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2 years ago

6. At the Winter Olympics, the ratio of Canadian medals to US to Russia was 1:8:5. If Russia won 25

Mathematics

1 answer:

rewona [7]2 years ago

5 0

Answer:

Step-by-step explanation:

Let x be the total number of medals won by the Russians.

The way to do this is to add the ratios together

1 + 8 + 5 = 14

(5/14) x = 25

Multiply by 14

5*x = 25 * 14

5x = 350

divide by 5

8/14 = x / 70

14x = 8 * 70

14x = 560

x = 560 / 14

x = 40

The USA won 40 medals.

1/14 = x / 70

14x = 70

x = 5

Canada Won 5 medals.

Check

Russia Won 25 medals

Canada Won 5 medals

USA Won 40 medals

Total 70

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3 years ago

Find the complex fourth roots of 81(cos(3π/8)+isin(3π/8)). a) Find the fourth root of 81. b) Divide the angle in the problem by

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Answer:

The answer is below

Step-by-step explanation:

Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:

$z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1$

Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:

$z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\$

$z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]$

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3 years ago

The distribution of prices for home sales in a certain New Jersey county is skewed to the right with a mean of $290,000 and a st

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Answer:

The probability that the mean of the sample is greater than $325,000

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Step-by-step explanation:

Step(i):-

Given the mean of the Population( )= $290,000

Standard deviation of the Population = $145,000

Given the size of the sample 'n' = 100

Given 'X⁻' be a random variable in Normal distribution

Let X⁻ = 325,000

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{325000-290000}{\frac{145000}{\sqrt{100} } } = 2.413$

Step(ii):-

The probability that the mean of the sample is greater than $325,000

$P( X > 3,25,000) = P( Z >2.413)$

= 0.5 - A(2.413)

= 0.5 - 0.4920

= 0.008

Final answer:-

The probability that the mean of the sample is greater than $325,000

$P( X > 3,25,000) = P( Z >2.413) = 0.008$

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