Daniel expanded the expression as shown -3(-8x-4y+3/4)=10x-8y-1 1/4 what areas did he make like three options
1 answer:
Question
Daniel expanded the expression as shown. What errors did he make? Select three options.
A. The first term should be positive.
B. The second term should be positive.
C. The last term should be -1 1/2, not -1 1/4.
D. He divided -8 by -2 instead of multiplying -8 by -2.
E. He did not simplify the expression completely.
Answer:
Daniel's errors are (a), (b) and (c)
Step-by-step explanation:
To do this, we only need to solve the expression on the left.
So, we have:
Open bracket
From the expression, we can see that:
- The first term is positive
- The second is also positive
- And the third term is
So, Daniel's errors are (a), (b) and (c)
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Answer:
a) The 95% confidence interval would be given by (0.341;0.499)
b) The 99% confidence interval would be given by (0.316;0.524)
c) n=335
d)n=649
Step-by-step explanation:
1) Notation and definitions
number of high speed internet users that had been interrupted one or more times in the past month.
random sample taken
estimated proportion of high speed internet users that had been interrupted one or more times in the past month.
true population proportion of high speed internet users that had been interrupted one or more times in the past month.
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
1) Part a
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 95% confidence interval would be given by (0.341;0.499)
2) Part b
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 99% confidence interval would be given by (0.316;0.524)
3) Part c
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=335
4) Part d
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=649