Answer:
g(n) = 180 - 20(n-1)
Step-by-step explanation:
Since your has its g(1) value as 180, we put 180 in front. Then, we subtract 20 multiplied by n-1, n being the sequence number. For example, if the recursive function has recursed 3 times, we do 3-1, which is 2. We multiply 2 with 20, which is 40. Finally, we subtract 40 from 180, which is 140. This equation is equivalent to g(3) = 180 - 20(3-1). When the sequence has g(3), we clearly see the answer is 140. When we look at the sequence, the third number is 140, proving this equation correct.
Answer:
20
Step-by-step explanation:
x = price
y = number of keyboard
xy = 540
(x-2)(y+3) = 540
x = 540/y
==> x = 20
==> y = 27
<span>Answer:
The probabilities that either a) the butterfly dies within 7 days or b) the butterfly lives longer than 7 days must add up to one. We know the second probability (lives longer than 7 days)--it is given. So now set up an equation and solve:
P(t > 7) = 36 / 13² = 36/169
-->
36/169 + x = 1 --> x = 1 - 36/169 = 133/169 ~ 0.7870 or 78.70%
b)
7% is the probability (the expected value) that a butterfly will survive more than t days. Again, this formula is given:
36/(t + 6)² = 0.07 --> (t + 6)² = 36/.07 --> t = âš(36/.07) - 6 ~ 16.68 days
This is the value of t that will give a probability of 7%.
c)
This one is a little trickier. Technically the mean lifetime should be calculated as:
â«t * p(t)dt where p(t) is the probability distribution function
But we have a cumulative probability distribution. I think we need to find the probability distribution from this cumulative one. Which is easy because the cumulative distribution function is an integral of the probability distribution function:
P(t) = â«p(x)dx, from x = t, to x = âž
Now hopefully it's easy to see that P(t) is an anti-derivative of p(x). Said the other way p(x) is the derivative of P(t):
P'(t) = -72/(t + 6)Âł
--> but p(t) shouldn't be negative--also you can convince yourself that it should be positive by using the above value (from t --> âž...you get -0 - a negative = a positive)
p(t) = 72/(t + 6)Âł
Now we can calculate the mean lifetime by integrating:
72â«t/(t + 6)Âłdt
--> there's a very easy u-substitution to use here:
u = t + 6 --> du = dt --> t = u - 6
-->
â«(u - 6)/uÂłdu = â«(1/u² - 6/uÂł)du = -1/u + 3/u² + C
--> now evaluate from t = 0 to t = âž or from u = 0 + 6 = 6 to u = âž
0 - (-1/6 + 3/36) = 1/6 - 1/12 = 1/12
--> multiply by the 72
72/12 = 6 days</span>
0.16÷0.3220=0.49689440993
Answer:
Option D.
Step-by-step explanation:
we have
-----> the parent function
The vertex of the function F(x) is the origin (0,0)
The vertex of the function G(x) is the point (0,-1)
so
The rule of the translation is equal to
(x,y)------> (x,y-1)
That means ------> The translation is 1 unit down
Applying the rule of the translation to F(x)
F(x)-------> G(x)