In this section we are going to see how knowledge of some fairly simple graphs can help us graph some more complicated graphs. Collectively the methods we’re going to be looking at in this section are called transformations.
Vertical Shifts
The first transformation we’ll look at is a vertical shift.
Answer:
y=29
Step-by-step explanation:
Since the angles are across a vertex from one another, they are congruent and equal. You can also see this by reflecting or folding it in half through the vertex. They will be the same. This means we can write the following equation and solve using inverse operations:
4y-8=79+y
4y-y-8=79+y-y
3y-8=79
3y-8+8=79+8
3y=87
y=29
If I understand the question, you have to get n alone. in this case, you have to subtract 7 from both sides, resulting in n (is less than) -10
Answer:
hmm.. very blurry repost please
Step-by-step explanation:
Answer:
a. We reject the null hypothesis at the significance level of 0.05
b. The p-value is zero for practical applications
c. (-0.0225, -0.0375)
Step-by-step explanation:
Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.
Then we have
,
,
and
,
,
. The pooled estimate is given by
a. We want to test
vs
(two-tailed alternative).
The test statistic is
and the observed value is
. T has a Student's t distribution with 20 + 25 - 2 = 43 df.
The rejection region is given by RR = {t | t < -2.0167 or t > 2.0167} where -2.0167 and 2.0167 are the 2.5th and 97.5th quantiles of the Student's t distribution with 43 df respectively. Because the observed value
falls inside RR, we reject the null hypothesis at the significance level of 0.05
b. The p-value for this test is given by
0 (4.359564e-10) because we have a two-tailed alternative. Here T has a t distribution with 43 df.
c. The 95% confidence interval for the true mean difference is given by (if the samples are independent)
, i.e.,
where
is the 2.5th quantile of the t distribution with (25+20-2) = 43 degrees of freedom. So
, i.e.,
(-0.0225, -0.0375)