What is the value of f(x)=6
1 answer:
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The measures of central tendency for this data set are as follows:
- Mean = 3.55.
- Median = 3.5.
- Mode = 3.
In Mathematics, there are three (3) main measures of central tendency and these include the following:
- Mean
- Median
- Mode
For the mean, we have:
Mathematically, the mean for this data set would be calculated by using this formula:
Mean = [F(x)]/n
For the total number of data, we have:
F(x) = 0 + 1 + 1 + 1 + 2 + 2 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7
F(x) = 71
Substituting the parameters into the formula, we have:
Mean = [F(x)]/n
Mean = 71/20
Mean = 3.55.
For the median, we have:
First of all, we would order the data from lowest to highest and then determine the median as follows:
Data = {0, 1, 1, 1, 2, 2, 3, 3, 3,} 3, 4, {4, 4, 5, 5, 5, 6, 6, 6, 7}
Median = {3 + 4}/2
Median = 7/2
Median = 3.5.
<h3>How to calculate the mode?</h3>A mode refers to the most frequently occurring number in a data set. Thus, the mode for this data set is equal to 3.
In conclusion, a box plot of the measures of central tendency for this data set is shown in the image attached below.
Read more on mean here: brainly.com/question/9550536
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Answer:
The coordinates of the explosion is (3300, -2750)
Step-by-step explanation:
I have plot the points and attached to thus answer for easy understanding.
Now, from the question, since station A is the first to hear the explosion, we'll make it the foci of the parabola in the graph I attached and it will be horizontal since the distance between station C and A is much more than that between station B and A. Thus, the reason why station C will have to be the other foci with the hyperbola centred at the origin.
Now, sound travels at a speed of 1100 ft/s and station B is located 1100 ft from station A. Thus, the explosion would likely have occurred at a point on the line x = 3300ft . Since station A is 3300ft from centre C = 3300,hence C² = 3300² = 10,890,000. Since it takes 4 seconds longer for the sound to reach station C than A, the sound has traveled 4(1100)= 4400 ft.
Thus, 4400 = d1 = d2 = 2a
So,2a = 4400 and so, a =2200
a² = 2200² = 4,840,000 where d1 is the distance from station C to the explosion and d2 is the distance from station A to the explosion. To find b², let's use the equation ;
c² = a² + b² and so; b² = c² - a² = 10,890,000 - 4,840,000 = 6,050,000
Equation of hyperbola is given as;
(x²/a²) - (y²/b²) = 1
Plugging in the values of a² and b², we obtain ;
(x²/4,840,000) - (y²/6,050,000) = 1
Since we have deduced that the explosion must occur on the line x= 3300, we'll put in 3300 for x to obtain ;
(3300²/4,840,000) - (y²/6,050,000) = 1
2.25 - 1 = (y²/6,050,000)
y² = (1.25 x 6,050,000)
y² = 7562500
y = √7562500
y = ± 2750
Due to the fact that the explosion will occur at a point further from station B than from station A, the explosion will take place in quadrant 4. Thus, we will take the negative value of y which is - 2750.
So explosion will occur at the coordinate (3300, -2750)
