1. A boat is 18 ft away from a point perpendicular to the shoreline. A person stands at a point down the shoreline so that a 68°
angle is formed between the closest point to the boat, the person, and the boat. How far is the person from the boat? Round your answer to the nearest tenth of a foot. Show your work please to help me understand
1 answer:
Answer:
19.4 feet
Step-by-step explanation:
When calculating distances using perpendicular angles, we use trig functions such as Sin, Cos, and Tan.
- Sine is defined in a perpendicular triangle as the ratio of the opposite side to the angle over the hypotenuse.
- Cosine is defined in a perpendicular triangle as the ratio of the adjacent side to the angle over the hypotenuse.
- Tangent is defined in a perpendicular triangle as the ratio of the opposite side over the adjacent side.
Because our angle and know side value are across from each other and we need to know the hypotenuse, we chose to use Sine.
We set up the equation .
We isolate h by multiplying h across the equal sign and dividing sin (68) across as well.
And finally we have . We input to calculator.
See the attached picture below showing the shore with the boat out at sea and the position of the person.
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Answer:
The Musician had $29 before performing at the fairs
Step-by-step explanation:
Let the initial amount musician has be x
At the first musician doubled his money and spent
$30 , this can be written as
2(x) -30---------------------------------(1)
At the second he tripled his money and spent $54.
3(2x -30) - 54
=> 6x-90-54
=> 6x- 144--------------------------------(2)
At the third, he quadrupled his money and spent $72
4( 6x- 144) - 72
24x - 576 - 72
24x -648-------------------------------(3)
At-last he had $48
24x -648 = 48
24x = 48+ -648
24x =696
x =
x = 29
Answer:
If we compare the p value and a significance level for example we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean it's not significantly less than 20 min.
Step-by-step explanation:
Data given and notation
represent the average lateral recumbency for the sample
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to apply a left tailed test.
What are H0 and Ha for this study?
Null hypothesis:
Alternative hypothesis :
Compute the test statistic
The statistic for this case is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
The degrees of freedom are given by:
Give the appropriate conclusion for the test
Since is a one side left tailed test the p value would be:
Conclusion
If we compare the p value and a significance level for example we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean it's not significantly less than 20 min.