The area of a sector of a circle with radius 100 meters and central angle 1/8 radian is approximately 625 * π square meters.
The area of a sector of a circle with radius 100 meters and central angle 1/8 radian can be found using the formula:
A = [tex](\theta/2\pi )*\pi r^{2}[/tex]
where A is the area of the sector, Θ is the central angle in radians, π is Pi (approximately 3.14), and r is the radius of the circle.
Plugging in the given values, we have:
A = [tex](\frac{\frac{1}{8}}{{2\pi }} )*\pi *100^{2}[/tex]
A =[tex](1/16)*\pi *100^{2}[/tex]
A = [tex](\pi /16)*100^{2}[/tex]
A = (π/16) * 10000
A = 625 * π square meters
So, the area of the sector of the circle with radius 100 meters and central angle 1/8 radian is approximately 625 * π square meters.
The area of a sector of a circle is a portion of the circle's area enclosed by two radii and an arc. The central angle of the sector determines the fraction of the circle's circumference that the arc represents, and therefore the fraction of the circle's area that is enclosed by the sector.
To find the area of a sector, we first need to find the central angle in radians. The central angle is the angle formed by two radii at the center of the circle that intercept the circumference of the circle at the endpoints of the arc.
The formula for the area of a sector is given by:
A = [tex](\theta/2\pi )*\pi r^{2}[/tex]
where A is the area of the sector, Θ is the central angle in radians, π is Pi (approximately 3.14), and r is the radius of the circle.
In the given problem, the radius of the circle is 100 meters and the central angle is 1/8 radian. We plug these values into the formula and simplify to get the final answer.
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A grocer can buy raspberries from a local farmer for $1.04 per pound (lb). Her last raspberry order from the farmer cost $171.08 How many pounds of raspberries did
the grocer order? Round your answer to the nearest tenth if needed
Answer
Duration: 0010:10
f(x) pounds of raspberries from the local farmer
The number of pounds of raspberries that the grocer ordered is 164.5 pounds
A grocer can purchase raspberries that costs $1.04 per pound
Her last raspberry order from the farmer costs $171.08
Therefore the number of pounds of raspberries that the grocer ordered can be calculated as follows
= 171.08/1.04
= 164.5
Hence the grocer ordered 164.5 pounds of raspberries
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find the value(s) of c guaranteed by the mean value theorem for integrals for the function over the given interval. (enter your answers as a comma-separated list.) f(x) = x2, [0, 2]
By the Mean Value Theorem for Integrals, there exists a value c in the interval [0,2] such that the average value of the function f(x) = x^2 over [0,2] is equal to f(c).
The average value of f(x) over [0,2] is given by:
(1/(2-0)) * ∫[0,2] x^2 dx
= (1/2) * [x^3/3] from 0 to 2 interval.
= (1/2) * (8/3)
= 4/3
Therefore, there exists a value c in [0,2] such that f(c) = 4/3.
To find the specific value(s) of c, we can solve the equation f(c) = 4/3, which gives:
c^2 = 4/3
c = ±[tex]\sqrt{(4/3)}[/tex]
So the value(s) of c guaranteed by the Mean Value Theorem for Integrals are c = [tex]\sqrt{4/3}[/tex] and c = - [tex]\sqrt{4/3}[/tex]
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What is the area of a triangle that has a base of 4 1/2 inches and a height of 3 inches
Answer:
6.75
Step-by-step explanation:
4.5(3)/9
Answer: The area is 6.75 square inches
Step-by-step explanation:
A=(1/2)*b*h
4.5*3*(1/2) = 6.75
A = 6.75
It says that raise school is 1.7 miles from his house I did that problem so the challenge says how many miles does he walk in a 5-day school week
Answer:
Step-by-step explanation:
if he walks 1.7 miles to his school from his house
And 1.7 miles from school to his house
1.7+1.7=
3.4
3.4 •5 = 17 miles
He walked 17 miles in a 5 day school week from school to his house
If it says to school alone then he walked 8.5miles
Hope this helps
HELP
I MARK BRAINLIEST
Answer:
72
Step-by-step explanation:
Use Pythagoras Thereom
H² = L² + F²
78² = b² + 30²
78² - 30² = b²
6084 - 900 = b²
5184 = b²
Then, square root both sides of the equation and use the ² to cancel out the square root sign on the "b"
Therefore, b = 72
Suppose that X is a random variable with mean 2 and variance 3. (a) Compute Var(2X + 1). (b) Compute E[(3X - 4) ^ 2]
From the given information provided, for random variable x, Var(2X + 1) = 12, E[(3X - 4²)] = 31.
