Given that lines a and b are parallel and that m∠6 = 65°, find m∠3.
2 answers:
Answer: The correct option is (B) 65°.
Step-by-step explanation: Given that the lines a and b are parallel and m∠6 = 65°.
We are to find the measure of angle 3.
From the figure, we note that
parallel lines a and b are cut by a tranversal. So, angle 2 and angle 6 are corresponding angles.
This implies that
Now, angle 2 and angle 3 are vertically opposite angles and so their measures should be equal.
That is,
Thus, the measure of angle 3 is 65°.
Option (B) is CORRECT.
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Answer:
<em>The domain of f is (-∞,4)</em>
Step-by-step explanation:
<u>Domain of a Function</u>
The domain of a function f is the set of all the values that the input variable can take so the function exists.
We are given the function
It's a rational function which denominator cannot be 0. In the denominator, there is a square root whose radicand cannot be negative, that is, 4-x must be positive or zero, but the previous restriction takes out 0 from the domain, thus:
4 - x > 0
Subtracting 4:
- x > -4
Multiplying by -1 and swapping the inequality sign:
x < 4
Thus the domain of f is (-∞,4)
Using the z-distribution, it is found that the 90% confidence interval is given by: (0.6350, 0.6984).
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
In this problem, we have a 90% confidence level, hence, z is the value of Z that has a p-value of
, so the critical value is z = 1.645.
The sample size and the estimate are given by:
Hence, the bounds of the interval are given by:
The 90% confidence interval is given by: (0.6350, 0.6984).
More can be learned about the z-distribution at brainly.com/question/25890103
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