Step-by-step explanation:
xy + 10 = 0. => y = -10/x.
2x + 3y = 7. => 3y = -2x + 7, y = -2/3 x + 7/3.
When -10/x = -2/3 x + 7/3,
-10 = -2/3 x² + 7/3 x, 2/3 x² - 7/3 x - 10 = 0.
=> 2x² - 7x - 30 = 0
=> (2x + 5)(x - 6) = 0
=> x = -2.5 or x = 6.
dy/dx = d/dx [-10/x] = 10/x².
When x = -2.5, dy/dx = 10 / (-2.5)² = 1.6.
When x = 6, dy/dx = 10 / (6)² = 5/18.
Hence the gradients at the points are 1.6 and 5/18.
R - Right Handed
L - Left Handed
R = 9L ( the number of right handed kids is equal to having 9*number of left handed kids)
9L + L = 30 ( since total number of people in class is 30)
10L = 30
( Divide by 10 both sides )
L = 3
so... There are 3 Left Handed kids and 27 Right Handed kids ( since R = 9L , R = 9(3) = 27)
Hope this helped!
Answer:
3×10^4
Step-by-step explanation:
The desired factor is found by calculating the ratio of the two numbers:
k = (9×10^2)/(3×10^-2) = (9/3)×10^(2 -(-2)) = 3×10^4
The first number is 3×10^4 = 30,000 times as much as the second number.
1 pound equals 16 ounces
10 times 16 equals 160 ounces plus 1/2 a pound which is 8
168 ounces
Answer:
42.1% of variation in the response is explained by the regression line
Step-by-step explanation:
Correlation coefficient is a measure which tells us that how strongly are two variables under study are linearly related to each other i.e correlation coefficient gives the strength of linear association between the variables.
If the magnitude of correlation coefficient is closer to 1, it indicates a strong linear relationship. If the magnitude of correlation coefficient is closer to 0, it indicates a weak linear relationship.
There is another variable known as "Coefficient of Determination", which is equal to square of Correlation Coefficient. Coefficient of Determination tells us that what percentage of variation in the response of the study can be explained by the regression line.
This means, for this question we need to calculate the Coefficient of Determination.
Correlation coefficient = r = 0.649
Coefficient of Determination = R = r² = (0.649)²= 0.421 = 42.1 %
This means that 42.1% of variation in the response is explained by the regression line.
