Answer:
22608 mm³/s
Step-by-step explanation:
Applying chain rule,
dV/dt = (dV/dr)(dr/dt)............... Equation 1
Where dV/dr = rate at which the volume is increasing
But,
V = 4πr³/3
Therefore,
dV/dr = 4πr²............... Equation 2
Substitute equation 2 into equation 1
dV/dt = 4πr²(dr/dt).............. Equation 3
From the question,
Given: dr/dt = 2 mm/s, r = 60/2 = 30 mm
Consatant: π = 3.14
Substitute these values into equation 3
dV/dt = 4×3.14×30²×2
dV/dt = 22608 mm³/s
In a mixture of 240 gallons, the ratio of ethanol and gasoline is 3:1. If the ratio is to be 1:3, then find the quantity of gasoline that is to be added.
Answer:
480 gallons.
Step-by-step explanation:
Given that in a mixture of 240 gallons, the ratio of ethanol and gasoline is 3: 1, if the ratio is to be 1: 3, to find the quantity of gasoline that is to be added the following calculation must be performed:
240/4 x 3 = Ethanol
240/4 = Gasoline
180 = Ethanol
60 = Gasoline
0.25 = 180
1 = X
180 / 0.25 = X
720 = X
720 - 180 - 60 = X
480 = X
Therefore, 480 gallons of gasoline must be added if the ratio is to be 1: 3.
At a snack food manufacturing facility, the quality control engineer must ensure that all products feature the appropriate expiration date. Suppose that a box of 60 candy bars includes 12 which do not have the proper printed expiration date. The quality control engineer, in inspecting the box, grabs a handful of seven candy bars. What is the probability that there are exactly 3 faulty candy bars among the seven
Answer:
0.1108 = 11.08% probability that there are exactly 3 faulty candy bars among the seven.
Step-by-step explanation:
The bars are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
60 total candies means that [tex]N = 70[/tex]
12 are faulty, which means that [tex]k = 12[/tex]
Seven are chosen, so [tex]n = 7[/tex]
What is the probability that there are exactly 3 faulty candy bars among the seven?
This is [tex]P(X = 3)[/tex]. So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,70,7,12) = \frac{C_{12,3}*C_{48,4}}{C_{60,7}} = 0.1108[/tex]
0.1108 = 11.08% probability that there are exactly 3 faulty candy bars among the seven.
Multiply (x2 + 3x + 5)(2x2 - 2x + 1).
A. 2A - 6x2 + 5
B. 3x2 + x + 6
C. 2A + 4x2 + 5x2 - 7x + 5
D. 2x4 + 8x3 + 17x2 + 13x+5
What is the area of the sector that is not shaded?
12Pi units squared
24Pi units squared
120Pi units squared
144Pi units squared
Answer:
120Pi units squared
Step-by-step explanation:
π*12²*(360-60)/360
= π*144*300/360
= π*144*5/6
= π*720/6
= π*120
= 120π or 120Pi units squared
Answer:
120Pi units squared
Step-by-step explanation:
on edge
1. Using the factorisation method, simplify the following √32
Answer:
[tex]4 \sqrt{2} [/tex]
[tex] \sqrt{32} = \sqrt{16 \times 2} = 4 \sqrt{2} [/tex]
Use cylindrical shells to find the volume of the solid generated when the region
R under y = x2 over the interval (0,2) revolved about the line y = -1
Answer:
[tex]\displaystyle V = \frac{176 \pi}{15}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsExpandingFunctionsFunction NotationGraphingExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method:
[tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] x is the radius[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is the volumeStep-by-step explanation:
Step 1: Define
Identify
Graph of region
y = x²
x = 2
y = 4
Axis of Revolution: y = -1
Step 2: Sort
We are revolving around a horizontal line.
