Answer: 0.9730
Step-by-step explanation:
Let A be the event of the answer being correct and B be the event of the knew the answer.
Given: ![P(A)=0.9](https://tex.z-dn.net/?f=P%28A%29%3D0.9)
![P(A^c)=0.1](https://tex.z-dn.net/?f=P%28A%5Ec%29%3D0.1)
![P(B|A^{C})=0.25](https://tex.z-dn.net/?f=P%28B%7CA%5E%7BC%7D%29%3D0.25)
If it is given that the answer is correct , then the probability that he guess the answer ![P(B|A)= 1](https://tex.z-dn.net/?f=P%28B%7CA%29%3D%201)
By Bayes theorem , we have
![P(A|B)=\dfrac{P(B|A)P(A)}{P(B|A)P(A)+P(C|A^c)P(A^c)}](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%5Cdfrac%7BP%28B%7CA%29P%28A%29%7D%7BP%28B%7CA%29P%28A%29%2BP%28C%7CA%5Ec%29P%28A%5Ec%29%7D)
![=\dfrac{(1)(0.9)}{(1))(0.9)+(0.25)(0.1)}\\\\=0.972972972973\approx0.9730](https://tex.z-dn.net/?f=%20%3D%5Cdfrac%7B%281%29%280.9%29%7D%7B%281%29%29%280.9%29%2B%280.25%29%280.1%29%7D%5C%5C%5C%5C%3D0.972972972973%5Capprox0.9730)
Hence, the student correctly answers a question, the probability that the student really knew the correct answer is 0.9730.
Given u/7 - 1 = 7 and plugging in values for u,
For u = 28; 28/7 - 1 = 4 - 1 = 3; No
For u = -49; -49/7 - 1 = -7 - 1 = -8; No
For u = 42; 42/7 - 1 = 6 - 1 = 5; No
For u = 0; 0/7 - 1 = -1; No
Another way to find out which value would be a solution to u/7 - 1 = 7 is to solve for u.
u/7 - 1 = 7
u/7 = 7 + 1
u/7 = 8
u = 8*7
u = 56
The only solution to this equation is when u = 56.
Answer:
Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.
Step-by-step explanation:
The equation of a circle with center (h,k) and radius r is given by:
![(x-h)^2 + (y-k)^2 = r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%20%2B%20%28y-k%29%5E2%20%3D%20r%5E2)
Given
Center = (h,k) = (-3,1)
=> h = -3
=> k = 1
The distance between the center of circle and the point through which the circle passes will be the radius.
The distance formula is given by:
![r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2)
Given
![(x_1,y_1) = (-3,1)\\(x_2,y_2) = (-5,3)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28-3%2C1%29%5C%5C%28x_2%2Cy_2%29%20%3D%20%28-5%2C3%29)
Putting the values in the formula
![r = \sqrt{(-5+3)^2+(3-1)^2}\\r = \sqrt{(-2)^2+(2)^2}\\r = \sqrt{4+4}\\r = \sqrt{8}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28-5%2B3%29%5E2%2B%283-1%29%5E2%7D%5C%5Cr%20%3D%20%5Csqrt%7B%28-2%29%5E2%2B%282%29%5E2%7D%5C%5Cr%20%3D%20%5Csqrt%7B4%2B4%7D%5C%5Cr%20%3D%20%5Csqrt%7B8%7D)
Putting the values of h,k and r in general form of equation
![\{x-(-3)}^2\} +(y-1)^2 = (\sqrt{8})^2\\(x+3)^2+(y-1)^2 = 8](https://tex.z-dn.net/?f=%5C%7Bx-%28-3%29%7D%5E2%5C%7D%20%2B%28y-1%29%5E2%20%3D%20%28%5Csqrt%7B8%7D%29%5E2%5C%5C%28x%2B3%29%5E2%2B%28y-1%29%5E2%20%3D%208)
Hence,
Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.
Step-by-step explanation:
it's an equilateral triangle so all sides are equal
using Pythagorean theorem
2(√6) raised to the power of 2 = √6 raised to the power of 2 + x raised to the power of 2
2(√6) raised to the power of 2 is 12
√6 raised to the power of 2 is 6
therefore 12=6 + x
x = 12-6
x=6
427+316
step one- add 400 and 300=700
step two- take 3 from the 16 and add it to the 27 and add - 27+3+13=43
step three- add 43 and 700
I think that the common core way just adds more steps and makes it more complicated than just adding it regularly, but that's just me.