letter - a character representing one or more of the sounds used in speech; any of the symbols of an alphabet.

A combination lock open with the correct 4 letter code. Each wheel roared through letters A-L. How m

A combination lock open with the correct 4 letter code. Each wheel roared through letters A-L. How many different 4 letter codes are possible
A-L = 12 letters
Possible combinations is found by:
12 * 12 * 12 * 12 = [B]20,736 combinations[/B]

a licence plate that has 3 numbers from 0 to 9 followed by 2 letters

a licence plate that has 3 numbers from 0 to 9 followed by 2 letters
How many license plate combinations can we form?
We multiply as follows:
[LIST]
[*][0-9] = 10 possible digits (D)
[*]A-Z = 26 possible letters (L)
[/LIST]
The problem asks for this:
DDDLL
So we have:
10 * 10 * 10 * 26 * 26 = [B]676,000[/B] plates

a license plate has 3 letters followed by 4 numbers

a license plate has 3 letters followed by 4 numbers
There are 26 letters A-Z and 10 numbers 0-9. So we have:
26 * 26 * 26 * 10 * 10 * 10 * 10
[B]175,760,000 different license plate combinations[/B]

A license plate is made up of 2 letter and 3 single digit numbers

A license plate is made up of 2 letter and 3 single digit numbers.
There are 26 letters (A-Z). And there are 10 single digit numbers [0-9]. So our total combinations are:
Letter - Letter - Number - Number - Number
26 * 26 * 10 * 10 * 10 = [B]676,000[/B]

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSION

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSIONS OF THE RECTANGLE?
Whoa... stop screaming with those capital letters! But I digress...
The perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]P = 196
[*]l = 6w
[/LIST]
Plug these into the perimeter formula:
2(6w) + 2w = 196
12w + 2w = 196
[URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B2w%3D196&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]w = 14[/B]
Now we put w = 14 into equation (2) above:
l = 6(14)
[B]l = 84
[/B]
So our length (l), width (w) of the rectangle is (l, w) = [B](84, 14)
[/B]
Let's check our work by plugging this into the perimeter formula:
2(84) + 2(14) ? 196
168 + 28 ? 196
196 = 196 <-- checks out

ADG,BEH,CFI,___,___,___

ADG,BEH,CFI,___,___,___
Looking at this pattern, we see:
[LIST=1]
[*]the first term starts with A and increments by 1 letter
[*]the second term starts with D and increments by 1 letter
[*]the third term starts with G and increments by 1 letter
[/LIST]
So terms 4, 5, and 6 are:
[LIST]
[*][B]DGJ[/B]
[*][B]EHK[/B]
[*][B]FIL[/B]
[/LIST]

Below are data showing the results of six subjects on a memory test. The three scores per subject ar

Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data.
A score trial B score trial 2 C Score trial 3
4 6 7
3 7 8
2 8 5
1 4 7
4 6 9
2 4 2
(a) Compute L for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject.
(b) Compute a one-sample t-test on this column (with the L values for each subject) you created. Formula t = To computer a one-sample t-test first know the meaning of each letter
(a) Each L column value is just -1(Column 1) + 0(Column2) + 1(Column 3)
A score trial B score trial 2 C Score trial 3 L = (-1)(a) + (0)(b) + (1)(c)
4 6 7 3
3 7 8 5
2 8 5 3
1 4 7 6
4 6 9 5
2 4 2 0
(b) Mean = (3 + 5 + 3 + 6 + 5 + 0)/6 = 22/6 = 3.666666667
Standard Deviation = 2.160246899
Use 3 as our test mean
(3.666667 - 3)/(2.160246899/sqrt(6)) = 0.755928946

Ben can write 153 letters in 3 minutes. At this rate, how many letters can he write in 10 minutes?

Ben can write 153 letters in 3 minutes. At this rate, how many letters can he write in 10 minutes?
We set up a proportion of letters to minutes where the number of letters in 10 minutes is l:
153/3 = l/10
We [URL='https://www.mathcelebrity.com/prop.php?num1=153&num2=l&den1=3&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into a search engine[/URL] and we get:
l =[B] 510[/B]

Braille Translator

Given a phrase with letters, numbers, and most punctuation symbols, the calculator will perform the following duties:

1) Translate that phrase to Braille

2) Calculate the number of dots in the message

3) Calculate the number of empty spaces in the message

1) Translate that phrase to Braille

2) Calculate the number of dots in the message

3) Calculate the number of empty spaces in the message

Dane wrote the letters of “NEW YORK CITY” on cards and placed them in a hat. What is the probability

Dane wrote the letters of “NEW YORK CITY” on cards and placed them in a hat. What is the probability that he will draw the letter “Y” out of the hat?
New York City has 11 letters.
Our probability of drawing a Y is denoted as P(Y):
P(Y) = Number of Y's / Total Letters
P(Y) = [B]2/11[/B]

Each of letters in the word PROPER are on separate cards, face down on the table. If you pick a card

