The area of a circular wave expands across a still pond such that its radius increases by 14 cm each second. Write a formula for
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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.
A polynomial is said to be in standard form if it is written in the order of degree from highest to lowest from left to right.
The degree of a term of a polynomial is the exponent of the variable or the sum of the exponents of the variables of that term of the polynomial.
Thus, given the expression
has a degree of 6, and
has a degree of 6.
Thus, the exponent of the variable or the sum of the exponents of the variables of the next term of the polynomial must be less than or equal to 6 for the polynomal to be said to be in standars form.
Therefore, the <span>terms that could be used as the last term of the given expression to create a polynomial written in standard form are
</span>
The degree of a term of a polynomial is the exponent of the variable or the sum of the exponents of the variables of that term of the polynomial.
Thus, given the expression
Thus, the exponent of the variable or the sum of the exponents of the variables of the next term of the polynomial must be less than or equal to 6 for the polynomal to be said to be in standars form.
Therefore, the <span>terms that could be used as the last term of the given expression to create a polynomial written in standard form are