range - Difference between the largest and smallest values in a number set

(2,3)(4,5)(6,7)(8,9) represents a function

(2,3)(4,5)(6,7)(8,9) represents a function
Domain is the x-values:
x = (2, 4, 6, 8)
Range is the y-values:
y = (3, 5, 7, 9)
The function y, or f(x) is:
y = x + 1 where x = (2, 4, 6, 8)
Test this function for x = 2:
y = 2 + 1
y = 3
Test this function for x = 4:
y = 4 + 1
y = 5
Test this function for x = 6:
y = 6 + 1
y = 7
Test this function for x = 8:
y = 8 + 1
y = 9

14 oranges $3.78

14 oranges $3.78
Using our [URL='http://www.mathcelebrity.com/unit-cost-calculator.php?num=14orangesfor3.78&pl=Calculate+Unit+Cost']unit cost calculator[/URL], we get:
[B]$0.27 per orange[/B].
You could also enter in the search engine:
14 oranges for $3.78

2 numbers that add up makes 5 but multiplied makes -36

2 numbers that add up makes 5 but multiplied makes -36
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*]x + y = 5
[*]xy = -36
[/LIST]
Rearrange equation (1) by subtracting y from each side:
[LIST=1]
[*]x = 5 - y
[*]xy = -36
[/LIST]
Substitute equation (1) for x into equation (2):
(5 - y)y = -36
5y - y^2 = -36
Add 36 to each side:
-y^2 + 5y + 36 = 0
We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=-y%5E2%2B5y%2B36%3D0&pl=Solve+Quadratic+Equation&hintnum=0']type it in our search engine and solve[/URL] to get:
y = ([B]-4, 9[/B])
We check our work for each equation:
[LIST=1]
[*]-4 + 9 = -5
[*]-4(9) = -36
[/LIST]
They both check out

4 rectangular strips of wood, each 30 cm long and 3 cm wide, are arranged to form the outer section

4 rectangular strips of wood, each 30 cm long and 3 cm wide, are arranged to form the outer section of a picture frame. Determine the area inside the wooden frame.
Area inside forms a square, with a length of 30 - 3 - 3 = 24. We subtract 3 twice, because we account for 2 rectangular strips with a width of 3.
Area of a square is side * side. So we have 24 * 24 = [B]576cm^2[/B]

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there?
Assumptions:
[LIST]
[*]Let the number of adults be a
[*]Let the number of kids be k
[/LIST]
Given with assumptions:
[LIST=1]
[*]a + k = 508
[*]2a + 1.25k = 885.50 (since cost = price * quantity)
[/LIST]
Rearrange equation (1) by subtracting c from each side to isolate a:
[LIST=1]
[*]a = 508 - k
[*]2a + 1.25k = 885.50
[/LIST]
Substitute equation (1) into equation (2):
2(508 - k) + 1.25k = 885.50
Multiply through:
1016 - 2k + 1.25k = 885.50
1016 - 0.75k = 885.50
To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=1016-0.75k%3D885.50&pl=Solve']type this equation into our search engine[/URL] and we get:
k = [B]174[/B]
Now, to solve for a, we substitute k = 174 into equation 1 above:
a = 508 - 174
a = [B]334[/B]

63 oranges is shared among 3 boys in the ratio of 2:3:4 how many oranges will the second boy receive

63 oranges is shared among 3 boys in the ratio of 2:3:4 how many oranges will the second boy receive?
Total sharing is 2 + 3 + 4 = 10.
[LIST]
[*]Boy 2 = 3/10 * 63 = [B]18.9 oranges[/B]
[/LIST]

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an ho

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey?
[U]Set up the relationship of still water speed and downstream speed[/U]
Speed down stream = Speed in still water + speed of the current
Speed down stream = x+2
Therefore:
Speed upstream =x - 2
Since distance = rate * time, we rearrange to get time = Distance/rate:
15/(x+ 2) + 15 /(x- 2) = 3
Multiply each side by 1/3 and we get:
5/(x + 2) + 5/(x - 2) = 1
Using a common denominator of (x + 2)(x - 2), we get:
5(x - 2)/(x + 2)(x - 2) + 5(x + 2)/(x + 2)(x - 2)
(5x - 10 + 5x + 10)/5(x - 2)/(x + 2)(x - 2)
10x = (x+2)(x-2)
We multiply through on the right side to get:
10x = x^2 - 4
Subtract 10x from each side:
x^2 - 10x - 4 = 0
This is a quadratic equation. To solve it, [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-10x-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine[/URL] and we get:
Speed of the boat in still water =X=5 +- sq. Root of 29 kmph
We only want the positive solution:
x = 5 + sqrt(29)
x = 10.38
[U]Calculate time for upstream journey:[/U]
Time for upstream journey = 15/(10.38 - 2)
Time for upstream journey = 15/(8.38)
Time for upstream journey = [B]1.79[/B]
[U]Calculate time for downstream journey:[/U]
Time for downstream journey = 15/(10.38 + 2)
Time for downstream journey = 15/(12.38)
Time for downstream journey = [B]1.21[/B]

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each pri

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $188,800?
Let x be the number of $24 tickets, and y be the number of $40 tickets. We have:
[LIST=1]
[*]24x + 40y = 188,800
[*]x + y = 6,000
[*]Rearrange (2) to solve for x: x = 6000 - y
[*]Plug in (3) to (1):
[/LIST]
24(6000 - y) + 40y = 188800
144,000 - 24y + 40y = 188,800
16y + 144,000 = 188,800
Subtract 144,000 from each side:
16y = 44,800
Divide each side by 16
y = 2,800 ($40 tickets)
Plug this into (2)
x + 2,800 = 6000
Subtract 2,800 from each side:
x = 3,200 ($24 tickets)

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many dif

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many different ways are there to arrange the batting order of 9 starting players if only one pitcher is used at a time and the pitcher always bats last.
(This means that 8 players are taken from the position players and one pitcher is then added at the end of the lineup.)
First 8 positions:
[URL='https://www.mathcelebrity.com/permutation.php?num=15&den=8&pl=Permutations']15P8[/URL] = 259,459,200
For the pitcher, we can have 10 different possibilities for the 9th player:
259,459,200 x 10 = [B]2,594,592,000 ways[/B]

A bowl contains 45 oranges. If ? of the oranges are bad; how many are good?

A bowl contains 45 oranges. If ? of the oranges are bad; how many are good?
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=2%2F3&pl=Subtract']fraction operator calculator[/URL], we see that:
1 - 2/3 = 1/3 of the oranges are good.
We want 1/3 of 45. [URL='https://www.mathcelebrity.com/fraction.php?frac1=45&frac2=1/3&pl=Multiply']Typing this expression into our search engine[/URL], we get:
[B]15 good oranges[/B]

A box has y oranges. 5 oranges are rotten and removed. The remaining oranges are placed equally into

A box has y oranges. 5 oranges are rotten and removed. The remaining oranges are placed equally into 2 containers . Each container has ______oranges
Remove 5 rotten oranges means we subtract 5 from y:
y - 5
If each of the two remaining boxes contains an equal amount of the remaining oranges, we have:
[B](y - 5)/2[/B] oranges in each box

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How many of each type of bill does the cashier have?
Let a be the amount of $10 bills and b be the amount of $20 bills. We're given two equations:
[LIST=1]
[*]a + b = 44
[*]10a + 20b = 730
[/LIST]
We rearrange equation 1 in terms of a. We subtract b from each side and we get:
[LIST=1]
[*]a = 44 - b
[*]10a + 20b = 730
[/LIST]
Now we substitute equation (1) for a into equation (2):
10(44 - b) + 20b = 730
Multiply through to remove the parentheses:
440 - 10b + 20b = 730
Group like terms:
440 + 10b = 730
Now, to solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=440%2B10b%3D730&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]29
[/B]
To get a, we take b = 29 and substitute it into equation (1) above:
a = 44 - 29
a = [B]15
[/B]
So we have [B]15 ten-dollar bills[/B] and [B]29 twenty-dollar bills[/B]

