162 results

formula - a fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.

$150,000; 7%; 25 yr ordinary annuity formula

$150,000; 7%; 25 yr ordinary annuity formula
[URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=150000&n=25&i=7&check1=1&pl=Calculate']Answer for PV and AV[/URL]

(98)^2 no calculator mental math

Round 98 to the nearest 10. This is 100. Call this a.
Calculate b which is a - our original number:
b = 100 - 98
b = 2
We can use this formula:
(a - b)^2 = a(a- 2b) + b^2
Given a = 100 and b = 2, we have:
(100 - 2)^2 = 100(100 - 2(2)) + 2^2
98^2 = 100(96) + 4
98^2 = 9600 + 4
98^2 = [B]9,604[/B]
[MEDIA=youtube]8lQdxVVo-Ps[/MEDIA]

-11, -9, -7, -5, -3 What is the next number? What is the 200th term in this sequence?

-11, -9, -7, -5, -3 What is the next number? What is the 200th term in this sequence?
We see that Term 1 is -11, Term 2 is -9, so we do a point slope equation of (1,-11)(2,-9) to get the [URL='https://www.mathcelebrity.com/search.php?q=%281%2C-11%29%282%2C-9%29']nth term of the formula[/URL]
f(n) = 2n - 13
The next number is the 6th term:
f(6) = 2(6) - 13
f(6) = 12 - 13
f(6) = [B]-1
[/B]
The 200th term is:
f(200) = 2(200) - 13
f(200) = 400 - 13
f(200) = [B]387[/B]

1, 1/2, 1/3, 1/4, 1/5 What is the next number? What is the 89th term of the sequence?

1, 1/2, 1/3, 1/4, 1/5
What is the next number?
What is the 89th term of the sequence?
Formula for nth term is 1/n
Next number is n = 5, so we have [B]1/5[/B]
With n = 89, we have [B]1/89[/B]

1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you wou

1, 1/2, 1/4, 1/8, 1/16
The next number in the sequence is 1/32. What is the function machine you would use to find the nth term of this sequence?
Hint: look at the denominators
We notice that
1/2^0 = 1/1 = 1
1/2^1 = 1/2
1/2^2 = 1/4
1/2^3 = 1/8
1/2^4 = 1/32
So we write our explicit formula for term n:
f(n) = [B]1/2^(n - 1)[/B]

1, 4, 9, 16, 25 What is the next number? What is the 50th term?

1, 4, 9, 16, 25
What is the next number?
What is the 50th term?
We see that 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25
We build a formula for the nth term:
f(n) = n^2
The next number means n = 6th term:
f(6) = 6^2 = [B]36
[/B]
The 50th term means n = 50:
f(50) = 50^2 = [B]2500[/B]

1.25, 2, 2.75, 3.5 What is the 100th term?

1.25, 2, 2.75, 3.5 What is the 100th term?
The formula of nth term is:
f(n) = 0.75n + 0.5
So the 100th term is:
f(100) = 0.75(100) + 0.5
f(100) = 75 + 0.5
f(100) = [B]75.5[/B]

2, 4, 6, 8....1000. What term is the number 1000?

2, 4, 6, 8....1000. What term is the number 1000?
Formula for nth term is 2n
If 2n = 1000, then dividing each side by 2, we see that:
2n/2 = 1000/2
n = [B]500[/B]

28 students in class and 16 are boys what is percent of girls?

28 students in class and 16 are boys what is percent of girls?
Calculate the number of girls:
Girls = Total Students - Boys
Girls = 28 - 16
Girls = 12
The percent of girls is found by this formula:
Percent of Girls = 100 * Number of Girls / Number of Students
Percent of Girls = 100 * 12 / 28
Percent of Girls = 1,200 / 28
Percent of Girls = [B]42.86%[/B]

35 m/s for 40 s. how far does it travel?

35 m/s for 40 s. how far does it travel?
This is a distance problem. The formula to relate, distance, rate, and time is:
d = rt
We are given r = 35 m/s and t = 40s. We want d
d = 35 m/s * 40s
d = [B]1,400 meters[/B]

5, 14, 23, 32, 41....1895 What term is the number 1895?

5, 14, 23, 32, 41....1895 What term is the number 1895?
Set up a point slope for the first 2 points:
(1, 5)(2, 14)
Using [URL='https://www.mathcelebrity.com/search.php?q=%281%2C+5%29%282%2C+14%29&x=0&y=0']point slope formula, our series function[/URL] is:
f(n) = 9n - 4
To find what term 1895 is, we set 9n - 4 = 1895 and solve for n:
9n - 4 = 1895
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=9n-4%3D1895&pl=Solve']equation solver[/URL], we get:
n = [B]211[/B]

5,10,15,20 What is the next number? What is the 100th term?

5,10,15,20
What is the next number?
What is the 100th term?
Increment is by 5, so next number is 20 + 5 = [B]25[/B]
Formula for nth number is 5 * n
With n = 100, we have 5 * 100 = [B]500[/B]

52% of a town's households have children and 25% have pets. If 12% have both, what percent have neit

52% of a town's households have children and 25% have pets. If 12% have both, what percent have neither
Let C represent households with children. Let P represents households with pets. We have the formula to determine households with Children or Pets as C U P (C Union P) or (C or P):
C U P = C + P - (C and P)
C U P = 52% + 25% - 12%
C U P = 65%
Now, if we want to find what percent have neither, we use (C U P)':
(C U P)' = 100% - (C U P)
(C U P)' = 100% - 65%
(C U P)' = [B]35%[/B]

8,11,14,17,20 What is the next number? What is the 150th term?

8,11,14,17,20
What is the next number?
What is the 150th term?
We're adding by 3 to the last number in the sequence, so we have the next number as:
20 + 3 = [B]23
[/B]
For the nth term, we have a formula of this:
3n + 5
3(1) + 5 = 8
3(2) + 5 = 11
3(3) + 5 = 14
With n = 150, we have:
3(150) + 5 = 450 + 5 = [B]455[/B]

9, 3, 1, 1/3, 1/9 What is the next number in this sequence? What is the function machine for this se

9, 3, 1, 1/3, 1/9
What is the next number in this sequence?
What is the function machine for this sequence?
We see the following pattern in this sequence:
9 = 9/3^0
3 = 9/3^1
1 = 9/3^2
1/3 = 9/3^3
1/9 = 9/3^4
Our function machine formula is:
[B]f(n) = 9/3^(n - 1)
[/B]
Next term is the 6th term:
f(6) = 9/3^(6 - 1)
f(6) = 9/3^5
f(6) = 9/243
f(6) = [B]1/27[/B]

A bag contains 8 marbles of different colors. How many ways unique ways or orders can you select 3 m

A bag contains 8 marbles of different colors. How many ways unique ways or orders can you select 3 marbles?
We want the combinations formula, 8 choose 3, or 8C3.
[URL='https://www.mathcelebrity.com/permutation.php?num=8&den=3&pl=Combinations']Type 8 C 3 into our search engine and we get:[/URL]
[B]56 unique ways[/B]

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a func

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a function to model the situation the value of the card in 2020.Let x be number of years since 1970
The formula for accumulated value of something with a percentage growth p and years x is:
V(x) = Initial Value * (1 + p/100)^x
Set up our growth equation where 8% = 0.08 and V(y) for the value at time x and x = 2020 - 1970 = 50, we have:
V(x) = 100 * (1 + 8/100)^50
V(x) = 100 * (1.08)^50
V(x) = 100 * 46.9016125132
V(x) = [B]4690.16[/B]

A binomial probability experient is conducted with the given parameters. Compute the probability of

A binomial probability experient is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 40, p = 0.05, x = 2
P(2) =
Answer is [B]0.2777[/B]. Using Excel formula of =BINOMDIST(2,40,0.05,FALSE) or using our [URL='http://www.mathcelebrity.combinomial.php?n=+40&p=0.05&k=2&t=+5&pl=P%28X+%3D+k%29']binomial probability calculator[/URL]

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the tree. How tall is the tree?
So we have a [U]right triangle[/U]. Hypotenuse is 15. Base is 12. We want the length of the leg.
The formula for a right triangle relation of sides is a^2 + b^2 = c^2 where c is the hypotenuse and a, b are the sides
Rearranging this equation to isolate a, we get a^2 = c^2 - b^2
Taking the square root of both sides, we get a = sqrt(c^2 - b^2)
a = sqrt(15^2 - 12^2)
a = sqrt(225 - 144)
a = sqrt(81)
a = [B]9 meters[/B]

A car worth $43,000 brand new, depreciates at a rate of $2000 per year. What is the formula that des

A car worth $43,000 brand new, depreciates at a rate of $2000 per year. What is the formula that describes the relationship between the value of the car (C) and the time after it has been purchased (t)?
Let t be the number of years since purchase. Depreciation means the value decreases, so we have:
[B]C = 43000 - 2000t[/B]

A catering service offers 3 appetizers, 6 main courses, and 4 desserts. A customer is to select 2 ap

A catering service offers 3 appetizers, 6 main courses, and 4 desserts. A customer is to select 2 appetizers, 3 main courses, and 3 desserts for a banquet. In how many ways can this be done?
We use the combinations formula, and since each event is independent of the others, we multiply:
2 appetizers, 3 main courses, and 3 desserts = [URL='https://www.mathcelebrity.com/permutation.php?num=3&den=2&pl=Combinations']3C2[/URL] * [URL='https://www.mathcelebrity.com/permutation.php?num=6&den=3&pl=Combinations']6C3[/URL] * [URL='https://www.mathcelebrity.com/permutation.php?num=4&den=3&pl=Combinations']4C3[/URL]
2 appetizers, 3 main courses, and 3 desserts = 3 * 20 * 4
2 appetizers, 3 main courses, and 3 desserts = [B]240[/B]

