On a can of sardines it is written that the can contains 10 sardines. You open up 100 cans and find the average is 9.75 sardines with a standard deviation of 1. What is the test statistic in a test of the null hypothesis that the population average is 10? Can you reject the null at the 5% significance level?
Answers
Answer:
The test statistic is -2.5
Yes, I can reject the null hypothesis at 5% significance level.
Step-by-step explanation:
Null hypothesis: The average number of sardines in a can is 9.75
Alternate hypothesis: The average number of sardines in a can is greater than 9.75
Test statistic (z) = (sample mean - population mean) ÷ sd/√n
sample mean = 9.75
population mean = 10
sd = 1
n = 100
z = (9.75 - 10) ÷ 1/√100 = -0.25 ÷ 0.1 = -2.5
The test is a one-tailed test. At 5% significance level, the critical value is 1.645
Conclusion:
Reject the null hypothesis because the test statistic -2.5 is less than the critical value 1.645
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Select all the correct answers.Which of the following should be subtracted from a check register balance when comparing it with a bank statement? ATM withdrawal fee outstanding deposit interest earned NSF fee
What is the greatest common factor osb42 and 63?
Simplify the following expression by using the distributive property 6(3a-4)
How is this number read out loud 0.034
4
B.
6
C.
12
D.
7
Answers
Answer:
the answer is C. 12
Step-by-step explanation:
Answers
Answer:
A) (3,-2)
Step-by-step explanation:
A) (3,-2)
Answers
Answer:
x = −π/2, x = π/2
Step-by-step explanation:
Given f(x) = 6x tan x and the interval −π/2 < x < π/2, we know that tan x has asymptotes in both extremes of the interval. To find the vertical asymptotes we evaluate the limit in the x-values we think asymptote can appear, in this case for x = −π/2 and x = π/2.
Then, x = −π/2 and x = π/2 are vertical asymptotes.
Answer: Does not exist.
Step-by-step explanation:
Since, given function, f(x) = 6x tan x, where −π/2 < x < π/2.
⇒ f(x) =
And, for vertical asymptote, cosx= 0
⇒ x = π/2 + nπ where n is any integer.
But, for any n x is does not exist in the interval ( -π/2, π/2)
Therefore, vertical asymptote of f(x) where −π/2 < x < π/2 does not exist.
2. Regular pentagon PENTA has side lengths that are 9 meters long. To the nearest square meter, find the area of the pentagon.
Area of pentagon PENTA = _____square centimeter
Answers
Given
1) Trapezoid BEAR with bases 11.5 and 6.5 and height 8.5, all in cm.
2) Regular pentagon PENTA with side lengths 9 m
Find
The area of each figure, rounded to the nearest integer
Solution
1) The area of a trapezoid is given by
... A = (1/2)(b1 +b2)h
... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77
The area of BEAR is about 77 cm².
2) The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...
... A = (1/2)ap
... A = (1/2)(s/(2tan(180°/n)))(ns)
... A = (n/4)s²/tan(180°/n)
We have a polygon with s=9 and n=5, so its area is
... A = (5/4)·9²/tan(36°) ≈ 139.36
The area of PENTA is about 139 m².
Answer:139 cm squared
The area of a trapezoid is given by
... A = (1/2)(b1 +b2)h
... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77
The area of BEAR is about 77 cm².
The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...
... A = (1/2)ap
... A = (1/2)(s/(2tan(180°/n)))(ns)
... A = (n/4)s²/tan(180°/n)
We have a polygon with s=9 and n=5, so its area is
... A = (5/4)·9²/tan(36°) ≈ 139.36
The area of PENTA is about 139 m².
Answers
Answer:
$15,000
Step-by-step explanation:
The $1500 interest on a home equity loan used for purposes other than home improvement is not deductible with other home loan interest as an itemized deduction.
However, the interest on a loan for qualified educational expenses may be considered an adjustment to income, within limits.
Only the $15,000 main mortgage interest can be an itemized deduction.
Final answer:
The total possible mortgage interest deduction for Mark in this scenario is $16,500. However, the actual amount he can deduct depends on his adjusted gross income and whether his itemized deductions exceed the standard deduction.
Explanation:
Under US tax law, taxpayers can deduct the interest on home mortgages and home equity loans, subject to some limitations. The interest expense on the main mortgage ($15,000) and the interest expense on the home equity loan ($1,500) can be combined for a total interest deduction of $16,500. However, the deduction may not be the full amount if there are other factors that would limit the amount of itemized deductions that Mark can claim. This can depend on his adjusted gross income and whether the total of his itemized deductions exceeds the standard deduction. It's also worth noting that the tax benefits of home ownership, such as the mortgage interest deduction, is a key reason why many people choose to buy rather than rent, as it can lead to significant financial savings.
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Answers
36 teams
Final answer:
To form teams, divide the total number of players by the number of players per team. In this case, 36 teams are needed.
Explanation:
To find out how many teams will be formed, we divide the total number of players by the number of players assigned to a team. In this case, there are 432 players and 12 players per team. So, we divide 432 by 12:
Number of teams = 432 ÷ 12 = 36 teams
Therefore, the league will need to form 36 teams to accommodate all the players.
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