Answer:
![1- \frac{1}{2^2} = 1-\frac{1}{4} = \frac{3}{4}](https://tex.z-dn.net/?f=%201-%20%5Cfrac%7B1%7D%7B2%5E2%7D%20%3D%201-%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D)
So then we will have at least 75% of the data within two deviations from the mean
.
![\bar x -2s = 98.32 -2*0.59 = 97.14](https://tex.z-dn.net/?f=%20%5Cbar%20x%20-2s%20%3D%2098.32%20-2%2A0.59%20%3D%2097.14)
![\bar x +2s = 98.32 +2*0.59 = 99.5](https://tex.z-dn.net/?f=%20%5Cbar%20x%20%2B2s%20%3D%2098.32%20%2B2%2A0.59%20%3D%2099.5)
So then the interval would be (97.14, 99.5)
Explanation:
Previous concepts
Chebyshev’s rule is appropriate for any distribution. "Chebyshev’s inequality applies to all distributions, regardless of shape". And is useful since provides a "minimum percentage of the observations that lies within k standard deviations of the mean. "
If k = 2, at least 3/4 of the measurements lie within 2 standard deviations to within the mean.
And the general formula is (1-1/k^2) represent the fraction of the data within the mean .
Solution to the problem
For this case we want to find the percentage of data that would be at least within two deviations from the mean so for this case the value of k =2 and if we replace we got:
![1- \frac{1}{2^2} = 1-\frac{1}{4} = \frac{3}{4}](https://tex.z-dn.net/?f=%201-%20%5Cfrac%7B1%7D%7B2%5E2%7D%20%3D%201-%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D)
So then we will have at least 75% of the data within two deviations from the mean
.
For the other part we have the mean and deviation provided
the interval would be:
![\bar x -2s = 98.32 -2*0.59 = 97.14](https://tex.z-dn.net/?f=%20%5Cbar%20x%20-2s%20%3D%2098.32%20-2%2A0.59%20%3D%2097.14)
![\bar x +2s = 98.32 +2*0.59 = 99.5](https://tex.z-dn.net/?f=%20%5Cbar%20x%20%2B2s%20%3D%2098.32%20%2B2%2A0.59%20%3D%2099.5)
So then the interval would be (97.14, 99.5)
The net force acting on the center O is 4.495 X 10⁹ N
<u>Explanation:</u>
Given:
Charge-
q₁ = 4C
q₂ = 3C
q₃ = -5C
q₄ = 2C
q₅ = 1C
Side of the square = 4cm
Net force acting on the center, F = ?
Length of the side of the square is 4cm
The length of the diagonal will be 4√2
The length of half diagonal = 4√2 / 2 = 2√2
Force acting on the center of the square is:
![F = k({\frac{Qq_1}{r^2} + \frac{Qq_2}{r^2} + \frac{Qq_3}{r^2} + \frac{Qq_4}{r^2} )\\\\\\](https://tex.z-dn.net/?f=F%20%3D%20k%28%7B%5Cfrac%7BQq_1%7D%7Br%5E2%7D%20%2B%20%5Cfrac%7BQq_2%7D%7Br%5E2%7D%20%2B%20%5Cfrac%7BQq_3%7D%7Br%5E2%7D%20%2B%20%5Cfrac%7BQq_4%7D%7Br%5E2%7D%20%29%5C%5C%5C%5C%5C%5C)
![F = \frac{kQ}{r^2} (q_1 + q_2 + q_3 + q_4)](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7BkQ%7D%7Br%5E2%7D%20%28q_1%20%2B%20q_2%20%2B%20q_3%20%2B%20q_4%29)
Here, k is coulomb's constant and the value is
k = 8.99 x 10⁹ N m2 / C2
On substituting the value, we get:
![F = \frac{8.99 X 10^9 X 1}{(2\sqrt{2} )^2} ( 4C + 3C - 5C + 2C)\\\\F = \frac{8.99 X 10^9}{8} (4C)\\\\F = 4.495 X 10^9 N](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B8.99%20X%2010%5E9%20X%201%7D%7B%282%5Csqrt%7B2%7D%20%29%5E2%7D%20%28%204C%20%2B%203C%20-%205C%20%2B%202C%29%5C%5C%5C%5CF%20%3D%20%5Cfrac%7B8.99%20X%2010%5E9%7D%7B8%7D%20%284C%29%5C%5C%5C%5CF%20%3D%204.495%20X%2010%5E9%20N)
Therefore, the net force acting on the center O is 4.495 X 10⁹ N
Answer:
a) L = 33.369 m
, b) 21
Explanation:
The analysis of the ocean depth can be performed assuming that at the bottom of the ocean there is a node and the surface must have a belly, so the expression for resonance is
λ = 4 L / n
n = 1, 3, 5, ...
The speed of the wave is
v = λ f
v = 4L / n f
L = n v / 4f
Let's write the expression for the two frequencies
L = n₁ 343/4 53.95
L = n₁ 1,589
L = n₂ 343/4 59
L = n₂ 1.4539
Let's solve the two equations
n₁ 1,589 = n₂ 1,459
n₁ / n₂ = 1.4539 / 1.589
n₁ / n2 = 0.91498
Since the two frequencies are very close the whole numbers must be of consecutive resonances, let's test what values give this value
n₁ n₂ n₁ / n₂
1 3 0.3
3 5 0.6
5 7 0.7
7 9 0.77
9 11 0.8
17 19 0.89
19 21 0.905
21 23 0.913
23 25 0.92
Therefore the relation of the nodes is n₁ = 21 and n₂ = 23
Let's calculate
L = n₁ 1,589
L = 21 1,589
L = 33.369 m
b) the number of node and nodes is equal therefore there are 21 antinode
Answer:
120 miles/hour
Explanation:
The average speed is the ratio of total distance covered by an object or a body to the total time taken to cover the distance.
Mathematically,
<em>Average speed = total distance covered/total time taken</em>
In the case of Connie:
total distance = 180 + 180 = 360 miles
In order to calculate the time for each trip
<em>speed = distance/time</em>
<em> time = distance/speed</em>
From Phoenix to flagstaff:
time = 180/180 = 1 hour
From flagstaff back to Phoenix:
time = 180/90 = 2 hours
total time taken = 1 + 2 = 3 hours
Average speed = 360/3 = 120 miles/hour
<em>Hence, the average speed is </em><em>120 miles per hour.</em>
Answer:
1.1 m
Explanation:
PE = mgh
6.7 J = (0.62 kg) (9.8 m/s²) h
h = 1.1 m