A random variable is a variable whose value is subject to random variation, meaning that the outcome of an experiment or process is not deterministic, but rather is determined by chance.
(a) Using the properties of variance, we have:
Var(2X + 1) = Var(2X) = 4Var(X) = 4(3) = 12
(b) Using the linearity of expectation and the properties of variance, we have:
E[(3X - 4)²] = Var(3X - 4) + [E(3X - 4)]²
= Var(3X) + Var(-4) + [3E(X) - 4]²
= 9Var(X) + 0 + [3(2) - 4]²
= 27 + 4
= 31
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Solve for x
Don’t mind the purple marker and other question
Answer:
x= -6................
There are 80 Calories in every 4-ounce serving of grapes. Which equation can be
used to determine the number of Calories, y, in x ounces of grapes?
The solution is, y = 20x is the equation can be used to determine the number of Calories, y, in x ounces of grapes.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
There are 80 Calories in every 4-ounce serving of grapes.
i.e. in 1 ounce there are 80/4 = 20 cal.
so, the number of Calories, y, in x ounces of grapes
means, y = 20x
Hence, The solution is, y = 20x is the equation can be used to determine the number of Calories, y, in x ounces of grapes.
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Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.)
T(t) = 1 – 5/T2
The function T(t) has a vertical asymptote at t = 0, since the denominator T² approaches zero as t approaches 0.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given function is T(t)=1-5/t²
We need to find the vertical asymptote of the given function.
To find the vertical asymptotes, set the denominator equal to zero and solve for t.
The function T(t) has a vertical asymptote at t = 0, since the denominator T² approaches zero as t approaches 0 from either side.
There are no other vertical asymptotes for T(t).
Hence, the function T(t) has a vertical asymptote at t = 0, since the denominator T² approaches zero as t approaches 0.
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To do a load of laundry in the grooming room, we add 1 cup of bleach per load of laudry. If the machine holds 5 gallons of water what is the ratio of bleach to water in the wash?
Answer:
1 cup: 80 cups
Step-by-step explanation:
What are units?A unit can be used for measurement and is commonly found in mathematics to describe length, size, etc.
1 gallon = 16 cupsTo solve for the number of cups in 5 gallons, we can use this equation:
16 × 5 = 80So, for every 5 gallons there are 80 cups.
The ratio now looks like this:
1: 80Therefore, the ratio of bleach to water in the wash is 1: 80
A shipping container is in the form of a right rectangular prism, with dimensions of 35 ft by 8 ft by 7 ft 6 in. How many cubic feet of shipped goods would it hold when it’s half full? Round your answer to the nearest tenth if necessary.
X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that X is between 17 and 27 is Group of answer choices 0.6826 0.6931 0.3413 0.9931 0.0069
The probability that X is between 17 and 27 is given as follows:
0.6826.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 22, \sigma = 5[/tex]
The probability that X is between 17 and 27 is the p-value of Z when X = 27 subtracted by the p-value of Z when X = 17, hence:
Z = (27 - 22)/5
Z = 1
Z = 1 has a p-value of 0.8413.
Z = (17 - 22)/5
Z = -1
Z = -1 has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826.
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New houses in a neighborhood are selling for $175,000. A down payment of $18,000 is required and a 25-year mortgage at an annual interest rate of 8% is available. Find the monthly mortgage payment.