A cereal box has dimensions of 12" x 3" x 18". How many square inches of cardboard are used in its c

A cereal box has dimensions of 12" x 3" x 18". How many square inches of cardboard are used in its construction?
A cereal box is a rectangular solid. The volume formula is V = lwh.
Substituting these values of the cereal box in, we have:
V = 12(3)(18)
V = [B]648 cubic inches[/B]

A circle has a center at (6, 2) and passes through (9, 6)

A circle has a center at (6, 2) and passes through (9, 6)
The radius (r) is found by [URL='https://www.mathcelebrity.com/slope.php?xone=6&yone=2&slope=+2%2F5&xtwo=9&ytwo=6&pl=You+entered+2+points']using the distance formula[/URL] to get:
r = 5
And the equation of the circle is found by using the center (h, k) and radius r as:
(x - h)^2 + (y - k)^2 = r^2
(x - 6)^2 + (y - 2)^2 = 5^2
[B](x - 6)^2 + (y - 2)^2 = 25[/B]

A colony of 995 bacteria doubles in size every 206 minutes. What will the population be 618 minutes

A colony of 995 bacteria doubles in size every 206 minutes. What will the population be 618 minutes from now?
Calculate the doubling time periods:
Doubling Time Periods = Total Minutes From Now / Doubling Period in Minutes
Doubling Time Periods = 618/206
Doubling Time Periods = 3
Calculate the new population using the doubling time formula below where t is the number of doubling periods:
Population = Initial Population * 2^2
Population = 995 * 2^3
Population = 995 * 8
Population = [B]7,960[/B]

A company had sales of $19,808 million in 1999 and $28,858 million in 2007. Use the Midpoint Formula

A company had sales of $19,808 million in 1999 and $28,858 million in 2007. Use the Midpoint Formula to estimate the sales in 2003
2003 is the midpoint of 1999 and 2007, so we use our [URL='https://www.mathcelebrity.com/mptnline.php?ept1=19808&empt=&ept2=28858&pl=Calculate+missing+Number+Line+item']midpoint calculator[/URL] to get:
[B]24,333[/B] sales in 2003

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants t

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this situation.
Perimeter of a rectangle:
P = 2l + 2w
We have P = 165 and l = x --> x>50 and width y <= 20. Plug these into the perimeter formula
[B]165 = 2x + 2y where x > 50 and y <= 20[/B]

A girl is pedaling her bicycle at a velocity of 0.10 km/hr. How far will she travel in two hours?

A girl is pedaling her bicycle at a velocity of 0.10 km/hr. How far will she travel in two hours?
The distance formula is:
d = rt
We're given a rate (r) of 0.10km/hr
We're given time (t) of 2 hours
Plug these values into the distance formula and we get:
d= 0.1 * 2
d = [B]0.2km
[MEDIA=youtube]w80E_YM-tDA[/MEDIA][/B]

A group of students at a school takes a history test. The distribution is normal with a mean of 25,

A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4.
(a) Everyone who scores in the top 30% of the distribution gets a certificate.
(b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state?
(a) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.70&pl=Calculate+Critical+Z+Value']Top 30% is 70% percentile[/URL]
Inverse of normal distribution(0.7) = -0.5244005
Plug into z-score formula, -0.5244005 = (x - 25)/4
[B]x = 22.9024[/B]
(b) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.95&pl=Calculate+Critical+Z+Value']Top 5% is 95% percentile[/URL]
Inverse of normal distribution(0.95) = 1.644853627
Plug into z-score formula, 1.644853627 = (x - 25)/4
[B]x = 31.57941451[/B]

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hour

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hours head start. How far from the starting point are the planes?
Use the formula D = rt where
[LIST]
[*]D = distance
[*]r = rate
[*]t = time
[/LIST]
The plan traveling 150 mph for 3 hours:
Time 1 = 150
Time 2 = 300
Time 3 = 450
Now at Time 3, the other plane starts
Time 4 = 600
Time 5 = 750
Time 6 =
450 + 150t = 550t
Subtract 150t
400t = 450
Divide each side by 400
t = 1.125
Plug this into either distance equation, and we get:
550(1.125) = [B]618.75 miles[/B]

A jet travels at 485 miles per hour. Which equation represents the distance, d, that the jet will tr

A jet travels at 485 miles per hour. Which equation represents the distance, d, that the jet will travel in t hours.
The distance formula is:
d = rt
We're given r = 485, so we have:
[B]d = 485t[/B]

a painter is painting a circular sculpture. The sculpture has a radius of 5 meters. How much paint s

a painter is painting a circular sculpture. The sculpture has a radius of 5 meters. How much paint should she use to paint the sculpture
Area of a circle (A) is:
A = ?r²
Substituting r = 5 into this formula, we get:
A = ? * 5²
A = [B]25?[/B]

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. Wh

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. What is the length of each of the other two sides?
A parallelogram is a rectangle bent on it's side. So we have the perimeter formula P below:
P = 2l + 2w
We're given w = 17 and P = 54. So we plug this into the formula for perimeter:
2l + 2(17) = 54
2l + 34 = 54
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B34%3D54&pl=Solve']equation calculator[/URL], we get [B]l = 10[/B].

A passenger train left station A at 6:00 P.M. Moving with the average speed 45 mph, it arrived at st

A passenger train left station A at 6:00 P.M. Moving with the average speed 45 mph, it arrived at station B at 10:00 p.m. A transit train left from station A 1 hour later than the passenger train, but it arrived at the station B at the same time with the passenger train. What was the average speed of the transit train?
[U]Passenger Train[/U]
[LIST]
[*]45 miles per hour and it got there in 4 hours.
[/LIST]
Using our formula D = rt where:
[LIST]
[*]D = Distance
[*]r = rate
[*]t = time
[/LIST]
[LIST]
[*]D = rt
[*]D = 45(4)
[*]D = 180 miles from Station A to Station B
[/LIST]
Transit Train
[LIST]
[*]It has to go the same distance, 180 miles, so D = 180
[*]It made it there in 3 hours. This is r
[*]We want to solve for t
[/LIST]
D = rt
180 = 3r
Divide each side by 3
[B]r = 60 miles per hour[/B]

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuousl

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuously. Using the formula V = Pe^{rt}V=Pe^rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 20 years
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=230&int=6.8&t=20&pl=Continuous+Interest']continuous compounding calculator[/URL], we get:
V = [B]896.12[/B]

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuou

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV = Pe^{rt} V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years.
Substituting our given numbers in where P = 96,300, r = 0.028, and t = 7, we get:
V = 96,300 * e^(0.028 * 7)
V = 96,300 * e^0.196
V = 96,300 * 1.21652690533
V = [B]$117,151.54[/B]

A pollster selected 4 of 7 people. How many different groups of 4 are possible?

A pollster selected 4 of 7 people. How many different groups of 4 are possible?
We want to use the combinations formula. [URL='https://www.mathcelebrity.com/permutation.php?num=7&den=4&pl=Combinations']So we type 7C4 into our search engine[/URL]. This is also known as 7 choose 4.
We get [B]35[/B] different groups.

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

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?
We know the rectangle has the following formulas:
Area = lw
Perimeter = 2l + 2w
Given an area of 238 and a perimeter of 62, we have:
[LIST=1]
[*]lw = 238
[*]2(l + w) = 62
[/LIST]
Divide each side of (1) by w:
l = 238/w
Substitute this into (2):
2(238/w + w) = 62
Divide each side by 2:
238/w + w = 31
Multiply each side by w:
238w/w + w^2 = 31w
Simplify:
238 + w^2 = 31w
Subtract 31w from each side:
w^2 - 31w + 238 = 0
We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get:
w = (14, 17)
We take the lower amount as our width and the higher amount as our length:
[B]w = 14
l = 17
[/B]
Check our work for Area:
14(17) = 238 <-- Check
Check our work for Perimeter:
2(17 + 14) ? 62
2(31) ? 62
62 = 62 <-- Check

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards b

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards because of a building code, what will the length need to be?
Perimeter of a rectangle (P) with length (l) and width (w) is:
2l + 2w = P
We're given P = 506 and w = 100. We plug this in to the perimeter formula and get:
2l + 2(100) = 506
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B2%28100%29%3D506&pl=Solve']type it in our search engine[/URL] and we get:
l = [B]153[/B]

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 fe

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 feet longer than the width, then how wide is the field?
We're given:
[LIST=1]
[*]l = w + 40
[/LIST]
And we know the perimeter of a rectangle is:
P = 2l + 2w
Substitute (1) into this formula as well as the given perimeter of 1120:
2(w + 40) + 2w = 1120
Multiply through and simplify:
2w + 80 + 2w = 1120
Group like terms:
4w + 80 = 1120
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B80%3D1120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 260[/B]

A salary after a 4.6% increase, of the original salary is x dollars

A salary after a 4.6% increase, of the original salary is x dollars
4.6% is also written as 0.046.
Our formula for the new salary S is:
S = (1 + 0.046)x
[B]S = 1.046x[/B]

