Answer:
Question 7:
∠L = 124°
∠M = 124°
∠J = 118°
Question 8:
∠Q = 98°
∠T = 98°
∠R = 82°
Question 15:
m∠G = 110°
Question 16:
∠G = 60°
Question 17:
∠G = 80°
Question 18:
∠G = 70°
Step-by-step explanation:
The angles can be solving using Symmetry.
Question 7.
The sum of interior angles in an isosceles trapezoid is 360°, and because it is an isosceles trapezoid
∠K = ∠J = 118°
∠L = ∠M
∠K+∠J+∠L +∠M = 360°
236° + 2 ∠L = 360°
Therefore,
∠L = 124°
∠M = 124°
∠J = 118°
Question 8.
In a similar fashion,
∠Q+∠T+∠S +∠R = 360°
and
∠R = ∠S = 82°
∠Q = ∠T
∠Q+∠T + 164° = 360°
2∠Q + 164° = 360°
2∠Q = 196°
∠Q = ∠T =98°.
Therefore,
∠Q = 98°
∠T = 98°
∠R = 82°
Question 15.
The sum of interior angles of a kite is 360°.
∠E + ∠G + ∠H + ∠F = 360°
Because the kite is symmetrical
∠E = ∠G.
And since all the angles sum to 360°, we have
∠E +∠G + 100° +40° = 360°
2∠E = 140° = 360°
∠E = 110° = ∠G.
Therefore,
m∠G = 110°
Question 16.
The angles
∠E = ∠G,
and since all the interior angles sum to 360°,
∠E + ∠G + ∠F +∠H = 360°
∠E + ∠G + 150 + 90 = 360°
∠E + ∠G = 120 °
∠E = 60° = ∠G
therefore,
∠G = 60°
Question 17.
The shape is a kite; therefore,
∠H = ∠F = 110°
and
∠H + ∠F + ∠E +∠G = 360°
220° + 60° + ∠G = 360°,
therefore,
∠G = 80°
Question 18.
The shape is a kite; therefore,
∠F = ∠H = 90°
and
∠F +∠H + ∠E + ∠G = 360°
180° + 110° + ∠G = 360°
therefore,
∠G = 70°.
Calculate the circumference of the two semi circles, which equals a full circle. Then add the two sides of the track.
Circumference is pi x diameter = 3.14 x 22.8 = 71.592, so, you would need to add 71.592 + 49.2 + 49.2 = 169.992 meters, and that would be the length of one lap of the track.
Answer:
The mean of X is 122.5 and the standard deviation is 7.9.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they believe that the overall state of moral values is poor, or they do not believe this. The probability of an adult believing this is independent of other adults. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
In this problem, we have that:
So
The mean of X is 122.5 and the standard deviation is 7.9.
0.001
Step- by-step explanation
