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3 years ago

ABC represents a race path. Find the total distance of the race. Round your answer to the nearest meter.

Mathematics

1 answer:

Oksanka [162]3 years ago

8 0

Answer:

Race covers 1911 meters.

Step-by-step explanation:

Triangle ABC represents a race path.

Total distance covered by the race = Perimeter of the triangle ABC

We will apply Sine rule in the given triangle to find the unknown sides.

By Sine rule,

$\frac{SinB}{AC}=\frac{SinA}{BC}=\frac{SinC}{AB}$

$\frac{Sin35}{450}=\frac{Sin85}{AC}=\frac{Sin60}{AB}$ [Since m∠A = 180° - (85 + 60)° = 35°]

$\frac{Sin35}{450}=\frac{Sin85}{AC}$

AC = $\frac{450\times \text{Sin85}}{\text{Sin35}}$

= 781.57 meters

$\frac{Sin35}{450}=\frac{Sin60}{AB}$

AB = $\frac{450\times \text{Sin60}}{\text{Sin35}}$

= 679.44 meters

Perimeter of the triangle = AB + BC + AC

= 679.44 + 450 + 781.57

= 1911.01

≈ 1911 meters

Therefore, the race covers 1911 meters.

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3 years ago

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Kruka [31]

Answer:

$x=17$

Step-by-step explanation:

$(6x+10)(x+17)(4x-34)$

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and $10+17-34=-7$

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2 years ago

At a raffle, 1500 tickets are sold at $2 each. There are four prizes given for $500, $250, $150, and $75. You buy one ticket. Us

wolverine [178]

Answer:

The expected value of every ticket is a loss of $ 1.35

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
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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

The expected value of every ticket is a loss of $ 1.35

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3 years ago

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