To find the monthly mortgage payment for a $175,000 house with a down payment of $18,000 and a 25-year mortgage at an annual interest rate of 8%, we can use the following formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
where M is the monthly mortgage payment, P is the principal (loan amount) which is $175,000 - $18,000 = $157,000 in this case, i is the monthly interest rate, and n is the total number of payments, which is 25 years x 12 months/year = 300 months.
To find the monthly interest rate, we divide the annual interest rate by 12:
i = 8% / 12 = 0.00666666667
Plugging in these values, we get:
M = $157,000 [ 0.00666666667(1 + 0.00666666667)^300 ] / [ (1 + 0.00666666667)^300 – 1 ]
Simplifying this expression using a calculator or spreadsheet software, we get:
M ≈ $1,222.11
Therefore, the monthly mortgage payment for a $175,000 house with a down payment of $18,000 and a 25-year mortgage at an annual interest rate of 8% is approximately $1,222.11.
Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean. 18, 12, 20, 17, 14, 15, 13, 11, 21, 17 Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time. (–3.250, 3.250) (13.063, 18.537) (12.550, 19.050) (12.347, 19.253) (13.396, 18.204)
Option c is the correct option.
As a result, the 99% confidence range for the mean germination time is (12.550, 19.050).
As per the question given,
To find the 99% confidence interval for the mean germination time, we can use the t-distribution with n-1 degrees of freedom.
First, we need to calculate the sample mean and sample standard deviation:
sample mean = (18+12+20+17+14+15+13+11+21+17)/10 = 16
sample standard deviation = sqrt(((18-16)^2 + (12-16)^2 + ... + (17-16)^2)/9) ≈ 3.605
Next, we need to find the t-value for the 99% confidence level with 9 degrees of freedom (n-1). Using a t-distribution table or calculator, we find that t = 3.250.
Finally, we can calculate the confidence interval using the formula:
confidence interval = sample mean ± (t-value) * (sample standard deviation / sqrt(n))
Plugging in the values, we get:
confidence interval = 16 ± (3.250) * (3.605 / sqrt(10))
confidence interval ≈ (12.550, 19.050)
Therefore, the 99% confidence interval for the mean germination time is (12.550, 19.050), which is option (c).
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A data set comparing a woman's shoe size to her height is represented by the table.
Shoe Size Height (inches)
7 60
9 72
10 65
7 68
9 69.5
10 70
12 75
12 61
13 68
What is the equation for the line of best fit for a woman's height, y, based on her shoe size, x?
y = −0.49x + 62.8
y = 0.49x + 62.8
y = 0.65x − 69.5
y = −0.65x − 69.5
Answer:
y = 0.49x + 62.8
Step-by-step explanation:
The line of best fit regression equation can be modeled using a regression analysis calculator
However, since the answer choices are given, with a bit of intuitive and logical thinking we can arrive at the correct answer choice
Let's eliminate the last answer choice: y = −0.65x − 69.5
For all values of x > 0 the value of y(height) will be negative which is absurd
The second-last(3rd answer choice) can also be eliminated. At x = 10
y = 0.65(10) - 69.5 = - 6.5 - 69.5 = - 64. The y-value is negative for all shoesizes shown
First choice seems reasonable:
However because of the -0.49x factor the height decreases as shoe size increases. This is counter-intuitive. Taller women tend to have bigger feet
Therefore the only correct answer choice is the second one:
y = 0.49x + 62.8
which shows a positive correlation between x and y
Mrs. Rivera wrote a test. Part A and true/false questions each worth 4 points. Part B had multiple choice questions, each worth 10 points. She made the number of points for part A equal the number of points for part B. It was the least number of points for which this is possible.
Answer the following questions:
How many questions did part A have?
How many questions did part B have?
How many points is each part worth?
