Which of the following sets of ordered pairs in the form (x,y) represent a function of x?
1 answer:
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The equation is 0.1x + 0.15(50-x)=1.20(50)
Step-by-step explanation:
Here you need 50ml of 12% alcohol solution.
You have 10% and 15% alcohol solutions.
Take volume of 10% alcohol solution to be x ml
Take volume of 15% alcohol solution to be y ml
Form equations;
x+y=50 ml--------------------------equation 1
0.1x +0.15 y= 12% of 50
0.1x+0.15y=6-----------------------equation 2
Now you have simultaneous equations, use a graph tool to solve for values of x and y as attached.
or use the mixture equation the get value of x
0.1x + 0.15(50-x)=1.20(50)
The values of x and y are ;
(x,y) (30,20) which means;
y is 20 ml of 15% alcohol
x is 30 ml of 10% alcohol
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Keywords : concentration, mixture
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Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 42 at 1% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is higher than 42, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, 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 if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one side test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 42 at 1% of signficance.