Each of letters in the word PROPER are on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be P or R?
PROPER has 6 letters in it. It has 2 P's and 2 R's. So we have:
Pr(P or R) = Pr(P) + Pr(R)
Pr(P or R) = 2/6 + 2/6
Pr(P or R) = 4/6
We can simplify this. So [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']we type this fraction in our search engine[/URL], choose simplify, and we get:
Pr(P or R) = [B]2/3[/B]

Each of the letters in the word PLOTTING are on separate cards, face down on the table. If you pick

Each of the letters in the word PLOTTING are on separate cards, face down on the table. If you pick a card at random, what is the probability that its letter will be T or G?
PLOTTING has to 8 letters. It has 2 T'sand 1 G, so we have:
P(T or G) = P(T) + P(G)
P(T or G) = 2/8 + 1/8
P(T or G) = [B]3/8[/B]

Grade Point Average (GPA)

Calculates Grade Point Average (GPA) based on letter grades entered.

How many distinct 3 letter arrangements can be made using P, R, I, M and E

How many distinct 3 letter arrangements can be made using P, R, I, M and E?
We have all unique letters. We want the combination formula 5 Choose 3, or C(5,3).
Using our [URL='http://www.mathcelebrity.com/permutation.php?num=5&den=3&pl=Combinations']combinations calculator[/URL], we get 10 unique 3 letter arrangements.

How many license plates can be made consisting of 3 letters followed by 2 digits

How many license plates can be made consisting of 3 letters followed by 2 digits
There are 26 letters A-Z and 10 digits 0-9. We have:
26 * 26 * 26 * 10 * 10 = [B]1,757,600 license plates[/B]

In how many ways can I arrange the 7 letters A, B, C, D, E, F, G?

In how many ways can I arrange the 7 letters A, B, C, D, E, F, G?
[B]5,040[/B] from our [URL='http://www.mathcelebrity.com/wordarrange.php?aword=ABCDEFG&pl=Calculate+Letter+Arrangements']letter arrangement calculator[/URL]

Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episod

Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episode airs, Jake receives a bunch of fan mail. He splits all the letters into 3 equal stacks to open with his mom and his sister. Each stack contains 21 letters. Which equation can you use to find the number of letters n Jake receives?
The number of letters n is represented by number of stacks (s) times letter per stack (l). We're given s = 3 and l = 21, so we have:
n = 21(3)
n = [B]63[/B]

L is the set of letters in the word Mississippi

L is the set of letters in the word Mississippi
We want only unique letters, so we have:
[B]L = {I, M, P, S}[/B]

Letter Arrangements in a Word

Given a word, this determines the number of unique arrangements of letters in the word.

License plate that is made up of 4 letters followed by 2 numbers

License plate that is made up of 4 letters followed by 2 numbers
Using the fundamental rule of counting, we have:
26 possible letters * 26 possible letters * 26 possible letters * 26 possible letters * 10 possible numbers * 10 possible numbers = [B]45,697,600 license plate combinations[/B]

license plate with 4 letter combinations and 3 number combinations

license plate with 4 letter combinations and 3 number combinations
There are 26 total letters and 10 digits [0-9].
We have 26 C 4 * 10 C 3.
[URL='http://www.mathcelebrity.com/permutation.php?num=26&den=4&pl=Combinations']26 C 4[/URL] = 14,950
[URL='http://www.mathcelebrity.com/permutation.php?num=10&den=3&pl=Combinations']10 C 3[/URL] = 120
Total license plate combinations:
14,950 * 120 = [B]1,794,000[/B]

License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetit

License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed.
We have 26 possible letters and 10 possible digits 0-9. Since repetition is allowed, we have:
26 * 26 * 26 * 10 * 10 = [B]1,757,600 possible license plates[/B]

License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetit

License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed
We have 26 letters A-Z and 10 possible digits 0-9. Using the fundamental rule of counting, we have:
26 * 26 * 26 * 10 * 10 = [B]1,757,600 possible choices[/B]

License plates are made using 3 letters followed by 3 digits. How many plates can be made of repetit

License plates are made using 3 letters followed by 3 digits. How many plates can be made of repetition of letters and digits is allowed
We have 26 letters in the alphabet
We have 10 digits [0-9]
The problem asks for the following license plate scenario of Letters (L) and Digits (D)
LLLDDD
The number of plates we can make using L = 26 and D = 10 using the fundamental rule of counting is:
Number of License Plates = 26 * 26 * 26 * 10 * 10 * 10
Number of License Plates = [B]17,576,000[/B]

Match each variable with a variable by placing the correct letter on each line.

Match each variable with a variable by placing the correct letter on each line.
a) principal
b) interest
c) interest rate
d) term/time
2 years
1.5%
$995
$29.85
[B]Principal is $995
Interest is $29.85 since 995 * .0.15 * 2 = 29.85
Interest rate is 1.5%
Term/time is 2 year[/B]s

Morse Code Translator

Given a phrase with letters, numbers, and most punctuation symbols, the calculator will perform the following duties:

1) Translate that phrase to Morse Code.

