You are wanting to simulate tossing a coin 20 times to determine the probability of getting tails. Starting with the first row, you use the list of random numbers shown to do so, letting 0-4 represent heads and 5-9 represent tails. What is the probability the coin lands on tails?
Answers
When you flip a fair coin, there is always a 50% chance of heads, and a 50% chance of tails. Not sure the rest of info is relevant here
Final answer:
Simulated coin tossing uses random numbers, where 0-4 and 5-9 represent heads and tails respectively. The theoretical probability of getting tails is 0.5, but empirical probabilities can differ. This discrepancy, assumed to reduce with more trials, is accounted for by the Law of Large Numbers.
Explanation:
In the context of the provided problem, you are attempting to simulate tossing a coin 20 times using a system of random numbers, where you've assigned 0-4 to represent heads and 5-9 to represent tails. Theoretically, in a fair coin toss, there's a 50% chance (0.5 probability) of getting either heads or tails.
However, experimental or empirical probability may not always align with this theoretical likelihood, especially in smaller samples. This discrepancy is due to randomness and doesn't necessarily imply the coin or system is biased. Over many trials, the relative frequency of getting tails should approach the theoretical probability, according to the law of large numbers.
To calculate the empirical probability of getting tails in your simulation, you would tally up the total number of 'tails' results (numbers 5-9) from your 20 trials, then divide that count by the total number of trials (20). So, if you get 12 'tails' results, your empirical probability would be 12/20 = 0.6.
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Name the pair of angle, Find the measure of angle b
9-x/5=3 what does x equal
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Martha has $180. she needs a total of $20000 to start an account. she earns $60 per day working, of which she saves $50. which equation can she use to determine the number days,d, she needs to work to reach her goal of $20000.
Answers
$835.90 + 15 = $850.90
Answers
Answer:
There are 27,720 ways to select the committee
Step-by-step explanation:
First, it is necessary to know how many ways are there to select 3 members, if there are 9 members of the mathematics department. This can be found using the following equation:
Where nCk gives as the number of ways in which we can select k elements from a group of n elements. So, replacing n by 9 and k by 3 members, we get:
So, there are 84 ways to select 3 members from 9 members of the mathematics department.
At the same way, we can calculate that there are 330 ways to select 4 members from the 11 that belong to the Computer science department as:
Finally the total number of ways in which we can form a committee with 3 faculty members from mathematics and 4 from the computer science department is calculated as:
9C3 * 11C4 = 84 * 330 = 27,720
A
R
х
S
If RT = 8, then
TX=
Answers
Answer:
4√3
Step-by-step explanation:
I did a²+b²=c²
RX²+XT²=RT²
4²+XT²=8²
16+XT²=64
XT²=48
√XT=√48
4√3
Answer:
TX=8, all sides of an equilateral triangle are congruent
v=u+at
Answers
Answer:
a =
Step-by-step explanation:
v = u + at
u + at = v
at = v - u
a =
Answers
n = 7
a = 10 m
r = 10.3826 m
R = 11.5238 m
A = 363.391 m2
P = 70 m
x = 128.571 °
y = 51.4286 °
Answers
The required, there is no part of the sphere x² + y² + z² = 16 that lies above the cone z = x² + y², where z > x² + y².
To find the part of the sphere x² + y² + z² = 16 that lies above the cone z = x² + y², where z > x² + y², we can use spherical coordinates. In spherical coordinates, the equations for the sphere and the cone are simpler.
Spherical coordinates are represented as (ρ, θ, φ), where ρ is the radial distance, θ is the azimuthal angle (measured from the positive x-axis in the xy-plane), and φ is the polar angle (measured from the positive z-axis).
For the sphere x² + y² + z² = 16, the spherical representation is:
ρ = 4 (since ρ² = x² + y² + z² = 16)
For the cone z = x² + y², the spherical representation is:
ρ = ρ (since ρ^2 = x² + y²)
Now, to find the part of the sphere that lies above the cone (z > x² + y^2), we need to restrict the values of φ.
When z > x² + y², we have z = ρ cos(φ) > ρ².
Since ρ = 4, we get 4 cos(φ) > 4², which simplifies to cos(φ) > 4.
However, the range of φ in spherical coordinates is 0 ≤ φ ≤ π, which means that the values of φ that satisfy cos(φ) > 4 are not within the valid range.
Therefore, there is no part of the sphere x² + y² + z² = 16 that lies above the cone z = x² + y², where z > x² + y².
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Final answer:
We use the given equations of the sphere and cone and express them in spherical coordinates. The sphere lies on or above the cone when z's value in the sphere equation is greater or equal than z's value in the cone equation. One method is to use spherical coordinates and represent the radius and polar angle in terms of u and v.
Explanation:
The question involves spherical and rectangular coordinates and the relationship between the two. We are given the sphere's equation as x^2 + y^2 + z^2 = 16 and the cone's equation as z = x^2 + y^2. Here's one way to think of the part of the sphere that lies on or above the cone. If we view z=x^2 + y^2 as a function of x and y, the sphere lies above this cone when z's value in the equation of the sphere is greater or equal to the value of z in the cone's equation. To express x, y, and z in terms of u and/or v, you can use a method such as spherical coordinates.
In spherical coordinates, the relationship between spherical and rectangular coordinates can be represented as:
- x = r sin θ cos φ
- y = r sin θ sin φ
- z = r cos θ
Here r, θ, and φ are the radius, polar, and azimuthal angles respectively, which we can let u and v represent. One potential assignment is to let r=u and θ=v, assuming we want only two parameters.
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