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Fi

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Find the numbers
Let the first number be a and the second number be b. We have:
[LIST=1]
[*]a + 2b = 7
[*]2a + b = 23
[/LIST]
Rearrange (1) into (3)
(3) a = 7 - 2b
Substitute (3) into (2):
2(7 - 2b) + b = 23
Multiply through:
14 - 4b + b = 23
Combine like terms:
14 - 3b = 23
Subtract 14 from each side:
-3b = 9
Divide each side by -3
[B]b = -3[/B]
Substitute this into (3)
a = 7 - 2b
a = 7 - 2(-3)
a = 7 + 6
[B]a = 13[/B]
[B](a, b) = (13, -3)[/B]

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from sel

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?
Let the number of drinks be d. Let the number of salads be s. We're given two equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d + s = 209
[/LIST]
We can use substitution to solve this system of equations quickly. The question asks for the number of salads (s). Therefore, we want all expressions in terms of s. Rearrange Equation 2 by subtracting s from both sides:
d + s - s = 209 - s
Cancel the s's, we get:
d = 209 - s
So we have the following system of equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d = 209 - s
[/LIST]
Substitute equation (2) into equation (1) for d:
2(209 - s) + 6.50s = 836.50
Multiply through to remove the parentheses:
418 - 2s + 6.50s = 836.50
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=418-2s%2B6.50s%3D836.50&pl=Solve']type it into our search engine and we get[/URL]:
s = [B]93[/B]

A fruit basket contains 458 apples And 139 oranges.How many more apples are there in the basket?

A fruit basket contains 458 apples And 139 oranges.How many more apples are there in the basket?
We want Apples - Oranges:
Apples - Oranges = 458 - 139
Apples - Oranges = [B]319[/B]

A grocer is selling oranges at 3 for $2. How much would it cost to buy a dozen oranges?

A grocer is selling oranges at 3 for $2. How much would it cost to buy a dozen oranges?
Set up a proportion of oranges per cost where c is the cost of a dozen oranges:
3/2 = 12/c <-- A dozen equals 12
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=12&den1=2&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
c = [B]8[/B]

A grocery store sells a bag of six oranges for $2.34 if Nova spends $1.95 on oranges how many did sh

A grocery store sells a bag of six oranges for $2.34 if Nova spends $1.95 on oranges how many did she buy
Unit cost is:
2.34/6 = 0.39 cents each
Nova spent $1.95
$1.95/0.39 = [B]5 oranges[/B]

A jug holds 1.2 litres of orange juice. All of the juice is poured equally into six glasses. How muc

A jug holds 1.2 litres of orange juice. All of the juice is poured equally into six glasses. How much orange is in each glass?
1.2 litres / 6 glasses = [B]0.2 litres[/B] in each glass.

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add the

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100
Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given:
[LIST=1]
[*]m = w + 5
[*]d = 0.5m
[*]d + m + w = 100
[/LIST]
Rearrange equation 1 in terms of w my subtracting 5 from each side:
[LIST=1]
[*]w = m - 5
[*]d = 0.5m
[*]d + m + w = 100
[/LIST]
Substitute equation (1) and equation (2) into equation (3)
0.5m + m + m - 5 = 100
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.5m%2Bm%2Bm-5%3D100&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get:
m = [B]42
[/B]
Now, substitute m = 42 into equation 2 to solve for d:
d = 0.5(42)
d = [B]21
[/B]
Now substitute m = 42 into equation 1 to solve for w:
w = 42 - 5
w = [B]37
[/B]
To summarize our ages:
[LIST]
[*]Man (m) = 42 years old
[*]Daughter (d) = 21 years old
[*]Wife (w) = 37 years old
[/LIST]

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket?
Declare variables:
[LIST]
[*]Let a be the number of adult's tickets
[*]Let c be the number of children's tickets
[/LIST]
Cost = Price * Quantity
We're given two equations:
[LIST=1]
[*]a + c = 20
[*]15a + 10c = 225
[/LIST]
Rearrange equation (1) in terms of a:
[LIST=1]
[*]a = 20 - c
[*]15a + 10c = 225
[/LIST]
Now that I have equation (1) in terms of a, we can substitute into equation (2) for a:
15(20 - c) + 10c = 225
Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225
We first need to simplify the expression removing parentheses
Simplify 15(20 - c): Distribute the 15 to each term in (20-c)
15 * 20 = (15 * 20) = 300
15 * -c = (15 * -1)c = -15c
Our Total expanded term is 300-15c
Our updated term to work with is 300 - 15c + 10c = 225
We first need to simplify the expression removing parentheses
Our updated term to work with is 300 - 15c + 10c = 225
[SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE]
(-15 + 10)c = -5c
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
-5c + 300 = + 225
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 300 and 225. To do that, we subtract 300 from both sides
-5c + 300 - 300 = 225 - 300
[SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE]
-5c = -75
[SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE]
-5c/-5 = -75/-5
c = [B]15[/B]
Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a:
a = 20 - 15
a = [B]5[/B]

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 poin

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?
Let's call the 5 point questions m for multiple choice. Let's call the 2 point questions t for true-false. We have two equations:
[LIST=1]
[*]m + t = 38
[*]5m + 2t = 100
[/LIST]
Rearrange (1) to solve for m - subtract t from each side:
3. m = 38 - t
Now, substitute (3) into (2)
5(38 - t) + 2t = 100
190 - 5t + 2t = 100
Combine like terms:
190 - 3t = 100
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=190-3t%3D100&pl=Solve']equation solver[/URL], we get [B]t = 30[/B].
Plugging t = 30 into (1), we get:
30 + t = 38
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=m%2B30%3D38&pl=Solve']equation solver[/URL] again, we get [B]m = 8[/B].
Check our work for (1)
8 + 30 = 38 <-- Check
Check our work for (2)
5(8) + 2(30) ? 100
40 + 60 ? 100
100 = 100 <-- Check
You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+38&term2=5m+%2B+2t+%3D+100&pl=Cramers+Method']simultaneous equations calculator[/URL]

A medium orange has 70 calories. This is 10 calories less then 1/4 of the calories in a sugar krunch

A medium orange has 70 calories. This is 10 calories less then 1/4 of the calories in a sugar krunchy. How many calories are in a sugar crunchy?
Let s = calories in a sugar crunch. Let o = 70 be the calories in a medium orange. Set up the equation:
o = 1/4s - 10
70 = 1/4s - 10
Add 10 to each side
1/4s = 80
Multiply each side by 4
[B]s = 320[/B]

A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of

A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of each coin are there?
Let d = the number of dimes and q = the number of quarters. We have two equations:
(1) d + q = 146
(2) 0.1d + 0.25q = 27.05
Rearrange (1) into (3) solving for d
(3) d = 146 - q
Substitute (3) into (2)
0.1(146 - q) + 0.25q = 27.05
14.6 - 0.1q + 0.25q = 27.05
Combine q's
0.15q + 14.6 = 27.05
Subtract 14.6 from each side
0.15q = 12.45
Divide each side by 0.15
[B]q = 83[/B]
Plugging that into (3), we have:
d = 146 - 83
[B]d = 63[/B]

A set of data has a range of 30. The least value in the set of data is 22. What is the greatest valu

A set of data has a range of 30. The least value in the set of data is 22. What is the greatest value in the set of data?
High Value - Low Value = Range
Let the high value be h. We're given:
h - 22 = 30
We [URL='https://www.mathcelebrity.com/1unk.php?num=h-22%3D30&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]52[/B]

A soccer team has picked its five best players to take part in penalty kicks to determine the winner

A soccer team has picked its five best players to take part in penalty kicks to determine the winner of a soccer match that is tied. Each of the five players will get one shot against the opposing team's goalie. The coach needs to decide the order in which the five players will take their shots. How many possible ways are there to arrange the five players?
First shot, 5 players can take the shot. Next shot is 4, then 3, then 2, then 1
5! = 5 x 4 x 3 x 2 x 1 = [B]120 ways[/B]

A thermometer has a range of 1.5 degrees of the temperature, what is the maximum and minimum at 87.4

