A given angle measures 90°.. Then, note that the total measurement of the triangle is 180°... Subtract 180° by 90°, and the other angles must add up to 90°!
Good luck!
Answer:
a) <u>0.4647</u>
b) <u>24.6 secs</u>
Step-by-step explanation:
Let T be interval between two successive barges
t(t) = λe^λt where t > 0
The mean of the exponential
E(T) = 1/λ
E(T) = 8
1/λ = 8
λ = 1/8
∴ t(t) = 1/8×e^-t/8 [ t > 0]
Now the probability we need
p[T<5] = ₀∫⁵ t(t) dt
=₀∫⁵ 1/8×e^-t/8 dt
= 1/8 ₀∫⁵ e^-t/8 dt
= 1/8 [ (e^-t/8) / -1/8 ]₀⁵
= - [ e^-t/8]₀⁵
= - [ e^-5/8 - 1 ]
= 1 - e^-5/8 = <u>0.4647</u>
Therefore the probability that the time interval between two successive barges is less than 5 minutes is <u>0.4647</u>
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b)
Now we find t such that;
p[T>t] = 0.95
so
t_∫¹⁰ t(x) dx = 0.95
t_∫¹⁰ 1/8×e^-x/8 = 0.95
1/8 t_∫¹⁰ e^-x/8 dx = 0.95
1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t = 0.95
- [ e^-x/8]¹⁰_t = 0.96
- [ 0 - e^-t/8 ] = 0.95
e^-t/8 = 0.95
take log of both sides
log (e^-t/8) = log (0.95)
-t/8 = In(0.95)
-t/8 = -0.0513
t = 8 × 0.0513
t = 0.4104 (min)
so we convert to seconds
t = 0.4104 × 60
t = <u>24.6 secs</u>
Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is <u>24.6 secs</u>
Answer:
40 Tickets
80 Tickets
Step-by-step explanation:
To find how many tickets it will take to break even, we use the formula:
Our variables are:
Fixed Cost = $200
Sales Price = $10
Variable Cost = $5
Let's plug in our values into the formula.
So the class needs to sell a total of 40 Tickets to break even.
Since we know that it takes 40 tickets to break even a $200 Fixed cost. To make a profit of $200, we simply multiply the number of tickets sold by 2.
Number of tickets for $200 profit = 40 x 2
Number of tickets for $200 profit = 80 Tickets.
So the class needs to sell 80 Tickets to make a $200 Profit.
You'd multiply both by 5, so the answer is 5x+15
