Two solutions of different concentrations of acid are mixed creating 40 mL of a solution that is 32% acid. One-quarter of the so
2 answers:
You might be interested in
Answer:
Comparing the p value with a significance level for example we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the mean for the Campus 1 is significantly higher than the mean for the group 2.
Step-by-step explanation:
Data given
Campus Sample size Mean Population deviation
1 330 33 8
2 310 31 7
represent the mean for sample 1
represent the mean for sample 2
represent the population standard deviation for 1
represent the population standard deviation for 2
sample size for the group 1
sample size for the group 2
Significance level provided
z would represent the statistic (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the mean for Campus 1 is higher than the mean for Campus 2, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We have the population standard deviation's, and the sample sizes are large enough we can apply a z test to compare means, and the statistic is given by:
(1)
z-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.
With the info given we can replace in formula (1) like this:
P value
Since is a one right tailed test the p value would be:
Comparing the p value with a significance level for example we see that
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the mean for the Campus 1 is significantly higher than the mean for the group 2.
Answer:
Step-by-step explanation:
Step 1: Divide the numbers
Step 2: Simplify
Step 3: Simplify
Therefore, the simplified answer is
Answer:
The Translation is 5 units to the right and 8 units up
Step-by-step explanation:
* Lets talk about some transformation
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Now lets solve the problem
∵ The parent function is y = (0.5)^x
∵ f(x) = (0.5)^x - 5 + 8 after translation
- The x in the first function is (x - 5) in the second function
∴ There is a horizontal translation to the right 5 units
- the first function is (0.5)^x in the second function y = (0.5)^x - 5 + 8
∴ There is a vertical translation up 8 units
* The Translation is 5 units to the right and 8 units up
- Look to the attached graph to more understand
- The purple graph is y = (0.5)^x
- The black graph is f(x) = (0.5)^x-5 + 8
- To check the answer take a point from the y = (0.5)^x as (0 , 1), the
image of this point on f(x) is (5 , 9)
-The point (0 , 1) is shifted 5 units to the right and 8 units up
∴ Its x- coordinate move from 0 to 5, y- coordinate move from 1 to 9
