I’m not sure but I never went over this
Answer:
117.3
Step-by-step explanation:
7*4=117.29=117.3
That expression is the expected value of your winnings, or "the average amount you will win (or lose) per game in the long run".
So the length of the arc is given by: l = r*theta, here theta is the intercepted angle in unit radian
So, 80 degrees = 80/360 * 2pi = 4/9 * pi
So l = r * (4/9 * pi), the constant ratio is 4/9 * pi
Answer:
yes
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem, so the triangle is a right triangle.
7.5² +10² = 12.5²
56.25 +100 = 156.25
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You may recognize that the ratios of side lengths are ...
7.5 : 10 : 12.5 = 3 : 4 : 5
A 3-4-5 triangle is a well-known right triangle, as this is the smallest set of integers that satisfy the Pythagorean theorem. They also happen to be consecutive integers, so form an arithmetic sequence. Any arithmetic sequence that satisfies the Pythagorean theorem will have these ratios.
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If you're familiar with trigonometry, you know the law of cosines tells you ...
c² = a² + b² - 2ab·cos(θ) . . . . where θ is the angle between sides a and b. This reduces to the Pythagorean theorem when θ=90°, which makes cos(θ)=0. If the sides do not satisfy the Pythagorean theorem, cos(θ)≠0 and the triangle is not a right triangle.