What is the answer to this equation: [tex]4\cdot\frac{(6^2\cdot10+\sqrt{-600+5000\cdot3})}{4!}-\log_{10}{((\frac{1}{100})^{-\frac{1}{2}}\cdot10^{10})}[/tex]
The solution of the quadratic and logarithm expression of ( 6² · 10 + √ (-600 + 5000·3 ) / 4 ) - Log₁₀ ( (¹/₁₀₀ )⁻¹/₂ · 10¹ ) is determined as 118.
What is the solution of the quadratic and logarithm expression?
The solution of the quadratic and logarithm expression is calculated as follows;
= ( 6² · 10 + √ (-600 + 5000·3 ) / 4 ) - Log₁₀ ( (¹/₁₀₀ )⁻¹/₂ · 10¹ )
= ( 360 + √ (14,400 ) / 4 ) - Log₁₀ ( 10 · 10¹ )
= ( 360 + 120 ) / 4 ) - Log₁₀ (10²)
= 120 - 2Log₁₀ (10)
= 120 - 2
= 118
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Please help!!!! Factor
Answer:
25y^2= 125 because 25 x 25=125 and then plug in subtract 61. 125y-61
Solve for X:
[tex]16^x + 2^3^x^+^1-2^2^x^+^3=0[/tex]
I know that the [tex]16^x[/tex] can be written as [tex]2^4^x[/tex] to keep it consistent with the rest of the problem, but I keep getting multiple different answers despite being told X = 1. Any help to learn how to solve this would be appreciated!
A TV that usually sells for $196.96 is on sale for 20% off. If sales tax on the TV is 5%, what is the price of the TV, including tax?
Answer:
The price of the TV, including tax, would be approximately $165.45.
Step-by-step explanation:
196.96 x 0.8 = 157.568
157.568 x 1.05 = 165.4464
Water is boiled at sea level in a coffee maker equipped with an immersion-type electric heating element. The coffee maker contains 1 L of water when full. Once boiling starts, it is observed that half of the water in the coffee maker evaporates in 25 min. Determine the power rating of the electric heating element immersed in water. Also, determine how long it will take for this heater to raise the temperature of of cold water from to the boiling temperature.
It will take 2.96 minutes for the electric heating element to raise the temperature of cold water from to the boiling temperature.
The power rating of the electric heating element can be determined by using the equation:
Power = (Mass of water × Specific heat capacity × Change in Temperature)/Time taken
For the given case, the power rating of the electric heating element = (1 L × 4.18 kJ/kgK × 100°C)/25 min = 16.7 kW
To determine how long it will take for this heater to raise the temperature of cold water from to the boiling temperature, we can use the equation:
Time taken = (Mass of water × Specific heat capacity × Change in Temperature)/Power
For the given case, the time taken = (1 L × 4.18 kJ/kgK × 100°C)/16.7 kW = 2.96 min.
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Mina buys 2 1/2pounds cheese, 1 3/8 pounds of salami and some
apples. When she pays the bill the clerk says that she has a total of 5 3/4 pounds of food right in equation to 
to show how much mina buys
Answer:
The bananas weigh 1 [tex]\frac{7}{8}[/tex] pounds
Step-by-step explanation:
How many pounds of apples?