A set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is th

A set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is the new mean?
We know the mean formula is:
Sum of scores / Number of Scores = Mean
We're given mean = 6.3 and number of scores = 19, so we have:
Sum of scores / 19 = 6.3
Cross multiply:
Sum of scores = 19 * 6.3
Sum of scores = 119.7
Now a new score is added of 8, so we have:
Sum of scores = 119.7 + 8 = 127.7
Number of scores = 19 + 1 = 20
So our new mean is:
Mean = Sum of scores / Number of Scores
Mean = 127.7/20
Mean = [B]6.385[/B]
[COLOR=rgb(0, 0, 0)][SIZE=5][FONT=arial][B][/B][/FONT][/SIZE][/COLOR]

A spinner is divided into 4 equal sections numbered 1 to 4. The theoretical probability of the spinn

A spinner is divided into 4 equal sections numbered 1 to 4. The theoretical probability of the spinner stopping on 3 is 25%. Which of the following is most likely the number of 3s spun in 10,000 spins?
We want Expected Value of s spins. Set up the expected value formula for any number 1-4
E(s) = 0.25 * n where n is the number of spins.
Using s = 3, n = 10,000, we have:
E(10,000) = 0.25 * 10,000
E(10,000) = [B]2,500[/B]

A student was trying to determine a formula for changing speeds that are written in feet per second

A student was trying to determine a formula for changing speeds that are written in feet per second into miles per hour. If a sprinter runs at a speed of n feet per second, what is her speed in miles per hour?
3600 seconds per hour = 3600n feet per hour
5280 feet per mile so we have:
3600n feet per hour / 5280 feet per mile = [B]0.6818n feet per second[/B]

A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a.

A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a. 40 years b. 50 years c. 30 years d. 60 years e. 80 years
Simple interest formula if we start with 1 dollar and double to 2 dollars:
1(1 + i(20)) = 2
1 + 20i = 2
Subtract 1 from each side:
20i = 1
Divide each side by 20
i = 0.05
Now setup the same simple interest equation, but instead of 2, we use 3:
1(1 + 0.05(t)) = 3
1 + 0.05t = 3
Subtract 1 from each side:
0.05t = 2
Divide each side by 0.05
[B]t = 40 years[/B]

A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For

A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For how many minutes does it walk?
Distance formula (d) for a rate (r) and time (t) is:
d = rt
We're given d = 12.5 and r = 5
12.5 = 5t
5t = 12.5
Solve for t. Divide each side of the equation by 5:
5t/5 = 12.5/5
Cancel the 5's on left side and we get:
t = [B]2.5[/B]

A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4

A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4 years.
Every 6 months means twice a year. So we have 4 years * twice a year increase = 8 compounding periods.
Our formula for compounding an initial population P at time t is P(t) at a compounding percentage i:
P(t) = P * (1 + i)^t
Since 8% is 0.08 as a decimal and t = 4 *2 = 8, we have:
P(8) = 50000 * (1.08)^8
P(8) = 50000 * 1.85093
P(8) = 92,546.51
Since we can't have a partial person, we round down to [B]92,545[/B]

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continuous at a constant speed of 40 feet per minute for the last 50 feet.
(i) Determine which animal won the race.
(ii). By how much time the animal won the race.
(iii) Explain one life lesson from the race.
We know the distance formula is:
d = rt
For the turtle, he has a rate (r) of 20 feet / minute and distance (d) of 100. We want to solve for time:
[URL='https://www.mathcelebrity.com/drt.php?d=+100&r=+20&t=&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 5
The rabbit has 3 parts of the race:
Rabbit Part 1: Distance (d) = 50 and rate (r) = 40
[URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 1.25
Rabbit Part 2: The rabbit stops for 3 minutes (t = 3)
Rabbit Part 3: Distance (d) = 50 and rate (r) = 40
[URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 1.25
Total time for the rabbit from the 3 parts is (t) = 1.25 + 3 + 1.25
Total time for the rabbit from the 3 parts is (t) = 5.5
[LIST]
[*](i) The [B]turtle won[/B] the race because he took more time to finish and they both started at the same time
[*](ii) We subtract the turtles time from the rabbit's time: 5.5 - 5 = [B]0.5 minutes which is also 30 seconds[/B]
[*](iii) [B]Slow and Steady wins the race[/B]
[/LIST]

a ^5 x a ^2 without exponents

a ^5 x a ^2 without exponents
When we multiply the same variable or number, we add exponents, so we have:
a^(5 + 2)
a^7
To write a variable raised to an exponent without exponents, we break it up. The formula to do this is:
a^n = a times itself n times
a^7 = [B]a * a * a * a * a * a * a[/B]

Accounting Formulas

Free Accounting Formulas Calculator - Shows various accounting formulas

Allan built an additional room onto his house. The length of the room is 3 times the width. The peri

Allan built an additional room onto his house. The length of the room is 3 times the width. The perimeter of the room is 60 feet. What is the length of the room
A room is a rectangle. We know the perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]l = 3w
[*]P = 60
[/LIST]
Plug (1) and (2) into our rectangle perimeter formula:
2(3w) + w = 60
6w + w = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2Bw%3D60&pl=Solve']Type this equation into our search engine[/URL] to solve for w:
w = 8.5714
Now plug w = 8.5714 into equation 1 to solve for l:
l = 3(8.5714)
l = [B]25.7142[/B]

An estate has 6 houses and each house has x lighting fittings which need 1 lamp each, and y fittings

An estate has 6 houses and each house has x lighting fittings which need 1 lamp each, and y fittings which need 3 lamps each. Write a formula to find z, the total number of lamps needed on the estate.
z = 6(x * 1 + 3 * y)
z = [B]6(x + 3y)[/B]

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how m

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how much is in the account after 7 years? How much of this is interest?
Let's assume payments are made at the end of each month, since the problem does not state it. We have an annuity immediate formula. Interest rate per month is 6.6%/12 = .55%, or 0.0055. 7 years * 12 months per year gives us 84 deposits.
Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=950&n=84&i=0.55&check1=1&pl=Calculate']present value of an annuity immediate calculator[/URL], we get the following:
[LIST=1]
[*]Accumulated Value After 7 years = [B]$101,086.45[/B]
[*]Principal = 79,800
[*]Interest Paid = (1) - (2) = 101,086.45 - 79,800 = [B]$21,286.45[/B]
[/LIST]

Arithmetic and Geometric and Harmonic Sequences

Free Arithmetic and Geometric and Harmonic Sequences Calculator - This will take an arithmetic series or geometric series or harmonic series, and an optional amount (n), and determine the following information about the sequence

1) Explicit Formula

2) The remaining terms of the sequence up to (n)

3) The sum of the first (n) terms of the sequence Also known as arithmetic sequence, geometric sequence, and harmonic sequence

1) Explicit Formula

2) The remaining terms of the sequence up to (n)

3) The sum of the first (n) terms of the sequence Also known as arithmetic sequence, geometric sequence, and harmonic sequence

As a salesperson, Lauren earns a base salary of $94 per week plus a commission of 10% of sales. If s

As a salesperson, Lauren earns a base salary of $94 per week plus a commission of 10% of sales. If she had $90 in sales last week, what was her total pay?
[B][U]Use the Base plus Commission formula above[/U][/B]
Salary = Base Salary + 10%(Total Sales)
Salary = $94 + 0.1(90)
Salary = $94 + $9
Salary = [B]$103[/B]

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?
b. What proportion of the vehicles would be going less than 50 mph?
c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?
d. In what way do you think the actual distribution of speeds differs from a normal distribution?
a. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=65&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<65) = [B]22.66%[/B]
b. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+50&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<50) = [B]0.4269%[/B]
c. [URL='http://www.mathcelebrity.com/zcritical.php?a=0.9&pl=Calculate+Critical+Z+Value']Inverse of normal for 90% percentile[/URL] = 1.281551566
Plug into z-score formula: (x - 71)/8 = 1.281551566
[B]x = 81.25241252[/B]
d. [B]The shape/ trail differ because the normal distribution is symmetric with relatively more values at the center. Where the actual has a flatter trail and could be expected to occur.[/B]

assume your math class has 10 sophomores and 7 juniors. there are 3 female sophomores and 4 male jun

assume your math class has 10 sophomores and 7 juniors. there are 3 female sophomores and 4 male juniors. what is the probability of randomly selecting a student who is a female or a junior
[U]Sophomores:[/U]
10 sophomores:
3 female
male = 10 - 3 = 7
[U]Juniors:[/U]
7 juniors
4 males
female = 7 - 4 = 3
[U]Females:[/U]
Total Females = Female Sophomores + Female Juniors
Total Females = 3 + 3
Total Females = 6
[U]Total Students:[/U]
Total Students = Total Sophomores + Total Juniors
Total Students = 10 + 7
Total Students = 17
[U]We want P(female or Junior). We use the formula below to avoid duplicates:[/U]
P(female or Junior) = P(female) + P(junior) - P(female and junior)
P(female or Junior) = Total Females / Total Students + Total Juniors / Total Students - Total Female Juniors / Total Students
P(female or Junior) = 6/17 + 7/17 - 3/17
P(female or Junior) = [B]10/17[/B]

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

Beth made a trip to the train station and back. On the trip there she traveled 45 km/h and on the re

Beth made a trip to the train station and back. On the trip there she traveled 45 km/h and on the return trip she went 30 km/h. How long did the trip there take if the return trip took six hours?
We use the distance formula: D = rt where D = distance, r = rate, and t = time.
Start with the return trip:
D = 45(6)
D = 270
The initial trip is:
270= 30t
Divide each side by 30
[B]t = 9 hours[/B]

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 fe

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W.
Plugging our numbers in for P = 22 and L = 5, we get:
22 = 2(5) + 2W
22 = 10 + 2w
Rewritten, we have:
10 + 2w = 22
[URL='https://www.mathcelebrity.com/1unk.php?num=10%2B2w%3D22&pl=Solve']Plug this equation into the search engine[/URL], we get:
[B]w = 6[/B]

Body Mass Index (BMI)

Free Body Mass Index (BMI) Calculator - Solves for the popular health measurement of Body Mass Index or Weight using inches and pounds input or meters and kilos input.

