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Alexandra [31]
3 years ago
15

Jacob and Ashley run an animal shelter that houses only cats and dogs. they have 37 adult animals 21 cats and 16 dogs. A group o

f 8 adult animals is chosen at random from the shelter. What is the most likely number of cats and dogs in this group and what is the probability of that arrangement happening? give your probability to four decimal placements. I'm pretty sure the arrangement is 5 cats to 3 dogs but i don't know how to get the probability
Mathematics
1 answer:
Bond [772]3 years ago
3 0
The most likely number of cats = 21/37 x 8 = 4.54 ≈ 5 cats
The most likely number of dogs = 16/37 x 8 = 3.46 ≈ 3 dogs

The probability of that arrangement happening = 1/8^2 = 1/64 = 0.00156
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3 years ago
Help with math pls cant figure it out
tatyana61 [14]

Answer:

\frac{5}{4}+or-\frac{3i\sqrt{7} }{4}

Step-by-step explanation:

You can solve this equation with the quadratic formula which is:

m_{1,2}=\frac{-b+or-\sqrt{b^{2}-4ac } }{2a}

All you need to do is rearrange the equation (add -\frac{11}{2} to both sides and then multiply both sides by 2) to get:

2m^2-5m+11=0

From this new equation, we can easily see that a = 2, b = -5, and c = 11 AND you don't have to work with as many fractions. Substitute the values for a, b, and c into the quadratic formula to get:

m_{1,2}=\frac{5+or-\sqrt{(-5)^{2}-4(2)(11) } }{2(2)}

That simplifies to:

\frac{5}{4}+or-\frac{\sqrt{25-88} }{4}

Which simplifies even further to:

\frac{5}{4}+or-\frac{\sqrt{-63} }{4}

Which gets you:

\frac{5}{4}+or-\frac{3i\sqrt{7} }{4}

P.S. The plus-minus sign wasn't working for me, so I had to just write, "+or-". I hope that didn't make it too confusing for you.

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7 0
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The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.954 grams and a standard devia
olga_2 [115]

Let <em>X</em> be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.

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where <em>Z</em> follows the standard normal distribution with mean 0 and standard deviation 1. (We just transform <em>X</em> to <em>Z</em> using the rule <em>Z</em> = (<em>X</em> - mean(<em>X</em>))/sd(<em>X</em>).)

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You can also estimate this probabilty using the empirical or 68-95-99.7 rule, which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. This is to say,

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The normal distribution is symmetric, so this means

P(<em>Z</em> ≤ -2) ≈ 1/2 × 0.05 = 0.025

which is indeed pretty close to what we found earlier.

4 0
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