Answer:
Option C is correct.
The test statistic for this question is -3.13
Step-by-step explanation:
To compute the z-test statistic, the formula is given as
z = (x - μ₀)/σₓ
x = p = sample proportion of the 500 college students sampled, that favor reducing the deficit using only spending cuts with no tax increase = (75/500) = 0.15
μ₀ = p₀ = the proportion to be compared against, that is, the proportion of Americans that favor reducing the U.S. budget deficit by using spending cuts only, with no tax increases = 20% = 0.20
σₓ = standard error of the sample proportion = √[p(1-p)/n]
p = 0.15
n = Sample size = 500
σₓ = √[0.15×0.85/500] = 0.01597
z = (0.15 - 0.20) ÷ 0.01597
z = -3.13
Hope this Helps!!!
By definition of tangent,
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
Recall the double angle identities:
sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)
cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):
sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))
and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.
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We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get
sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5
Then
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)
tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)
tan(2<em>θ</em>) = 24/7
Answer:
3. π
4. it occurs when x = 0
Step-by-step explanation:
Answer:
0.001
Step-by-step explanation:
i hope this helps :)
A). They are not similar, because 6/13 is not equal to 8/20
For triangles to be similar, the ratios of sides need to be the same (shortest to shortest, middle to middle, longest to longest). The shortest sides are 6 and 13, respectively, the middle ones are 8 and 20. Because 6/13 is not equal to 8/20, the triangles are not similar.
