What is the perimeter of a square with an area of 81 cm2
2 answers:
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Answer:
The maximum power generated by the circuit is 300 watts.
Step-by-step explanation:
A quadratic function is one that can be written as an equation of the form:
f (x) = ax² + bx + c
where a, b and c (called terms) are any real numbers and a is nonzero.
In this case, f(x) is P(c) [the power generated], x is the current c (in amperes), a = -12, b = 120 and c = 0.
The vertex is a point that is part of the parabola, which has the value as ordered minimum or maximum function. If the scalar a> 0, the parabola opens or faces up and the vertex is the minimum of the function. In contrast, if a <0, the parabola opens downward and the vertex is the maximum of the function.
The calculation of the vertex, which in this case will be the maximum of the function, is carried out as follows:
- The value of x, in this case the value of current c in amperes, can be calculated with the formula
. In this case:
So c= 5 amperes. The current is 5 amperes.
- The value of y, in this case the value of the electric current in watts, is obtained by substituting the value of c previously obtained in the function. In this case: P(5)= -12*5²+120*5. So P(5)= 300 watts
<u><em>The maximum power generated by the circuit is 300 watts.</em></u>
Answer:
a)
b) For this case we need to find a critical value that accumulates of the area on each tail, we know that
, so then
, using the normal standard table or excel we see that:
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.
Step-by-step explanation:
Data given and notation
n=420+174=594 represent the random sample taken
X=174 represent the number of yellow peas
estimated proportion of yellow peas
is the value that we want to test
represent the significance level
Confidence=99% or 0.99
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 yellow peas is 0.23:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, 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 significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis.
b) Critical value
For this case we need to find a critical value that accumulates of the area on each tail, we know that
, so then
, using the normal standard table or excel we see that:
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.