Answer:
There will be 50 bacteria remaining after 28 minutes.
Step-by-step explanation:
The exponential decay equation is
[tex]N=N_0e^{-rt}[/tex]
N= Number of bacteria after t minutes.
[tex]N_0[/tex] = Initial number of bacteria when t=0.
r= Rate of decay per minute
t= time is in minute.
The sample begins with 500 bacteria and after 11 minutes there are 200 bacteria.
N=200
[tex]N_0[/tex] = 500
t=11 minutes
r=?
[tex]N=N_0e^{-rt}[/tex]
[tex]\therefore 200=500e^{-11r}[/tex]
[tex]\Rightarrow e^{-11r}=\frac{200}{500}[/tex]
Taking ln both sides
[tex]\Rightarrow ln| e^{-11r}|=ln|\frac{2}{5}|[/tex]
[tex]\Rightarrow {-11r}=ln|\frac{2}{5}|[/tex]
[tex]\Rightarrow r}=\frac{ln|\frac{2}{5}|}{-11}[/tex]
To find the time when there will be 50 bacteria remaining, we plug N=50, [tex]N_0[/tex]= 500 and [tex]r}=\frac{ln|\frac{2}{5}|}{-11}[/tex] in exponential decay equation.
[tex]50=500e^{-\frac{ln|\frac25|}{-11}.t}[/tex]
[tex]\Rightarrow \frac{50}{500}=e^{\frac{ln|\frac25|}{11}.t}[/tex]
Taking ln both sides
[tex]\Rightarrow ln|\frac{50}{500}|=ln|e^{\frac{ln|\frac25|}{11}.t}|[/tex]
[tex]\Rightarrow ln|\frac{1}{10}|={\frac{ln|\frac25|}{11}.t}[/tex]
[tex]\Rightarrow t= \frac{ln|\frac{1}{10}|}{\frac{ln|\frac25|}{11}.}[/tex]
[tex]\Rightarrow t= \frac{11\times ln|\frac{1}{10}|}{{ln|\frac25|}}[/tex]
[tex]\Rightarrow t\approx 28[/tex] minutes
There will be 50 bacteria remaining after 28 minutes.
Final answer:
To solve this problem, we use the formula for exponential decay and solve for the time when there are 50 bacteria remaining.
Explanation:
To solve this problem, we can use the formula for exponential decay: A = A0 * e^(kt), where A is the final population, A0 is the initial population, e is Euler's number (approximately 2.71828), k is the decay constant, and t is the time in minutes.
First, let's determine the value of k. We know that after 11 minutes, the population is 200 bacteria, so we can substitute these values into the formula to solve for k: 200 = 500 * e^(11k).
Divide both sides of the equation by 500: 0.4 = e^(11k).
Take the natural logarithm of both sides to solve for k: ln(0.4) = 11k.
Divide both sides by 11 to find the value of k: k ≈ -0.07761.
Now we can use the formula to solve for t when there are 50 bacteria remaining: 50 = 500 * e^(-0.07761t).
Divide both sides by 500: 0.1 = e^(-0.07761t).
Take the natural logarithm of both sides to solve for t: ln(0.1) = -0.07761t.
Divide both sides by -0.07761 to find the value of t: t ≈ 13.857 minutes.
Therefore, after approximately 14 minutes (rounded to the nearest whole number), there will be 50 bacteria remaining.
What is the value of d?
Answer:
57
Step-by-step explanation:
the angles of a triangle together make 180 degrees.
using this, we can find the unknown angle is 115 degrees.
from here, we subtract 1 from both sides of 2d+1=115, then divide by 2, to get the d alone.
114/2=57
d=57
Answer:
d=57
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees
38 +27 +2d+1=180
Combine like terms
(38+27+1) +2d= 180
66+2d=180
Now, solve for d by isolating it
Subtract 66 from both sides
66-66 +2d=180-66
2d=114
Divide both sides by 2
d=57
Joshua is reading a book for history class. He has read 180 pages so far. This number represents 30% of the total
number of pages in the book.
What is the total number of pages in the book?
54 pages
126 pages
385 pages
600 pages
Oo oo
600 is the total number of pages in the book
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Joshua is reading a book for history class.