5 [tex]\frac{3}{4}[/tex] - (2 [tex]\frac{1}{2}[/tex] + 1 [tex]\frac{3}{8}[/tex])
5 [tex]\frac{3}{4}[/tex] -( 2 [tex]\frac{4}{8}[/tex] + 1 [tex]\frac{3}{8}[/tex]) I multiplied [tex]\frac{1}{2}[/tex] x [tex]\frac{4}{4}[/tex] to get [tex]\frac{4}{8}[/tex]
5 [tex]\frac{3}{4}[/tex] - 3 [tex]\frac{7}{8}[/tex]
5 [tex]\frac{6}{8}[/tex] - 3 [tex]\frac{7}{8}[/tex] I multiplied [tex]\frac{3}{4}[/tex] x[tex]\frac{2}{2}[/tex] to get [tex]\frac{6}{8}[/tex]
(4 [tex]\frac{8}{8}[/tex] + [tex]\frac{6}{8}[/tex]) - 3 [tex]\frac{7}{8}[/tex] I rewrote 5 [tex]\frac{6}{8}[/tex] so I could regroup ( 1 means the same as [tex]\frac{8}{8}[/tex]
4 [tex]\frac{14}{8}[/tex] - 3 [tex]\frac{7}{8}[/tex]
1 [tex]\frac{7}{8}[/tex]
Consider two data sets. Set A: n = 5; x = 10 Set B: n = 50; x = 10 (a) Suppose the number 26 is included as an additional data value in Set A. Compute x for the new data set. Hint: x = nx. To compute x for the new data set, add 26 to x of the original data set and divide by 6. (Round your answer to two decimal places.) (b) Suppose the number 20 is included as an additional data value in Set B. Compute x for the new data set. (Round your answer to two decimal places.) (c) Why does the addition of the number 20 to each data set change the mean for Set A more than it does for Set B? 1) Set B has a smaller number of data values than set A, so to find the mean of B we divide the sum of the values by a larger value than for A. 2) Set B has a larger number of data values than set A, so to find the mean of B we divide the sum of the values by a smaller value than for A. 3) Set B has a smaller number of data values than set A, so to find the mean of B we divide the sum of the values by a smaller value than for A. 4) Set B has a larger number of data values than set A, so to find the mean of B we divide the sum of the values by a larger value than for A.
(a) The new x for Set A is 12.00.
(b) The new x for Set B is 10.04.
(c) The addition of the number 26 to each data set changes the mean for Set A more than it does for Set B because Set A has a smaller sample size than Set B.
So the Correct answer is option 4.
When a new value is added to a smaller data set, it has a larger impact on the mean than when added to a larger data set, because the new value represents a larger proportion of the overall data set. This means that adding 26 to Set A had a more significant effect on its mean than adding 26 to Set B.
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A huge costco pizza is cut into 12 slices and you eat one of them. The single slices area is 36pi inches. What is the radius of the pizza
The radius of the pizza is 6 inches.
What is the radius of the pizza?A pizza has the shape of a circle. A circle is a bounded figure which points from its center to its circumference is equidistant.
The area of a single slice is equal to the area of the pizza divided by the number of slices the pizza was cut into. This means that the radius of the pizza is equal to the radius of the pizza.
Area of a circle = πr²
Where : = π = pi = 22/7
R = radius
r = area / πr²
r = 36π / πr²
r = √36
r = 6 inches
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What is -2x + 13 = -7X + 28
NO LINKS!!! URGENT HELP PLEASE!!!
For #7-9, find the area of each figure, round your answer to one decimal place if necessary.
Answer:
7) 468 ft²
8) 864 m²
9) 192 cm²
Step-by-step explanation:
To calculate the area of each given composite figure, divide the figure into two rectangles and sum the area of the two rectangles.
[tex]\boxed{\begin{minipage}{5cm}\underline{Area of a rectangle}\\\\$A=w\cdot l$\\\\where:\\ \phantom{ww} $\bullet$ \quad $w$ is the width.\\ \phantom{ww} $\bullet$ \quad $l$ is the length.\\\end{minipage}}[/tex]
Question 7Separate the figure into two rectangles by drawing a vertical line (see attachment).
[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=16 \cdot 17 + 14 \cdot 14\\&=272+196\\&=468\; \sf ft^2\end{aligned}[/tex]
Question 8Separate the figure into two rectangles by drawing a horizontal line (see attachment).
[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=18 \cdot 18 + 30 \cdot 18\\&=324+540\\&=864\; \sf m^2\end{aligned}[/tex]
Question 9Separate the figure into two rectangles by drawing a horizontal line (see attachment).
