Answer:
The variance is ![\sigma ^2 =25](https://tex.z-dn.net/?f=%5Csigma%20%5E2%20%20%3D25)
Step-by-step explanation:
From the question we are told that
The sample size is n = 21
The sum of squares is ![SS = 500](https://tex.z-dn.net/?f=SS%20%3D%20%20500)
Generally the variance is mathematically represented as
![\sigma ^2 = \frac{SS}{n- 1}](https://tex.z-dn.net/?f=%5Csigma%20%5E2%20%20%3D%20%5Cfrac%7BSS%7D%7Bn-%201%7D)
substituting values
![\sigma ^2 = \frac{ 500}{21- 1}](https://tex.z-dn.net/?f=%5Csigma%20%5E2%20%20%3D%20%5Cfrac%7B%20500%7D%7B21-%201%7D)
![\sigma ^2 =25](https://tex.z-dn.net/?f=%5Csigma%20%5E2%20%20%3D25)
Answer:
A = 20 degree
B = 160 degree
C = 160 degree
D = 20 degree
Step-by-step explanation:
If the measure of angle C is eight timeseight times the measure of angle A
That means C = 8A
But According to the question, angles A and D have the same measure as well as angles C and B.
That is, B = 8A and D = A
If A + B + C + D = 360
Let us substitute for B, C and D
A + 8A + 8A + A = 360
18A = 360
A = 360/18 = 20
Therefore
A = 20 degree
B = 8 × 20 = 160 degree
C = 8× 20 = 160 degree
D = 20 degree
The difference between both unit rates rounded off to the nearest tenth is: 0.4 meters per second
Step-by-step explanation:
We have to calculate his unit rate for both type of races
So,
<u>Unit rate for 400m race:</u>
Distance = 400m
Time = 43 sec
![Unit\ rate = U_1= \frac{Distance}{Time}\\=\frac{400}{43}\\=9.30\ meters\ per\ second](https://tex.z-dn.net/?f=Unit%5C%20rate%20%3D%20U_1%3D%20%5Cfrac%7BDistance%7D%7BTime%7D%5C%5C%3D%5Cfrac%7B400%7D%7B43%7D%5C%5C%3D9.30%5C%20meters%5C%20per%5C%20second)
<u>Unit rate for 300m Race:</u>
Distance = 300m
Time = 31 sec
![Unit\ Rate= U_2=\frac{300}{31}\\=9.68\ meters\ per\ second](https://tex.z-dn.net/?f=Unit%5C%20Rate%3D%20U_2%3D%5Cfrac%7B300%7D%7B31%7D%5C%5C%3D9.68%5C%20meters%5C%20per%5C%20second)
The difference between both unit rates is:
![U_2-U_1 = 9.68-9.30\\=0.38 => 0.4\ meters\ per\ sec](https://tex.z-dn.net/?f=U_2-U_1%20%3D%209.68-9.30%5C%5C%3D0.38%20%3D%3E%200.4%5C%20meters%5C%20per%5C%20sec)
Hence,
The difference between both unit rates rounded off to the nearest tenth is: 0.4 meters per second
Keywords: Unit rate, Speed
Learn more about unit rate at:
#LearnwithBrainly
Answer:
Step-by-step explanation:
5
Answer:
a). m∠AED = 70°
b). x = 10°
Step-by-step explanation:
a). Quadrilateral ABDE is a cyclic quadrilateral.
Therefore, by the theorem of cyclic quadrilateral,
Sum of either pair of opposite angle is 180°
m(∠AED) + m(∠ABD) = 180°
m(∠AED) = 180° - 110°
m(∠AED) = 70°
Since, ∠AED ≅ ∠EAD
Therefore, m∠AED = m∠EAD = 70°
b). By triangle sum theorem in ΔABD,
m∠ABD + m∠BDA + m∠DAB = 180°
110° + 40° + m∠DAB = 180°
m∠DAB = 180° - 150°
m∠DAB = 30°
m∠BAE = m∠EAD + m∠BAD
= 70° + 30° = 100°
By angle sum theorem in ΔACE,
m∠EAC + m∠AEC + m∠ACE = 180°
100° + 70° + x° = 180°
x = 180° - 170°
x = 10°