Also calculates the estimated surface area of the body using the Mosteller Formula

Also calculates the estimated surface area of the body using the Mosteller Formula

Bond Price Formulas

Free Bond Price Formulas Calculator - Given a face value, coupon percent, yield percent, term, and redemption value, this calculates the price of a bond using the four price formulas for bonds

1) Basic

2) Premium/Discount

3) Base

4) Makeham

1) Basic

2) Premium/Discount

3) Base

4) Makeham

Bretschneiders Formula

Free Bretschneiders Formula Calculator - Calculates the area of a quadrilateral using Bretschneiders Formula

can someone help me with how to work out this word problem?

Have you tried the rate of change formula?

can someone help me with how to work out this word problem?

Could you please post said formula?

Centripetal Acceleration

Free Centripetal Acceleration Calculator - Solves for any of the 3 items in the centripetal acceleration formula, centripetal acceleration, rotational speed, and radius.

Chemical Compounds

Free Chemical Compounds Calculator - Shows details of the chemical compounds including name, formula, and molar mass

Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve

Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve for a, b, or h? Why? Solve for each of these variables to demonstrate.
The variable "h" is the easiest to solve for. Because you only have one step. Let's review:
Divide each side of the equation by 12(a + b)
h = 12(a + b)/A
Solving for "a", we two steps. Divide each side by 12h:
A/12h = a + b
Subtract b from each side
a = A/12h - b
Solving for "b" takes two steps as well. Divide each side by 12h:
A/12h = a + b
Subtract a from each side
b = A/12h - a

Density

Free Density Calculator - Solves for any of the 3 items in the Density Formula, Density (D), Mass (M), and Volume (V) (Capacity), with 2 given items.

Determine the formula of the given statement by following the procedures. Choose any number then add

Determine the formula of the given statement by following the procedures. Choose any number then add 2. Multiply your answer to 3 and minus 2
For the phrase [I]choose any number[/I] we can use an arbitrary variable, let's call it x.
Add 2:
x + 2
Multiply your answer to 3:
3(x + 2)
And minus 2 which means we subtract:
[B]3(x + 2) - 2[/B]

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time pe

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.
Our givens are:
[LIST]
[*]I = 450
[*]P = 3000
[*]t = 3
[*]We want r
[/LIST]
450 = 3000(r)(3)
450 = 9000r
Divide each side by 9000
[B]r = 0.05[/B]

difference between 2 positive numbers is 3 and the sum of their squares is 117

difference between 2 positive numbers is 3 and the sum of their squares is 117
Declare variables for each of the two numbers:
[LIST]
[*]Let the first variable be x
[*]Let the second variable be y
[/LIST]
We're given 2 equations:
[LIST=1]
[*]x - y = 3
[*]x^2 + y^2 = 117
[/LIST]
Rewrite equation (1) in terms of x by adding y to each side:
[LIST=1]
[*]x = y + 3
[*]x^2 + y^2 = 117
[/LIST]
Substitute equation (1) into equation (2) for x:
(y + 3)^2 + y^2 = 117
Evaluate and simplify:
y^2 + 3y + 3y + 9 + y^2 = 117
Combine like terms:
2y^2 + 6y + 9 = 117
Subtract 117 from each side:
2y^2 + 6y + 9 - 117 = 117 - 117
2y^2 + 6y - 108 = 0
This is a quadratic equation:
Solve the quadratic equation 2y2+6y-108 = 0
With the standard form of ax2 + bx + c, we have our a, b, and c values:
a = 2, b = 6, c = -108
Solve the quadratic equation 2y^2 + 6y - 108 = 0
The quadratic formula is denoted below:
y = -b ± sqrt(b^2 - 4ac)/2a
[U]Step 1 - calculate negative b:[/U]
-b = -(6)
-b = -6
[U]Step 2 - calculate the discriminant ?:[/U]
? = b2 - 4ac:
? = 62 - 4 x 2 x -108
? = 36 - -864
? = 900 <--- Discriminant
Since ? is greater than zero, we can expect two real and unequal roots.
[U]Step 3 - take the square root of the discriminant ?:[/U]
?? = ?(900)
?? = 30
[U]Step 4 - find numerator 1 which is -b + the square root of the Discriminant:[/U]
Numerator 1 = -b + ??
Numerator 1 = -6 + 30
Numerator 1 = 24
[U]Step 5 - find numerator 2 which is -b - the square root of the Discriminant:[/U]
Numerator 2 = -b - ??
Numerator 2 = -6 - 30
Numerator 2 = -36
[U]Step 6 - calculate your denominator which is 2a:[/U]
Denominator = 2 * a
Denominator = 2 * 2
Denominator = 4
[U]Step 7 - you have everything you need to solve. Find solutions:[/U]
Solution 1 = Numerator 1/Denominator
Solution 1 = 24/4
Solution 1 = 6
Solution 2 = Numerator 2/Denominator
Solution 2 = -36/4
Solution 2 = -9
[U]As a solution set, our answers would be:[/U]
(Solution 1, Solution 2) = (6, -9)
Since one of the solutions is not positive and the problem asks for 2 positive number, this problem has no solution

Don wants to bring some sand home from his vacation at the beach. He has a box that is 3 inches wide

Don wants to bring some sand home from his vacation at the beach. He has a box that is 3 inches wide, 4 inches long, and 2 inches tall. How much sand can he fit in the box?
We want the volume. The volume of a rectangular solid is found with the formula:
V = lwh
V = 4 * 3 * 2
V = [B]24 cubic inches[/B]

Donna bought 4 bags of dog treats for $9.36. What is the cost per bag of dog treats?

Donna bought 4 bags of dog treats for $9.36. What is the cost per bag of dog treats?
Using our unit cost formula, we get:
$9.36/4
[B]$2.34 per bag[/B]

Eulers Formula for Planar Geometry

Free Eulers Formula for Planar Geometry Calculator - This calculator solves for any one of the 3 following items using Eulers Formula for planar geometry:

* Vertices (v)

* Faces (f)

* Edges (e)

* Vertices (v)

* Faces (f)

* Edges (e)

Falling Object

Free Falling Object Calculator - Calculates any of the 3 items in the falling object formula, distance (s), acceleration (a), and time (t).

Fantasia decided to paint her circular room which had a diameter of 25 feet. She started painting in

Fantasia decided to paint her circular room which had a diameter of 25 feet. She started painting in the center and when she had painted a circle with a 5-foot diameter, she used one quart of paint. How many more quarts of paint must Fantasia buy to finish her room?
The area formula for a circle is:
Area = pir^2
Area of full room
Radius = D/2
Radius = 25/2
Radius = 12.5
Area = 3.1415 * 12.5 * 12.5
Area = 490.625
Area of 5-foot diameter circle
Radius = D/2
Radius = 5/2
Radius = 2.5
Area = 3.1415 * 2.5 * 2.5
Area = 19.625
So 1 quart of paint covers 19.625 square feet
Area of unpainted room = Area of Room - Area of 5-foot diameter circle
Area of unpainted room = 490.625 - 19.625
Area of unpainted room = 471
Calculate quarts of paint needed:
Quarts of paint needed = Area of unpainted Room / square feet per quart of paint
Quarts of paint needed = 471/19.625
Quarts of paint needed = [B]24 quarts[/B]

Fibonacci Sequence

Free Fibonacci Sequence Calculator - Generates a list of the first 100 Fibonacci numbers.
Also shows how to generate the nth Fibonacci number using Binet's Formula

Find r in P(7, r)

Find r in P(7, r)
Recall the permutations formula:
7! / (7-r!) = 840.
We [URL='https://www.mathcelebrity.com/factorial.php?num=7!&pl=Calculate+factorial']run 7! through our search engine[/URL] and we get:
[URL='https://www.mathcelebrity.com/factorial.php?num=7!&pl=Calculate+factorial']7![/URL] = 5040
5040 / (7 - r)! = 840
Cross multiply, and we get:
5040/840 = 7 - r!
6 = (7 - r)!
Since 6 = 3*2*! = 3!, we have;
3! = (7 - r)!
3 = 7 - r
To solve for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=3%3D7-r&pl=Solve']type this equation into our search engine[/URL] and we get:
r = [B]4[/B]

Find the explicit formula of the sequence 3,12,48

Find the explicit formula of the sequence 3,12,48
We [URL='https://www.mathcelebrity.com/sequenceag.php?num=3,12,48&n=10&pl=Calculate+Series']type in 3,12,48 into our search engine[/URL]. Choose series, and we get:
[B]a(n) = 3 * 4^(n - 1)[/B]

Find the number of polygon sides given an interior angle sum of 2700°

Formula for finding sides of a polygon given interior angle sum I:
[B][URL='https://www.mathcelebrity.com/polygon-side-calculator.php?num=2700&pl=Calculate+Sides']Formula[/URL][/B]
n = I/180 + 2
[B]Solve for n when I = 2700[/B]
n = 2700/180 + 2
n = 15 + 2
n = [B]17
[MEDIA=youtube]MlhulFxUzXY[/MEDIA][/B]

Find y if the line through (1, y) and (2, 7) has a slope of 4.