He has read 180 pages so far.
This number represents 30% of the total number of pages in the book.
We need to find total number of pages in the book.
Let x be the number of pages in the book.
30% of x=180
Convert 30% to decimal
30/100x=180
0.3x=180
Divide both sides by 0.3
x=600
Hence, 600 is the total number of pages in the book
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Eliminate the parameter to find the cartesian equation of the curve: x=7sinθ,y=cos2θ,−π2≤θ≤π2 x=7sinθ,y=cos2θ,−π2≤θ≤π2 the equation of the curve is: y = equation editorequation editor from x = equation editorequation editor to x =
To eliminate the parameter and find the Cartesian equation of the curve x = 7sinθ,y = cos2θ, we can express x in terms of θ, rearrange the equation, and substitute it into the other equation to eliminate the parameter θ. The resulting equation 2(x/7)² + y - 1 = 0 represents the Cartesian equation of the curve.
Explanation:To eliminate the parameter and find the Cartesian equation of the curve, we can express x in terms of θ using the given equation x = 7sinθ. Rearranging this equation, we get sinθ = x/7. Similarly, we can express y in terms of θ using the given equation y = cos2θ, which can be rewritten as cos(2θ) = y.
Now we can use the trigonometric identity cos(2θ) = 1 - 2sin²θ to eliminate θ from the equations. Substituting this identity into the second equation, we get 1 - 2(sinθ)² = y.
Simplifying this equation, we have 2(sinθ)² + y - 1 = 0. Finally, we can express sinθ in terms of x using the equation sinθ = x/7, and substitute it into the simplified equation to eliminate θ. This gives us 2(x/7)² + y - 1 = 0, which represents the Cartesian equation of the given curve.
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Erin opened a savings account that earns 3% simple interest. If she deposits $2,750 and doesn't make any additional deposits or withdrawals how much money will be in her account at the end of 6 years?
Answer:
$3,245
Step-by-step explanation:
For a money saved at Simple Interest,
Amount =Simple Interest+Principal
Principal, P=$2750
Rate, r=3%
Time, T=6 Years
[TeX] Simple \: Interest= \frac{Principal X Rate X Time}{100}[/TeX]
[TeX] = \frac{2750X 3 X 6}{100}[/TeX]=$495
Therefore, Amount in Erin's Account after 6 years =2750+495
=$3,245
A farmer sells 9.1 kilograms of apples and pears at the farmer's market. 2 5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answer:
5.46 kilograms or 6.6 kilograms
Step-by-step explanation:
Assume that 2 5 in your question has two possible meaning:
2/5 of this weight is applesLet divide 9.1 kilograms into 5 equal part
=> 1 equal part = 9.1 / 5 = 1.82 kilograms
Because 2/5 of this weight is apples, so the weight of apples accounted for 2 equal parts
=> the weight of apples is: 2*1.82 kilograms = 3.64 kilograms
=> the weight of pears is: 9.1 kilograms - 3.64 kilograms = 5.46 kilograms
2.5 kg of this weight is applesGiven the total weight is 9.1 kilograms
=> the weight of pears is: 9.1 kilograms - 2.5 kilograms = 6.6 kilograms
Final answer:
To find the amount of pears sold, calculate two-fifths of the total weight for the apples and subtract this from the total weight. The farmer sold 5.46 kilograms of pears.
Explanation:
The student has asked a question that requires understanding of basic fractions and weight calculation in a real-life context, specifically within a farmer's market scenario. To solve the problem, we note that the total weight of apples and pears sold is 9.1 kilograms. If two-fifths (2/5) of this weight is apples, then to find the weight of pears, we first calculate the weight of apples and then subtract this from the total weight to get the weight of pears.
Step 1: Calculate the weight of apples by multiplying the total weight by the fraction that represents apples. This is 2/5 of 9.1 kg.
Step 2: Subtract the weight of the apples from the total weight to find the weight of pears.
Here are the calculations:
Weight of apples = (2/5) × 9.1 kg = 3.64 kg
Weight of pears = Total weight - Weight of apples = 9.1 kg - 3.64 kg = 5.46 kg
Therefore, the farmer sold 5.46 kilograms of pears at the farmer's market.
