Perform the following division problem using both long division and synthetic division to show that they both give the same answ
er. Show your work.
( x 5 - 8x 4 +8x - 64 ) ÷ ( x - 8)
Second using a graphing calculator graph f(x)=x 5 - 8x 4 +8x - 64. Try Desmos.com
Analyze the graph. Do you see a connection between the x - 8 and the graph? What is the connection?
Include the picture of the graph with the long division and synthetic division.
( x 5 - 8x 4 +8x - 64 ) ÷ ( x - 8)
Second using a graphing calculator graph f(x)=x 5 - 8x 4 +8x - 64. Try Desmos.com
Analyze the graph. Do you see a connection between the x - 8 and the graph? What is the connection?
Include the picture of the graph with the long division and synthetic division.
1 answer:
Answer:
Step-by-step explanation:
a) Perform the following division problem using both long division and synthetic division to show that they both give the same answer. Show your work.
Attached in Figure 1
The quotient is: x^4+8
and the remainder is: 0
b) Second using a graphing calculator graph f(x)=x 5 - 8x 4 +8x - 64. Try Desmos.com
The graph is shown in Figure 2
c) Analyze the graph. Do you see a connection between the x - 8 and the graph? What is the connection?
The graph shows that the value of x is 8, for any value of y.
x-8 =0 => x=8 The value of x is 8 (The graph is attached in figure 3)
Both have same graph.
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Answer:
a) The 99% confidence interval for the difference of proportions is (0.0844, 0.3012).
b) We are 99% sure that the true difference in proportions is between 0.0844 and 0.3012. Since all values are positive, there is significant evidence at the 1 - 0.99 = 0.01 significance level to conclude that the proportion is the Fort Defiance region is higher than in the Indian Wells region.
Step-by-step explanation:
Before finding the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Fort Defiance:
69 out of 210, so:
Indian Wells:
22 out of 162, so:
Distribution of the difference:
a. Find a 99% confidence interval for p1 -p2.
The confidence interval is:
In which
z is the z-score that has a p-value of .
99% confidence level
So , z is the value of Z that has a p-value of
, so
.
The lower bound of the interval is:
The upper bound of the interval is:
The 99% confidence interval for the difference of proportions is (0.0844, 0.3012).
Question b:
We are 99% sure that the true difference in proportions is between 0.0844 and 0.3012. Since all values are positive, there is significant evidence at the 1 - 0.99 = 0.01 significance level to conclude that the proportion is the Fort Defiance region is higher than in the Indian Wells region.
Answer:
4
Step-by-step explanation:
since it's all addition, we can remove the parentheses
Now we combine like terms
We subtract both sides by 12 to get,
now we divide both sides by 11