Answer:
134.0 in^3
Step-by-step explanation:
Volume = (radius^2 * pi * height)/3 = (4^2 * pi * 8)/3 = 134.0 in^3
Let us determine the product of 438 and 17 by partial products.
Consider 
and 
So, 
= 
= 7446
Therefore, the product of 438 and 17 is 7446.
No, Sandra's answer is not correct.
Because she should have expressed 17 as (10+7), then if she multiplied (438 by 10) and (438 by 7). And, then added the results.Then her answer would be correct.
14.
Angles 4 and 6 are supplementary, because they are on the same line. Supplementary angles add up to 180 degrees, and a line must be 180 degrees.
15.
Angles 1 and 8 are congruent, because they are alternate exterior angles
16.
m = y2 - y1 / x2 - x1
m = 7 - 2 / 4 - 5
m = 5 / -1
m = -5
17.
m = 3 - 3 / 7 - (-5)
m = 0 / 12
m = 0
18.
m = 1 - (-2) / 5 - (-4)
m = 3 / 9
m = 1/3
19.
A = (0, 3) - B = (3,0)
m = 0 - 3 / 3 - 0
m = -3 / 3
<em>m = -1</em>
C = (0, -2) - D = (4, 2)
m = 2 - (-2) / 4 - 0
m = 4 / 4
<em>m = 1</em>
Perpendicular, because the slopes are opposite reciprocals.
20.
E = (1, 2) - F = (0, 0)
m = 0 - 2 / 0 - 1
m = -2 / -1
<em>m = 2</em>
G = (1, -3) - H = (3, 0)
m = 0 - (-3) / 3 - 1
<em>m = 3 / 2</em>
Neither, because the slopes are different.
21.
I = (0, 1) - J = (2, -4)
m = -4 - 1 / 2 - 0
<em>m = -5/2</em>
K = (-1, -2) - L = (4, 0)
m = 0 - (-2) / 4 - (-1)
<em>m = 2/5</em>
Perpendicular, because the slopes are opposite reciprocals.
22.
M = (-2, 2) - N = (2, 2)
Horizontal line
<em>m = 0</em>
O = (3, 0) - P = (-3, 0)
Horizontal line
<em>m = 0
</em>Parallel, because the slopes are the same.
<em>
</em>23.
Angle 2 is congruent to angle 1 because of the alternate exterior angle theorem.
Angle 1 is congruent to angle 3 because of the vertical angle theorem.
Angle 2 is congruent to angle 3 because of substitution.
Line l is parallel to line m because the corresponding angles are congruent.
Answer:
0.214 ; 0.064 ; 0.3859 ; 0.9966 ; 0.135
Step-by-step explanation:
Given the distribution :
Poor ___ Acceptable ____ Excellent
0.25 _____ 0.6 _________ 0.15
The data scientist receives three items produced by the manufacturing process.
Find the chance that:
a. all of items are Acceptable
0.6 * 0.6 * 0.6 = 0.6^3 = 0.214
b. none of the items is Acceptable
P(not acceptable) = 1 - p(acceptable) = 1 - 0.6 = 0.4
0.4 * 0.4 * 0.4 = 0.4^3 = 0.064
c. at least one of the items is Excellent
P(atleast one) = 1 - P(none)
P(not excellent) = 1 - 0.15 = 0.85
P(none is excellent) = 0.85^3 = 0.614125
Hence,
P(atleast one is excellent) = 1 - 0.614125 = 0.3859
d. not all of the items are Excellent
P(not all) = 1 - p(All)
P(all excellent) = 0.15^3 = 0.003375
P(not all are excellent) = 1 - 0.003375 = 0.9966
e. there is one item of each class:
P(poor) * p(acceptable) * p(excellent) * (number of classes)!
0.25 * 0.6 * 0.15 * 3!
= 0.135
