Solve the inequality -23x>23
1 answer:
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Answer:
a=3
b=24
Step-by-step explanation:
If is a factor of
, then the factors of
must also be factors of
.
So what are the factors of ? Well the cool thing here is the coefficient of
is
.
The zeros of are therefore x=-4 and x=3. We know those are zeros of
by the factor theorem.
So x=-4 and x=3 are also zeros of because we were told that
was a factor of it.
This means that when we plug in -4, the result will be 0. It also means when we plug in 3, the result will be 0.
Let's do that.
Equation 1.
Equation 2.
Let's simplify Equation 1 a little bit:
Let's simplify Equation 2 a little bit:
So we have a system of equations to solve:
16a-b=24
9a-b=3
---------- This is setup for elimination because the b's are the same. Let's subtract the equations.
16a-b=24
9a-b= 3
------------------Subtracting now!
7a =21
Divide both sides by 7:
a =3
Now use one the equations with a=3 to find b.
How about 9a-b=3 with a=3.
So plug in 3 for a.
9a-b=3
9(3)-b=3
27-b=3
Subtract 27 on both sides:
-b=-24
Multiply both sides by -1:
b=24
So a=3 and b=24
Answer:
a) The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
b) The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
Step-by-step explanation:
Question a:
The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms.
At the null hypothesis, we test if this is the average resistance, that is:
We are interested in testing the hypothesis that the resistors conform to the specifications.
At the alternative hypothesis, we test if it is not conforming, that is, the mean is different of 0.15, so:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.15 is tested at the null hypothesis:
This means that
Sample mean of 0.152, sample of 10, population standard deviation of 0.005.
This means that
Value of the test statistic:
P-value of the test and decision:
The p-value of the test is the probability of the sample mean differing from 0.15 by at least 0.152 - 0.15 = 0.002, which is P(|z| > 1.26), given by two multiplied by the p-value of z = -1.26.
Looking at the z-table, z = -1.26 has a p-value of 0.1038.
2*0.1038 = 0.2076
The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
Question b:
We have to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Z-table as such z has a p-value of .
That is z with a p-value of , so Z = 1.96.
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 0.15 - 0.003 = 0.147.
The upper end of the interval is the sample mean added to M. So it is 0.15 + 0.003 = 0.153.
The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.