A thermometer has a range of 1.5 degrees of the temperature, what is the maximum and minimum at 87.4 degrees
Range = Max - Min
Divide this by 2 to get the lesser half and larger half:
Half-Range = 1.5/2
Half-Range = 0.75
[U]Our Maximum temperature is:[/U]
Max Temp = Current Temp + Half-Range
Max Temp = 87.4 + 0.75
Max Temp = [B]88.15
[/B]
[U]Our Minimum temperature is:[/U]
Min Temp = Current Temp - Half-Range
Min Temp = 87.4 - 0.75
Min Temp = [B][B]86.65[/B][/B]

A traveler is walking on a moving walkway in an airport. the traveler must walk back on the walkway

A traveler is walking on a moving walkway in an airport. the traveler must walk back on the walkway to get a bag he forgot. the traveler's ground speed is 2 ft/s against the walkway and 6 ft/s with the walkway. what is the traveler's speed off the walkway? What is the speed of the moving walkway.
We have two equations, where w is the speed of the walkway and t is the speed of the traveler.
[LIST=1]
[*]t - w = 2
[*]t + w = 6
[*]Rearrange (1) to solve for t: t = w + 2
[/LIST]
Now plug (3) into (2)
(w + 2) + w = 6
Combine like terms:
2w + 2 = 6
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B2%3D6&pl=Solve']equation solver[/URL], we get [B]w = 2[/B]
Plug this into (1)
t - 2 = 2
Add 2 to each side
[B]t = 4[/B]

A+B+D=255 B+15=A D+12=B A=

A+B+D=255 B+15=A D+12=B A=
[LIST=1]
[*]A + B + D = 255
[*]B + 15 = A
[*]D + 12 = B
[*]A = ?
[*]Rearrange (3) to solve for D by subtracting 12 from each side: D = B - 12
[/LIST]
Substitute (2) and (5) into 1
(B + 15) + B + (B - 12) = 255
Combine like terms:
3B + 3 = 255
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3b%2B3%3D255&pl=Solve']equation solver[/URL], b = 84
Substitute b = 84 into equation (2):
A = 84 + 15
[B]A = 99[/B]

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were col

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were collected for a total of 10,078.75, how many students attended the fair
Let the number of students be s and the others be o. We're given two equations:
[LIST=1]
[*]o + s = 2848
[*]3.75o + 2.50s = 10078.75
[/LIST]
Since we have no coefficients for equation 1, let's solve this the fast way using substitution. Rearrange equation 1 by subtracting o from each side to isolate s
[LIST=1]
[*]o = 2848 - s
[*]3.75o + 2.50s = 10078.75
[/LIST]
Now substitute equation 1 into equation 2:
3.75(2848 - s) + 2.50s =10078.75
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3.75%282848-s%29%2B2.50s%3D10078.75&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]481[/B]

Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the siste

Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara?
Let a be Alice's age, b be Barbara's age, and c be Carol's age. We have 3 given equations:
[LIST=1]
[*]a = b - 3
[*]b = c - 5
[*]a + b + c = 68
[/LIST]
Rearrange (2)
c = b + 5
Now plug in (1) and (2) revised into (3). We want to isolate for b.
a + b + c = 68
(b - 3) + b + (b + 5) = 68
Combine like terms:
(b + b + b) + (5 - 3) = 68
3b + 2 = 68
Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2B2%3D68&pl=Solve']equation calculator[/URL], and we get b = [B]22[/B]

All the colors of the rainbow

All the colors of the rainbow
You can find this with the acronym: ROYGBIV
[LIST=1]
[*][B]Red[/B]
[*][B]Orange[/B]
[*][B]Yellow[/B]
[*][B]Green[/B]
[*][B]Blue[/B]
[*][B]Indigo[/B]
[*][B]Violet[/B]
[/LIST]
[U]Written as a set, we have 7 elements:[/U]
{[B]Red, Orange, Yellow, Green, Blue, Indigo, Violet[/B]}

An eccentric millionaire has 5 golden hooks from which to hang her expensive artwork. She wants to h

An eccentric millionaire has 5 golden hooks from which to hang her expensive artwork. She wants to have enough paintings so she can change the order of the arrangement each day for the next 41 years. (The same five paintings are okay as long as the hanging order is different.) What is the fewest number of paintings she can buy and still have a different arrangement every day for the next 41 years?
365 days * 41 years + 10 leap year days = 14,975 days
what is the lowest permutations count of n such that nP5 >= 14,975
W[URL='https://www.mathcelebrity.com/permutation.php?num=9&den=5&pl=Permutations']e see that 9P5[/URL] = 15,120, so the answer is [B]9 paintings[/B]

An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How ma

An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How many trees are there in each row?
We have r rows and t trees per row. We're give two equations:
[LIST=1]
[*]rt = 378
[*]r = t + 3
[/LIST]
Substitute equation (2) into equation (1) for r:
(t + 3)t = 378
Multiply through:
t^2 + 3t = 378
We have a quadratic equation. To solve this equation, we [URL='https://www.mathcelebrity.com/quadratic.php?num=t%5E2%2B3t%3D378&pl=Solve+Quadratic+Equation&hintnum=+0']type it in our search engine [/URL]and we get:
t = 18 and t = -21
Since t cannot be negative, we get trees per row (t):
[B]t = 18[/B]

Andrea has one hour to spend training for an upcoming race she completes her training by running ful

Andrea has one hour to spend training for an upcoming race she completes her training by running full speed in the distance of the race and walking back the same distance to cool down if she runs at a speed of 9 mph and walks back at a speed of 3 mph how long should she plan on spending to walk back
Let r = running time. Let w = walking time
We're given two equations
[LIST=1]
[*]r + w = 1
[*]9r = 3w
[/LIST]
Rearrange equation (1) by subtract r from each side:
[LIST=1]
[*]w = 1 - r
[*]9r = 3w
[/LIST]
Now substitute equation (1) into equation (2):
9r = 3(1 - r)
9r = 3 - 3r
To solve for r, [URL='https://www.mathcelebrity.com/1unk.php?num=9r%3D3-3r&pl=Solve']we type this equation into our search engine[/URL] and we get:
r = 0.25
Plug this into modified equation (1) to solve for w, and we get:
w = 1. 0.25
[B]w = 0.75[/B]

Basic Statistics

Given a number set, and an optional probability set, this calculates the following statistical items:

Expected Value

Mean = μ

Variance = σ^{2}

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Expected Value

Mean = μ

Variance = σ

Standard Deviation = σ

Standard Error of the Mean

Skewness

Mid-Range

Average Deviation (Mean Absolute Deviation)

Median

Mode

Range

Pearsons Skewness Coefficients

Entropy

Upper Quartile (hinge) (75th Percentile)

Lower Quartile (hinge) (25th Percentile)

InnerQuartile Range

Inner Fences (Lower Inner Fence and Upper Inner Fence)

Outer Fences (Lower Outer Fence and Upper Outer Fence)

Suspect Outliers

Highly Suspect Outliers

Stem and Leaf Plot

Ranked Data Set

Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range

Root Mean Square

Weighted Average (Weighted Mean)

Frequency Distribution

Successive Ratio

Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money

Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money in terms of the number of quarters and dimes. b)Rearrange the equation to isolate for the number of dimes (D)
a) The equation is:
[B]0.1d + 0.25q = 4.5[/B]
b) Isolate the equation for d. We subtract 0.25q from each side of the equation:
0.1d + 0.25q - 0.25q = 4.5 - 0.25q
Cancel the 0.25q on the left side, and we get:
0.1d = 4.5 - 0.25q
Divide each side of the equation by 0.1 to isolate d:
0.1d/0.1 = (4.5 - 0.25q)/0.1
d = [B]45 - 2.5q[/B]

Cards in a pack are either orange or purple. 80% of the cards are orange. Write the ratio of orange

Cards in a pack are either orange or purple. 80% of the cards are orange. Write the ratio of orange cards to purple cards.
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=80&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']80% as a fraction [/URL]is 4/5.
Fractions to ratios can be written as numerator : denominator, so we have:
[B]4:5[/B]

Chi-Square χ

This calculator determines a χ^{2} chi-square test on a test statistic and determines if it is outside an accepted range with critical value test and conclusion.