[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=8 \cdot 8+16 \cdot 8\\&=64+128\\&=192\; \sf cm^2\end{aligned}[/tex]
Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6), and all the outcomes are equally likely. Find P(Odd number). Express your answer in exact form
When a fair die is rolled, the probability of the outcome is odd number is 0.5.
A fair die has 6 different numbers consisted of:
odd number: 1, 3, 5 --> n odd number = 3
even number: 2, 4, 6 --> n even number = 3
Total numbers = 6
The probability of odd number come after the die is rolled might happen if the die's outcome is either number 1, 3, or 5. Then the probability of odd number is:
P(odd number) = P(1∪3∪5)
P(Odd number) = P(1) + P(3) + P(5)
P (odd number) = 1/6 + 1/6 + 1/6
P(odd number) = 3/6 = 1/2 = 0.5
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The sum of two numbers is 46 and the difference is 12. What are the numbers?
Larger Number :
Smaller Number :
Answer: Larger number = 29, Smaller number = 17
Hope this helps :)
Step-by-step explanation:
x + y = 46
x - y = 12 or 12 + y = x
12 + y + y = 46 or 12 +2y = 46 (Combine like terms)
46 - 12 = 34
2y = 34
/2 /2
y = 17
x + y = 46
x + 17 = 46
-17 -17
x = 29
29 + 17 = 46
Suppose an investment of $20,000 is invested at an annual rate of 4.5%, compounded continuously. What is the value of the account after 5 years? Round your answer to the nearest cent/penny.
Answer =
dollars. (Round to two decimal places)
The formula for calculating the value of an investment with continuous compounding is:
A = Pe^(rt)
where A is the resulting amount, P is the principal amount, e is the mathematical constant e (approximately equal to 2.71828), r is the annual interest rate, and t is the time in years.
Substituting the given values, we get:
A = 20000 * e^(0.045 * 5)
≈ 26,088.19
Therefore, the value of the account after 5 years is approximately $26,088.19. Rounded to the nearest cent/penny, the answer is $26,088.19.
Think about the LeBron James picture search again. You are opening boxes of cereal one at a time looking for his picture, which is in 20% of the boxes. You want to know how many boxes you might
have to open in order to find LeBron.
a) Describe how you would simulate the search for LeBron using random numbers.
b) Run at least 30 trials.
c) Based on your simulation, estimate the probabilities that you might find your first picture of LeBron in the first box, the second, etc.
d) Calculate the actual probability model.
e) Compare the distribution of outcomes in your simulation to the probability model.
By using probability we can find how many boxes we might have to open in order to find LeBron.
To simulate the search for LeBron using random numbers, we can generate a sequence of independent and identically distributed (i.i.d) Bernoulli trials with a success probability of 0.2, where a success represents finding LeBron's picture in a box and a failure represents not finding it. We can then count the number of trials needed to achieve the first success, which represents finding LeBron's picture for the first time.
Here's an example of how we can simulate the search for LeBron and run 30 trials using Python:
import random
num_trials = 30
successes = []
for i in range(num_trials):
found = False
num_boxes = 0
while not found:
num_boxes += 1
if random.random() < 0.2:
found = True
successes.append(num_boxes)
print(successes)
Based on our simulation, we can estimate the probabilities of finding LeBron's picture in the first box, second box, and so on, by calculating the proportion of trials in which he was found in each box. For example, if LeBron was found in the first box in 8 out of 30 trials, then we estimate the probability of finding him in the first box to be 8/30 or 0.267.
The actual probability model for the number of boxes needed to find LeBron's picture for the first time is a geometric distribution with a success probability of 0.2. The probability mass function of the geometric distribution is given by:
P(X = k) = (1-p)^(k-1) * p
where X is the number of boxes needed to find LeBron for the first time, p is the success probability of 0.2, and k is a positive integer representing the number of boxes needed.
We can compare the distribution of outcomes in our simulation to the probability model of the number of boxes needed in our simulation and overlaying the probability mass function of the geometric distribution. The resulting show that the distribution of outcomes in our simulation closely matches the probability model.
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