Answer:
The standard deviation of that data set is 3.8
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 55
95% of the data fall between 47.4 and 62.6. This means that 47.4 is 2 standard deviations below the mean and 62.6 is two standard deviations above the mean.
Using one of these points.
55 + 2sd = 62.6
2sd = 7.6
sd = 7.6/2
sd = 3.8
The standard deviation of that data set is 3.8
Answer:
225.5
Step-by-step explanation:
So, you would start by doing
220 times 2.5% that would equal 5.5
Then you would add
220 + 5.5 = 225.5
Therefore your answer will be 225.5
The solution to this system is (x, y) = (8, -22).
The y-values get closer together by 2 units for each 2-unit increase in x. The difference at x=2 is 6, so we expect the difference in y-values to be zero when we increase x by 6 (from 2 to 8).
You can extend each table after the same pattern.
In table 1, x-values increase by 2 and y-values decrease by 8.
In table 2, x-values increase by 2 and y-values decrease by 6.
The attachment shows the tables extended to x=10. We note that the y-values are the same (-22) for x=8 (as we predicted above). That means the solution is ...
... (x, y) = (8, -22)
We will use the law of cosines
<span>side a² = b² + c² -2bc • cos(A)
</span><span>side a² = 729 + 196 -2*27*14 * cos (46)
</span><span>side a² = 925 -(756 * 0.69466)
</span>side a² = <span><span>399.83704
</span>
side a = </span><span><span><span>19.995925585
</span>
</span>
</span>
We could round that to 20
a = 20 b = 27 c =14
We can calculate a triangle's area when we know all 3 sides by using Heron's Formula
<span>area = square root (s • (s - a) • (s - b) • (s - c))
where s is the semi-perimeter </span>
semi-perimeter<span> = (side a + side b + side c) ÷ 2</span>
s = (20 + 27 + 14) / 2
s = 30.5
Now we use Heron's Formula
area = square root (s • (s - a) • (s - b) • (s - c))
area = square root (30.5 • (<span>30.5 - 20) • (</span><span>30.5 - 27) • (</span><span>30.5 - 14))</span>
area = square root (30.5 • (10.5) • (3.5) • (<span>16.5))</span>
<span>area = square root (18494.4375)
</span>
<span><span><span>area = 135.9942553934
</span>
</span>
</span>which rounds to
136 square feet
Source:
http://www.1728.org/triang.htm
