How many liters of a 40% sugar solution must be mixed with 30 liters of a 60% sugar solution to make a 56 % sugar solution?
2 answers:
Answer:
7.5 liters of a 40% sugar solution
Step-by-step explanation:
Let
x ----> liters of a 40% sugar solution
Remember that
we know that
The amount of liters of a 40% sugar solution (x) multiplied by 0.40 plus the amount of liters of a 60% sugar solution (30 L) multiplied by 0.60 must be equal to the total amount of liters mixed (x+30) multiplied by 0.56
solve for x
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Answer:
a) Null hypothesis:
Alternative hypothesis:
b)
For this case the p value is given
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 15 at 5% of signficance.
c) Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.
So for this case a type I of error would be reject the hypothesis that the true mean is less or equal than 15 and is actually true.
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)
Part a: State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean for vacation days is higher than 15, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and 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".
Part b: P-value and conclusion
The first step is calculate the degrees of freedom, on this case:
For this case the p value is given
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 15 at 5% of signficance.
Part c
Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.
So for this case a type I of error would be reject the hypothesis that the true mean is less or equal than 15 and is actually true.
ANSWER:
The average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.
STEP-BY-STEP EXPLANATION:
The cental limit theorem states, that id the sample size is large (30 or more), then the sampling distribution of the sample means is approximately normal with mean ц and standar deviation б/
Thus the correct answer is the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.
Answer:
See attachment for cube
Step-by-step explanation:
Given
Required
The net of the cuboid
A cuboid has 6 faces.
The dimension of these faces are:
Length and Width; Length and Height;
Length and Width; Length and Height;
Width and Height; Width and Height;
This means that the faces will have the following dimensions:
6cm by 3cm; 6cm by 2cm
6cm by 3cm; 6cm by 2cm
3cm by 2cm; 3cm by 2 cm
Taking into account the above measurements and dimensions, you draw 6 faces, then join similar sides lengths.
<em>See attachment for net of the cuboid</em>