[Function] Rewrite in terms of y: x = √y[Graph] Identify bounds of integration: [0, 4]Step 3: Find Volume Pt. 1
[Shell Method] Find distance of radius x: [tex]x = y + 1[/tex][Shell Method] Find circumference variable f(x) [Area]: [tex]\displaystyle f(x) = 2 - \sqrt{y}[/tex][Shell Method] Substitute in variables: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - \sqrt{y})} \, dy[/tex][Integral] Rewrite integrand [Exponential Rule - Root Rewrite]: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - y^\bigg{\frac{1}{2}})} \, dy[/tex][Integral] Expand integrand: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(-y^\bigg{\frac{3}{2}} + 2y - y^\bigg{\frac{1}{2}} + 2)} \, dy[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{-2y^\bigg{\frac{5}{2}}}{5} + y^2 - \frac{2y^\bigg{\frac{3}{2}}}{3} + 2y \bigg) \bigg| \limits^4_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = 2\pi (\frac{88}{15})[/tex]Multiply: [tex]\displaystyle V = \frac{176 \pi}{15}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
A classmate walks into class and states that he has an extra ticket to a chamber orchestra concert on Friday night. He asks everyone in the class to put their name on a piece of paper and put it in a basket. He plans to draw from the basket to choose the person who will attend the concert with him. If there are 38 other people in class that night, what is your chance of being chosen to attend the concert
Answer:
2.56% chance of being selected
Step-by-step explanation:
Given
[tex]n = 39[/tex] --- you and 38 others
Required
Chance of you being selected
To do this, we simply calculate the probability using:
[tex]Pr(x) = \frac{n(x)}{n}[/tex]
Where:
[tex]n(x)= 1[/tex] --- i.e you are just 1 person
So:
[tex]Pr(x) = \frac{1}{39}[/tex]
[tex]Pr(x) = 0.0256[/tex]
Express as percentage
[tex]Pr(x) = 2.56\%[/tex]
Solve the following quadratic by factoring.
x² – 3x – 4=0
List the answers separated by a comma. For example, if you found solutions x = 1 and x = 2, you would enter 1, 2.
Answer:
4, -1
Step-by-step explanation:
We can reverse the FOIL (First, outside, inside, last) method to break down the equation. The question is asking to solve by factoring so you want to find the right combination of numbers this equation can be broken down into:
x^2 - 3x - 4 = 0
Because we want x squared, x needs to be multiplied by itself, so we can put x in the first slot for each.
(x + or - ?) ( x + or - ?) = 0
Then we need to find numbers that could be added to get -3 and multiplied to get -4. The only set of numbers that works for this is -4 and 1. Note that the sign you put in front of each number has an impact on your answers. With this we get:
(x - 4) (x + 1) = 0
To test that this is equal to the original equation, simply multiply it out using FOIL.
x * x = x^2
x * 1 = x
x * -4 = -4x
-4 * 1 = -4
Putting each component into an equation:
x^2 + x - 4x - 4 = 0
Simplifying:
x^2 - 3x - 4 = 0
Once we are sure it is still the same equation, we find the solutions. We know 0 multiplied by anything equals 0, so to get 0 as the answer, one of the sets in the parentheses must equal 0. (It doesn't matter what the other one is as long is one equals 0)
Therefore, we have 2 solutions, 4, and -1 because if x is 4, 4-4 is 0 which solves the equation, and if x is -1, then -1 + 1 is 0 which also solves the equation.
You can also check your answers by plugging them back into the original equation.
Write a polynomial f (x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.
The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).
The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320
(0+4)^3*(0-1)*k = 320
-64k = 320
k = -5
Combining all three conditions, f(x)
= -5(x+4)^3*(x-1)
= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)
= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)
= -5(x^4 + 11x^3 + 36x^2 + 16x -64)
= -5x^3 -55x^3 - 180x^2 - 80x + 320
Answer:
Step-by-step explanation:
-4 is a root for 3 times and 1 is root for once
so (x+4)^3 * (x-1) is part of f(x)
the constant term there is 4^3*(-1)=-64
so there is a multiplier of 320/-64=-5
f(x) = -5 * (x+4)^3 * (x-1)
find 9 rational no. between 8/7 and 17/10.
Answer:
[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]
Step-by-step explanation:
We need to find 9 rational number between [tex]\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}[/tex]
We make the denominators of both fractions same. So,
[tex]\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}[/tex]
and
[tex]\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}[/tex]
The rational number are:
[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]
XYZ ∆ where Angle Y =90° , XZ= 14 m , XY = 6 m . Find YZ ?
