What is the value of the expression 1/2 (m÷3) +n A. 13/5 B. 13/10 C. 15/11 D. 15/17
1 answer:
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When we approach limits, we are finding values that are infinitesimally approaching this x-value. Essentially, we consider the approximate location that this root or limit appears. This is essential when it comes to taking Calculus, and finding the limit or rate of change of a function.
When we are attempting limits questions, there are several tests we attempt first.
1. Evaluate the limit by substituting the value of the x-value as it approaches the value (direct evaluation of a limit)
2. Rearrangement of the function, such that we can evaluate the limit.
3. (TRIGONOMETRIC PROPERTIES)
4. Using L'Hopital's Rule for indeterminate limits, such as 0/0, -infinity/infinity, or infinity/infinity.
For example:
1)
We can do this using the first and second method.
<em>Method 1: Direct evaluation:</em>
Substitute x = 0 to the function.
<em>Method 2: Rearranging the function
</em>
We can see that x - 25 can be rewritten as: (√x - 5)(√x + 5)
By rewriting it in this form, the top will cancel with the bottom easily, and our limit comes out the same.
Every example works exactly the same way, and by remembering these criteria, every limit question should come out pretty naturally.
When we are attempting limits questions, there are several tests we attempt first.
1. Evaluate the limit by substituting the value of the x-value as it approaches the value (direct evaluation of a limit)
2. Rearrangement of the function, such that we can evaluate the limit.
3. (TRIGONOMETRIC PROPERTIES)
4. Using L'Hopital's Rule for indeterminate limits, such as 0/0, -infinity/infinity, or infinity/infinity.
For example:
1)
We can do this using the first and second method.
<em>Method 1: Direct evaluation:</em>
Substitute x = 0 to the function.
<em>Method 2: Rearranging the function
</em>
We can see that x - 25 can be rewritten as: (√x - 5)(√x + 5)
By rewriting it in this form, the top will cancel with the bottom easily, and our limit comes out the same.
Every example works exactly the same way, and by remembering these criteria, every limit question should come out pretty naturally.
Answer:
Yes, since the test statistic value is greater than the critical value.
Step-by-step explanation:
Data given and notation
represent the mean for the downtown restaurant
represent the mean for the freeway restaurant
represent the sample standard deviation for downtown
represent the sample standard deviation for the freeway
sample size for the downtown restaurant
sample size for the freeway restaurant
t would represent the statistic (variable of interest)
significance level provided
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the true mean of revenue for downtown is higher than for freeway restaurant, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:
(1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Determine the critical value.
Based on the significance level and
we can find the critical values from the t distribution dith degrees of freedom df=36+36-2=55+88-2=70, we are looking for values that accumulates 0.025 of the area on the right tail on the t distribution.
For this case the value is
Calculate the value of the test statistic for this hypothesis testing.
Since we have all the values we can replace in formula (1) like this:
What is the p-value for this hypothesis test?
Since is a right tailed test the p value would be:
Based on the p-value, what is your conclusion?
Comparing the p value with the significance level given we see that
so we can conclude that we reject the null hypothesis, and the true mean for the downtown revenue restaurant seems higher than the true mean revenue for the freeway restaurant.
The best option would be:
Yes, since the test statistic value is greater than the critical value.