Answer:
D
Step-by-step explanation:
Using the Sine rule in Δ QRS , that is
=
, that is
=
( cross- multiply )
12× sinQ = 15 × sin50.1° ( divide both sides by 12 )
sinQ =
, thus
Q =
(
) ≈ 73.5° ( to the nearest tenth )
Answer: y=-6/5x+3
Step-by-step explanation:
To find the equation of the line that passes through the points, you want to first find the slope by using the formula
, then solve for the y-intercept.
![m=\frac{15-(-3)}{-10-5} =\frac{18}{-15} =-\frac{6}{5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B15-%28-3%29%7D%7B-10-5%7D%20%3D%5Cfrac%7B18%7D%7B-15%7D%20%3D-%5Cfrac%7B6%7D%7B5%7D)
Now that we have the slope, we can plug in a given point and solve for the y-intercept.
15=-6/5(-10)+b [multiply]
15=12+b [subtract both sides by 12]
b=3
Now that we have the y-intercept, we know the equation is y=-6/5x+3.
Answer:
or ![x = -\dfrac{11}{3}](https://tex.z-dn.net/?f=%20x%20%3D%20-%5Cdfrac%7B11%7D%7B3%7D%20)
Step-by-step explanation:
I assume the denominators are x + 5 and x + 4 although that is not what you wrote.
![\dfrac{4x}{x+5} = \dfrac{x}{x+4}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B4x%7D%7Bx%2B5%7D%20%3D%20%5Cdfrac%7Bx%7D%7Bx%2B4%7D%20)
![(x + 4)(x + 5)\times \dfrac{4x}{x+5} = (x + 4)(x + 5) \times \dfrac{x}{x+4}](https://tex.z-dn.net/?f=%20%28x%20%2B%204%29%28x%20%2B%205%29%5Ctimes%20%5Cdfrac%7B4x%7D%7Bx%2B5%7D%20%3D%20%28x%20%2B%204%29%28x%20%2B%205%29%20%5Ctimes%20%5Cdfrac%7Bx%7D%7Bx%2B4%7D%20)
![(x + 4)(4x) = (x + 5)(x)](https://tex.z-dn.net/?f=%20%28x%20%2B%204%29%284x%29%20%3D%20%28x%20%2B%205%29%28x%29%20)
![4x^2 + 16x = x^2 + 5x](https://tex.z-dn.net/?f=%204x%5E2%20%2B%2016x%20%3D%20x%5E2%20%2B%205x%20)
![3x^2 + 11x = 0](https://tex.z-dn.net/?f=%203x%5E2%20%2B%2011x%20%3D%200%20)
![x(3x + 11) = 0](https://tex.z-dn.net/?f=%20x%283x%20%2B%2011%29%20%3D%200%20)
or ![3x + 11 = 0](https://tex.z-dn.net/?f=%203x%20%2B%2011%20%3D%200%20)
or ![3x = -11](https://tex.z-dn.net/?f=%203x%20%3D%20-11%20)
or ![x = -\dfrac{11}{3}](https://tex.z-dn.net/?f=%20x%20%3D%20-%5Cdfrac%7B11%7D%7B3%7D%20)
Answer:
![P(A) = 0.25, P(B= 0.3](https://tex.z-dn.net/?f=%20P%28A%29%20%3D%200.25%2C%20P%28B%3D%200.3)
And if we want to find
we can use this formula from the definition of independent events :
![P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3DP%28A%29%20%2AP%28B%29%20%3D%200.25%2A0.3%3D%200.075)
And the best option would be:
![P(A \cap B) =0.075](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D0.075)
Step-by-step explanation:
For this case we have the following events A and B and we also have the probabilities for each one given:
![P(A) = 0.25, P(B= 0.3](https://tex.z-dn.net/?f=%20P%28A%29%20%3D%200.25%2C%20P%28B%3D%200.3)
And if we want to find
we can use this formula from the definition of independent events :
![P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3DP%28A%29%20%2AP%28B%29%20%3D%200.25%2A0.3%3D%200.075)
And the best option would be:
![P(A \cap B) =0.075](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D0.075)