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san4es73 [151]
3 years ago
6

How do I prove that these are the vertices of an isosceles triangle: (-3,0), (0,4), (3,0)?

Mathematics
1 answer:
castortr0y [4]3 years ago
3 0
In an isoceles triangle two angles are equal
if u take the coordinates and apply it in the graph it makes and isoceles triangle
as the y-axis is zero two of the ends will be level and x-axis is equal on both sides of the origin so (0,4) will be the third non equal angle
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Find the distance between each pair of numbers on the number line; then find the coordinate of their midpoint.
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Answer:

d = 1 7/24 or 31/24;  midpoint would be half of that,or 31/48

Step-by-step explanation:

Since distance is absolute value, add 2/3 and 5/8 to get the entire distance.  Midpoint is that distance divided by 2.

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My triangle solver says EF ≈ 7.5 ft.

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The law of cosines is usually used for this.

EF^2 = DE^2 +DF^2 -2*DE*DF*cos(D)
.. = 6^2 +11^2 -2*6*11*cos(40°)
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EF ≈ √55.88 ≈ 7.5 . . . ft

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A poll of 1068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At a
zubka84 [21]

Answer:

Z = -1.333

P-value  = 0.09176

Decision Rule: Reject H_o if ∝  is greater than the P-value

Conclusion: Since P-value is >  the level of significance ∝, we fail to reject the null hypothesis, therefore there is insufficient evidence to conclude that at least half of all voters prefer the Democrat.

Step-by-step explanation:

Given that:

The sample size of the poll = 1068

The proportion of voters that preferred Democratic candidate is \hat p = 0.48

To test the claim that at least half of all voters prefer the Democrat, i.e 1/2 = 0.5

The null hypothesis and the alternative hypothesis can be computed as:

H_o : p \geq 0.50

H_1 : p < 0.50

Using the Z test statistics which can be expressed by the formula:

Z = \dfrac{\hat p - p}{\dfrac{\sqrt{p(1-p) }}{n}}}

Z = \dfrac{0.48 - 0.5}{\dfrac{\sqrt{0.5(1-0.5) }}{1068}}}

Z = \dfrac{-0.02}{\sqrt{\dfrac{{0.5(0.5) }}{1068}}}

Z = \dfrac{-0.02}{\sqrt{\dfrac{{0.25}}{1068}}}

Z = \dfrac{-0.02}{0.015}

Z = -1.333

P-value = P(Z< -1.33)

From z tables,

P-value  = 0.09176

The level of significance ∝ = 0.05

Decision Rule: Reject H_o if ∝  is greater than the P-value

Conclusion: Since P-value is >  the level of significance ∝, we fail to reject the null hypothesis, therefore there is insufficient evidence to conclude that at least half of all voters prefer the Democrat.

5 0
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