1,3,5,8,12

Partitioned Intervals

1,3,5,8,12

Pascal-Floyd-Leibniz Triangle

floyds triangle 6 rows
5 rows of pascal triangle
leibniz 8 rows

Password Generator

10 character password

Percent Math

60 + 35% - 10% + 40

Percent Off Problem

50% off 90
35 percent off 80
45.80 - 22.5%
200 decreased by 40%

Percentage of the Pie Word Problem

A parent died and left an estate to four children. one inherited 4/9 of the estate, the second inherited 7/81 and the third inherited 10/27 how much did the fouth inherit?

Percentage-Decimal-Fraction Relations

20% of 50
42 percent of 80
1/8 to decimal
convert 5/9 to decimal
88.596 to fraction
45 is 10% of what number
55 is 60% of what?
80% of what number =40
What is the percent change from 90 to 110
What percent of 20 is 30?
45% of what is 9
10% more than 90
30% less than 120
What percent of 3000 is 389.4

Permutations and Combinations

10 permutations of 6
5 combinations of 3
9 combination 4
8 combination 2
6 permutation 2
10 permutations of 5
6P3
7c4
how many subsets of at least 3 elements can be formed from a set of 4 elements

Phonetic Algorithms

CELEBRITY TO SOUNDEX
homework to metaphone
algebra to NYSIIS

Place Value

12345.987 place value
place value for 56987.2365

Power Sets

a,b,c,d,e
2,4,6,8,10

Pressure Conversions

4 mbar
6 atmospheres
3 pascal

Pressure Law

p1=200,p2=80,t1=75
t1=70,t2=80,p1=300

Prime and Composite and Even and Odd Numbers

generate 30 prime numbers
50 composite numbers
175 even numbers
88 odd numbers
generate composite numbers
show prime numbers

Primitive Root Calculator

Is 3 a primitive root of 7

Proportions

a/10=6/12
2/3x=6/9
-5/6=y/24
1/2=4/2z
1/0=6/12
-8/9x > -61/81
1/2=?/10
x:8=4/32

Pythagorean Theorem

a=3,b=4
a=3,c=5
b=4,c=5
find the hypotenuse of a right triangle that has legs of 4 inches and 5 inches

Quadratic Equations and Inequalities

4x^2+11x-3
a^2-a+6
x^2 + 7x + 6>=0
x^2+2x=35

Quadrilateral

(0,0),(5,10),(10,15),(5,5)

Quartic Equations

3x^4 + 6x^3 - 123x^2 - 126x + 1080

Radical Expressions

2sqrt(28) + 3sqrt(63) - sqrt(49)
sqrt(40x^4y^8)
sqrt(2/16)+sqrt(98/9)

Random Number Generator

6 random numbers between 10 and 100
generate 5 random numbers
12 random numbers

Rational Exponents

27^2/3
-243^1/5
w^7/4
What is the 5th root of 243

Rational,Irrational,Natural,Integer Property

is 34 natural
is 85.6 rational
prove 99.7 is rational
is 45 an integer

Ratios

80:200
the ratio of 100 to 25000
7:5 for 100
9 to 4 for 30
9:5 and 7:2
a:b = 5:4 and b:c = 6:5

Relative Coordinates

Starting at a point of (1,5), you move 2 spaces up, 3 spaces left
Starting at a point of (1,5), you move 2 spaces up, 8 spaces right, 7 spaces down, 3 spaces left

Resistor Color Codes

red,blue,orange,silver
green,orange,yellow

RGB and HEX conversions

R:255,G:255,B:255
r=100,g=150,B=230
£CCCCCC

Roman Numeral Conversions

DCXVII
XIV
456 to Roman
convert 1934 to roman number
345 to a roman numeral
3589
465

Roulette

roulette evens
roulette odds
roulette red
roulette black
roulette 1-12
roulette 13-24
roulette 25-36
roulette 1 number
roulette 2 numbers
roulette 4 numbers

Rounding and Truncating Numbers and Ceiling and Floor Function

round 50,6
round 76 to 3
round (80,7)
round 123 to nearest 7
truncate 95.687543 to 4
[92.5]
]78.432[
floor 98.54
ceiling(32.57)

Rule of 72

rule 72 @ 5%
rule of 72 at 6.54 percent
rule72 8.54%
rule of 72 6.53
how long to double money at 7.54%

Salary Converter

100000 salary

Sales Tax Calculator

You bought jewelery that was priced at $6.52, and the total bill was $7.99. What is the sales tax rate?
You paid 8.25 for a meal purchased at a price of 7.02. How much was the tax?
You bought a sandwich for 8.50. You paid 10.00. How much was the tax?

