Answer:
Measure of minor angle JOG is ![95.5^{\circ}](https://tex.z-dn.net/?f=95.5%5E%7B%5Ccirc%7D)
Step-by-step explanation:
Consider a circular track of radius 120 yards. Assume that Cherie starts from point J and runs 200 yards up to point G.
.
Now the measure of minor arc is same as measure of central angle. Therefore minor angle is the central angle
.
To calculate the central angle, use the arc length formula as follows.
Where
is measured in radian.
Substituting the value,
Dividing both side by 120,
Reducing the fraction into lowest form by dividing numerator and denominator by 40.
Therefore value of central angle is
, since angle is in radian
Now convert radian into degree by using following formula,
![1^{c}=\left(\dfrac{180}{\pi}\right)^{\circ}](https://tex.z-dn.net/?f=1%5E%7Bc%7D%3D%5Cleft%28%5Cdfrac%7B180%7D%7B%5Cpi%7D%5Cright%29%5E%7B%5Ccirc%7D)
So multiplying
with
to convert it into degree.
![\left(\dfrac{5}{3}\right)^{c}=\left(\dfrac{5}{3}\right) \times \left(\dfrac{180}{\pi}\right)^{\circ}](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B5%7D%7B3%7D%5Cright%29%5E%7Bc%7D%3D%5Cleft%28%5Cdfrac%7B5%7D%7B3%7D%5Cright%29%20%5Ctimes%20%5Cleft%28%5Cdfrac%7B180%7D%7B%5Cpi%7D%5Cright%29%5E%7B%5Ccirc%7D)
Simplifying,
![\therefore \theta = 95.49^{circ}](https://tex.z-dn.net/?f=%20%5Ctherefore%20%5Ctheta%20%3D%2095.49%5E%7Bcirc%7D)
So to nearest tenth, ![\angle JOG=95.5^{circ}](https://tex.z-dn.net/?f=%20%5Cangle%20JOG%3D95.5%5E%7Bcirc%7D)
Answer:
36.36% probability that she gave birth to quadruplets
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcoes.
Desired outcomes:
Giving births to quadruplets.
She has 4 sets of quadruplets.
So ![D = 4](https://tex.z-dn.net/?f=D%20%3D%204)
Total outcomes:
At least 3 children(triplets).
7 sets of triplets and 4 sets of quadruplets.
So ![T = 7 + 4 = 11](https://tex.z-dn.net/?f=T%20%3D%207%20%2B%204%20%3D%2011)
Probability:
![p = \frac{D}{T} = \frac{4}{11} = 0.3636](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7BD%7D%7BT%7D%20%3D%20%5Cfrac%7B4%7D%7B11%7D%20%3D%200.3636)
36.36% probability that she gave birth to quadruplets
Answer:
State A was the <u>12th</u> state to enter the Union. State B was the <u>11th</u> state to enter the Union.
Step-by-step explanation:
Let's call x to the order-of-entry of State B, therefore the order-of-entry of State A is x+1. Given that he product of their order-of-entry numbers is 132:
x*(x+1) = 132
x² + x - 132 = 0
Using quadratic formula:
![x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2%20-4%28a%29%28c%29%7D%7D%7B2%28a%29%7D%20)
![x = \frac{-1 \pm \sqrt{1^2 -4(1)(-132)}}{2(1)}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-1%20%5Cpm%20%5Csqrt%7B1%5E2%20-4%281%29%28-132%29%7D%7D%7B2%281%29%7D%20)
![x = \frac{-1 \pm 23}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-1%20%5Cpm%2023%7D%7B2%7D%20)
![x_1 = \frac{-1 + 23}{2}](https://tex.z-dn.net/?f=x_1%20%3D%20%5Cfrac%7B-1%20%2B%2023%7D%7B2%7D%20)
![x_1 = 11](https://tex.z-dn.net/?f=x_1%20%3D%2011%20)
![x_2 = \frac{-1 - 23}{2}](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cfrac%7B-1%20-%2023%7D%7B2%7D%20)
![x_2 = -12](https://tex.z-dn.net/?f=x_2%20%3D%20-12)
The negative solution has no sense in the context of our problem, then the solution is x = 11.
Answer:
its answer b
Step-by-step explanation:
B:(m∠1 + m∠2) = 180° and (m∠3 + m∠4) = 180°