The equation does not fit the table
Answer:
At least 75% of the observations lie between 16 and 28.
Step-by-step explanation:
The Chebyshev’s Theorem says:
For any numerical data set, at least
of the data lie within k standard deviations of the mean, that is, in the interval with endpoints
for populations, where k is any positive whole number that is greater than 1.
Given:
![\mu=22\\\sigma=3](https://tex.z-dn.net/?f=%5Cmu%3D22%5C%5C%5Csigma%3D3)
The interval (16, 28) is the one that is formed by adding and subtracting two standard deviations from the mean.
![(\mu - k\sigma,\mu +k\sigma)\\(22 - 2\cdot3,22 + 2\cdot3)\\(16,28)](https://tex.z-dn.net/?f=%28%5Cmu%20-%20k%5Csigma%2C%5Cmu%20%2Bk%5Csigma%29%5C%5C%2822%20-%202%5Ccdot3%2C22%20%2B%202%5Ccdot3%29%5C%5C%2816%2C28%29)
For k = 2, we see that
, which is 75% of the data must always be within two standard deviations of the mean.
At least 75% of the observations lie between 16 and 28.
Answer:
ft tall
Step-by-step explanation:
We must follow the indications:
Ryan is 4 1/2 ft. tall.
Ryan = ![4\frac{1}{12} ft](https://tex.z-dn.net/?f=4%5Cfrac%7B1%7D%7B12%7D%20ft)
He is 3 in. taller than his sister Lizzie. to find how tall is Lizzie we need to substract 3 inches from the height of Ryan, but we can only substract the quantities if they are in the same units.
Thus we convert the 3 inches to feet, since we 1 feet = 12 inches:
![\frac{1}{4} feet=3inches](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20feet%3D3inches)
so the height of lizzie:
![4\frac{1}{12}ft-\frac{1}{4}ft\\ \\](https://tex.z-dn.net/?f=4%5Cfrac%7B1%7D%7B12%7Dft-%5Cfrac%7B1%7D%7B4%7Dft%5C%5C%20%20%5C%5C)
we convert the first mixed number to fraction by multiplying 4 by 12 and adding the numerator 1:
![4\frac{1}{12}=\frac{4*12+1}{12}=\frac{49}{12}](https://tex.z-dn.net/?f=4%5Cfrac%7B1%7D%7B12%7D%3D%5Cfrac%7B4%2A12%2B1%7D%7B12%7D%3D%5Cfrac%7B49%7D%7B12%7D)
the subtraction becomes:
![\frac{49}{12}ft-\frac{1}{4}ft\\ \\=\frac{49*4-12*1}{12*4}\\ \\=\frac{196-12}{48}\\\\=\frac{184}{48}\\ \\=\frac{46}{12} \\](https://tex.z-dn.net/?f=%5Cfrac%7B49%7D%7B12%7Dft-%5Cfrac%7B1%7D%7B4%7Dft%5C%5C%20%20%5C%5C%3D%5Cfrac%7B49%2A4-12%2A1%7D%7B12%2A4%7D%5C%5C%20%5C%5C%3D%5Cfrac%7B196-12%7D%7B48%7D%5C%5C%5C%5C%3D%5Cfrac%7B184%7D%7B48%7D%5C%5C%20%5C%5C%3D%5Cfrac%7B46%7D%7B12%7D%20%5C%5C)
![=\frac{23}{6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B23%7D%7B6%7D)
Lizzie is 23/6 ft tall.
She is 3/4 of a foot taller than her sister Emma, thus we must substract 3/4 from the height of Lizzie to find the height of Emma:
![\frac{23}{6}ft-\frac{3}{4}ft\\ \\=\frac{23*4-6*3}{6*4}\\ \\=\frac{92-18}{24}\\ \\=\frac{74}{24}\\ \\=\frac{37}{12}\\ \\=3\frac{1}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B23%7D%7B6%7Dft-%5Cfrac%7B3%7D%7B4%7Dft%5C%5C%20%20%5C%5C%3D%5Cfrac%7B23%2A4-6%2A3%7D%7B6%2A4%7D%5C%5C%20%5C%5C%3D%5Cfrac%7B92-18%7D%7B24%7D%5C%5C%20%5C%5C%3D%5Cfrac%7B74%7D%7B24%7D%5C%5C%20%5C%5C%3D%5Cfrac%7B37%7D%7B12%7D%5C%5C%20%5C%5C%3D3%5Cfrac%7B1%7D%7B12%7D)
Emma is
ft tall.
Answer:
explain whtlat?
Step-by-step explanation:
comment what i could do for u.