Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8
centimeters, and the length of A C is 6.9 centimeters.
Which expressions can be used to find m∠BAC? Select three options.
Which expressions can be used to find m∠BAC? Select three options.
1 answer:
Answer: We can find angle BAC by using (1) SinA = 9.8/12
(2) CosA = 6.9/12
(3) TanA = 9.8/6.9
Step-by-step explanation: The question indicates that we have a right angled triangle ABC with the right angle at point C (that is, angle ACB is the right angle). Also the three sides have been labeled as AB equals 12 cm, CB equals 9.8 cm and AC equals 6.9 cm. Line AB has been identified as the hypotenuse and angle A (that is, BAC) is the reference angle. If angle A is the reference angle, then line CB facing angle A shall be the opposite side, while line AC is the adjacent (which lies between the reference angle and the right angle). Please see the attached diagram for details.
Having these details available, we can actually find angle A by using any of the three trigonometric ratios, since all three sides are given. Hence,
SinA = opposite/hypotenuse
SinA = 9.8/12
SinA = 0.8167
Checking with your calculator or table of values, A = 54.76 (approximately 55)
Also CosA = adjacent/hypotenuse
CosA = 6.9/12
CosA = 0.5750
Checking with your calculator or table of values A = 54.90 (approximately 55).
Finally TanA = opposite/adjacent
TanA = 9.8/6.9
TanA = 1.4203
Checking with your calculator or table of values A = 54.83 (approximately 55).
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Null hypothesis:
Alternative hypothesis:
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Step-by-step explanation:
Data given and notation
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sample 1
sample 2
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represent the proportion of renters who would buy the security system
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Concepts and formulas to use
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Null hypothesis:
Alternative hypothesis:
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(1)
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Statistical decision
For this case we don't have a significance level provided , but we can calculate the p value for this test.
Since is a two sided test the p value would be:
So the p value is a very low value and using any significance level for example always
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions NOT differs significantly.