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse i

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. How old is each one of them?
Set up the relational equations where a = Alex's age, c = Chris's aged and j = Jesse's age
[LIST=1]
[*]a = c + 5
[*]j = a + 6
[*]a + c + j = 31
[*]Rearrange (1) in terms of c: c = a - 5
[/LIST]
[U]Plug in (4) and (2) into (3)[/U]
a + (a - 5) + (a + 6) = 31
[U]Combine like terms:[/U]
3a + 1 = 31
[U]Subtract 1 from each side[/U]
3a = 30
[U]Divide each side by 3[/U]
[B]a = 10[/B]
[U]Plug in 1 = 10 into Equation (4)[/U]
c = 10 - 5
[B]c = 5[/B]
Now plug 1 = 10 into equation (2)
j = 10 + 6
[B]j = 16[/B]

Circular Permutation

Calculates the following:

Number of ways to arrange n distinct items arranged on a circle

Number of ways to arrange n distinct items arranged on a circle

Derangements - Subfactorials

Calculates the number of derangements/subfactorial !n.

Donna buys a bag of 11 oranges for 2.86. Find the unit price in dollars per orange.

Set up a proportion in dollars to oranges
2.86/11 oranges = x/1
[URL='http://www.mathcelebrity.com/unit-cost-calculator.php?num=11poundbagfor2.86&pl=Calculate+Unit+Cost']Using our unit cost calculator[/URL]
[B]0.26 per orange[/B]

Each unit on a map of a forest represents 1 mile. To the nearest tenth of a mile, what is the distan

Each unit on a map of a forest represents 1 mile. To the nearest tenth of a mile, what is the distance from a ranger station at (1, 2) on the map to a river crossing at (2, 4) ?
We use our 2 point calculator and we get a distance of 2.2361.
Since each unit represents 1 mile, we have:
2.2361 units * 1 mile per unit = [B]2.2361 miles[/B]

eight oranges are $1.00 how much would 5 dozen oranges cost?

eight oranges are $1.00 how much would 5 dozen oranges cost?
Set up a proportion of oranges to cost where c is the cost for 5 dozen = 60 oranges:
8/1 = 60/c
To solve this proportion, [URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=60&den1=1&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
c = [B]7.5[/B]

Express the confidence interval 0.039 < p < 0.479 in the form of p ± E.

Express the confidence interval 0.039 < p < 0.479 in the form of p ± E.
We find the range of this interval:
Range = Upper Bound - Lower Bound
Range = 0.479 - 0.039
Range = 0.44
Each piece on opposite sides of p gets:
0.44/2 = 0.22
So our expression becomes
[B]p ± 0.22[/B]

Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?

Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?
Let Faith's age be f. Let her mother's age be m. We're given:
[LIST=1]
[*]f = m/5
[*]f + m = 30
[/LIST]
Rearrange (1) by cross-multiplying:
m = 5f
Substitute this into equation (2):
f + 5f = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=f%2B5f%3D30&pl=Solve']Type this equation into our search engine[/URL] and we get:
f = [B]5[/B]

Function

Takes various functions (exponential, logarithmic, signum (sign), polynomial, linear with constant of proportionality, constant, absolute value), and classifies them, builds ordered pairs, and finds the y-intercept and x-intercept and domain and range if they exist.

Given that E[Y]=2 and Var [Y] =3, find E[(2Y + 1)^2]

Given that E[Y]=2 and Var [Y] =3, find E[(2Y + 1)^2]
Multiply through
E[(2Y + 1)^2] = E[4y^2 + 4y + 1]
We can take the expected value of each term
E[4y^2] + E[4y] + E[1]
For the first term, we have:
4E[Y^2]
We define the Var[Y] = E[Y^2] - (E[Y])^2
Rearrange this term, we have E[Y^2] = Var[Y] + (E[Y])^2
E[Y^2] = 3+ 2^2
E[Y^2] = 3+ 4
E[Y^2] = 7
So our first term is 4(7) = 28
For the second term using expected value rules of separating out a constant, we have
4E[Y] = 4(2) = 8
For the third term, we have:
E[1] = 1
Adding up our three terms, we have:
E[4y^2] + E[4y] + E[1] = 28 + 8 + 1
E[4y^2] + E[4y] + E[1] = [B]37[/B]

H multiplied by 2x

H multiplied by 2x
h * 2x
If we arrange variables alphabetically, we have:
[B]2hx[/B]

How many different ways could you arrange 5 books on a shelf

How many different ways could you arrange 5 books on a shelf?
[URL='https://www.mathcelebrity.com/factorial.php?num=5!&pl=Calculate+factorial']Using permutations, you can type in 5![/URL] and we get:
[B]120 different ways.[/B]

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.

I have 5 apples and oranges, 4 are apples, how many oranges do i have

I have 5 apples and oranges, 4 are apples, how many oranges do I have?
5 apples and oranges - 4 apples = [B]1 orange[/B]

If f={(4,2),(5,1),(6,2),(7,3),(8,6)} then the range of f is what

If f={(4,2),(5,1),(6,2),(7,3),(8,6)} then the range of f is what
The range is the full set of all possible y-values:
{1, 2, 2, 3, 6}
Remove duplicates, we get:
[B]{1, 2, 3, 6}[/B]

If Jody had $3 more she would have twice as much as Lars together they have $60

If Jody had $3 more she would have twice as much as Lars together they have $60.
Let j be Jody's money and l be Lars's money. We have two equations:
[LIST=1]
[*]j + l = 60
[*]j + 3 = 2l
[/LIST]
Rearrange (2) to solve for j by subtracting 3
j = 2l - 3
Now substitute this into (1)
(2l - 3) + l = 60
Combine like terms
3l - 3 = 60
Enter this into our [URL='http://www.mathcelebrity.com/1unk.php?num=3l-3%3D60&pl=Solve']equation calculator[/URL], and we get:
[B]l = 21[/B]
Now plug l = 21 into our rearranged equation above:
j = 2(21) - 3
j = 42 - 3
[B]j = 39[/B]

If the max time that John can spend on Client A ($20/hr) in one week is 32 hours, and the min time i

If the max time that John can spend on Client A ($20/hr) in one week is 32 hours, and the min time is 8 hours, while the max time on Client B ($14/hr) is 8 hours and the min 5 hours, what is the RANGE (max, min) of total pay he can earn in one week (40 hours)
[LIST]
[*]Client A Minimum = 20 x 8 hours = $160
[*]Client A Maximum = 20 x 32 hours = $640
[*]Client B Minimum = 14 x 5 hours = $70
[*]Client B Maximum = 14 x 8 hours = $112
[/LIST]
[U]The Total Maximum Pay is found by adding Client A Maximum and Client B Maximum[/U]
Total Maximum = Client A Maximum + Client B Maximum
Total Maximum = 640 + 112
Total Maximum = 752
[U]The Total Minimum Pay is found by adding Client A Minimum and Client B Minimum[/U]
Total Minimum = Client A Minimum + Client B Minimum
Total Minimum = 160 + 70
Total Minimum = 230
[U]The Range is the difference between the Total maximum and the Total minimum[/U]
Range(Total Maximum, Total Minimum) = Total Maximum - Total Minimum
Range(752, 230) = 752 - 230
Range(752, 230) = [B]522[/B]

in a city, the record monthly high temperature for March is 56°F. The record monthly low for March i

in a city, the record monthly high temperature for March is 56°F. The record monthly low for March is -4°F. What is the range of temperatures for the month of March
Range = High - Low
Range = 56 - -4
Range = 56 + 4 [I]since double negative is positive[/I]
Range = [B]60[/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]

In Maricopa County, 5 persons are to be elected to the Board of Supervisors. If 8 persons are candid

In Maricopa County, 5 persons are to be elected to the Board of Supervisors. If 8 persons are candidates, how many different arrangements are possible?
We want 8 choose 5, or 8C5. [URL='http://www.mathcelebrity.com/permutation.php?num=8&den=5&pl=Combinations']Typing this into the search engine[/URL] we get [B]56[/B].

