Answer:
∠STU = 69°
Step-by-step explanation:
The angle with vertex T is called an "inscribed angle." It intercepts arc SU. The relationship you are asked to remember is that the measure of the inscribed angle (T) is half the measure of the arc SU.
Point V is taken to be the center of the circle. The angle with vertex V is called a "central angle." It also intercepts arc SU. The relationship you are asked to remember is that the measure of the central angle (V) is equal to the measure of arc SU.
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Using these two relationships together, we realize angle V is twice the measure of angle T:
∠SVU = 2×∠STU
18x +12° = 2(18x -57°) . . . . . . relationship between the marked angles
18x +12° = 36x -114° . . . . . eliminate parentheses
126° = 18x . . . . . . . . . . . add 114°-18x
∠STU = 18x -57° = 126° -57°
∠STU = 69°
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<em>Additional comment</em>
You may notice we did not solve for x. We only needed to know the value of 18x, so we stopped when we found that value. (Actually, we only need the value of 18x-57°. See below.)
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<em>Alternate solution</em>:
(18x +12°) -(18x -57°) = 18x -57° . . . . . . . subtract 18x -57° from both sides of the first equation.
69° = 18x -57° . . . . . simplify. This is the answer to the problem.
Answer:
<h2>x < 2</h2>
Step-by-step explanation:
Solving inequalities is easy, you just need to follow the standard rules of algebra. Also, when multiplying or dividing by a negative number, the inequality sign is reversed.
Step 1: Divide by 5
x < 2
Step 2: Check
5(1) < 10
5 < 10✔️
Step 3: Check Again
Since an inequality has multiple solutions, it is important to check at least 2, to determine if the entire range of solutions is true.
5(-6) < 10
-30 < 10✔️
Step 4: Verified Answer
x < 2
I'm always happy to help :)
Answer:
Sure, what do you need
Step-by-step explanation:
Answer: D. two-sample z-test for a difference in population proportions
Step-by-step explanation:
The options for the given questions were missing. The options are as follows:
A one-sample z-test for a sample proportion
B one-sample z-test for a population proportion
A
C two-sample z-test for a difference in sample proportions
D two-sample z-test for a difference in population proportions
Solution:
Sample proportions are used to estimate population proportions.
We are given the sample proportion of students from one state who ordered a yearbook = 70/150
We are also given the sample proportion of students from the other state who ordered a yearbook = 65/100
Since there are 2 samples and we want to investigate if there is a difference between 2 population of students,
Therefore, the most appropriate method for analyzing the results is
D. two-sample z-test for a difference in population proportions