( Show all your workings )
[tex]4 \sqrt{10} [/tex]
Step-by-step explanation:
Use Pythagoras
A^2 + b^2 = c^2
(6)^2 + b^2 = (14)^2
36 + b^2 = 196
B^2 =160
[tex]b = \sqrt{160} [/tex]
[tex]b = 4 \sqrt{10} [/tex]
what is the cost to drive from san francisco to los angeles (405 mi) if the cost of gasoline is $2.34/gal and the automobile gets 8.5 mi/L
Answer:
The cost is $ 29.5.
Step-by-step explanation:
distance = 405 miles
Cost = $ 2.34 /gal
Average = 8.5 miles per litre
So, the amount of gasoline to travel for 405miles
= 405/8.5 = 47.65 liter
1 gal = 3.785 liters
So,
47.65 liter = 47.65 / 3.785 = 12.6 gal
So, the cots is
= $ 2.34 x 12.6 = $29.5
what is the quotient?
Answer:
the result gaven by dividing one number by another
In 1999, a company had a profit of $173,000. In 2005, the profit was
$206,000. If the profit increased by the same amount each year, find the
rate of change of the company's profit in dollars per year. *
$5,500
$4,004
$379,000
$33,000
O $102.74
Answer:
A. $5500Step-by-step explanation:
The difference of years:
2005 - 1999 = 6The difference in profit over 6 years:
206000 - 173000 = 33000Average rate of change:
33000/6 = 5500It has been 6 years,
The main difference in profit over 6 years between 1999 and 2005 is,
→ 206000 - 173000
→ 33000
Then the average rate of change is,
→ 33000/6
→ 5500
Hence, $ 5500 is the correct option.
please simplify this one. I need answers fast as possible .(chapter name : surds )
[tex] \sqrt[5]{32} \times 2 \sqrt[3]{81} \\ = {32}^{ \frac{1}{5} } \times 2 {(81)}^{ \frac{1}{3} } \\ = ({{2}^{5}})^{ \frac{1}{5} } \times {2({3}^{3})}^{ \frac{1}{3} } \\ = {2}^{1} \times 2({3}^{1}) \\ = 2 \times 2 \times 3 \\ = 4 \times 3 \\ = 12[/tex]
This is the answer.
Hope it helps!!
Find the probability that when a couple has children, at least one of them is a . (Assume that boys and girls are equally likely.)
Answer:
[tex]P(At\ least\ one\ girl) = 0.875[/tex]
Step-by-step explanation:
Given
[tex]n = 3[/tex]
[tex]B \to boys[/tex]
[tex]G \to girls[/tex]
[tex]P(G) = P(B) = 0.5[/tex] --- equal probability
See comment for complete question
Required:
[tex]P(At\ least\ one\ girl)[/tex]
To do this, we make use of complement rule:
[tex]P(At\ least\ one\ girl) = 1 - P(No\ girl)[/tex]
The event that there is no girl out of the 3 children is: B B B
And the probability is:
[tex]P(No\ Girl) = P(B) * P(B) * P(B)[/tex]
[tex]P(No\ Girl) = 0.5*0.5*0.5[/tex]
[tex]P(No\ Girl) = 0.125[/tex]
So:
[tex]P(At\ least\ one\ girl) = 1 - P(No\ girl)[/tex]
[tex]P(At\ least\ one\ girl) = 1 - 0.125[/tex]
[tex]P(At\ least\ one\ girl) = 0.875[/tex]
HELP ME FAST WILL GIVE BRAINLY
A bag contains 16 white marbles, 10 blue marbles and 12 red marbles. Give each ratio as a reduced fraction.
A) The ratio of white marbles to blue marbles.
B) The ratio of red marbles to total marbles.
the total of marbles = 16 + 10 +12 =38
A) white : blue = 16/10 = 8/5
B) red : total = 12/38 = 6/19
Step-by-step explanation:
1. find the total of marbles
From the table below, determine whether the data shows an exponential function. Explain why or why not.
x
3
2
1
–1
y
8
2
0.5
0.125
a. No; the domain values are at regular intervals and the range values have a common factor 0.25. b. No; the domain values are not at regular intervals although the range values have a common factor. c. Yes; the domain values are at regular intervals and the range values have a common factor 4. d. Yes; the domain values are at regular intervals and the range values have a common factor 0.25.
9514 1404 393
Answer:
b. No; the domain values are not at regular intervals although the range values have a common factor.
Step-by-step explanation:
The differences between x-values are ...
