How to to determine if two polygons have the same side and shape
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Answer:
The function that could be the function described is;
Step-by-step explanation:
The given parameters of the cosine function are;
The period of the cosine function = 3
The maximum value of the cosine function = 20
The minimum value of the cosine function = 0
The general form of the cosine function is presented as follows;
y = A·cos(ω·x - ∅) + k
Where;
= The amplitude = Constant
The period, T = 2·π/ω
The phase shift, = ∅/ω
k = The vertical translation = Constant
Therefore, by comparison, we have;
T = 3 = 2·π/ω
∴ ω = 2·π/3
The range of value of the cosine of an angle are;
-1 ≤ cos(θ) ≤ 1
Therefore, when A = 10, cos(ω·x - ∅) = 1 (maximum value of cos(θ)) and k = 10, we have;
y = A × cos(ω·x - ∅) + k
y = 10 × 1 + 10 = 20 = The maximum value of the function
Similarly, when A = 10, cos(ω·x - ∅) = -1 (minimum value of cos(θ)) and k = 10, we get;
y = 10 × -1 + 10 = 0 = The minimum value of the function
Given that the function is a reflection of the parent function, we can have;
A = -10, cos(ω·x - ∅) = -1 (minimum value of cos(θ)) and k = 10, to get;
y = -10 × -1 + 10 = 20 = The maximum value of the function
Similarly, for cos(ω·x - ∅) = 1 we get;
y = -10 × 1 + 10 = 0 = The minimum value of the function
Therefore, the likely values of the function are therefore;
A = -10, k = 10
The function is therefore presented as follows;
y = -10 × cos(2·π/3·x) + 10
Answer:
If we compare the p value obtained with the significance level assumed we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of homes in Omaha with one or more lawn mowers is not ignificantly higher than 0.65
Step-by-step explanation:
Data given and notation
n=497 represent the random sample taken
X=340 represent the homes in Omaha with one or more lawn mowers
estimated proportion of homes in Omaha with one or more lawn mowers
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 true proportion of homes in Omaha with one or more lawn mowers is higher than 0.65.:
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:
If we compare the p value obtained with the significance level assumed we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of homes in Omaha with one or more lawn mowers is not ignificantly higher than 0.65