This is a really interesting question! One thing that we can notice right off the bat is that each of the circles has the same amount of area swept out of it - namely, the amount swept out by one of the interior angles of the hexagon. Let’s call that interior angle θ. We know that the amount of area swept out in the circle is proportional to the angle swept out - mathematically
θ/360 = a/A
Where “a” is the area swept out by θ, and A is the area of the whole circle, which, given a radius of r, is πr^2. Substituting this in, we have
θ/360 = a/(πr^2)
Solving for “a”:
a = π(r^2)θ/360
So, we have the formula for the area of one of those sectors; all we need to do now is find θ and multiply our result by 6, since we have 6 circles. We can preempt this but just multiplying both sides of the formula by 6:
6a = 6π(r^2)θ/360
Which simplifies to
6a = π(r^2)θ/60
Now, how do we find θ? Let’s look first at the exterior angles of a hexagon. Imagine if you were taking a walk around a hexagon. At each corner, you turn some angle and keep walking. You make 6 turns in all, and in the end, you find yourself right back at the same place you started; you turned 360 degrees in total. On a regular hexagon, you’d turn by the same angle at each corner, which means that each of the six turns is 360/6 = 60 degrees. Since each interior and exterior angle pair up to make 180 degrees (a straight line), we can simply subtract that exterior angle from 180 to find θ, obtaining an angle of 180 - 60 = 120 degrees.
Finally, we substitute θ into our earlier formula to find that
6a = π(r^2)120/60
Or
6a = 2πr^2
So, the area of all six sectors is 2πr^2, or the area of two circles with radii r.
Answer:
The most appropriate inferential statistic test in the present situation is the;
b. Two-sample t-test
Step-by-step explanation:
From the question, we have;
The number of subjects in each sample, n₁ = 100
The number of samples = 2
The nature of the test = To compare the two means
The value of the population standard deviation, σ = Unknown
From the given parameters, we have;
The t-test is a method of inferential statistics for determining whether the difference between the mean of two groups is significant, that is if the observed difference are due to chance, where the groups are likely to have some characteristics that are related
The t-test is utilized when testing an hypothesis, and it is used for small samples, where the population standard deviation is unknown
The types of t-test used are;
a) One-sample t-test
b) Two-sample t-test
c) Paired Sample t-test
Therefore, a two-sample t-test is most appropriate.
Answer:
anything above 1
Step-by-step explanation:
-3/2 = -1.5.
3 x -2 = -6
Nope
3 x -1 = -3
Nope
3 x 1 = 3 Yes!!
Answer:
1. $132.24
2. $55.89
3. $1336.66
4. $258.19
5. $57.86
Step-by-step explanation:
Simply use this equation.
Substitute in our values, using No.1 as our example.
Cross multiply
922.575 = x100
Solve for x by dividing by 100.
x = 9.22575
Now add x to the initial value.
9.22575 + 123.01 = 132.23575
Round to the nearest hundredth for the answer.
$132.24
First find the area. 39*332=12,948. 12,948 is less than 15,000, so yes, she has enough bricks.
