A large emerald with a mass of 812.04 grams was recently discovered in a mine. If the density of the emerald is 2.76grams over c
2 answers:
You might be interested in
Answer:
A cone with base radius of 17 in
Step-by-step explanation:
Given
Triangle ABC
Where
AB = BC = 24in
D = Midpoint of AC
Required
Which best describes the resulting three-dimensional figure?
First, the length of the third side of the triangle has to be calculated
The sides of triangle ABC are AB, AC and BC
Given that the perimeter = 82 in
AB + AC + BC = 82
Recall that AB = BC = 24in; The equation becomes
Collect like terms
Given that, the triangle is rotated at D, the midpoint of AC
The length of the midpoint has to be calculated
At this point, we can dismiss options C and D.
This is because; a triangular pyramid is formed by more than 1 triangles (at least 3 triangle) and in this case, we're dealing with only 1 triangle.
So, we have option A and B to select from.
When the triangle is rotated at point D, it generates a cone such that the radius of the cone is the distance at point D.
This implies that, a cone with base radius D is generated.
Recall that D = 17.
Hence, <em>A cone with base radius of 17 in</em>
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)
Given:
There are 4 quarts in a gallon.
She wants to convert 6 quarts to a gallon.
To find:
Whether she should multiply 6 by 4 or divide 6 by 4 to find her answer.
Solution:
We have,
Here, 6 quarts is equal to gallon. It means we need to multiply 6 by 4 in
to find the answer.