The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to
1 answer:
Answer:
An equation that represents this path is described below in detail.
Step-by-step explanation:
The equalization that describes the pathway of the swimmer to the shoreline can be described in the slope-intercept pattern, given as.
Where,
Slope (m) = the adverse reciprocal of the incline of the shoreline, considering it is perpendicular to it = ??
y-intercept (b) = ??
Find the incline of the shoreline using, (0, 1) and (4, 4):
.
Considering the incline of the shoreline is ¾. The incline of the pathway of the swimmer would be the adverse reciprocal of ¾.
The adverse reciprocal of ¾ = -⁴/3.
The incline of the swimmer's path = -⁴/3.
Applying the coordinate of the position of the swimmer (6, 1), and the incline of the way, we can find b, the y-intercept of the way.
Substitute x = 6, y = 1 and m = -⁴/3 into y = mx + b, to find b.
Thus:
1 = (-⁴/3)(6) + b
1 = -8 + b
Add 8 to both sides
1 + 8 = b
9 = b
b = 9
Substitute m = -⁴/3 and b = 9 into y = mx + b.
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Answer:
(a) The value of <em>x</em> is 5.
(b) The value of <em>y</em> is 15.
Step-by-step explanation:
Let the random variable <em>X</em> represent the number of electric toasters produced that require repairs within 1 year.
And the let the random variable <em>Y</em> represent the number of electric toasters produced that does not require repairs within 1 year.
The probability of the random variables are:
P (X) = 0.20
P (Y) = 1 - P (X) = 1 - 0.20 = 0.80
The event that a randomly selected electric toaster requires repair is independent of the other electric toasters.
A random sample of <em>n</em> = 20 toasters are selected.
The random variable <em>X</em> and <em>Y</em> thus, follows binomial distribution.
The probability mass function of <em>X</em> and <em>Y</em> are:
(a)
Compute the value of <em>x</em> such that P (X ≥ x) < 0.50:
Use the Binomial table for <em>n</em> = 20 and <em>p</em> = 0.20.
The least value of <em>x</em> that satisfies the inequality P (X ≥ x) < 0.50 is:
<em>x</em> - 1 = 4
<em>x</em> = 5
Thus, the value of <em>x</em> is 5.
(b)
Compute the value of <em>y</em> such that P (Y ≥ y) > 0.80:
Use the Binomial table for <em>n</em> = 20 and <em>p</em> = 0.20.
The least value of <em>y</em> that satisfies the inequality P (Y ≥ y) > 0.80 is:
20 <em>- y</em> = 5
<em>y</em> = 15
Thus, the value of <em>y</em> is 15.