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Irina-Kira [14]
3 years ago
7

Trig questions:

Mathematics
1 answer:
navik [9.2K]3 years ago
8 0
Question 1
Because the period is 2π, and the amplitude is 1obtain
f(x) = sin(x)
Because the horizontal shift is π, obtain
f(x) = sin(x - π)
Because the vertical shift is -4, obtain
f(x) = sin(x - π) - 4

Answer: 1. f(x) = sin(x - π) - 4

Question 2
The radius is 36/2 = 18 in.
1 revolution (360°) is the circumference, which is
2π(18) = 36π in
When the revolution is 62°, the distance traveled is
(62/360)*(36π) = (31/5)π in

Answer: 3. (31π)/5

Question 3.
Consider f(x) = 3cos(2x-π) - 1
f(0) = 3cos(-π) - 1 = -4
f(π/2) = 3cos(0) - 1 = 2
Rate of change = (2+4)/(π/2) = 12/π

From the graph, the rate of change of g(x)  is
3/(π/2) = 6/π

Consider h(x) = sin(x) - 4
h(0) = 0 - 4 = -4
h(π/2) = 1 - 4 = -3
Rate of change = (-3+4)/(π/2) = 2/π
Therefore h(x) has the smallest rate of change

Answer: h(x)

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3 Simplify 36+236+2 to 3838
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4 Convert 3\frac{1}{4}3
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\frac{38}{3}\times \frac{3\times 4+1}{4}
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5 Simplify 3\times 43×4 to 1212
\frac{38}{3}\times \frac{12+1}{4}
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Answer:

<u>The expected value of every ticket is a loss of $ 1.35</u>

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Number of tickets sold at the raffle = 1,500

Price of each ticket = $ 2

Total prizes = 1 * $ 500 + 1 * $ 250 + 1 * $ 150 + 1 * $ 75

2. Use a probability distribution table to calculate the expected value of your gain. Your expected value is_____ ?

Let's answer the question using a probability distribution for the gains, this way:

  • Probability of 1st prize of $ 498 (500 - ticket) = 1/1,500
  • Probability of 2nd prize of $ 248 (250 - ticket) = 1/1,500
  • Probability of 3rd prize of $ 148 (150 - ticket) = 1/1,500
  • Probability of 4th prize of $ 73 (75 - ticket) = 1/1,500
  • Probability of losing $ 2 (ticket) = 1,496/1,500

Now, we calculate the mean for all the tickets (winners and non-winners), this way:

Expected value = [(1,496 * -2) + (1 * 498) + (1 * 248) + ( 1 * 148) + ( 1 * 73)]/1,500

Expected value = [- 2,992 +498 + 248 + 148 + 73)/1,500

Expected value = -2,025/1,500 = - 1,35

<u>The expected value of every ticket is a loss of $ 1.35</u>

8 0
3 years ago
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