Answer:
The area of the shaded region is about 38.1 square centimeters.
Step-by-step explanation:
We want to find the area of the shaded region.
To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.
The given circle has a radius of 6 cm.
And the given sector has a central angle of 150°.
The area for a sector is given by the formula:
In this case, r = 6 and θ = 150°. Hence, the area of the sector is:
Now, we can find the area of the triangle. We can use an alternative formula:
Where a and b are the side lengths, and C is the angle between them.
Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.
And the angle C is 150°. Hence, the area of the triangle is:
The area of the shaded region is equivalent to the sector minus the triangle:
Therefore:
Use a calculator:
The area of the shaded region is about 38.1 square centimeters.
#6 is incorrect
it's 6 7/8
#7 is correct
Answer:
P ( X > 5 ) = 72,2 %
Step-by-step explanation:
The probability of success ( outcomes bigger than 5 )
If dice 1 outcome is 6 no matter wich outcome we get from dice 2 all events are successful, the we have 6 outcomes
If dice 1 outcome is 5 we also have 6 outcomes
If dice 1 outcomes is 4 we have 5 positive outcomes
If dice 1 outcome is 3 we have 4 positive outcomes
If dice 1 outcome is 2 we have 3 positive outcomes
if dice 1 outcome is 1 we have 2 positive outcomes
Total evaluating dice 1: positive outcomes 26
We will get the sames results analysing dice 2 then we have a total of
52 successful events
And total numbers of outcomes is 36 + 36 = 72
Then
P ( X > 5 ) = 52/72
P ( X > 5 ) = 0,722
P ( X > 5 ) = 72,2 %
Answer:
The value of a₁₀ is -1352
Step-by-step explanation:
a₂ = -8
a₅ = -512
Now,
a₂ = -8 can be written as
a + d = -8 ...(1) and
a₅ = -512 can be written as
a + 4d = -512 ...(2)
Now, from equation (2) we get,
a + 4d = - 512
a + d + 3d = - 512
(-8) + 3d = - 512 (.°. <u>a + d = </u><u>-8</u><u>)</u>
3d = - 512 + 8
3d = - 504
d = - 504 ÷ 3
d = - 168
Now, for the value of a put the value of d = -168 in equation (1)
a + d = -8
a + (-168) = -8
a - 168 = -8
a = 168 - 8
a = 160
Now, For a₁₀
a₁₀ = a + 9d
a₁₀ = 160 + 9(-168)
a₁₀ = 160 - 1512
a₁₀ = -1352
Thus, The value of a₁₀ is -1352
<u>-TheUnknownScientist</u>
