Find the next three terms in the geometric sequence: 400, 200, 100, 50
2 answers:
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Answer:
The plates will not fit into the box.
Step-by-step explanation:
Each plate is 0.5 inches tall; therefore, the stack of 8 plates will have a height of .
Also, the diameter of the largest plate is 10 inches or has a radius of 5 inches, which matches the radius of the cylindrical box; therefore, we know that the stack of plates can fit into the base area of the cylindrical box.
What we want to figure out now is the height of the cylindrical box <em>to see if it is greater than or equal to 4 inches</em>—<em>the height of the stack of plates. </em>
The volume of a cylinder is , and since for our cylindrical box the volume is 150 cubic inches; therefore,
putting in and solving for height
we get
,
which is not greater than 4 inches, which means the plates will not fit into the box since the height of the stack is greater than the height of the box.
Answer:
r² = 0.5652 < 0.7 therefore, the correlation between the variables does not imply causation
Step-by-step explanation:
The data points are;
X, Y
0.7, 1.11
21.9, 3.69
18, 4
16.7, 3.21
18, 3.7
13.8, 1.42
18, 4
13.8, 1.42
15.5, 3.92
16.7, 3.21
The correlation between the values is given by the relation
Y = b·X + a
Where;
N = 10
∑XY = 499.354
∑X = 153.1
∑Y = 29.68
∑Y² = 100.546
∑X² = 2631.01
(∑ X)² = 23439.6
(∑ Y)² = 880.902
From which we have;
r² = 0.5652 which is less than 0.7 therefore, there is a weak relationship between the variables, and it does not imply causation.