Jack bought 7 tickets for a movie. He paid $7 for each adult ticket and $4 for each child ticket. Ja

Jack bought 7 tickets for a movie. He paid $7 for each adult ticket and $4 for each child ticket. Jack spent $40 for the tickets
Let a = Number of adult tickets and c be the number of child tickets.
[LIST=1]
[*]7a + 4c = 40
[*]a + c = 7
[*]Rearrange (2): a = 7 - c
[/LIST]
Now substitute a in (3) into (1):
7(7 - c) + 4c = 40
49 - 7c + 4c = 40
49 - 3c = 40
Add 3c to each side and subtract 40:
3c = 9
Divide each side by 3:
[B]c = 3
[/B]
Substitute c = 3 into Equation (2)
a + 3 = 7
Subtract 3 from each side:
[B]a = 4[/B]

Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined

Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined distance thrown by the 3 friends is 124 metres, how far did Angus throw the javelin?
Assumptions and givens:
[LIST]
[*]Let a be the distance Angus threw the javelin
[*]Let c be the distance Cameron threw the javelin
[*]Let j be the distance Jenny threw the javelin
[/LIST]
We're given 3 equations:
[LIST=1]
[*]j = a + 4
[*]j = c - 5
[*]a + c + j = 124
[/LIST]
Since j is the common variable in all 3 equations, let's rearrange equation (1) and equation (2) in terms of j as the dependent variable:
[LIST=1]
[*]a = j - 4
[*]c = j + 5
[*]a + c + j = 124
[/LIST]
Now substitute equation (1) and equation (2) into equation (3) for a and c:
j - 4 + j + 5 + j = 124
To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=j-4%2Bj%2B5%2Bj%3D124&pl=Solve']type it in our math engine[/URL] and we get:
j = 41
The question asks how far Angus (a) threw the javelin. Since we have Jenny's distance j = 41 and equation (1) has j and a together, let's substitute j = 41 into equation (1):
a = 41 - 4
a = [B]37 meters[/B]

John had x mangos and p oranges. How many fruits did he have

John had x mangos and p oranges. How many fruits did he have
Fruits = mangos + oranges
Fruits = [B]x + p[/B]

Juan spent at most $2.50 on apples and oranges. He bought 5 apples at $0.36 each. What is the most h

Juan spent at most $2.50 on apples and oranges. He bought 5 apples at $0.36 each. What is the most he spent on oranges?
Let a be spending apples and o be spending on oranges, we have:
[LIST=1]
[*]a + o <= 2.36 <-- At most means less than or equal to
[*]a = 5 * 0.36 = 1.8
[/LIST]
Substitute (2) into (1)
1.8 + o <= 2.36
Subtract 1.8 from each side
[B]o <= 0.56[/B]

Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most

Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most She spent on oranges
[U]Assumptions and givens:[/U]
[LIST]
[*]Let a be the total cost of apples
[*]Let o be the total cost of oranges
[/LIST]
The phrase [I]at most[/I] means less than or equal to, so we have:
a + o <= 2.50
[U]Find the cost of apples (a)[/U]
a = price per apple * quantity of apples
a = 0.36 * 5
a = 1.8
Our new inequality with a = 1.8 is:
1.8 + o <= 2.50
[URL='https://www.mathcelebrity.com/1unk.php?num=1.8%2Bo%3C%3D2.50&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]o <= 0.7[/B]

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of sla

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each shirt, each pair of slacks, and each sports coat?
Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given:
[LIST=1]
[*]4s + p = 11.45
[*]5s + 3p + c = 27.41
[*]5s + c = 16.94
[/LIST]
Rearrange (1) by subtracting 4s from each side:
p = 11.45 - 4s
Rearrange (3)by subtracting 5s from each side:
c = 16.94 - 5s
Take those rearranged equations, and plug them into (2):
5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41
Multiply through:
5s + 34.35 - 12s + 16.94 - 5s = 27.41
[URL='https://www.mathcelebrity.com/1unk.php?num=5s%2B34.35-12s%2B16.94-5s%3D27.41&pl=Solve']Group like terms using our equation calculator [/URL]and we get:
[B]s = 1.99 [/B] <-- Shirt Cost
Plug s = 1.99 into modified equation (1):
p = 11.45 - 4(1.99)
p = 11.45 - 7.96
[B]p = 3.49[/B] <-- Slacks Cost
Plug s = 1.99 into modified equation (3):
c = 16.94 - 5(1.99)
c = 16.94 - 9.95
[B]c = 6.99[/B] <-- Sports Coat cost

Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a to

Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive?
Let t = number of 20 bills and f = number of 50 bills. We have two equations.
(1) 20t + 50f = 390
(2) t + f = 15
[U]Rearrange (2) into (3) for t, by subtracting f from each side:[/U]
(3) t = 15 - f
[U]Now substitute (3) into (1)[/U]
20(15 - f) + 50f = 390
300 - 20f + 50f = 390
[U]Combine f terms[/U]
300 + 30f = 390
[U]Subtract 300 from each side[/U]
30f = 90
[U]Divide each side by 30[/U]
[B]f = 3[/B]
[U]Substitute f = 3 into (3)[/U]
t = 15 - 3
[B]t = 12[/B]

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The tot

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The total value of the jar is $7.85. How many of each type?
Let d be dimes and q be quarters. Set up two equations from our givens:
[LIST=1]
[*]d + q = 41
[*]0.1d + 0.25q = 7.85
[/LIST]
[U]Rearrange (1) by subtracting q from each side:[/U]
(3) d = 41 - q
[U]Now, substitute (3) into (2)[/U]
0.1(41 - q) + 0.25q = 7.85
4.1 - 0.1q + 0.25q = 7.85
[U]Combine q terms[/U]
0.15q + 4.1 = 7.85
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.15q%2B4.1%3D7.85&pl=Solve']equation calculator[/URL], we get:[/U]
[B]q = 25[/B]
[U]Substitute q = 25 into (3)[/U]
d = 41 - 25
[B]d = 16[/B]

Lagrange Four Square Theorem (Bachet Conjecture)

Builds the Lagrange Theorem Notation (Bachet Conjecture) for any natural number using the Sum of four squares.

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?
Declare variables for the 2 numbers:
[LIST]
[*]Let l be the larger number
[*]Let s be the smaller number
[/LIST]
We're given two equations:
[LIST=1]
[*]l = s + 4
[*]l + s = 40
[/LIST]
To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l.
Subtract 4 from each side in equation (1)
l - 4 = s + 4 - 4
Cancel the 4's and we get:
s = l - 4
Our given equations are now:
[LIST=1]
[*]s = l - 4
[*]l + s = 40
[/LIST]
Substitute equation (1) into equation (2) for s:
l + l - 4 = 40
Grouping like terms for l, we get:
2l - 4 = 40
Add 4 to each side:
2l - 4 + 4 = 40 + 4
Cancelling the 4's on the left side, we get
2l = 44
Divide each side of the equation by 2 to isolate l:
2l/2 = 44/2
Cancel the 2's on the left side and we get:
l = [B]22[/B]

Laura has three errands to complete. She must wash the dishes, mow the lawn, and paint a fence. How

Laura has three errands to complete. She must wash the dishes, mow the lawn, and paint a fence. How many ways can Laura arrange the order of the three errands?
3! = 3 * 2 * 1 = [B]6 ways[/B]

Letter Arrangements in a Word

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

Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes.

Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes. If the total value of the coins is 2.18, how many of each denomination does she have?
[U]Set up two equations where p is the number of pennies and d is the number of dimes:[/U]
(1) d + p = 47
(2) 0.1d + 0.01p = 2.18
[U]Rearrange (1) into (3) by solving for d[/U]
(3) d = 47 - p
[U]Substitute (3) into (2)[/U]
0.1(47 - p) + 0.01p = 2.18
4.7 - 0.1p + 0.01p = 2.18
[U]Group p terms[/U]
4.7 - 0.09p = 2.18
[U]Add 0.09p to both sides[/U]
0.09p + 2.18 = 4.7
[U]Subtract 2.18 from both sides[/U]
0.09p = 2.52
[U]Divide each side by 0.09[/U]
[B]p = 28[/B]
[U]Now substitute that back into (3)[/U]
d =47 - 28
[B]d = 19[/B]

Marissa has 24 coins in quarters and nickels. She has 3 dollars. How many of the coins are quarters?

