Answer:
Step-by-step explanation:
This limit can be written as follows
Direct substitution means that we substitute in the value for x to get our limit
Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe the restriction o
n the value of x.
Please explain your work--I need to know how to work this problem more than I need an answer.
Please explain your work--I need to know how to work this problem more than I need an answer.
1 answer:
Answer:
The inequality is:
The result is:
Step-by-step explanation:
1. According to the Hinge Theorem, when you have two triangles and two sides of both triangles are congruent, and the included angle of the first triangle is larger than the included angle of the other triangle, the third side of the first one is longer than the third side of the second one.
2. Keeping this on mind, as you can see in the figure, both triangles has two equal sides, and the included angle of the first one is larger than the angle of the second one:
°>
°
3. Therefore, the third side of the first one is longer than the third side of the second triangle. So, you have the following inequality:
4. Solve for . Therefore, you obtain:
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The value of Z would be 225°
<h3>What is the angle at a point?</h3>The angle at a point are angles that add up to 360°
Thus, X + Y + Z = 360°
X = 20°
Y = 135°
Then, Z = 360° - X - Y
Z = 360° - 20° + 135°
Z = 360° - 155°
Z = 205°
Therefore, the value of Z is 205°
Learn more about angle at a point here:
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Answer:
The 98% confidence interval for population proportion of people who refuse evacuation is {0.30, 0.33].
Step-by-step explanation:
The sample drawn is of size, <em>n</em> = 5046.
As the sample size is large, i.e. <em>n</em> > 30, according to the Central limit theorem the sampling distribution of sample proportion will be normally distributed with mean and standard deviation
.
The mean is:
The confidence level (CL) = 98%
The confidence interval for single proportion is:
Here = critical value and <em>α </em>= significance level.
Compute the value of <em>α</em> as follows:
For <em>α</em> = 0.02 the critical value can be computed from the <em>z</em> table.
Then the value of is ± 2.33.
The 98% confidence interval for population proportion is:
Thus, the 98% confidence interval [0.30, 0.33] implies that there is a 0.98 probability that the population proportion of people who refuse evacuation is between 0.30 and 0.33.