What is the y-intercept of (5,8) and (12,36)
2 answers:
Answer:
(0, -12)
Step-by-step explanation:
In order to find the y-intercept of the equation y = mx + b ( where m is the slope and b is the y-intercept), we first have to find the slope. We can do this by using the two points given to us.
To find the slope:
The slope is equal to:
Let's plug (5,8) and (12,36) into the equation:
Now let's solve for the slope:
36 -8 = 28
12 - 5 = 7
So we get:
Now that we've found the value of the slope, we can put it into the equation:
y = x + b
To find the value of b, we can input the values of one of the given points into the equation and solve for b. Let's use (5,8):
Input the values of x and y into the equation: 8 = (5) + b
Multiple by 5: 8 =
+ b
Divide 140 by 7: 8 = 20 + b
Subtract 20 from both sides of the equation to isolate b:
8 - 20 = 20 - 20 + b
-12 = b
The y-intercept is (0, -12).
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Answer:
a) X has geometric distribution with parameter 0.2
b) The expected number of attempts before hitting the target is 5
c) The variance is 20, the standard deviation is √20
d) The probability that less than 5 throws are needed before hitting the target is 0.5904.
Step-by-step explanation:
a) X has geometric distribution, with parameter p=0.2.
b) If X is geometric with parameter p, then its mean is 1/p and the variance is . With p = 0.2, the mean is 1/0.2 = 5. As a consecuence, the expected number of attempts before hitting the target is 5.
c) The variance with p = 0.2 is 0.8/0.2² = 20. The standard deviation is √20.
d) The probability that it takes less than 5 throws before hitting the target can be computed with the probability of the complementary event: the probability that the first 4 targets miss. That probability is 0.8⁴=0.4096. Therefore, the probability that it will take less than 5 throws before hitting the target is 1-0.4096 = 0.5904.