What is the value of y?
1 answer:
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Answer:
∠6=116°
Step-by-step explanation:
Buckle up :)
- We are given the values of ∠4
and ∠8
.
- Vertical angles are congruent. Angle 4 and angle 1 are vertical angles, so angle 1 is also
.
- ∠1 and ∠8 are alternate exterior angles. The transversal is the line that crosses over the parallel lines. When two angles are on opposite sides of the transversal, they are alternate angles. When the two angles are on the outside of the parallel lines, they are exterior angles. This makes them alternate-exterior angles.
- Alternate exterior angles are congruent. This means that ∠1≅∠8. Write an equation in order to solve for x:
Solve for x. Subtract 94 from both sides:
Add 5x to both sides:
Divide both sides by 3:
Insert the value of x into angle 4 because they are same-side interior angles. This is because they are on the same side of the transversal and within the parallel lines. Same-side interior angles are supplementary, so their value will add up to 180°. Therefore, in order to find angle 6, we need to first find the true value of angle 4:
∠4 is 64°. Use ∠a+∠b=180 to find angle 6:
a represents angle 6. Subtract 64 from both sides:
Angle 6 has a measure of 116°.
:Done
<h2>Answer with explanation:</h2>
Given : In a restaurant, the proportion of people who order coffee with their dinner is p.
Sample size : n= 144
x= 120
The null and the alternative hypotheses if you want to test if p is greater than or equal to 0.85 will be :-
Null hypothesis : [ it takes equality (=, ≤, ≥) ]
Alternative hypothesis : [its exactly opposite of null hypothesis]
∵Alternative hypothesis is left tailed, so the test is a left tailed test.
Test statistic :
Using z-vale table ,
Critical value for 0.05 significance ( left-tailed test)=-1.645
Since the calculated value of test statistic is greater than the critical value , so we failed to reject the null hypothesis.
Conclusion : We have enough evidence to support the claim that p is greater than or equal to 0.85.