Students in Mr. Tallow's class are reading a book that has 280 pages. Ramon decides to read 25% of the book each night. How many
2 answers:
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Answer:
Hence the function which has the smallest minimum is: h(x)
Step-by-step explanation:
We are given function f(x) as:
- f(x) = −4 sin(x − 0.5) + 11
We know that the minimum value attained by the sine function is -1 and the maximum value attained by sine function is 1.
so the function f(x) receives the minimum value when sine function attains the maximum value since the term of sine function is subtracted.
Hence, the minimum value of f(x) is: 11-4=7 ( when sine function is equal to 1)
- Also we are given a table of values for function h(x) as:
x y
−2 14
−1 9
0 6
1 5
2 6
3 9
4 14
Hence, the minimum value attained by h(x) is 5. ( when x=1)
- Also we are given function g(x) ; a quadratic function passing through (2,7),(3,6) and (4,7)
so, the equation will be:
Hence on putting these coordinates we will get:
a=1,b=3 and c=7.
Hence the function g(x) is given as:
So,the minimum value attained by g(x) could be seen from the graph is at the point (3,6).
Hence, the minimum value attained by g(x) is 6.
Hence the function which has the smallest minimum is h(x)
Answer:
(a) Null Hypothesis, :
41
Alternate Hypothesis, :
> 41
(b) The value of z test statistics is 1.08.
(c) We conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.
Step-by-step explanation:
We are given that in a random sample of 40 such periods from Spanish colonial times, the sample mean is x¯ = 47.0. Previous studies of sunspot activity during this period indicate that σ = 35.
It is thought that for thousands of years, the mean number of sunspots per 4-week period was about µ = 41.
Let = <u><em>mean sunspot activity during the Spanish colonial period.</em></u>
(a) Null Hypothesis, :
41 {means that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41}
Alternate Hypothesis, :
> 41 {means that the mean sunspot activity during the Spanish colonial period was higher than 41}
The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean = 47
σ = population standard deviation = 35
n = sample of periods from Spanish colonial times = 40
So, <em><u>the test statistics</u></em> =
= 1.08
(b) The value of z test statistics is 1.08.
(c) <u>Now, the P-value of the test statistics is given by;</u>
P-value = P(Z > 1.08) = 1 - P(Z < 1.08)
= 1 - 0.8599 = <u>0.1401</u>
Since, the P-value of the test statistics is higher than the level of significance as 0.1401 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.