The length of Joseph’s rectangular poster is two times it’s width. If the perimeter is 24 inches, what is the area of the poster
1 answer:
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Answer:
The boat turned <u>39°</u> degrees when it made its first turn.
Step-by-step explanation:
The question is as following:
A boat traveled north for 28 miles, then tuned x° south west and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.
By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.
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See the attached figure which represent explanation of the problem.
The boat start from point A to point B then stopped at point C
AB = 28 miles, BC = 25 miles and AC = 18 miles.
It is required to find the angle x
By applying the cosine Rule:
AC² = AB² + BC² - 2 * AB * BC * cos x
18² = 28² + 25² - 2 * 28 * 25 * cos x
2 * 28 * 25 * cos x = 28² + 25² - 18²
1400 cos x = 1085
Cos x = 1085/1400 = 0.775
x = Cos⁻¹ 0.775 = 39.2° = 39° to the nearest degree.
So, the boat turned <u>39°</u> degrees when it made its first turn.
Hi there!
We are given the equation:
x² - 2y = 7
To verify if each ordered pair is apart of the function, we can plug in their respective x and y values:
1. (5)² - 2(8) = 7
25 - 16 = 9 ≠ 7. This is NOT correct.
2. (-1)² - 2(-3) = 7
1 + 6 = 7. This is correct.
3. (-4)² - 2(-11.5) = 7
16 + 23 = 39 ≠ 7. This is NOT correct.
4. (1.2)² - 2(-2.78) = 7
1.44 +5.56 = 7. This is correct.
Thus, only 1 and 4 are the correct answers.
Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 5% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z 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 conduct a hypothesis in order to check if the mean is equal to 12, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-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:
P-value
Since is a right tailed test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 5% of signficance.