Answer:
12/104 or around 11% chance
Step-by-step explanation:
This is because there is a total of 26 red cards (1/2) and a total of 12 face cards (12/52). So, you multiply 1/2 x 12/52 and get 12/104 or around 11% chance
Answer:
Step-by-step explanation:
Okay, so I think I know what the equations are, but I might have misinterpreted them because of the syntax- I think when you ask a question you can use the symbols tool to input it in a more clear way, otherwise you can use parentheses and such.
Problem 1:
(x²)/4 +y²= 1
y= x+1
*substitute for y*
Now we have a one-variable equation we can solve-
x²/4 + (x+1)² = 1
x²/4 + (x+1)(x+1)= 1
x²/4 + x²+2x+1= 1
*subtract 1 from both sides to set equal to 0*
x²/4 +x^2+2x=0
x²/4 can also be 1/4 * x²
1/4 * x² +1*x² +2x = 0
*combine like terms*
5/4 * x^2+2x+ 0 =0
now, you can use the quadratic equation to solve for x
a= 5/4
b= 2
c=0
the syntax on this will be rough, but I'll do my best...
x= (-b ± √(b²-4ac))/(2a)
x= (-2 ±√(2²-4*(5/4)*(0))/(2*(5/4))
x= (-2 ±√(4-0))/(2.5)
x= (-2±2)/2.5
x will have 2 answers because of ±
x= 0 or x= 1.6
now plug that back into one of the equations and solve.
y= 0+1 = 1
y= 1.6+1= 2.6
Hopefully this explanation was enough to help you solve problem 2.
Problem 2:
x² + y² -16y +39= 0
y²- x² -9= 0
Answer:
a) ![r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%28333%29-%28200%29%285.37%29%7D%7B%5Csqrt%7B%5B4%2812000%29%20-%28200%29%5E2%5D%5B4%289.3501%29%20-%285.37%29%5E2%5D%7D%7D%3D0.9857)
The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables
b) 
Now we can find the means for x and y like this:
So the line would be given by:
Step-by-step explanation:
Part a
The correlation coeffcient is given by this formula:
![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D)
For our case we have this:
n=4 
The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables
Part b
Where:
With these we can find the sums:
And the slope would be:
Now we can find the means for x and y like this:
And we can find the intercept using this:
So the line would be given by:
Answer:
Someone is spending 80 cents daily from their bank account, starting out with $5.6
