Answer:
Z = -1.333
P-value = 0.09176
Decision Rule: Reject 
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 
= 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:
Using the Z test statistics which can be expressed by the formula:
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 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.
Answer:
a = 82
b = 130
c = 118
Step-by-step explanation:
A quadrilateral is inscribed in a circle. So, it is a cyclic quadrilateral.
Opposite angles of a cyclic quadrilateral are supplementary.
Therefore,
a° + 98° = 180°
a° = 180° - 98°
a° = 82°
a = 82
By inscribed angle theorem:
a° = 1/2(b° + 34°)
82° * 2 = b° + 34°
164° - 34° = b°
b° = 130°
b = 130
Again by inscribed angle theorem:
76° = 1/2(c° + 34°)
76° *2 = c° + 34°
152° - 34° = c°
c° = 118°
c = 118
<span>You can solve this problem using this equation: 34x + 14 = 30x + 22.
The x stands for how many points each multiple choice question is worth. 34x is the number of multiple choice questions Francine got correct multiplied by the currently unknown number each point is worth, while 14 represents the 14 points that Francine was given for her essay. 30x is the number of multiple choice questions Cheryl got correct multiplied by the currently unknown number each point is worth, while 22 represents the 22 points that Cheryl was given for her essay.
To solve, we can subtract 30x from 34x on the left side of the equation, and subtract 14 from 22 on the right side of the equation. That leaves, 4x = 8. Next step would be dividing 4 from each side which gives us x = 2. In order for Francine and Cheryl to receive the same test score, each multiple choice questions would have to be worth 2 points.</span>