Find y if the line through (1, y) and (2, 7) has a slope of 4.
Given two points (x1, y1) and (x2, y2), Slope formula is:
slope = (y2 - y1)/(x2 - x1)
Plugging in our coordinates and slope to this formula, we get:
(7 - y)/(2 - 1) = 4
7 - y/1 = 4
7 - y = 4
To solve this equation for y, w[URL='https://www.mathcelebrity.com/1unk.php?num=7-y%3D4&pl=Solve']e type it in our search engine[/URL] and we get:
y = [B]3[/B]

Find y if the line through (1,y) and (4,5) has a slope of 3

Find y if the line through (1,y) and (4,5) has a slope of 3.
Slope formula is:
m = (y2 - y1)/(x2 - x1)
With m = 3, we have:
3 = (5 - y)/(4 - 1)
3 = (5 - y)/3
Cross multiply:
5 - y = 9
Subtract 5 from each side
-y = 4
Multiply each side by -1
[B]y = -4[/B]

Geometry Summary

Free Geometry Summary Calculator - This is a table which lists out the formulas for geometric shapes

Given P(A) = 0.37, find P ( not A )

Given P(A) = 0.37, find P ( not A )
Not A is also written as A'.
We use the formula below:
P(A') = 1 - P(A)
P(A') = 1 - 0.37
P(A') = [B]0.63[/B]

Help on problem

[B]I need 36 m of fencing for my rectangular garden. I plan to build a 2m tall fence around the garden. The width of the garden is 6 m shorter than twice the length of the garden. How many square meters of space do I have in this garden?
List the answer being sought (words) ______Need_________________________
What is this answer related to the rectangle?_Have_________________________
List one piece of extraneous information____Need_________________________
List two formulas that will be needed_______Have_________________________
Write the equation for width_____________Have_________________________
Write the equation needed to solve this problem____Need____________________[/B]

Help on problem

[B]List the answer being sought (words) ______Area of the garden
What is this answer related to the rectangle?_Have_________________________
List one piece of extraneous information____2m tall fence
List two formulas that will be needed_______P = 36. P = 2l + 2w
Write the equation for width_____________w = 2l - 6
Write the equation needed to solve this problem A = lw, P = 2l + 2w[/B]

High and Low Method

Free High and Low Method Calculator - Calculates the variable cost per unit, total fixed costs, and the cost volume formula

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 straight lines can be formed by 8 points of which 3 are collinear?

The formula is nC2 - rC2 + 1
In this problem:
n = 8 and r = 3
[URL='https://www.mathcelebrity.com/permutation.php?num=8&den=2&pl=Combinations']8C2 [/URL]= 28
[URL='https://www.mathcelebrity.com/permutation.php?num=3&den=2&pl=Combinations']3C2[/URL] = 3
Evaluating, we have:
28 - 3 + 1
[B]26
[MEDIA=youtube]B3MGSmXOiY8[/MEDIA][/B]

How to Shade Fractions

The formula is:
Numerator = One color
Denominator - Numerator = Another Color
[MEDIA=youtube]mJD2acCpol4[/MEDIA]

I have $789 in the bank and make 1% interest a month. How much money do I have at the end of 6 month

I have $789 in the bank and make 1% interest a month. How much money do I have at the end of 6 months?
Our balance is found using our compound interest formula:
New Balance = Starting Balance * (1 + i/100)^t
With I = 1% and t = 6, we have:
New Balance = 789 * (1 + 1/100)^6
New Balance = 789 * (1.01)^6
New Balance = 789 * 1.0615201506
New Balance = [B]837.54[/B]

If $9000 grows to $9720 in 2 years find the simple interest rate.

If $9000 grows to $9720 in 2 years find the simple interest rate.
Simple interest formula is Initial Balance * (1 + tn) = Current Balance
We have
[LIST]
[*]Initial Balance = 9000
[*]Current Balance = 9720
[*]n = 2
[/LIST]
Plugging in these values, we get:
9000 * (1 + 2t) = 9720
Divide each side by 9000
1 + 2t = 1.08
Subtract 1 from each sdie
2t = 0.08
Divide each side by 2
t = [B]0.04 or 4%[/B]

If 5 is transformed into 11, and 12 is transformed into 25, then what does 15 become?

If 5 is transformed into 11, and 12 is transformed into 25, then what does 15 become?
Taking a look at potential patterns, we see:
5 * 2 + 1 = 11
12 * 2 + 1 = 25
Using this formula, we have:
15 * 2 + 1 =[B]31[/B]

If 5000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the

If 5000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the amount in the bank after 9 years if interest is compounded annually.
We assume the interest is compounded at the end of the year. Use the [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=9&i=10&check1=1&pl=Calculate']annuity immediate formula[/URL]:
[B]67,897.39[/B]

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A U B)=

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A U B)=?
We know the following formula for the probability of 2 events:
P(A U B) = P(A) + P(B) - P(A intersection B)
We're told A and B are independent, which makes P(A intersection B) = 0. So we're left with:
P(A U B) = P(A) + P(B) - P(A intersection B)
P(A U B) = 0.2 + 0.6 - 0
P(A U B) = [B]0.8[/B]

If a tutor charges $35 an hour and works for 286 minutes, what is the dollar amount she is owed?

If a tutor charges $35 an hour and works for 286 minutes, what is the dollar amount she is owed?
Dollar Amount Owed = Hourly Rate * Number of Hours Worked
Convert Minutes worked to hours worked
Hours worked = Minutes Worked / 60
Hours worked = 286 minutes / 60 minutes per hour
Hours worked = 4.77
So now back to our main formula...
Dollar Amount Owed = Hourly Rate * Number of Hours Worked
Dollar Amount Owed = $35 * 4.77
Dollar Amount Owed = [B]$166.95[/B]

If a universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'.

If a universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'.
We know from set theory that:
n(A U B) = n(A) + n(B) - n(A ? B)
Plugging in our given values, we get:
n(A U B) = 90 + 125 - 35
n(A U B) = 180
The problem asks for n(A U B)'. This formula is found with:
n(A U B)' = n(U) - n(A U B)
n(U) is the universal set which is 250, so we have:
n(A U B)' = 250 - 180
n(A U B)' = [B]70[/B]

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find th

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find the time taken by aeroplane to cover 1200m initially.
We know from the distance formula (d) using rate (r) and time (t) that:
d = rt
Regular speed:
1200 = rt
Divide each side by t, we get:
r = 1200/t
Reduced speed. 20 minutes = 60/20 = 1/3 of an hour. So we multiply 1,200 by 3
3600 = (r - 40)(t + 1/3)
If we multiply 3 by (t + 1/3), we get:
3t + 1
So we have:
3600 = (r - 40)(3t + 1)
Substitute r = 1200/t into the reduced speed equation:
3600 = (1200/t - 40)(3t + 1)
Multiply through and we get:
3600 = 3600 - 120t + 1200/t - 40
Subtract 3,600 from each side
3600 - 3600 = 3600 - 3600 - 120t + 1200/t - 40
The 3600's cancel, so we get:
- 120t + 1200/t - 40 = 0
Multiply each side by t:
-120t^2 - 40t + 1200 = 0
We've got a quadratic equation. To solve for t, [URL='https://www.mathcelebrity.com/quadratic.php?num=-120t%5E2-40t%2B1200%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this in our search engine[/URL] and we get:
t = -10/3 or t = 3. Since time [I]cannot[/I] be negative, our final answer is:
[B]t = 3[/B]

If you put $1 a day away and every day you add a dollar to the previous days amount, how much would

If you put $1 a day away and every day you add a dollar to the previous days amount, how much would you have after 100 days
Day 1, you have 1
Day 2, you have 1 + 1 = 2
Day 3, you have 1 + 2 = 3
So our formula for day n is:
D(n) = n
D(100) = [B]100[/B]

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like either tea or coffee
We don't want to count duplicates, so we have the following formula
Tea Or Coffee = Tea + Coffee - Both
Tea Or Coffee = 40 + 30 - 10
Tea Or Coffee = [B]60[/B]

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula to compute a mortgage payment, M, is shown below, where P is the principal amount of the loan, r is the monthly interest rate, and N is the number of monthly payments. Janice's bank offers a monthly interest rate of 0.325% for a 12-year mortgage. How many monthly payments must Janice make?
12 years * 12 months per year = [B]144 mortgage payments[/B]

Janice says that the sum of the measures of the interior angles of an octagon is 900°. Is Janice cor

Janice says that the sum of the measures of the interior angles of an octagon is 900°. Is Janice correct? Why or why not?
She's [B]incorrect.
[/B]
The interior angle sum for a polygon is found with this formula:
Interior Angle Sum = (sides - 2) x 180°
Since an octagon has 8 sides, we have:
Interior Angle Sum = (8 - 2) x 180°
Interior Angle Sum = 6 x 180°
Interior Angle sum = 1080°

Jason is 9 miles ahead of Joe running at 5.5 miles per hour and Joe is running at the speed of 7 mil