Let n be the number of nickels and q be the number of quarters.
We have two equations:
(1) n + q = 24
(2) 0.05n + 0.25q = 3
Rearrange (1) to solve for n in terms of q for another equation (3)
(3) n = 24 - q
Plug (3) into (2)
0.05(24 - q) + 0.25q = 3
Multiply through:
1.2 - 0.05q + 0.25q = 3
Combine q terms
0.2q + 1.2 = 3
Subtract 1.2 from each side:
0.2q = 1.8
Divide each side by 0.2
[B]q = 9[/B]

Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00 bob bought 3 burgers and

Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00. Bob bought 3 burgers and 1 drink for $5.50. How much is each burger and drink?
[U]Set up the givens where b is the cost of a burger and d is the cost of a drink:[/U]
Max: 2b + 2d = 5
Bob: 3b + d = 5.50
[U]Rearrange Bob's equation by subtracting 3b from each side[/U]
(3) d = 5.50 - 3b
[U]Now substitute that d equation back into Max's Equation[/U]
2b + 2(5.50 - 3b) = 5
2b + 11 - 6b = 5
[U]Combine b terms:[/U]
-4b + 11 = 5
[U]Subtract 11 from each side[/U]
-4b = -6
[U]Divide each side by -4[/U]
b = 3/2
[B]b = $1.50[/B]
[U]Now plug that back into equation (3):[/U]
d = 5.50 - 3(1.50)
d = 5.50 - 4.50
[B]d = $1.00[/B]

Mr. Crimmins bought 15 apples and 15 oranges. Each apple cost $1.00, each orange cost $1.50. How muc

Mr. Crimmins bought 15 apples and 15 oranges. Each apple cost $1.00, each orange cost $1.50. How much more did he spend on oranges than apples?
[U]Calculate apple spend:[/U]
Apple Spend = Apple Cost * Number of Apples
Apple Spend = $1.00 * 15
Apple Spend =[B] [/B]$15
[B][/B]
[U]Calculate apple spend:[/U]
Orange Spend = Orange Cost * Number of Oranges
Orange Spend = $1.50 * 15
Orange Spend = $22.50
[B][/B]
[U]Calculate the additional amount spent on oranges over apples:[/U]
Additional Orange Spend = Orange Spend - Apple Spend
Additional Orange Spend = $22.50 - $15.00
Additional Orange Spend = [B]$7.50[/B]

Multiple Fractions (Addition or Ordering)

This adds 3 or more fractions or arranges a list of fractions from lowest to highest and highest to lowest (ordering fractions or sorting fractions)

Normal Distribution

Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem).

Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability

Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability

Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each c

Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each class is $13, otherwise it is $18 for each class. After how many classes is the total cost with the fitness pass the same as the total cost without the fitness pass?
Let the number of classes be c.
For the fitness pass plan, we have the total cost of:
13c + 100
For the flat rate plan, we have the total cost of:
18c
The question asks for c when both plans are equal. So we set both costs equal and solve for c:
13c + 100 = 18c
We [URL='https://www.mathcelebrity.com/1unk.php?num=13c%2B100%3D18c&pl=Solve']type this equation into our math engine[/URL] and we get:
c = [B]20[/B]

Percentile for Normal Distribution

Given a mean, standard deviation, and a percentile range, this will calculate the percentile value.

Permutations and Combinations

Calculates the following:

Number of permutation(s) of n items arranged in r ways =_{n}P_{r}

Number of combination(s) of n items arranged in r__unique__ ways = _{n}C_{r} including subsets of sets

Number of permutation(s) of n items arranged in r ways =

Number of combination(s) of n items arranged in r

Rearrange the following equation to make x the subject, and select the correct rearrangement from th

Rearrange the following equation to make x the subject, and select the correct rearrangement from the list below
3x + 2y 1
-------- = ---
4x + y 3
[LIST]
[*]x = 7y/13
[*]x = 7y/5
[*]x = -7y
[*]x = -3y
[*]x = 3y/5
[*]x = -5y/13
[*]x = -y
[/LIST]
Cross multiply:
3(3x - 2y) = 4x + y
Multiply the left side through
9x - 6y = 4x + y
Subtract 4x from each side and add 6y to each side
5x = 7y
Divide each side by 5 to isolate x, the subject of an equation is the variable to the left
[B]x = 7y/5[/B]

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]

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked bot

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of $690. How long did Giselle work as a carpenter and how long did she work as a blacksmith?
Assumptions:
[LIST]
[*]Let b be the number of hours Giselle worked as a blacksmith
[*]Let c be the number of hours Giselle worked as a carpenter
[/LIST]
Givens:
[LIST=1]
[*]b + c = 30
[*]25b + 20c = 690
[/LIST]
Rearrange equation (1) to solve for b by subtracting c from each side:
[LIST=1]
[*]b = 30 - c
[*]25b + 20c = 690
[/LIST]
Substitute equation (1) into equation (2) for b
25(30 - c) + 20c = 690
Multiply through:
750 - 25c + 20c = 690
To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=750-25c%2B20c%3D690&pl=Solve']type this equation into our search engine[/URL] and we get:
c = [B]12
[/B]
Now, we plug in c = 12 into modified equation (1) to solve for b:
b = 30 - 12
b = [B]18[/B]

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large redwood tree was, the ranger said that he wouldn't tell its height, but would give Sonia a clue. How tall is the redwood tree Sonia asked about?
Sonia said the tree is 64 times my height. The tree is also 112 feet taller than the tree next to it. The two trees plus my height total 597.5 feet.
[LIST]
[*]Rangers's height = n
[*]Tree height = 64n
[*]Smaller tree height = 64n - 112
[*]Total height = 64n - 112 + 64n = 597.5
[/LIST]
Solve for [I]n[/I] in the equation 64n - 112 + 64n = 597.5
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(64 + 64)n = 128n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
128n - 112 = + 597.5
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants -112 and 597.5. To do that, we add 112 to both sides
128n - 112 + 112 = 597.5 + 112
[SIZE=5][B]Step 4: Cancel 112 on the left side:[/B][/SIZE]
128n = 709.5
[SIZE=5][B]Step 5: Divide each side of the equation by 128[/B][/SIZE]
128n/128 = 709.5/128
n = 5.54296875
Tree height = 64 * ranger height
Tree height = 64 * 5.54296875
Tree height = [B]354.75 feet[/B]

Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin doe

Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin does she have?
Set up two equations where d is the number of dimes and q is the number of quarters:
(1) d + q = 10
(2) 0.1d + 0.25q = 1.45
Rearrange (1) into (3) to solve for d
(3) d = 10 - q
Now plug (3) into (2)
0.1(10 - q) + 0.25q = 1.45
Multiply through:
1 - 0.1q + 0.25q = 1.45
Combine q terms
0.15q + 1 = 1.45
Subtract 1 from each side
0.15q = 0.45
Divide each side by 0.15
[B]q = 3[/B]
Plug our q = 3 value into (3)
d = 10 - 3
[B]d = 7[/B]

Susan has 10 apples and 6 oranges. How many fruits does she have?

Since apples and oranges are both fruits, we add 10 + 6 to get [B]16[/B] fruits.

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. Wh?

