Answer:
The proportion of the variability seen in math achievement that can be predicted by math attitude is 0.78, the same value as the correlation coefficient.
Step-by-step explanation:
The correlation coefficient r between this two variables is found to be 0.78.
This coefficient can be calculated as:
where SSY' is the sum of the squares deviation from the mean for the predicted value and SSY is the sum of the squares deviation from the mean for the criterion variable.
Then, the value of the coefficient r is giving the proportion of the variability seen in the criterion value Y that can be explained by the predictor variable X.
Answer:
f(2) = 9
Step-by-step explanation:
It's give in the question,
Two different functions are,
f(x) = 4x + 1
g(x) = -2x
Then we have to find the output value of function 'f' for the input value x = 2.
By substituting the value of x in the function 'f',
f(2) = 4(2) + 1
= 9
f(2) = 9
Answer:
d
Step-by-step explanation:
Soooo,
d = 2r
(29) = 2r
29/2 = 2r/2
14.5 = r
Answer:
The magnitude is 
The direction is 
i.e toward the x-axis
Step-by-step explanation:
From the question we are told that
The function is 
The point considered is 
Generally the maximum rate of change of f at the given point and the direction is mathematically represented as
![\Delta f(x,y) = [\frac{\delta f(x,y)}{\delta x } i + \frac{\delta f(x,y)}{\delta y } j ]](https://tex.z-dn.net/?f=%5CDelta%20f%28x%2Cy%29%20%3D%20%20%5B%5Cfrac%7B%5Cdelta%20%20f%28x%2Cy%29%7D%7B%5Cdelta%20x%20%7D%20i%20%2B%20%5Cfrac%7B%5Cdelta%20%20f%28x%2Cy%29%7D%7B%5Cdelta%20y%20%7D%20j%20%20%5D)
![\Delta f(x,y) = [\frac{\delta (9sin(xy))}{\delta x} i + \frac{\delta (9sin(xy))}{\delta y} i ]](https://tex.z-dn.net/?f=%5CDelta%20f%28x%2Cy%29%20%3D%20%20%5B%5Cfrac%7B%5Cdelta%20%20%289sin%28xy%29%29%7D%7B%5Cdelta%20x%7D%20i%20%20%2B%20%5Cfrac%7B%5Cdelta%20%20%289sin%28xy%29%29%7D%7B%5Cdelta%20y%7D%20i%20%20%20%5D)
![\Delta f(x,y) = [9y cos (x,y) i + 9xcos (x,y) j]](https://tex.z-dn.net/?f=%5CDelta%20f%28x%2Cy%29%20%3D%20%5B9y%20cos%20%28x%2Cy%29%20i%20%2B%20%209xcos%20%28x%2Cy%29%20j%5D)
At
![\Delta f (0,8) = [9(8) cos(0* 8)i + 9(8) sin(0* 8)j ]](https://tex.z-dn.net/?f=%5CDelta%20%20f%20%280%2C8%29%20%3D%20%20%5B9%288%29%20cos%280%2A%208%29i%20%20%2B%209%288%29%20sin%280%2A%208%29j%20%20%5D)
Assuming the man works 8 hours straight without breaks:
25% is the same as 1/4 of something.
So, we just have to figure out what 1/4 (one quarter) of 8 equals.
You can think of it as a pizza cut into 8 slices. One slice is equivalent to one hour for the patrolman.
If we take away 1/2 (half) of the pizza, we have 4 slices, right? Since we start with 8 slices, half of that equals 4 slices. In other words, 50% (half) of the pizza = 4 slices.
Now, 25% (one quarter) of the pizza will equal half of what is left:
If we know that 50%=4 slices (or 4 hours), then 25% must be 2 slices (or 2 hours).
That's it! 25% of 8 hours = 2 hours.
***So, the patrolman spends 2 hours each day completing paperwork.***
Lets check our work:
We know 8 hours (or 8 slices)= 100%
(We know this because
8 slices = 1 whole pizza, or 100% of a pizza. Similarly,
8 hours = 1 whole shift or 100% of the man's shift ).
So
25% + 25% + 25% + 25% = 100%
If 100% of the mans shift = 8 hours:
2+2+2+2 = 8
It checks out!
Hope this helps!
