The base of a solid right pyramid is a regular hexagon with
2 answers:
Answer: Last option.
Step-by-step explanation:
Observe the base of the pyramid, which is a regular hexagon. You can see that there is a right triangle.
The area of the triangle can be calculated with this formula:
Where "b" is the base and "h" is the height.
You can say that the apothem is the height of the right triangle, then, you need to find the base applying the Pythagorean Theorem:
Then, the area of the triangle is:
Since the base of the pyramid is a regular hexagon, then you can multiply by 12 the area of the right triangle calculated above, in order to find the area of the hexagon. Then you get:
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Answer:
Null hypothesis:
Alternative hypothesis:
So the p value obtained was a very low value and using the significance level assumed we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of applicants who request financial aid is significantly higher than 0.35
Step-by-step explanation:
Data given and notation
n=150 represent the random sample taken
X=67 represent the applicants who request financial aid
estimated proportion of applicants who request financial aid
is the value that we want to test
represent the significance level
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion of applicants who request financial aid is higher than 0.35.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
So the p value obtained was a very low value and using the significance level assumed we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of applicants who request financial aid is significantly higher than 0.35
Answer:
Student A and Student B both answered 2 questions correctly.
See explanation below
Step-by-step explanation:
Note: that answers in the form:
ARE ALL EQUIVALENT.
First of all, 4/5 is equivalent to 0.8 if we do long division.
and 19/20 is 0.95 if we do long division.
Now, <u>Student A:</u>
Both of the fractions are correct and the negative sign is equivalent and makes the answer correct, so both are correct.
For <u>Student B:</u>
Similarly, both answers are correct for this student as well, looking at the equivalence we showed first.
Also, "-" (negative) in front of the parenthesis and inside parenthesis here doesn't matter.
Hence,
Student A and Student B both answered 2 questions correctly.