Tutor profile: Stephanie D.
Please translate the following sentences into Mandarin characters: Hello, my name is John, I am 10 years old. I enjoy playing soccer on the weekends.
你好, 我叫 John, 我十岁。 周末的时候我喜欢踢祝秋。
An individual flips a two sided coin three times, and gets the results: Heads, Heads, Tails. A) Are the results heads and tails mutually exclusive? B) What is the probability of getting heads on the second flip given that the first flip was heads? C) What is the probability of getting a result of: Heads, Heads, Tails on three consecutive coin flips?
A) When flipping a two sided coin the results Heads and Tails are mutually exclusive, because on any given flip you can only have a result of Heads or Tails, you cannot have both results simultaneously. B) The probability of getting a result of Heads on the second flip is 50%. Since the results of the second flip are independent of the previous coin flip, we only consider the probability of this individual flip. Since you have two equally likely options, Heads and Tails, the probability of getting Heads is 50%. C) For this question we will use the multiplication rule because we want to find the probability of three independent events occurring together. We can model this question with the equation P(H,H,T) = P(H) x P(H) x P(T). Given that the probability of heads or tails is 50% on any given throw, we can use .5 for P(H) and P(T). Therefore, P(H,H,T) = .5 x .5 x .5 = 1/8 or 12.5%.
Given the equation y=2x+5, find the y-intercept, x-intercept, and slope of the line.
A) Since this equation is in slope-intercept form y=mx+b, we will find the y-intercept by looking at the term b in the equation. Since b=5, the y-intercept of the line will be (0,5). We can check this answer by plugging 0 into the x term and solving for y: y=2(0) + 5. This gives us the answer when x=0, y=5. B) To find the x-intercept we will plug in 0 for y in the above equation. 0=2x+5 -5=2x x= -2.5 Therefore the x-intercept will be (-2.5,0) C) Since this slope is in y-intercept form, and m=slope, we know that the slope of the line is 2.
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