[SIZE=6]Jason is 9 miles ahead of Joe running at 5.5 miles per hour and Joe is running at the speed of 7 miles per hour. How long does it take Joe to catch Jason?
A. 3 hours
B. 4 hours
C. 6 hours
D. 8 hours
Distance formula is d = rt
Jason's formula (Add 9 since he's ahead 9 miles):
d = 5.5t + 9
Joe's formula:
d = 7t
Set both distance formulas equal to each other:
5.5t + 9 = 7t
Subtract 5.5t from each side:
5.5t - 5.5t + 9 = 7t - 5.5t
1.5t = 9
Divide each side by 1.5:
1.5t/1.5 = 9/1.5
t = [B]6 hours[/B]
[U]Check our work with t = 6[/U]
Joe = 7(6) = 42
Jason = 5.5(6) + 9= 33 + 9 = 42
[MEDIA=youtube]qae3WCq9wzM[/MEDIA]
[/SIZE]

Jessie invests $3345 in the stock market. Over the 3 years she has this invested she gets an average

Jessie invests $3345 in the stock market. Over the 3 years she has this invested she gets an average return of 7.8%. How much will her investment be worth after the 3 years?
7.8% = 0.078, so we use our compound interest formula to find our balance after 3 years.
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=3345&nval=3+&int=7.8&pl=Annually']compound interest balance calculator[/URL], we get:
[B]$4,190.37[/B]

Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sal

Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sales were $100,235. How much money did he earn in May?
[U]The commission and salary formula is:[/U]
Earnings = Salary + Commission Percent * Sales
Plugging in our numbers with 4% as 0.04, we get:
Earnings = 500 + 0.04 * 100235
Earnings = 500 + 4009.40
Earnings = [B]4,509.40[/B]

Lever Systems Formula

Free Lever Systems Formula Calculator - Solves for F_{1}, F_{2}, d, or x.

Logarithms

Free Logarithms Calculator - Using the formula Log a_{b} = e, this calculates the 3 pieces of a logarithm equation:

1) Base (b)

2) Exponent

3) Log Result

In addition, it converts

* Expand logarithmic expressions

1) Base (b)

2) Exponent

3) Log Result

In addition, it converts

* Expand logarithmic expressions

Midpoint formula

Midpoint formula
Given two points (x1, y1) and (x2, y2), the midpoint is found as the average distance between the 2 points:
[LIST]
[*]x value is: (x1 + x2)/2
[*]y value is: (y1 + y2)/2
[/LIST]
So our midpoint is:
((x1 + x2)/2, (y1 + y2)/2)

Olga wrote all the natural numbers from 1 to k. Including 1 and k. How many numbers did she write?

Olga wrote all the natural numbers from 1 to k. Including 1 and k. How many numbers did she write?
The formula for the number of numbers including A to B is:
B - A + 1
With A = 1 and B = k, we have:
k - 1 + 1
[B]k[/B]

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded contin

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend? Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (?2.71828), r is the interest rate expressed as a decimal, and t is the time in years. Round your answer to the nearest cent.
[URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=3&t=14&pl=Continuous+Interest']Using our continuous interest calculator[/URL], we get:
A = [B]1,521.96[/B]

Out of 53 teachers 36 drink tea 18 drink coffee, 10 drink neither. how many drink both?

Out of 53 teachers 36 drink tea 18 drink coffee, 10 drink neither. how many drink both?
Let T be tea drinkers
Let C be coffee drinkers
Let (T & C) be Tea & Coffee drinkers.
And 53 are total. So we use the Union formula relation:
C U T = C + T - (C & T)
53 = 18 + 36 - (C & T)
C & T = 53 - (Not C & Not T) since we subtract people who don't drink coffee and don't drink tea
C & T = 53 - 10 = 43
C U T = 18 + 36 - 43
C U T = [B]11[/B]

Percentiles

Free Percentiles Calculator - Given a set of scores and a target score, this will determine the percentile of the target score using two different formulas.

porportion problems

Im not really good with proportion and rates word problems and I need some help with it in my homework
If Leah walks 5 miles in 60 minutes, then Leah will walk how far in 110 minutes if she walks at the same speed the whole time? If necessary, round your answer to the nearest tenth of a mile.
I wanna know how i get this answer and copy the formula. Please help me thank you.

Problems Involving Rational Expressions

We are given, using the word word problem combined formula, that:
1/j + 1/p + 1/m = 1/3
However, you state the hours working alone, but then ask how much it would take working alone. I'm confused on the last part. Can you clarify?

Prove 0! = 1

Prove 0! = 1
Let n be a whole number, where n! represents the product of n and all integers below it through 1.
The factorial formula for n is:
n! = n · (n - 1) * (n - 2) * ... * 3 * 2 * 1
Written in partially expanded form, n! is:
n! = n * (n - 1)!
[U]Substitute n = 1 into this expression:[/U]
n! = n * (n - 1)!
1! = 1 * (1 - 1)!
1! = 1 * (0)!
For the expression to be true, 0! [U]must[/U] equal 1. Otherwise, 1! <> 1 which contradicts the equation above

Prove 0! = 1

[URL='https://www.mathcelebrity.com/proofs.php?num=prove0%21%3D1&pl=Prove']Prove 0! = 1[/URL]
Let n be a whole number, where n! represents:
The product of n and all integers below it through 1.
The factorial formula for n is
n! = n · (n - 1) · (n - 2) · ... · 3 · 2 · 1
Written in partially expanded form, n! is:
n! = n · (n - 1)!
[SIZE=5][B]Substitute n = 1 into this expression:[/B][/SIZE]
n! = n · (n - 1)!
1! = 1 · (1 - 1)!
1! = 1 · (0)!
For the expression to be true, 0! [U]must[/U] equal 1.
Otherwise, 1! ? 1 which contradicts the equation above
[MEDIA=youtube]wDgRgfj1cIs[/MEDIA]

Quadratic Equations and Inequalities

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax^{2} + bx + c = 0. Also generates practice problems as well as hints for each problem.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)^{2} + k

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

Quadrilateral

Free Quadrilateral Calculator - Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much inte

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 years?
The formula for [U]interest[/U] using simple interest is:
I = Prt where P = Principal, r = interest, and t = time.
We're given P = 500, r =0.04, and t = 4. So we plug this in and get:
I = 500(0.04)(4)
I = [B]80[/B]

Reece made a deposite into an account that earns 8% simple interest. After 8 years reece has earned

Reece made a deposite into an account that earns 8% simple interest. After 8 years Reece has earned 400 dollars. How much was Reece's initial deposit?
Simple interest formula:
A = P(1 + it) where P is the amount of principal to be invested, i is the interest rate, t is the time, and A is the amount accumulated with interest.
Plugging in our numbers, we get:
400 = P(1 + 0.08(8))
400 = P(1 + 0.64)
400 = 1.64P
1.64P = 400
[URL='https://www.mathcelebrity.com/1unk.php?num=1.64p%3D400&pl=Solve']Typing this problem into our search engine[/URL], we get:
P = [B]$243.90[/B]

Relevancy Page Formula

[URL]https://soundcloud.com/mathcelebrity/organic-seo-part-2-relevancy-page-formula[/URL]

Select 6 bills from a combination of 5 different bills

We use the combination formula, 6 choose 5, or 6C5.
Using our [URL='http://www.mathcelebrity.com/permutation.php?num=6&den=5&pl=Combinations']combinations calculator[/URL], or entering 6C6 into the search engine, we get
[B]6 ways to select.[/B]

Simple and Compound and Continuous Interest

Free Simple and Compound and Continuous Interest Calculator - Calculates any of the four parameters of the simple interest formula or compound interest formula or continuous compound formula

1) Principal

2) Accumulated Value (Future Value)

3) Interest

4) Time.

1) Principal

2) Accumulated Value (Future Value)

3) Interest

4) Time.

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is runn

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second.
i. After how many seconds will Sophie catch Claire?
ii. If the race is 500 feet, who wins?
i.
Sophie's distance formula is given as D = 5s
Claire's distance formula is given as D = 3s + 100
Set them equal to each other
5s = 3s + 100
Subtract 3s from both sides:
2s = 100
Divide each side by 2
[B]s = 50[/B]
ii. [B]Sophie since after 50 seconds, she takes the lead and never gives it back.[/B]

Statistics Summary

Free Statistics Summary Calculator - This is a summary of formulas, pointers, and decision trees for statistics.

