SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given set of values
STEP 2: Write the formula for calculating the Standard deviation of a set of numbers
![\begin{gathered} S\tan dard\text{ deviation=}\sqrt[]{\frac{\sum^{}_{}(x_i-\bar{x})^2}{n-1}} \\ where\text{ }x_i\text{ are data points,} \\ \bar{x}\text{ is the mean} \\ \text{n is the number of values in the data set} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20S%5Ctan%20dard%5Ctext%7B%20deviation%3D%7D%5Csqrt%5B%5D%7B%5Cfrac%7B%5Csum%5E%7B%7D_%7B%7D%28x_i-%5Cbar%7Bx%7D%29%5E2%7D%7Bn-1%7D%7D%20%5C%5C%20where%5Ctext%7B%20%7Dx_i%5Ctext%7B%20are%20data%20points%2C%7D%20%5C%5C%20%5Cbar%7Bx%7D%5Ctext%7B%20is%20the%20mean%7D%20%5C%5C%20%5Ctext%7Bn%20is%20the%20number%20of%20values%20in%20the%20data%20set%7D%20%5Cend%7Bgathered%7D)
STEP 3: Calculate the mean
STEP 4: Calculate the Standard deviation
![\begin{gathered} S\tan dard\text{ deviation=}\sqrt[]{\frac{\sum^{}_{}(x_i-\bar{x})^2}{n-1}} \\ \sum ^{}_{}(x_i-\bar{x})^2\Rightarrow\text{Sum of squares of differences} \\ \Rightarrow10332.7225+657.9225+18591.3225+982.8225+2740.52251+9731.8225+3522.4225+18319.6225+2878.3225 \\ +8163.1225+1417.5225+3925.0225+1321.3225+386.1225+5677.6225+2953.9225+3800.7225 \\ +3209.2225+2565.4225+10537.0225 \\ \text{Sum}\Rightarrow108974.0275 \\ \\ S\tan dard\text{ deviation}=\sqrt[]{\frac{111714.55}{20-1}}=\sqrt[]{\frac{111714.55}{19}} \\ \Rightarrow\sqrt[]{5879.713158}=76.67928767 \\ \\ S\tan dard\text{ deviation}\approx76.68 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20S%5Ctan%20dard%5Ctext%7B%20deviation%3D%7D%5Csqrt%5B%5D%7B%5Cfrac%7B%5Csum%5E%7B%7D_%7B%7D%28x_i-%5Cbar%7Bx%7D%29%5E2%7D%7Bn-1%7D%7D%20%5C%5C%20%5Csum%20%5E%7B%7D_%7B%7D%28x_i-%5Cbar%7Bx%7D%29%5E2%5CRightarrow%5Ctext%7BSum%20of%20squares%20of%20differences%7D%20%5C%5C%20%5CRightarrow10332.7225%2B657.9225%2B18591.3225%2B982.8225%2B2740.52251%2B9731.8225%2B3522.4225%2B18319.6225%2B2878.3225%20%5C%5C%20%2B8163.1225%2B1417.5225%2B3925.0225%2B1321.3225%2B386.1225%2B5677.6225%2B2953.9225%2B3800.7225%20%5C%5C%20%2B3209.2225%2B2565.4225%2B10537.0225%20%5C%5C%20%5Ctext%7BSum%7D%5CRightarrow108974.0275%20%5C%5C%20%20%5C%5C%20S%5Ctan%20dard%5Ctext%7B%20deviation%7D%3D%5Csqrt%5B%5D%7B%5Cfrac%7B111714.55%7D%7B20-1%7D%7D%3D%5Csqrt%5B%5D%7B%5Cfrac%7B111714.55%7D%7B19%7D%7D%20%5C%5C%20%5CRightarrow%5Csqrt%5B%5D%7B5879.713158%7D%3D76.67928767%20%5C%5C%20%20%5C%5C%20S%5Ctan%20dard%5Ctext%7B%20deviation%7D%5Capprox76.68%20%5Cend%7Bgathered%7D)
Hence, the standard deviation of the given set of numbers is approximately 76.68 to 2 decimal places.
STEP 5: Calculate the First and third quartile
STEP 6: Find the Interquartile Range
Hence, the interquartile range of the data is 116
Using the asymptote concept, the function with a vertical asymptote at x = 3 and an horizontal asymptote at 
is given by:
<h3>What are the asymptotes of a function f(x)?</h3>
- The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
- The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.
The vertical asymptote at x = 3 means that x = 3 is a root of the denominator, hence:
The horizontal asymptote at y = -1/2 means that:
Which happens if 
, hence the function is:
More can be learned about asymptotes at brainly.com/question/16948935
#SPJ1
Answer: The answer to your question is infinitely many solutions
Step-by-step explanation: There is two solutions to the system of equations, which means there is complex solutions, or in other words many solutions. And when you have more than one solution, you have infinitely many solutions. Hope this helps:)
And please mark my answer the brainliest
Answer:
The correct option is 1.
Step-by-step explanation:
Two triangles are called similar if all the corresponding angles are congruent or all corresponding sides are in same proportion.
In triangle MNO and triangle RTS.
(Given)
(Given)
According to the angle sum property, the sum of all interior angles of a triangle is 180 degree. Since two corresponding angles are congruent, therefore third angle is also congruent.
Since all corresponding angles are congruent, therefore the triangles MNO and RTS similar.
The triangle are congruent by AA rule of similarity. Each triangle has two congruent angles, therefore both triangles are similar. Option 1 is correct.
5.6mile
7 x
-- = --
80 64
7×64=80x
448=80x
x=5.6