Find the area of a circle with a diameter of \color{green}{16}16start color green, 16, end color green.
Answer:
if you can write a comment so that makes sense, i might be able to help you
Step-by-step explanation:
sorry
Answer:
The answer is 64pi
Step-by-step explanation:
Barry needs to find the area of a rectangular room with a length that is 2 feet longer than the width. Write an expression for the area of the rectangle in terms of the width.
Final answer:
The area of the rectangular room with length 2 feet longer than the width can be expressed as w^2 + 2w square feet, where w represents the width of the room.
Explanation:
Barry needs to calculate the area of a rectangular room where the length is 2 feet longer than the width. If we denote the width as w, then the length will be w + 2 feet. The area of a rectangle is found by multiplying the length by the width.
Therefore, the expression for the area in terms of the width will be:
Area = width × length
Area = w × (w + 2 feet)
Area = w² + 2w square feet
This expression will give us the area of the rectangle in square feet.
In 24 games, Jaime has 48 scoring attempts. Which unit rate describes Jaime’s scoring attempts?
a. 1/2 a scoring attempt per game
b. 2 scoring attempts per game
c. 24 scoring attempts per game
d. 72 scoring attempts per game
Answer:
2 Scoring Attempts
Step-by-step explanation:
There are 48 attempts divided by 24 game which equals 2.
Answer:
it is b
Step-by-step explanation:
India joining figured PNP be intelligent trumpet with circle with Center see if angle APB is going to 40 degree then find angle ACB
Step-by-step explanation:
40° + 90° + 90° + angle ACB = 360°
220° + angle ACB = 360°
angle ACB = 360° - 220°
Therefore angle ACB = 140°
Hope it will help :))
Combine the like terms
Answer: -4
Step-by-step explanation:
[tex]3x-7x=x\\-4x=-4x[/tex]
Answer:
The answer is -4x.
Step-by-step explanation:
You can just substract easily by writing 7-3 but remember to add negative to the final value as 3 is smaller than 7 and lastly, you only have to add x to the final answer.
If you punch a wall with a force of 30 N, what force will you feel in your fist??
Answer:
30N
Step-by-step explanation:
Normal reaction
The force feel by fist is 30N.
What is Force?
A Force is a push or pull upon an object resulting from the object's interaction with another object.
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.
Since you punch a wall with a force of 30N, the fist will feel the same force in the opposite direction as per the Newton's Third Law of Motion.
Hence The force feel by fist is 30N.
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find the area of the circle. round your answer to the nearest hundredths. the diameter is 2cm
Answer:
3.14 cm squared
Step-by-step explanation:
First, identify the formula necessary to calculate the area of the circle.
Area of a circle = pi x r^2
Remember, the radius is just half of the diameter! Then to square a number, is to multiply it by itself once.
pi x 1^2 =?
pi x 1
Pi
The circumference of your circle is approximately 3.14 cm squared.
Find the solutions/ show steps
Sin2x+sin(4x) =0
Answer:
x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3
Step-by-step explanation:
sin(2x) + sin(4x) = 0
Use double angle formula.
sin(2x) + 2 sin(2x) cos(2x) = 0
Factor.
sin(2x) (1 + 2 cos(2x)) = 0
Solve.
sin(2x) = 0, cos(2x) = -½
2x = 0, 2π/3, π, 4π/3, 2π, 8π/3, 3π, 10π/3
x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3
The Drama Club is showing a video of their recent play. The first showing begins at 3:45 p.M. The second showing is scheduled at 6:25 p.M. With a 1 2 −hour break between the showings. How long is the video in hours and minutes? Pt. 2 The second showing started 20 minutes late. Will the second showing be over by 8:45 p.M.?
