Helppp what’s is itttttt
1 answer:
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Answer:
His parents should invest $15,278.16 to reach this goal ⇒ 4th answer
Step-by-step explanation:
* Lets explain how to solve the problem
- Derrick will need $39,500 in 10 years for college tuition
∴ The future amount is $39,500
∴ The time for investment is 10 years
- P is the money his parents invest now at 9.5% annual interest,
compounded daily
∴ The rate is 9.5% per year compounded daily
- The formula of the compounded interest is:
, where
# A is the future value of money
# P is the value of investment
# r is the rate of interest in decimal
# t is the time of investment
# n is the period of the time
∵ A = $39,500
∵ t = 10
∵ r = 9.5/100 = 0.095
∵ n = 365 ⇒ compounded daily
- Lets use the formula above to find P
∴
∴
- Divide both sides by 2.58539
∴ P = $15278.16
∴ His parents should invest $15,278.16 to reach this goal
Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
For this case the p value is given
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 15 at 5% of signficance.
c) Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.
So for this case a type I of error would be reject the hypothesis that the true mean is less or equal than 15 and is actually true.
Step-by-step explanation:
Data given and notation
represent the sample mean
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)
Part a: State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean for vacation days is higher than 15, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic 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".
Part b: P-value and conclusion
The first step is calculate the degrees of freedom, on this case:
For this case the p value is given
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 15 at 5% of signficance.
Part c
Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.
So for this case a type I of error would be reject the hypothesis that the true mean is less or equal than 15 and is actually true.
Answer:
option C.
Step-by-step explanation:
we have that
The point (-5,-12) belong to the III quadrant
so
The value of the cosine is negative
Applying the Pythagoras Theorem
Find the value of the hypotenuse
The value of cosine of angle θ is the ratio between the side adjacent to angle θ and the hypotenuse