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. What are the numbers?
Let the smaller number be x. Let the larger number be y. We're given:
[LIST=1]
[*]y - x = 108
[*]6x = y + 2
[/LIST]
Rearrange (1) by adding x to each side:
[LIST=1]
[*]y = x + 108
[/LIST]
Substitute this into (2):
6x = x + 108 + 2
Combine like terms
6x = x +110
Subtract x from each side:
5x = 110
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D110&pl=Solve']Plugging this equation into our search engine[/URL], we get:
x = [B]22[/B]

The difference between two positive numbers is 5 and the square of their sum is 169

The difference between two positive numbers is 5 and the square of their sum is 169.
Let the two positive numbers be a and b. We have the following equations:
[LIST=1]
[*]a - b = 5
[*](a + b)^2 = 169
[*]Rearrange (1) by adding b to each side. We have a = b + 5
[/LIST]
Now substitute (3) into (2):
(b + 5 + b)^2 = 169
(2b + 5)^2 = 169
[URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']Run (2b + 5)^2 through our search engine[/URL], and you get:
4b^2 + 20b + 25
Set this equal to 169 above:
4b^2 + 20b + 25 = 169
[URL='https://www.mathcelebrity.com/quadratic.php?num=4b%5E2%2B20b%2B25%3D169&pl=Solve+Quadratic+Equation&hintnum=+0']Run that quadratic equation in our search engine[/URL], and you get:
b = (-9, 4)
But the problem asks for [I]positive[/I] numbers. So [B]b = 4[/B] is one of our solutions.
Substitute b = 4 into equation (1) above, and we get:
a - [I]b[/I] = 5
[URL='https://www.mathcelebrity.com/1unk.php?num=a-4%3D5&pl=Solve']a - 4 = 5[/URL]
[B]a = 9
[/B]
Therefore, we have [B](a, b) = (9, 4)[/B]

The difference of two numbers is 12 and their mean is 15. Find the two numbers

The difference of two numbers is 12 and their mean is 15. Find the two numbers.
Let the two numbers be x and y. We're given:
[LIST=1]
[*]x - y = 12
[*](x + y)/2 = 15. <-- Mean is an average
[/LIST]
Rearrange equation 1 by adding y to each side:
x - y + y = y + 12
Cancelling the y's on the left side, we get:
x = y + 12
Now substitute this into equation 2:
(y + 12 + y)/2 = 15
Cross multiply:
y + 12 + y = 30
Group like terms for y:
2y + 12 = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B12%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 9[/B]
Now substitute this into modified equation 1:
x = y + 12
x = 9 + 12
[B]x = 21[/B]

The domain of a relation is all even negative integers greater than -9. The range y of the relation

The domain of a relation is all even negative integers greater than -9. The range y of the relation is the set formed by adding 4 to the numbers in the domain. Write the relation as a table of values and as an equation.
The domain is even negative integers greater than -9:
{-8, -6, -4, -2}
Add 4 to each x for the range:
{-8 + 4 = -4, -6 + 4 = -2. -4 + 4 = 0, -2 + 4 = 2}
For ordered pairs, we have:
(-8, -4)
(-6, -2)
(-4, 0)
(-2, 2)
The equation can be written:
y = x + 4 on the domain (x | x is an even number where -8 <= x <= -2)

The Oakdale High School Speech and Debate Club hosted its annual car wash fundraiser. Each club memb

The Oakdale High School Speech and Debate Club hosted its annual car wash fundraiser. Each club member brought a bottle of car wash soap, so there were 8 total bottles. 6 of the bottles contained orange soap. If a club member randomly selects 5 bottles to pour into the first soap bucket, what is the probability that all of them contain orange soap?
This is assumed to be draw without replacement, so we have:
[LIST=1]
[*]Draw 1: 6/8
[*]Draw 2: 5/7
[*]Draw 3: 4/6
[*]Draw 4: 3/5
[*]Draw 5: 2/4
[/LIST]
Since they are independent events, we multiply:
6/8 * 5/7 * 4/6 * 3/5 * 2/4
(6 * 5 * 4 * 3 * 2)/(8 * 7 * 6 * 5 * 4)
720/6720
[B]0.1071[/B]

The sum of 2 numbers is 18. 3 times the greater number exceeds 4 times the smaller number by 5. Find

The sum of 2 numbers is 18. 3 times the greater number exceeds 4 times the smaller number by 5. Find the numbers.
Let the first number be x. The second number is y. We have:
[LIST=1]
[*]x + y = 18
[*]3x = 4y + 5
[/LIST]
Rearrange (2), by subtracting 4y from each side:
3x - 4y = 5
So we have a system of equations:
[LIST=1]
[*]x + y = 18
[*]3x - 4y = 5
[/LIST]
Using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y+%3D+18&term2=3x+-+4y+%3D+5&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[B]x = 11
y = 7[/B]

The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age

The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age. How old are they now?
Let Jocelyn's age be a
Let Joseph's age be b.
We're given two equations:
[LIST=1]
[*]a + b = 40
[*]2(a + 5) = b + 5
[/LIST]
We rearrange equation (1) in terms of a to get:
[LIST=1]
[*]a = 40 - b
[*]2a = b + 5
[/LIST]
Substitute equation (1) into equation (2) for a:
2(40 - b) = b + 5
80 - 2b = b + 5
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=80-2b%3Db%2B5&pl=Solve']type it in our search engine[/URL] and we get:
[B]b (Joseph's age) = 25[/B]
Now, substitute b = 25 into equation (1) to solve for a:
a = 40 - 25
[B]a (Jocelyn's age) = 15[/B]

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. Ho

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now?
Let Levi's current age be l. Let Renee's current age be r. Were given two equations:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4(r - 7)
[/LIST]
Simplify equation 2 by multiplying through:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4r - 28
[/LIST]
Rearrange equation 1 to solve for r and isolate l by subtracting l from each side:
[LIST=1]
[*]r = 89 - l
[*]l - 7 = 4r - 28
[/LIST]
Now substitute equation (1) into equation (2):
l - 7 = 4(89 - l) - 28
l - 7 = 356 - 4l - 28
l - 7 = 328 - 4l
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get:
l = [B]67[/B]

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number.
Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given:
[LIST=1]
[*]x + y = 10
[*]10x+ y = 15y + 4
[/LIST]
Simplifying Equation (2) by subtracting y from each side, we get:
10x = 14y + 4
Rearranging equation (1), we get:
x = 10 - y
Substitute this into simplified equation (2):
10(10 - y) = 14y + 4
100 - 10y = 14y + 4
[URL='https://www.mathcelebrity.com/1unk.php?num=100-10y%3D14y%2B4&pl=Solve']Typing this equation into our search engine[/URL], we get:
y = 4
Plug this into rearranged equation (1), we get:
x = 10 - 4
x = 6
So our number xy is [B]64[/B].
Let's check our work against equation (1):
6 + 4 ? 10
10 = 10
Let's check our work against equation (2):
10(6)+ 4 ? 15(4) + 4
60 + 4 ? 60 + 4
64 = 64

There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How

There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How many of each animal are there?
Chickens have 2 legs, pigs have 4 legs. Let c be the number of chickens and p be the number of pigs. Set up our givens:
(1) c + p = 13
(2) 2c + 4p = 40
[U]Rearrange (1) to solve for c by subtracting p from both sides:[/U]
(3) c = 13 - p
[U]Substitute (3) into (2)[/U]
2(13 - p) + 4p = 40
26 - 2p + 4p = 40
[U]Combine p terms[/U]
2p + 26 = 40
[U]Subtract 26 from each side:[/U]
2p = 14
[U]Divide each side by 2[/U]
[B]p = 7[/B]
[U]Substitute p = 7 into (3)[/U]
c = 13 - 7
[B]c = 6[/B]
For a shortcut, you could use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+p+%3D+13&term2=2c+%2B+4p+%3D+40&pl=Cramers+Method']simultaneous equations calculator[/URL]

There are 5 orange books, 12 black books, and 8 tan books on Mr. Johnsons bookshelf. Calculate the p

There are 5 orange books, 12 black books, and 8 tan books on Mr. Johnsons bookshelf. Calculate the probability of randomly selecting a black book and then a tan book without replacement. Write your answer as a percent.
P(black book first draw)
P(black book first draw) = 12 black / (5 orange + 12 black + 8 tan)
P(black book first draw) = 12 / 25
P(tan book second draw)
P(tan book second draw) = 8 tan / (5 orange + 11 black + 8 tan) <-- 11 black because we already drew one black
P(tan book second draw) = 8 / 24
Using our fraction reduction calculator, this simplifies to 1/3
Since each draw is independent, we multiply both probabilities:
P(black book first draw, tan book second draw) = 12/25 * 1/3
P(black book first draw, tan book second draw) = 12/75
P(black book first draw, tan book second draw) = [B]16%[/B]

There are 5 pencil-cases on the desk. Each pencil-case contains at least 10 pencils, but not more th