2) Translate the Morse Code to a Dit-Dah message

3) Calculate the number of dots in the message

4) Calculate the number of dashes in the message

This also translates__from__ Morse Code back to English.

1) Translate that phrase to Morse Code.

2) Translate the Morse Code to a Dit-Dah message

3) Calculate the number of dots in the message

4) Calculate the number of dashes in the message

This also translates

N-Grams

Takes a phrase and displays chracter unigrams, character bigrams, character trigrams, and character n-grams as well as word unigrams, word bigrams, word trigrams, and word n-grams. (ngrams)

Also performs frequency analysis (number of instances of each letter)

Also performs frequency analysis (number of instances of each letter)

Phone Number Translator

Given a phone number with letters in it, this calculator will determine the numeric phone number for you to dial.

Sara wants to arrange the seven scrabble letters she has in every possible way so she can determine

Sara wants to arrange the seven scrabble letters she has in every possible way so she can determine if she has a 7-letter word. how many different ways are there for Sara to arrange all seven letters?
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = [B]5,040 ways[/B]

Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be t

Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be taken from the first 8 letters of the alphabet with no repeats. The digits are taken from numbers 0-9 with no repeats. How many serial numbers can be generated
The serial number is organized with letters (L) and digits (D) like this:
LLLDDDD
Here's how we get the serial number:
[LIST=1]
[*]The first letter can be any of 8 letters A-H
[*]The second letter can be any 7 of 8 letters A-H
[*]The third letter can be any 6 of 8 letters A-H
[*]The fourth digit can be any of 10 digits 0-9
[*]The fifth digit can be any 9 of 10 digits 0-9
[*]The sixth digit can be any 8 of 10 digits 0-9
[*]The seventh digit can be any 7 of 10 digits 0-9
[/LIST]
We multiply all possibilities:
8 * 7 * 6 * 10 * 9 * 8 * 7
[B]1,693,440[/B]

Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are t

Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are to be taken from the first 5 letters of the alphabet with repeats possible and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated?
First 5 letters of the alphabet are {A, B, C, D, E}
The 4 letters can be chosen as possible:
5 * 5 * 5 * 5
The number are not repeatable, so the 4 numbers can be chosen as:
10 * 9 * 8 * 7 since we have one less choice with each pick
Grouping letters and numbers together, we have the following serial number combinations:
5 * 5 * 5 * 5 * 10 * 9 * 8 * 7 = [B]3,150,000[/B]

Set B is the set of distinct letters in the word GIFT

Set B is the set of distinct letters in the word GIFT
Set B has 4 elements below:
B = [B]{G, I, F, T}[/B]

set of all letters in Australia

set of all letters in Australia
We remove duplicate "a's" and treat A and a as the same letters. Our set S is:
S = [B]{a, i, l, r, s, t, u}[/B]
If we want to find the properties of this set, we visit our [URL='https://www.mathcelebrity.com/powerset.php?num=%7Ba%2Ci%2Cl%2Cr%2Cs%2Ct%2Cu%7D&pl=Show+Power+Set']set notation calculator[/URL].

Set of consonants in the word EDUCATION

Set of consonants in the word EDUCATION
Consonants are all letters not vowels, so anything that is not {A, E, I, O, U}
Our set of consonants in the word EDUCATION is:
[B]{C, D, N, T}[/B]

set of days with the letter n

set of days with the letter n
We have the set below:
{Mo[B]n[/B]day, Wed[B]n[/B]esday, Su[B]n[/B]day}

States that begin with the letter C

States that begin with the letter C
Our set has 3 elements:
[B]{California, Colorado, Connecticut}[/B]

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a l

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter that is not “A”?
ALGEBRA has 7 letters
Of the 7 letters, we have 2 A's.
So we have 7 - 2 = 5 letters which are not A
P(Not A) = Letters not A / Total letters
P(Not A) = [B]5/7[/B]

The set of all letters in the word p lus is

The set of all letters in the word p lus is
The cardinality of this set is 4 with the elements below:
[B]{p, l, u, s}[/B]

The set of all letters in the word true is

The set of all letters in the word true is:
We have [B]{t, r, u, e}[/B]

The set of months of a year ending with the letters “ber”.

The set of months of a year ending with the letters “ber”.
We build set S below:
[B]S = {September, October, November, December}[/B]
The cardinality of S, denoted |S|, is the number of items in S:
[B]|S| = 4[/B]

To create an entry code, you must first choose 2 letters and then, 4 single-digit numbers. How ma

To create an entry code, you must first choose 2 letters and then, 4 single-digit numbers. How many different entry codes can you create?
List total combinations using the product of all possibilities:
26 letters * 26 letters * 10 digits (0-9) * 10 digits (0-9) * 10 digits (0-9) * 10 digits (0-9)
[B]6,760,000[/B]

Truth Tables

Sets up a truth table based on a logical statement of 1, 2 or 3 letters with statements such as propositions, equivalence, conjunction, disjunction, negation. Includes modus ponens.