Answer:
the movie is 2 hours and 10 min long
no it will not be over by 8:45pm
Step-by-step explanation:
if the movie begins at 3:45 pm and the next begins at 6:25pm with a half hour break you need to take 30 min from 6:25 to see what time the movie ended which is 5:55pm then you figure the time between 3:45pm and 5:55pm which is 2hours and 10 min.
since thw movie is starting 20 min late from 6:25pm that is now a start time of 6:45pm if the movie is 2hours and 10 min it will not be over by 8:45pm since that is only 2 hours
A rectangular red sticker is 8 millimeters wide and 5 millimeters tall. What is it’s area
Answer:
40 milimeters
Step-by-step explanation:
8*5=40
7 t-shirts cost £67.55. How much do 11 t-shirts cost?
Answer:
11 tshirts would cost £106.15
Step-by-step explanation:
67.55 divided by 7 = 9.65
9.65 x 11 = 106.15
Therefore the total would be £106.15.
Answer: 106.15
Step-by-step explanation:
Which of these pieces of data about a football team is considered numerical data?
Answer:
1. Points scored
Step-by-step explanation:
A numerical data is defined as a data that is made up of numbers representing the quantity of a measurement. It is a measurable data such as weight or height, at it can be arranged in ascending or descending order as well as being able to provide an average.
The two types of numeric data are discrete and continuous data
A categorical data is made up of item labels, names or description, that are qualitative in their nature.
Information about a football team that is considered as numeric includes
1. Points scored
Which represents a quantifiable measurement that can be different with different teams and matches
2. Attendance this year.
The 22 members of a baseball team are trying to raise at least $1968.00 to cover the traveling cost for a holiday tournament. If they have already raised $421.00, at least how much should each member still raise, on average, to meet the goal
About $70.31.
You would take $1968.00 and subtract $421.00 from it. Once you've subtracted, you would have gotten $1547.00. You would divide $1547.00 by the 22 people and get about $70.31 per person. :)
ABC is a triangle.
work out angle x. give your answer to 3 significant figures.
Answer:
x = 50.5°
Step-by-step explanation:
∠ BDC and ∠ BDA are adjacent and supplementary, thus
∠ BDC = 180° - 78° = 102°
Calculate ∠ BCD using the Sine rule in Δ ABC, that is
[tex]\frac{5.6}{sinC}[/tex] = [tex]\frac{9.3}{sin50}[/tex] ( cross- multiply )
9.3 × sinC = 5.6 × sin50° ( divide both sides by 9.3 )
sinC = [tex]\frac{5.6sin50}{9.3}[/tex] ≈ 0.4613, thus
C = [tex]sin^{-1}[/tex] (0.4613 ) ≈ 27.5°
The sum of the 3 angles in Δ BCD = 180°, thus
x = 180° - (102 + 27.5)° = 180° - 129.5° = 50.5°
The angle x is also 52 degrees.
To find the measure of angle x in triangle ABC, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Given that angle A is 78 degrees and angle B is 50 degrees, we can find angle C using the following equation:
Angle C + Angle B + Angle A = 180 degrees
Angle C + 50 degrees + 78 degrees = 180 degrees
Now, subtract the known angles from 180 degrees to find the measure of angle C:
Angle C = 180 degrees - (50 degrees + 78 degrees)
Angle C = 180 degrees - 128 degrees
Angle C = 52 degrees
Now that we know angle C is 52 degrees, we can use the fact that the angles in a triangle add up to 180 degrees to find angle x:
Angle A + Angle B + Angle x = 180 degrees
78 degrees + 50 degrees + Angle x = 180 degrees
Now, subtract the known angles from 180 degrees to find angle x:
Angle x = 180 degrees - (78 degrees + 50 degrees)
Angle x = 180 degrees - 128 degrees
Angle x = 52 degrees
So, angle x is also 52 degrees.
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In order for you to answer the question correctly, please use the following image below:
Find the value of x.
X=(blank)
What is the value of X?
Please show all the work on how you got your answer. (Note- If you are unable to explain your work then it's completely fine. The only thing that I'm asking for is for you to show all the work so I can understand how you got your answer)
Answer:
The value of x is 16°
Step-by-step explanation:
Using the formula, angle = 1/2(θ°-x°) :
Let θ = 96°, x = x°, angle = 40°,
1/2×(96°-x°) = 40°
96° - x° = 80°
-x° = 80° - 96°
-x° = -16°
x = 16°
erin ran 7 1/2 miles around the track. Each lap is 1 1/2 miles. How many laps did Erin run
Answer:
She ran 5 laps
Step-by-step explanation:
Why? Because with each lap stating to be one and a half miles; you first and only step is to divide, seeing how each time you put 1 1/2 into the value of this 7 1/2 miles, you got a lap each time.
you divide 7 1/2 by 1 1/2,
this results in getting, 5
Answer: Erin ran 5 laps.
