Answer: No, A and B are not independent events.
Step-by-step explanation:
Since we have given that
Number of outcomes that a die comes up with = 6
A be the event that the red die comes up even.
A={2,4,6}
B be the event that the sum on the two dice is 8.
B={(2,4),(4,2),(5,3),(3,5),(44)}
P(A) = ![\dfrac{3}{6}=\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B6%7D%3D%5Cdfrac%7B1%7D%7B2%7D)
P(B) = ![\dfrac{5}{36}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B36%7D)
P(A∩B) = ![\dfrac{3}{36}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B36%7D)
But,
P(A).P(B) ≠ P(A∩B)
![\dfrac{1}{2}\times \dfrac{5}{36}\neq \dfrac{3}{36}\\\\\dfrac{5}{72}\neq\dfrac{1}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20%5Cdfrac%7B5%7D%7B36%7D%5Cneq%20%5Cdfrac%7B3%7D%7B36%7D%5C%5C%5C%5C%5Cdfrac%7B5%7D%7B72%7D%5Cneq%5Cdfrac%7B1%7D%7B12%7D)
Hence, A and B are dependent events.
Answer
A) y = x - 7
Step-by-step
Part 1: Convert to slope-intercept form
The equation -x + y = 5 has to be converted from standard form to slope-intercept form before we can begin solving this problem. The slope-intercept form is y = mx + b, where m is the slope of the line and b is its y-intercept. To convert it, just get y by itself on the left side.
-x + y = 5
y - x = 5
y - x + x = 5 + x
y = 5 + x
y = x + 5
This equation tells us the slope of the line (1) and the line's y-intercept (5)
Part 2: Find the equation of the line that is parallel to y = x + 5 and passes through the point (2, -5)
Parallel lines have equal slopes, so the slope of the line we are looking for will be 1 (or just x). So we can rule out answer choice D because it has a slope of -1 (or -x). To find the y-intercept for the line, we need to find the point where x = 0. We can work backwards with the rise over run method to find this point.
m = rise / run = change in y / change in x
1 = 1 / 1
We can use this information to perform a series of transformations (down 1 unit then left 1 unit) that will bring us to the y-intercept.
(2, -5) --> (1, -6)
(1, -6) --> (0, -7)
The point (0, -7) has an x-coordinate of 0, which means that the line intercepts the y-axis at this point.
The slope of the desired line is 1 and its y-intercept is -7.
Part 3: Substitute into the slope-intercept equation
y = mx + b
m = slope = 1 = x
b = y-intercept = -7
y = x - 7
Solving
for v gives ![v=\frac{h}{t}+2t](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bh%7D%7Bt%7D%2B2t)
Solving
for b1 gives ![b_1=2A-b_2](https://tex.z-dn.net/?f=b_1%3D2A-b_2)
Step-by-step explanation:
Given
![h=vt-2t^2](https://tex.z-dn.net/?f=h%3Dvt-2t%5E2)
To solve for v, we have to isolate v on one side of the equation
![h=vt-2t^2\\Adding\ 2t^2\ on\ both\ sides\\h+2t^2=vt-2t^2+2t^2\\h+2t^2=vt\\Dividing\ both\ sides\ by\ t\\\frac{h+2t^2}{t}=\frac{vt}{t}\\v=\frac{h+2t^2}{t}\\v=\frac{h}{t}+\frac{2t^2}{t}\\v=\frac{h}{t}+2t](https://tex.z-dn.net/?f=h%3Dvt-2t%5E2%5C%5CAdding%5C%202t%5E2%5C%20on%5C%20both%5C%20sides%5C%5Ch%2B2t%5E2%3Dvt-2t%5E2%2B2t%5E2%5C%5Ch%2B2t%5E2%3Dvt%5C%5CDividing%5C%20both%5C%20sides%5C%20by%5C%20t%5C%5C%5Cfrac%7Bh%2B2t%5E2%7D%7Bt%7D%3D%5Cfrac%7Bvt%7D%7Bt%7D%5C%5Cv%3D%5Cfrac%7Bh%2B2t%5E2%7D%7Bt%7D%5C%5Cv%3D%5Cfrac%7Bh%7D%7Bt%7D%2B%5Cfrac%7B2t%5E2%7D%7Bt%7D%5C%5Cv%3D%5Cfrac%7Bh%7D%7Bt%7D%2B2t)
Given
![A=\frac{1}{2}(b_1+b_2)}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28b_1%2Bb_2%29%7D)
To isolate b1 we have to isolate b1
So,
![A=\frac{1}{2}(b_1+b_2)}\\Multiplying\ both\ sides\ by\ 2\\2A=2*\frac{1}{2}(b_1+b_2)}\\2A=b_1+b_2\\Subtracting\ b_2\ from\ both\ sides\\2A-b_2=b_1+b_2-b_2\\b_1=2A-b_2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28b_1%2Bb_2%29%7D%5C%5CMultiplying%5C%20both%5C%20sides%5C%20by%5C%202%5C%5C2A%3D2%2A%5Cfrac%7B1%7D%7B2%7D%28b_1%2Bb_2%29%7D%5C%5C2A%3Db_1%2Bb_2%5C%5CSubtracting%5C%20b_2%5C%20from%5C%20both%5C%20sides%5C%5C2A-b_2%3Db_1%2Bb_2-b_2%5C%5Cb_1%3D2A-b_2)
Hence,
Solving
for v gives ![v=\frac{h}{t}+2t](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bh%7D%7Bt%7D%2B2t)
Solving
for b1 gives ![b_1=2A-b_2](https://tex.z-dn.net/?f=b_1%3D2A-b_2)
Keywords: Variable, Linear equations
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Answer:
y= 4x -1
Step-by-step explanation:
m is the slope so it goes next to the x and b is the y intercept so it goes last