A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat
of the individual. The following scores are recorded.
Individual 1 2 3 4 5
Exercise (min) 10 18 26 33 44
% Fat 30 25 18 17 14
Individual: 1, 2, 3, 4, 5
Excercise (min): 10, 18, 26, 33, 44
% Fat: 30, 25, 18, 17, 14
a) Based on the above data, if an individual exercises 20 minutes daily, his predicted % body fat would be
a. 21.63
b. 27.74
c. 27.88
d. 23.75
Individual 1 2 3 4 5
Exercise (min) 10 18 26 33 44
% Fat 30 25 18 17 14
Individual: 1, 2, 3, 4, 5
Excercise (min): 10, 18, 26, 33, 44
% Fat: 30, 25, 18, 17, 14
a) Based on the above data, if an individual exercises 20 minutes daily, his predicted % body fat would be
a. 21.63
b. 27.74
c. 27.88
d. 23.75
1 answer:
Answer:
Option D is correct.
If exercise time = 20 mins,
Body fat = 23.75%
Step-by-step explanation:
After plotting a graph of the variables given, with body fat on the x-axis and exercise time on the y-axis.
The equation of the graph was obtained to be
Y = -1.931X + 65.936
If exercise time = 20 mins,
Y = 20
20 = -1.98X + 66.936
-1.98X = -46.936
X = 23.7 = 23.75% From the options.
The problem can also be solved by doing the least squares regression line method, but this is more straight forward.
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Answer:
x=6
Step-by-step explanation:
First, let 
be a point in our parabola. Since we know that the focus of our parabola is the point (0,8), we are going to use the distance formula to find the distance between the two points:
Next, we are going to find the distance between the directrix and the point in our parabola. Remember that the distance between a point (x,y) of a parabola and its directrix,
, is: 
. Since our directrix is y=-8, the distance to our point will be:
Now, we are going to equate those two distances, and square them to get rid of the square root and the absolute value:
Finally, we can expand and solve for
:
We can conclude that t<span>he standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8 is </span>
Next, we are going to find the distance between the directrix and the point in our parabola. Remember that the distance between a point (x,y) of a parabola and its directrix,
Now, we are going to equate those two distances, and square them to get rid of the square root and the absolute value:
Finally, we can expand and solve for
We can conclude that t<span>he standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8 is </span>