Step-by-step explanation
if he ran 7 1/2 miles and one lap is 1 1/2 miles then you need to add 1 1/2 miles up until you get the distance he ran which is 7 1/2 miles and when u keep adding 1 1/2 miles to get to 7 1/2 you get 5 laps. hope this helps :)
el Bowen borrowed $10,000 for 3 years
13.75% rate of interest. Find the simple
interest.
Answer:$4125
Step-by-step explanation:
Using the I = P x R x T formula, we can find the simple interest. Substitute all the values into this equation and you get : I = 10,000 x 13.75 x 3. Once you multiply all the values, $4125 is the answer you get. :)
A company knows that unit cost C and unit revenue R from the production and sale of x units are related by Upper C equals StartFraction Upper R squared Over 220 comma 000 EndFraction plus 3221.C= R2 220,000+3221. Find the rate of change of revenue per unit when the cost per unit is changing by $ 9$9 and the revenue is $1 comma 0001,000.
Answer:
$990 per unit.
Step-by-step explanation:
The Unit Cost (C) and Unit Revenue R from the production and sale of x units are related by the function:
[tex]C=\dfrac{R^2}{220000} +3221[/tex]
We are required to find the rate of change of revenue per unit when the cost per unit is changing by $9 and the revenue is $1,000.
Rate of Change of C,
[tex]\dfrac{dC}{dt}=\dfrac{R}{110000} \dfrac{dR}{dt} \\\dfrac{dC}{dt}=\$9, R=\$1000\\9=\dfrac{1000}{110000} \dfrac{dR}{dt}\\\dfrac{dR}{dt}=9 \div \dfrac{1000}{110000}\\=9 X \dfrac{110000}{1000}\\\dfrac{dR}{dt}=\$990 $ per unit$[/tex]
The Revenue is changing at a rate of $990 per unit.
The problem is solved by first finding the derivative of the given equation to determine the rate of change. Given that the cost per unit is changing by $9, we substitute this in the derivative equation to get the revenue. Real-world applications of such problems help understand the concepts of marginal revenue and marginal cost.
Explanation:As per the equation C = R2/220000 + 3221, we first need to find the derivative to determine the rate of change. So, C'(R) = 2R/220000 where C' represents the derivative of the cost with respect to revenue.
Given that the cost per unit is changing by $9, we can represent this as C' = 9 and solve for R using the derivative equation. Hence, R = sqrt(220000 * 9 / 2) = $1000. Therefore, the rate of change of revenue per unit when the cost per unit is changing by $9 and the revenue is $1,000 is found by substituting the revenue value into derivative equation.
These types of problems demonstrate how rates of change can be evaluated using calculus concepts in real-world applications such as understanding marginal revenue and marginal cost in economics and business studies.
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Find all degree solutions in the interval 0° ≤ θ < 360°. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify the solution graphically. (Enter your answers as a comma-separated list.) 5 sin2 θ − 9 cos 2θ = 03
Answer:
[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]
[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]
[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]
[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]
Step-by-step explanation:
The equation needs to be rearranged in terms of one trigonometric function:
[tex]5\cdot \sin 2\theta - 9\cdot \cos 2\theta = 0[/tex]
[tex]5\cdot \tan 2\theta - 9 = 0[/tex]
[tex]5\cdot \tan 2\theta = 9[/tex]
[tex]\tan 2\theta = \frac{9}{5}[/tex]
[tex]\theta = \frac{1}{2}\cdot \tan^{-1} \left(\frac{9}{5} \right)[/tex]
The tangent function has positive values in the 1st and 3rd Quadrants. Then, the solutions are:
[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]
[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]
[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]
[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]
Suppose that 17 inches of wire costs 85 cents.