[SIZE=4]There are 5 pencil-cases on the desk. Each pencil-case contains at least 10 pencils, but not more than 14 pencils. Which of the following could be the total number of pencils in all 5 cases?
A) 35
B) 45
C) 65
D) 75
[U]Determine the minimum amount of pencils (At least means greater than or equal to):[/U]
Minimum Amount of pencils = Cases * Min Quantity
Minimum Amount of pencils = 5 * 10
Minimum Amount of pencils = 50
[SIZE=4][U]Determine the maximum amount of pencils (Not more than means less than or equal to):[/U]
Maximum Amount of pencils = Cases * Min Quantity
Maximum Amount of pencils = 5 * 14
Maximum Amount of pencils = 70[/SIZE]
So our range of pencils (p) is:
50 <= p <= 70
Now take a look at our answer choices. The only answer which fits in this inequality range is [B]C, 65[/B].
[B][/B][/SIZE]

There are 72 boys and 90 girls on the Math team For the next math competition Mr Johnson would like

There are 72 boys and 90 girls on the Math team For the next math competition Mr Johnson would like to arrange all of the students in equal rows with only girls or boys in each row with only girls or boys in each row. What is the greatest number of students that can be put in each row?
To find the maximum number (n) of boys or girls in each row, we want the GCF (Greatest Common Factor) of 72 and 90.
[URL='https://www.mathcelebrity.com/gcflcm.php?num1=72&num2=90&num3=&pl=GCF+and+LCM']Using our GCF calculator for GCF(72,90)[/URL], we get 18.
[LIST]
[*]72 boys divided by 18 = [B]4 rows of boys[/B]
[*]90 girls divided by 18 = [B]5 rows of girls[/B]
[/LIST]

Triangle Inequality

This calculator displays 2 scenarios

1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle

2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle

2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

Tristian bought an orange that was 1/5 pound. He cut the orange into 8 slices. How much does each sl

Tristian bought an orange that was 1/5 pound. He cut the orange into 8 slices. How much does each slice weigh?
1/5 pound / 8 slices = 1/5 * 1/8 = [B]1/40 pound[/B]

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worke

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of 1225. what was the rate charged per hour by each mechanic if the sum of the two rates was 170 per hour?
Set up two equations:
(1) 10x + 5y = 1225
(2) x + y = 170
Rearrange (2)
x = 170 - y
Substitute that into (1)
10(170 - y) + 5y = 1225
1700 - 10y + 5y = 1225
1700 - 5y = 1225
Move 5y to the other side
5y + 1225 = 1700
Subtract 1225 from each side
5y =475
Divide each side by 5
[B]y = 95[/B]
Which means x = 170 - 95, [B]x = 75[/B]

two numbers have an average of 2100 and one number is $425 more than the other number. What are the

two numbers have an average of 2100 and one number is $425 more than the other number. What are the numbers
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*](x + y)/2 = 2100 (Average)
[*]y = x + 425
[/LIST]
Rearrange equation (1) by cross multiplying
x + y = 2 * 2100
x + y = 4200
So we have our revised set of equations:
[LIST=1]
[*]x + y = 4200
[*]y = x + 425
[/LIST]
Substituting equation (2) into equation (1) for y, we get:
x + (x + 425) = 4200
Combining like terms, we get:
2x + 425 = 4200
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B425%3D4200&pl=Solve']equation solver[/URL], we get:
x = [B]1887.5[/B]
Which means using equation (2), we get
y = 1887.5 + 425
y = [B]2312.5[/B]

Two numbers total 83 and have a difference of 17 find the two numbers

Let the numbers be x and y. Set up our givens:
[LIST=1]
[*]x + y = 83
[*]x - y = 17
[*]Rearrange (2), by adding y to each side, we have: x = 17 + y
[/LIST]
[U]Substitute (3) into (1):[/U]
(17 + y) + y = 83
[U]Group y terms[/U]
2y + 17 = 83
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2y%2B17%3D83&pl=Solve']equation solver[/URL], we get:[/U]
[B]y = 33
[/B]
[U]Substitute that into (3)[/U]
x = 17 + 33
[B]x = 50
[/B]
So our two numbers (x, y) = (33, 50)

Wan bought 2 salad rolls and 1 bottle of orange juice. If each salad roll costs x cents and the oran

Wan bought 2 salad rolls and 1 bottle of orange juice. If each salad roll costs x cents and the orange juice costs $1.50, write the expression for the total cost (in cents) for the food and drink
The cost C is:
C = 2x + 1.50(1)
Simplify:
[B]C = 2x + 1.50[/B]

What is a Function

This lesson walks you through what a function is, how to write a function, the part of a function, and how to evaluate the outputs of a function.

This lesson also shows you the domain and range of a function. This lesson shows you the y-intercept of a function and the x-intercept of a function. Also shows Relation and function

This lesson also shows you the domain and range of a function. This lesson shows you the y-intercept of a function and the x-intercept of a function. Also shows Relation and function

What is the range of possible values for a coefficient of correlation?

What is the range of possible values for a coefficient of correlation?
[B]The range is -1.0 to +1.0[/B]

Which of the following descriptions of confidence interval is correct? (Select all that apply) a. I

Which of the following descriptions of confidence interval is correct? (Select all that apply)
a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0
b. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0
c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1
d. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1
[B]a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0
c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1
[/B]
[I]The lower the confidence interval, the wider the range, so if a higher confidence interval contains a point, a lower confidence interval will contain that point as well.[/I]

Which of the following equations represents a line that is parallel to the line with equation y = -3

Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4?
A) 6x + 2y = 15
B) 3x - y = 7
C) 2x - 3y = 6
D) x + 3y = 1
Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we want a line with a slope of -3, like our given line.
If we rearrange A) by subtracting 6x from each side, we get:
2y = -6x + 15
Divide each side by 2, we get:
y = -3x + 15/2
This line is in the form y = mx + b, where m = -3. So our answer is [B]A[/B].

x is a multiple of 6 and 1 ? x ? 16

x is a multiple of 6 and 1 ? x ? 16.
We want multiples of 6 between 1 and 16.
We start with 6.
Another multiple of 6 is 12
The next multiple of 6 is 18, which is out side the range of 1 ? x ? 16.
So our number set is [B]x = {6, 12}[/B]

you and 5 friends go to a concert. how many different ways can you sit in the assigned seats

You and 5 friends go to a concert. how many different ways can you sit in the assigned seats?
With 6 possible seats, the [URL='https://www.mathcelebrity.com/factorial.php?num=6!&pl=Calculate+factorial']number of unique arrangements is[/URL]:
6! = 6 x 5 x 4 x 3 x 2 x 1 = [B]720[/B]

You and your friend are saving for a vacation. You start with the same amount and save for the same

You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save 75 per week, and your friend saves 50 per week. When vacation time comes, you have 950, and your friend has 800. How much did you start with, and for how many weeks did you save?
[U]Let w be the number of weeks. Set up two equations where s is the starting amount:[/U]
(1) s + 75w =950
(2) s + 50w = 800
[U]Rearrange (1) into (3) to solve for s by subtracting 75w[/U]
(3) s = 950 - 75w
[U]Rearrange (2) into (4) to solve for s by subtracting 50w[/U]
(4) s = 800 - 50w
[U]Set (3) and (4) equal to each other so solve for w[/U]
950 - 75w = 800 - 50w
[U]Add 75w to each side, and subtract 950 from each side:[/U]
25w = 150
[U]Divide each side by w[/U]
[B]w = 6[/B]
Now plug w = 6 into (3)
s = 950 - 75(6)
s = 950 - 450
[B]s = 500[/B]

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pi

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of $12.50 to buy snacks. The fruit drinks are $1.50 and the chips are $1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you able to purchase?
Let c be the number of chips. Let f be the number of fruit drinks. We're given two equations:
[LIST=1]
[*]c + f = 10
[*]c + 1.5f = 12.50
[/LIST]
Rearrange equation 1 by subtracting f from both sides:
[LIST=1]
[*]c = 10 - f
[*]c + 1.5f = 12.50
[/LIST]
Substitute equation (1) into equation (2):
10 - f + 1.5f = 12.50
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=10-f%2B1.5f%3D12.50&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]f = 5[/B]
Now, substitute this f = 5 value back into modified equation (1) above:
c = 10 - 5
[B]c = 5[/B]

{x | x is an even integer between -3 and 5}

{x | x is an even integer between -3 and 5}
We list even integers out in this range:
[B]{-2, 0, 2, 4}[/B]