Scientific Notation

456 to scientific
6.543x10^6
(4.2 x 10e5) x (2.1 x 10e6)

Sectoral Balance

PI=20,GS=40,T=10,E=200,I=50

Sieve of Eratosthenes

sieve of Eratosthenes less than 40
prime numbers less than 50

Simple and Compound and Continuous Interest

Solution Mixture

how much pure acid should be added to 18 L of 30% acid to increase the concentration of 50% acid?

Special Triangles: Isosceles and 30-60-90

The hypotenuse of a 30-60-90 triangle is 16, calculate the small side.

Spheres

sphere radius = 3
sphere diameter equal to 10
sphere volume is 6
sphere surface area = 10

Square Root Table

square root table for 200 rounded to 5 digits
square root table through 325

Square Roots and Exponents

sqrt(124)
sqrt(-58)
Square root of 136
square root 247
sqrt300
8^3
2 to the 4 power
25root767
sqrt(5)sqrt(7)
sqrt3sqrt12sqrt40sqrt48
7x7x7x7x7
(3^4)^2
2^4*2^7

Squares

square side = 3
square perimeter equal to 10
square area is 6
square diagonal = 5

Static Determinacy and Stability

m=10,j=5

Stock Price Information

GOOG
JPM
WWE

Stopping-Braking Distance for a Car

50mph
75 miles per hour

Sum of the First (n) Numbers

sum of the first 9 natural numbers
what is the sum of the first 10 cube numbers
show sum of the first 10 square numbers
sum first 15 even numbers
sum first 18 odd numbers

T-Bill

f=300,w=45,y=20

Tally Marks

Tally for 62
59 tallies

Target Heart Rate Calculator

target heart rate age 50
target heart rate for age 40
target heart rate of age 67

Temperature converter

65 Celsius
-45 Fahrenheit
97 Kelvin
150 Reaumur
225 Newton
100 Fahrenheit
34 Celsius
56 Kelvin
130 Rankine
225 Newton

Time Conversions

3 seconds
1 minute
8 fortnights

Triangle Coordinate Items

(1,1),(2,3),(4,5)
(2,2)(3,4)(8,9)

Triangle Solver and Classify Triangles

Find the area of the triangle with side lengths measuring 48 cm, 55 cm, and 73 cm

Trigonometry Relations

tan x= 1.98 and sin x = .89, what is cos x

Unix Time Translation

1234567890 to unix time

Verbal Phrase

Walking Distance (Pedometer)

10000 steps at 3 feet
15000 steps at 2.4 ft.

Weather Calculator

weather for Chicago
Boston weather

Weight Conversions

3 ounces
2 pounds
5lbs.
8 milligrams

Y Intercept and X Intercept

2x + 4y = 18
3y + 5x - 16=0

Yahtzee-1st Roll

yahtzee
yahtzee Full House
Yahtzee Large Straight
small straight yahtzee
3 of a kind Yahtzee
yahtzee 4 of a kind
Yahtzee chance

Z Score Lookup

P(Z<1.5)
P(z > 0.25)
p(0 < z < 2.16)

Other notes: If you just enter an integer, the decision engine will give you a list of choices you can make with the number you entered
We have made the decision engine case insensitive to make your life easier.

Standard Searches
Regular searches still work the same as they used to, i.e., you want to see what Math Celebrity has relating to quadratics. Type quadratic and press the button. This will return lessons that relate to quadratics in any way. If your keyword search identifies to exactly one of our lessons, the decision engine will whisk you there immediately

Subjects