-1, -1, -1, -2 . . . . not a constant difference
The ratios of y-values are ...
2/8 = 0.5/2 = 0.125/0.5 = 0.25 . . . . a constant difference
The fact that the domain values do not have a common difference renders the common factor of the range values irrelevant. The relation is not exponential.
solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!
Answer:
[0.25, 2]
Step-by-step explanation:
We have
4t² ≤ 9t-2
subtract 9t-2 from both sides to make this a quadratic
4t²-9t+2 ≤ 0
To solve this, we can solve for 4t²-9t+2=0 and do some guess and check to find which values result in the function being less than 0.
4t²-9t+2=0
We can see that -8 and -1 add up to -9, the coefficient of t, and 4 (the coefficient of t²) and 2 multiply to 8, which is also equal to -8 * -1. Therefore, we can write this as
4t²-8t-t+2=0
4t(t-2)-1(t-2)=0
(4t-1)(t-2)=0
Our zeros are thus t=2 and t = 1/4. Using these zeros, we can set up three zones: t < 1/4, 1/4<t<2, and t>2. We can take one random value from each of these zones and see if it fits the criteria of
4t²-9t+2 ≤ 0
For t<1/4, we can plug in 0. 4(0)²-9(0) + 2 = 2 >0 , so this is not correct
For 1/4<t<2, we can plug 1 in. 4(1)²-9(1) +2 = -3 <0, so this is correct
For t > 2, we can plug 5 in. 4(5)²-9(5) + 2 = 57 > 0, so this is not correct.
Therefore, for 4t^2 ≤ 9t-2 , which can also be written as 4t²-9t+2 ≤ 0, when t is between 1/4 and 2, the inequality is correct. Furthermore, as the sides are equal when t= 1/4 and t=2, this can be written as [0.25, 2]
A businessman spends 1/5 of his travel expense funds on a hotel room and 4/10 on airfare. What percentage of his travel expenses are left over?
Answer: 40%
Step-by-step explanation:
1/5=20%, 4/10=40%. 20 + 40 = 60. [ 100% - 60% = 40%]
What is the domain of this function y= 1/ square root 2-x
Answer:
Domain:
( − ∞ , 2 ] , { x | x ≤ 2 }
Range:
[ 0 , ∞ ) , { y | y ≥ 0 }
A full glass of water can hold 1/6 of a bottle.
How many glasses of water can be filled with 3 bottles of water
When you compute with decimals you should always check your answer is reasonable why
Answer:
Ang pangit mo
Kamuka mo Yong clown
What is the product (4.42 x 103)(5 x 10^) written in
scientific notation?
Answer:
2.2763 x 10 to the power of 4
for some reason it doesn't let me put in the explanation
The Goodman Tire and Rubber Company periodically tests its tires for tread wear under simulated road conditions. To study and control the manufacturing process, 20 samples, each containing three radial tires, were chosen from different shifts over several days of operation; the data collected are shown below. Assuming that these data were collected when the manufacturing process was believed to be operating in control, develop the R and charts.
R Chart: (to 2 decimals)
UCL =
LCL =
Chart: (to 1 decimal)
UCL =
LCL =
Answer:
Range:
UCL = 4.73
LCL = 18.08
MEAN :
UCL = 27.115
LCL = 31.219
Step-by-step explanation:
Given the data:
The mean and range of each sample :
Sample __ Thread wear __ xbar __ R
1 ___31 __ 42 ___ 28 ____ 33.67 _14
2___ 26 _ 18 ____35____ 26.33 _17
3___25 __30 ___ 34____29.67 _ 9
4 __ 17 __ 25 ___ 21 _____ 21 ___ 8
5 __ 38 _ 29 ___ 35 _____ 34 __ 9
6 __ 41 __42 ___36 _____39.67_ 6
7 __ 21 __ 17 ___29 _____22.33 _12
8 __ 32 __26___28 ____ 28.67 _ 6
9 __ 41 __ 34 __ 33 ______ 36 __8
10__29___17___30 _____25.33_ 13
11 __26 __ 31 __ 40 _____32.33_ 14
12__23 __ 19 __ 45 _____12.33 __6
13 __17 __ 24 __ 32_____24.33__15
14 __43__ 35___17_____ 31.67 _ 26
15__18 ___25__ 29_____ 24 ___ 11
16__30___42___31 ____34.33__ 12
17__28___36 __ 32____ 32 ____8
18__40 __ 29 __ 31 ____33.33 __ 11
19__18 ___29__ 28____ 25 ____11
20_ 22 __ 34 __ 26 ___ 27.33 __12
Size per sample, sample size, n = 3
Number of samples, k = 20
We calculate the sample mean and range average :
Sample mean, x-- = Σxbar/n = 29.167
Range average, Rbar = ΣR/n = 11.4
The mean control limit :
x-- ± A2Rbar
From the x chart ;
A2 for n = 20 is A2 = 0.180
29.167 ± 0.180(11.40)
LCL = 29.167 - 0.180(11.40) = 27.115
UCL = 29.167 + 0.180(11.40) = 31.219
The Range control limit :
Rbar(1 ± 3(d3/d2))
From the R-chart :
d2 at n = 20 ; d2 = 3.735
d3 at n = 20 ; d3 = 0.729
LCL = 11.40(1 - 3(0.729/3.735)) = 4.725
UCL = 11.40(1 + 3(0.729/3.735)) = 18.075
Which could be the function graphed below?
