Answer:
(29.14 ; 30.06)
Step-by-step explanation:
Given that'
Sample size (n) = 57
Mean (m) = 29.6
Population standard deviation (σ) = 2.7
Confidence interval = 80%
= (1 - 0.8) / 2 = 0.1
Mean ± z * σ/√n
Using the Z probability calculator : Z0. 1 = 1.28
Hence,
29.6 ± 1.28 * (2.7 / √57)
29.6 - (1.28 * 0.3576237) ; 29.6 + (1.28 * 0.3576237)
29.142241664 ; 30.057758336
(29.14 ; 30.06)
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

well then therefore

so we're really looking for the equation of a line with slope of -1/3 and that passes through (1, -3 )

Answer: Choice A. sin(A) = cos(B)
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Explanation:
The rule is that sin(A) = cos(B) if and only if A+B = 90.
Note how
- sin(A) = opposite/hypotenuse = BC/AB
- cos(B) = adjacent/hypotenuse = BC/AB
Since both result in the same fraction BC/AB, this helps us see why sin(A) = cos(B). Similarly, we can find that cos(A) = sin(B).
In the diagram below, the angles A and B are complementary, meaning they add to 90 degrees. So this trick only applies to right triangles.
The side lengths can be anything you want, as long as you're dealing with a right triangle.
Step-by-step explanation:
5x=1-6
5x=-5
<h3> x=-1</h3>
-5(-1)-8y=2
5-8y=2
-8y =2-5
-8y=-3
<h3> y=3/8</h3>
60×4=240
so 240/1 and 60×4
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1
both are equal to 240