Stress

Free Stress Calculator - Solves for any of the 3 items in the stress formula: Stress, Force, and Area

Substitute the given values into given formula and solve for the unknown variable. S=4LW + 2 WH; S=

Substitute the given values into given formula and solve for the unknown variable. S = 4LW + 2 WH; S= 144, L= 8, W= 4. H=
S = 4LW + 2 WH
Substituting our given values, we have:
144 = 4(8)(4) + 2(4)H
144 = 128 + 8H
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=128%2B8h%3D144&pl=Solve']equation calculator[/URL], we get:
[B]H = 2[/B]

Sum to Product and Product to Sum Formulas

Free Sum to Product and Product to Sum Formulas Calculator - Given two angles in degrees of u and v, this determines the following:

* Sin(u) ± Sin(v)

* Cos(u) ± Cos(v)

* Sin(u)Sin(v)

* Cos(u)Cos(v)

* Sin(u)Cos(v)

* Cos(u)Sin(v)

* Sin(u + v)

* Sin(u - v)

* Cos(u + v)

* Cos(u - v)

* Tan(u + v)

* Tan(u - v)

* Sin(u) ± Sin(v)

* Cos(u) ± Cos(v)

* Sin(u)Sin(v)

* Cos(u)Cos(v)

* Sin(u)Cos(v)

* Cos(u)Sin(v)

* Sin(u + v)

* Sin(u - v)

* Cos(u + v)

* Cos(u - v)

* Tan(u + v)

* Tan(u - v)

Suppose that Sn = 3 + 1/3 + 1/9 + ... + 1/3(n-2)

Suppose that Sn = 3 + 1/3 + 1/9 + ... + 1/3(n-2)
a) Find S10 and S?
b) If the common difference in an arithmetic sequence is twice the first term, show that Sn/Sm = n^2/m^2
a) Sum of the geometric sequence is
a = 3 and r = 1/3
(a(1 - r)^n)/(1 - r)
(3(1 - 1/3)^9)/(1 - 1/3)
[B]S10 = 4.499771376[/B]
For infinity, as n goes to infinity, the numerator goes to 1
so we have [B]S? = 3(1)/2/3 = 4.5[/B]
b) Sum of an arithmetic sequence formula is below:
n(a1 + an)/2
an = a1 + (n - 1)2a1 since d = 2a1
n(a1 + a1 + (n - 1)2a1)/2
(2a1n + n^2 - 2a1n)/2
n^2/2
For Sm
m(a1 + am)/2
am = a1 + (m - 1)2a1 since d = 2a1
m(a1 + 1 + (m - 1)2a1)/2
(2a1m + m^2 - 2a1m)/2
m^2/2
Sn/Sm = n^2/m^2 (cancel the 2's)
S10/S1 = 10^2/1^2
We know S_{1} = 3
So we have 100(3)/1
[B]S10 = 300[/B]

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls.
a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80^{th} percentile of the distribution of the average of 49 fly balls
a. N(250, 50/sqrt(49)) = [B]0.42074[/B]
b. Calculate Z-score and probability = 0.08 shown [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+240&mean=+250&stdev=+7.14&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
c. Inverse of normal distribution(0.8) = 0.8416. Use NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Using the Z-score formula, we have
0.8416 = (x - 250)/50
x = [B]292.08[/B]

b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.

c. Find the 80

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed wit

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and
a standard deviation of 50 feet.
a. If X = distance in feet for a fly ball, then X ~
b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement.
a. [B]N(250, 50/sqrt(1))[/B]
b. Calculate [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+220&mean=250&stdev=50&n=+1&pl=P%28X+%3C+Z%29']z-score[/URL]
Z = -0.6 and P(Z < -0.6) = [B]0.274253[/B]
c. Inverse of normal distribution(0.8) = 0.8416 using NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL]
Z-score formula: 0.8416 = (x - 250)/50

x = [B]292.08[/B]

x = [B]292.08[/B]

T-Bill

Free T-Bill Calculator - Calculates any of the four items of the T-Bill (Treasury Bill or TBill) formula:

1) Price (P)

2) Face Value (F)

3) Number of Weeks (w)

4) Yield Rate (y)

1) Price (P)

2) Face Value (F)

3) Number of Weeks (w)

4) Yield Rate (y)

Take a look at the following sums: 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 +

Take a look at the following sums:
1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
a. Come up with a conjecture about the sum when you add the first *n* odd numbers. For example, when you added the first 5 odd numbers (1 + 3 + 5 + 7 + 9), what did you get? What if wanted to add the first 10 odd numbers? Or 100?
b. Can you think of a geometric interpretation of this pattern? If you start with one square and add on three more, what can you make? If you now have 4 squares and add on 5 more, what can you make?
c. Is there a similar pattern for adding the first n even numbers?
2 = 2
2 + 4 = 6
2 + 4 + 6 = 12
2 + 4 + 6 + 8 = 20
a. The formula is [B]n^2[/B].
The sum of the first 10 odd numbers is [B]100[/B] seen on our s[URL='http://www.mathcelebrity.com/sumofthefirst.php?num=10&pl=Odd+Numbers']um of the first calculator[/URL]
The sum of the first 100 odd numbers is [B]10,000[/B] seen on our [URL='http://www.mathcelebrity.com/sumofthefirst.php?num=100&pl=Odd+Numbers']sum of the first calculator[/URL]
b. Geometric is 1, 4, 9 which is our [B]n^2[/B]
c. The sum of the first n even numbers is denoted as [B]n(n + 1)[/B] seen here for the [URL='http://www.mathcelebrity.com/sumofthefirst.php?num=+10&pl=Even+Numbers']first 10 numbers[/URL]

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of th

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of the triangle is less than 10 units. Write and solve an inequality that represents the possible area A of the triangle
We're given:
b=2/7A
We're also told that b is less than 10. So we have:
2/7A < 10
2A/7 < 10
Cross multiply:
2A < 7 * 10
2A < 70
Divide each side of the inequality by 2 to isolate A
2A/2 < 70/2
Cancel the 2's on the left side and we get:
A < [B]35[/B]

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased by x cm and its width i

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased
by x cm and its width is increased by x cm, its area is increased by 35 sq. cm.
a. Express the new length and the new width in terms of x.
b. Express the new area of the rectangle in terms of x.
c. Find the value of x.
Calculate the current area. Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=30&w=18&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 30 and width = 18[/URL], we get:
A = 540
a) Decrease length by x and increase width by x, and we get:
[LIST]
[*]length = [B]30 - x[/B]
[*]width = [B]18 + x[/B]
[/LIST]
b) Our new area using the lw = A formula is:
(30 - x)(18 + x) = 540 + 35
Multiplying through and simplifying, we get:
540 - 18x + 30x - x^2 = 575
[B]-x^2 + 12x + 540 = 575[/B]
c) We have a quadratic equation. To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=-x%5E2%2B12x%2B540%3D575&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine, choose solve[/URL], and we get:
[B]x = 5 or x = 7[/B]
Trying x = 5, we get:
A = (30 - 5)(18 + 5)
A = 25 * 23
A = 575
Now let's try x = 7:
A = (30 - 7)(18 + 7)
A = 23 * 25
A = 575
They both check out.
So we can have

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. Wh

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room?
The mean formulas is denoted as:
Mean = Sum of Ages / Total People
We're given Mean = 38 and Total People = 5, so we plug in our numbers:
28 = Sum of Ages / 5
Cross multiply, and we get:
Sum of Ages = 28 * 5
Sum of Ages = 140
One more person enters the room. The mean age is now 39. Set up our Mean formula:
Mean = Sum of Ages / Total People
With a new Mean of 39 and (5 + 1) = 6 people, we have:
39 = Sum of Ages / 6
But the new sum of Ages is the old sum of ages for 5 people plus the new age (a):
Sum of Ages = 140 + a
So we have:
29 = (140 + a)/6
Cross multiply:
140 + a = 29 * 6
140 + a = 174
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D174&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]34[/B]

The mean height of a class of 20 children is 1.27 the mean height of 12 boys in the class is 1.29 wh

The mean height of a class of 20 children is 1.27 the mean height of 12 boys in the class is 1.29 what is the mean height of the girls in the class?
The mean of sums is the sum of means. So we have:
Total Height / 20 = 1.27
Cross multiplying, we get:
Total Height = 20 * 1.27
Total Height = 25.4
Boys Height / 12 = 1.29
Cross multiplying, we get:
Boys Height = 12 * 1.29
Boys Height = 15.48
The Problem asks for mean height for girls. The formula is:
Girls Height / # of Girls = Mean of Girls Height
# of Girls = Total children - # of boys
# of Girls = 20 - 12
# of Girls = 8
Girls Height = Total Height - Boys Height
Girls Height = 25.4 - 15.48
Girls Height = 9.92
Plugging this into the Mean of girls height, we get:
9.92 /8 = [B]1.24[/B]

The moon's diameter is 2,159 miles. What is the surface area of the moon? Round to the nearest mile.

The moon's diameter is 2,159 miles. What is the surface area of the moon? Round to the nearest mile.
The moon is a sphere. So our Surface Area formula is:
S =4pir^2
If diameter is 2,159, then radius is 2,159/2 = 1079.5. Plug this into the Surface Area of a sphere formula:
S = 4 * pi * 1079.5^2
S = 4 * pi *1165320.25
S = 4661281 pi
S = [B]14,643,846.15 square miles[/B]

The perimeter of a college basketball court is 102 meters and the length is twice as long as the wid

The perimeter of a college basketball court is 102 meters and the length is twice as long as the width. What are the length and width?
A basketball court is a rectangle. The perimeter P is:
P = 2l + 2w
We're also given l = 2w and P = 102. Plug these into the perimeter formula:
2(2w) + 2w = 102
4w + 2w = 102
6w = 102
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%3D102&pl=Solve']Typing this equation into our calculator[/URL], we get:
[B]w = 17[/B]
Plug this into the l = 2w formula, we get:
l = 2(17)
[B]l = 34[/B]

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is it’s width?
The formula for a rectangles perimeter P, is:
P = 2l + 2w where l is the length and w is the width.
Plugging in our P = 340 and l = 97, we have:
2(97) + 2w = 340
Multiply through, we get:
2w + 194 = 340
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B194%3D340&pl=Solve']Type this equation into our search engine[/URL], we get:
[B]w = 73[/B]

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. Wh

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. What are the dimensions of the patio?
Perimeter of a rectangle is:
P = 2l + 2w
We're given l = w + 3 and P = 54. So plug this into our perimeter formula:
54= 2(w + 3) + 2w
54 = 2w + 6 + 2w
Combine like terms:
4w + 6 = 54
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B6%3D54&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 12[/B]
Plug this into our l = w + 3 formula:
l = 12 + 3
[B]l = 15[/B]

The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?