At the same rate, how much (in cents) will 39 inches of wire cost?
Answer:
195¢
Step-by-step explanation:
1 inch of the wire costs
[tex]\frac{85}{17}[/tex] cents
So we just multiply by 39 to get the total cost.
[tex]\frac{85}{17} * 39 = 195[/tex]
Answer: 195 cents
Explanation:
17 inches cost 85 cent
Means 1-inch will cost 85/17 = 5 cents
At the same rate 39 inches will cost 39×5= 195 cents
an
Diego and Lin are drinking milkshakes. Lin starts with 12 ounces and drinks
ounce per second. Diego starts with 20 ounces and drinks.How long will it take lin and Diego to finish their milkshakes?
It will take Lin 12 seconds to finish her milkshake. The time it takes Diego to finish his milkshake cannot be determined without the rate at which he drinks.
Explanation:The problem is about how long it will take for Diego and Lin to finish their milkshakes. Lin is drinking her milkshake at a rate of 1 ounce per second and began with a total of 12 ounces. Therefore, it will take her 12 seconds to finish. For Diego, it doesn't specify how quickly he is drinking his milkshake, which began with 20 ounces, it is impossible to calculate how long it would take him to finish his drink without this information. Hence, to fully solve this problem, you need additional rate information for Diego.
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A bag contains 5 red marbles, 3 green marbles, 2 purple marbles, 2 orange marbles, and 1 blue marble.
Which color marble is less likely to be picked than purple?
Answer:
blue marble is the right answer
If a fair die is rolled 4 times, what is the probability, to the
nearest thousandth, of getting exactly o threes?
The probability of not getting a '3' when a fair die is rolled four times, rounded to the nearest thousandth, is approximately 0.482.
Explanation:In a fair die, the probability of getting any one number, such as a 3, is 1/6 because a die has 6 possible outcomes (1 through 6). So, the probability of not getting a 3 is 5/6. If the die is rolled four times, the probability of not getting a 3 on each roll is (5/6)^4. To find this, multiply 5/6 by itself 4 times. The result is approximately 0.482, or rounded to the nearest thousandth, 0.482. So, "the probability of not getting a 3 on four rolls of a die to the nearest thousandth is 0.482."
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CONGRATS! Your parents bought you a car for graduation. They paid $9000 for it. The bad news is that it depreciates at 12% per year. Write a function to represent the value of the car versus time
Answer:
If the price before depretiation be P and price after depreciation be Pt..
The eqn would be,
Pt=P(1-12/100)^t
Hope it helps!!
Final answer:
The function to represent the value of a car over time, with an initial value of $9000 and depreciating at 12% per year, is V = 9000(1 - 0.12)^t. This exponential decay function calculates the car's value at any time t years after purchase.
Explanation:
The question asks for a function to represent the value of a car over time, given that the car was purchased for $9000 and depreciates at a rate of 12% per year. To model this, we can use an exponential decay function. The general form of an exponential decay function is V = P(1 - r)^t, where V represents the value of the car at time t, P is the initial purchase price, r is the rate of depreciation, and t is the time in years.
Substituting the given values into the formula, we get V = 9000(1 - 0.12)^t. This function can be used to calculate the value of the car at any given time t years after the purchase. The rate of depreciation (12%) and the initial purchase price ($9000) are the critical factors that determine the car's value over time.
Rico does not work for Street Bikes Company,but wrongfully obtains inside information concerning the firm.Based on the information,Rico buys and sells Street Bikes stock for personal gain.The Securities and Exchange Commission prosecutes Rico,arguing that he is liable because he stole information rightfully belonging to another.This argument is:_________.
A) the blue-sky theory.
B) the misappropriation theory.
C) the free-writing prospectus theory.
D) the tipper/tippee theory.
Answer:
B) The misappropriation theory
Step-by-step explanation:
The misappropriation theory states that a person who uses insider information in trading securities has committed securities fraud against the information source.
In this case, Street Bikes Company is the information source because the information rightfully belong to them, Rico trades Street Bikes Stocks because he stole the firm's information which does not belong to him, according to the misappropriation theory, Rico is liable to the offence of insider trading.