[tex]f(x)=\sqrt{x} -2[/tex] is the correct option
CHECK MY ANSWERS PLEASE
____
The sequence is geometric:
3, 13, 23, 33,...
True
False***
_____________________
The sequence is geometric:
5, -25, 125, -625,...
True***
False
Answer:
1. False 2. True
Step-by-step explanation:
For a geometric sequence,
[tex]\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}[/tex]
1. The sequence is :
3, 13, 23, 33,...
[tex]\dfrac{13}{3}\ne \dfrac{23}{13}[/tex]
It is not geometric. It is false
2. The sequence is :
5, -25, 125, -625
[tex]\dfrac{-25}{5}=\dfrac{125}{-25}\\\\-5=-5[/tex]
So, the sequence is geometric as the common ratio is same. It is true.
If 19,200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Step-by-step explanation:
√19200cm²
=138.56cm
then the highest possible volume
=(138.56)³
=2660195.926cm³
The largest possible volume of the box is; V = 25600 cm³
Let us denote the following of the square box;
Length = x
Width = y
height = h
Formula for volume of a box is;
V = length * width * height
Thus; V = xyh
but we are dealing with a square box and as such, the base sides are all equal and so; x = y. Thus;
V = x²h
The box has an open top and as such, the surface are of the box is;
S = x² + 4xh
We are given S = 19200 cm². Thus;
19200 = x² + 4xh
h = (19200 - x²)/4x
Put (19200 - x²)/4x for h in volume equation to get;
V = x²(19200 - x²)/4x
V = 4800x - 0.25x³
To get largest possible volume, it will be dimensions when dV/dx = 0. Thus;
dV/dx = 4800 - 0.75x²
At dV/dx = 0, we have;
4800 - 0.75x² = 0
0.75x² = 4800
x² = 4800/0.75
x² = 6400
x = √6400
x = 80 cm
From h = (19200 - x²)/4x;
h = (19200 - 80²)/(4 × 80)
h = (19200 - 6400)/3200
h = 4 cm
Largest possible volume = 80² × 4
Largest possible volume = 25600 cm³
Read more at; https://brainly.com/question/19053087
Consider a relation on the set of all states in the United States given by: two states are related if they have a border in common. Is it an equivalence relation
Answer:
Yes it is an equivalence relation
Explanation:
An equivalence relation is a binary relation between two values that are symmetric, transitive and reflexive. In other words, when we say a value x is equal(using "=") to a value y, there is an equivalence relation between them.
Example, given set {x, y, z} where ~ means equivalence:
x ~ y if y ~ z means symmetric
since x ~ y and y ~ z, then x ~ z means transitive
x ~ x means reflexive
Equivalence relations share a common attribute or attributes(example, a satisfying condition)
The above condition that two states are related from the set of all US states if they have a border in common satisfies the condition of equivalence listed hence it is an equivalence relation.
What is the answer
5 10 25 100 × ÷ ÷
Answer: 1/50, or 0.02
Step-by-step explanation:
I'm assuming this is 5*10/25/100. if you just follow the equation, you get 50/25/100, which is 2/100, or 1/50.