The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?
The perimeter for a rectangle is given below:
P = 2l + 2w
We're given l = 7 and P = 60. Plug this into the perimeter formula:
60 = 2(7) + 2w
60 = 14 + 2w
Rewritten, it's 2w + 14 = 60.
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B14%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get [B]w = 23[/B].

The teacher is handing out note cards to her students. She gave 20 note cards to the first student,

The teacher is handing out note cards to her students. She gave 20 note cards to the first student, 30 note cards to the second student, 40 note cards to the third student, and 50 note cards to the fourth student. If this pattern continues, how many note cards will the teacher give to the fifth student?
[LIST]
[*]Student 1 has 20
[*]Student 2 has 30
[*]Student 3 has 40
[*]Student 4 has 50
[/LIST]
The teacher adds 10 note cards to each student. Or, if we want to put in a sequence formula, we have:
S(n) = 10 + 10n where n is the student number
Simplified, we write this as:
S(n) = 10(1 + n)
The question asks for S(5)
S(5) = 10(1 + 5)
S(5) = 10(6)
[B]S(5) = 60
[/B]
If we wanted to simply add 10 and not use a sequence formula, we see that S(4) = 50.
So S(5) = S(4) + 10
S(5) = 50 + 10
[B]S(5) = 60[/B]

the university of california tuition in 1990 was $951 and tuition has been increasing by a rate of 2

the university of california tuition in 1990 was $951 and tuition has been increasing by a rate of 26% each year, what is the exponential formula
Let y be the number of years since 1990. We have the formula T(y):
[B]T(y) = 951 * 1.26^y[/B]

There are 100 people in a sport centre. 67 people use the gym. 62 people use the swimming pool. 5

There are 100 people in a sport centre. 67 people use the gym. 62 people use the swimming pool. 56 people use the track. 38 people use the gym and the pool. 31 people use the pool and the track. 33 people use the gym and the track. 16 people use all three facilities. A person is selected at random. What is the probability that this person doesn't use any facility?
WE use the compound probability formula for 3 events:
[LIST=1]
[*]Gym use (G)
[*]Swimming pool use (S)
[*]Track (T)
[/LIST]
P(G U S U T) = P(G) + P(S) + P(T) - P(G Intersection S) - P(G Intersection T) - P(S Intersection T) + P(G Intersection S Intersection T)
[LIST]
[*]Note: U means Union (Or) and Intersection means (And)
[/LIST]
Plugging our numbers in:
P(G U S U T) = 67/100 + 62/100 + 56/100 - 38/100 - 31/100 - 33/100 + 16/100
P(G U S U T) = (67 + 62 + 56 - 38 - 31 - 33 + 16)/100
P(G U S U T) = 99/100 or 0.99
What this says is, the probability that somebody uses at any of the 3 facilities is 99/100.
The problem asks for none of the 3 facilities, or P(G U S U T)'
P(G U S U T)' = 1 - P(G U S U T)
P(G U S U T)' = 1 - 99/100
P(G U S U T)' = 100/100 - 99/100
P(G U S U T)' = [B]1/100 or 0.1[/B]

There are 113 identical plastic chips numbered 1 through 113 in a box. What is the probability of re

There are 113 identical plastic chips numbered 1 through 113 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is greater than 44?
We want 45, 46, … 113
The formula to get inclusive number count between and including 2 numbers is:
Total numbers = L - S + 1
Total numbers = 113 - 45 + 1
Total numbers = 69
That is 69 possible numbers. We draw this out of a total of 113
[B]P(Number > 44) = 69/113
[B]P(Number > 44) [/B]= 0.610619
[MEDIA=youtube]BLBVcpdHqXU[/MEDIA][/B]

To convert from Celsius to Fahrenheit, multiply by 1.8 and add 32. Write a formula to describe this

To convert from Celsius to Fahrenheit, multiply by 1.8 and add 32. Write a formula to describe this relationship.
Given C as Celsius and F as Fahrenheit, we have the following equation:
[B]F = 1.8C + 32[/B]

Triangle Solver and Classify Triangles

Free Triangle Solver and Classify Triangles Calculator - Solves a triangle including area using the following solving methods

Side-Angle-Side (SAS) Side Angle Side

Angle-Side-Angle (ASA) Angle Side Angle

Side-Side-Angle (SSA) Side Angle Side

Side-Side-Side (SSS) Side Side Side

Area (A) is solved using Herons Formula

Law of Sines

Law of Cosines

Also classifies triangles based on sides and angles entered.

Side-Angle-Side (SAS) Side Angle Side

Angle-Side-Angle (ASA) Angle Side Angle

Side-Side-Angle (SSA) Side Angle Side

Side-Side-Side (SSS) Side Side Side

Area (A) is solved using Herons Formula

Law of Sines

Law of Cosines

Also classifies triangles based on sides and angles entered.

Trigonometry Summary

Free Trigonometry Summary Calculator - This is a list of important angle formulas and identities in trigonometry

Twelve students tried out for the football team. Coach Moorhead only has 5 openings. In how many way

Twelve students tried out for the football team. Coach Moorhead only has 5 openings. In how many ways, can he pick 5 of the 12 students to be on the team?
We use the combinations formula. We can write this as 12C5. [URL='https://www.mathcelebrity.com/permutation.php?num=12&den=5&pl=Combinations']Type this into our search engine[/URL] and we get:
[B]792 ways[/B]

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that s

Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that starts with 13 and continues to add seven to each output. For now, van needs to know what the 15th output will be. Complete the steps needed to determine the 15th term in sequence.
Given a first term a1 of 13 and a change amount of 7, expand the series
The explicit formula for an [I]arithmetic series[/I] is an = a1 + (n - 1)d
d represents the common difference between each term, an - an - 1
Looking at all the terms, we see the common difference is 7, and we have a1 = 13
Therefore, our explicit formula is an = 13 + 7(n - 1)
If n = 15, then we plug it into our explicit formula above:
an = 13 + 7(n - 1)
a(15) = 15 + 7(15 - 1)
a(15) = 15 + 7 * 14
a(15) = 15 + 98
a(15) = [B]113[/B]

What is the 1000th term in the series 0, 7, 14, 21, … ?

Map this out as a function with term number n and value
1, 0
2, 7
3, 14
4, 21
The values jump by 7, but they do so as the n - 1 term.
We have the series formula S(n) = 7(n - 1)
The problem asks for S(1000)
S(1000) = 7(1000 - 1)
S(1000) = 7(999)
S(1000) = [B]6,993[/B]
[MEDIA=youtube]ZF10Ec29XKo[/MEDIA]

What is the formula for the area of a circle?

What is the formula for the area of a circle?
Given a radius r, we have Area (A) of:
[B]A = ?r^2[/B]

What is the formula for the circumference of a circle?

What is the formula for the circumference of a circle?
Given radius r and diameter d, the circumference C is:
[B]C = 2?r or ?d[/B]

What is the formula for the volume of a cylinder?

What is the formula for the volume of a cylinder?
The Volume (V) of a cylinder with radius (r) and height (h) is:
[B]V = ?r^2h[/B]

Which of the followings can increase the value of t? (select all the apply) a. Increase the standar

Which of the followings can increase the value of t? (select all the apply)
a. Increase the standard deviation of difference scores
b. Decrease the standard deviation of difference scores
c. Increase the difference between means
d. Decrease the difference between means
[B]b. Decrease the standard deviation of difference scores
c. Increase the difference between means[/B]
[I]Increase numerator or decrease denominator of the t-value formula[/I]

Work

Free Work Calculator - Solves for any of the 3 variables, Work (W), Force (F) and Distance (d) in the work formula

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for inter

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for interest. What was the annual simple interest rate that he charged you? Use the formula: I = Prt.
We have I = 2, P = 25, t = 0.5
2 = 25(r)0.5
Divide each side by 0.5
4 = 25r
Divide each side by 25
r = 4/25
[B]r = 0.16[/B]
As a percentage, this is [B]16%[/B]

You conduct 50,000 tests, 1500 people test positive, what's the positivity rate?

You conduct 50,000 tests, 1500 people test positive, what's the positivity rate?
[U]Our Positivity Rate formula is below:[/U]
Positivity Rate = 100% * positive tests / Total tests
[U]Plugging in our numbers from the problem, we get:[/U]
Positivity Rate = 100% * 1500/50000
Positivity Rate = 100% * 0.03
Positivity Rate = [B]3%[/B]

You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must yo

You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest?
The simple interest formula for the accumulated balance is:
Prt = I
We are given P = 2,000, r = 0.04, and I = 500.
2000(0.04)t = 500
80t = 500
Divide each side by 80
t = [B]6.25 years
[MEDIA=youtube]Myz0FZgwZpk[/MEDIA][/B]

You start reading on page 342 and end on 531. How many pages did you read?

You start reading on page 342 and end on 531. How many pages did you read?
The pages read formula is:
Pages Read = End Page - Start Page + 1
Pages Read = 531 - 342 + 1
Pages Read = [B]190[/B]