Answer:
a. 0.45 b. 1
Step-by-step explanation:
We will be using Poisson Approximation of Binomial because n = 80,000 is large and probability (<em>p) </em>is very small.
We calculate for (a) as follows:
The probability that both partners were born on April 30 is
<em>p </em>= 1/365 X 1/365
<em>p </em>= 1/133,225
<em>p </em>= 0.00000751
Using Poisson Approximation, we have:
λ = n<em>p</em>
λ = 80,000 X 0.00000751
λ = 0.6
We use λ to calculate thus:
P (X 
1) = 1 - P ( X = 0)
= 1 - e^-λ
= 1 - e^-0.6
= 0.451
There is a 45.1% probability that, for at least one of these couples, both partners were born on April 30.
(b) To calculate the probability that both partners celebrated their birthday on the same day:
<em>p </em>(same birthday) = 365 X 1/365 X 1/365
= 1/365
λ = n<em>p</em>
λ = 80,000 X 1/365
λ = 219.17
P (X 1) = 1 - P ( X = 0)
= 1 - e^-λ
= 1 - e^-219.17
≈ 1
There is almost 100% probability that, for at least one of these couples, both partners celebrate their birthday on the same day of the year.
Answer:
x = 8 sqrt(2)
Step-by-step explanation:
Since this is a right triangle
sin 45 = opp side/ hypotenuse
sin 45 = 8/x
Multiply each side by x
x sin 45 = 8/x *x
x sin 45 = 8
Divide each side by sin 45
x sin 45 /sin 45 = 8 /sin 45
x = 8 / sin 45
We know sin 45 = 1/ sqrt (2)
x = 8 / 1 / sqrt(2)
x = 8 sqrt(2)
Answer:
w = 33
Step-by-step explanation:
w ÷ 3.3 = 10
multiply both sides by 3.3:
w ÷ 3.3 x 3.3 = 10 x 3.3
⇒ w = 33
The point-slope form of the equation of the line is:
(y - y1) = m (x - x1)
So, (y + 2) = - 1/3 (x - 4) in the point-slope form is:
[y - (-2) ] = (-1/3) [ x - 4 ]
You must, then realize that the line passes through the point (4,-2) and its slope is - 1 /3.
That slope, -1 / 3, means that the function is decresing (because the slope is negative), and it decreases one unit when x increases 3 units.
Now you can fill in the blanks in this way:
Plot the point (4, -2), move 1 unit down, and 3 units over to find the next point on the line.
Note that the 2nd equation can be re-written as y=8x-10.
According to the second equation, y=x^2+12x+30.
Equate these two equations to eliminate y:
8x-10 = x^2+12x+30
Group all terms together on the right side. To do this, add -8x+10 to both sides. Then 0 = x^2 +4x +40. You must now solve this quadratic equation for x, if possible. I found that this equation has NO REAL SOLUTIONS, so we must conclude that the given system of equations has NO REAL SOLUTIONS.
If you have a graphing calculator, please graph 8x-10 and x^2+12x+30 on the same screen. You will see two separate graphs that do NOT intersect. This is another way in which to see / conclude that there is NO REAL SOLUTION to this system of equations.
