Answer:
6
<em>BRAINLIEST, PLEASE!</em>
Step-by-step explanation:
-19p - 2p + 16p + 12 = -18
-5p + 12 = -18
-5p = -30
p = 6
Apply the product rule to
7
11
7
11
.
(
2
7
)
2
⋅
7
2
11
2
(
2
7
)
2
⋅
7
2
11
2
Raise
7
7
to the power of
2
2
.
(
2
7
)
2
⋅
49
11
2
(
2
7
)
2
⋅
49
11
2
Raise
11
11
to the power of
2
2
.
(
2
7
)
2
⋅
49
121
(
2
7
)
2
⋅
49
121
Multiply
2
(
49
121
)
2
(
49
121
)
.
Tap for more steps...
(
2
7
)
98
121
(
2
7
)
98
121
Apply the product rule to
2
7
2
7
.
2
98
121
7
98
121
2
98
121
7
98
121
The result can be shown in multiple forms.
Exact Form:
2
98
121
7
98
121
2
98
121
7
98
121
Decimal Form:
0.36253492
…
0.36253492
…
(
2
7
)
2
⋅
(
7
1
1
)
2
(
2
7
)
2
⋅
(
7
1
1
)
2
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)
Answer:
C; 4
Step-by-step explanation:
Mathematically, when two lines are perpendicular, the product of their slopes equal -1
in that case, we have it that;
m1 * m2 = -1
where m1 is the slope of the first line and m2 is the slope of the second line
Hence,
m2* -1/4 = -1
-m2/4 = -1
-m2 = -4
m2 = 4
