Two cargo ships spot a signal fire on a small island. The captains know they are 140 feet

At a gymnastics meet, twenty gymnasts compete for first, second, and third place. How many ways can first, second, and third pla

ExtremeBDS [4]

Part A:

Given that at a gymnastics meet, twenty gymnasts compete for first, second, and third place. The number of ways first, second, and third place can be assigned is given by

$^{20}P_3= \frac{20!}{(20-3)!} \\ \\ = \frac{20!}{17!} =20\times19\times18 \\ \\ =6,840\ ways$

Part B:

Given that at a gymnastics meet, twenty gymnasts compete for first, second, and third place. If the third place has been announced the number of ways that the remaining two places can be assigned is given by :

 $^{19}P_2= \frac{19!}{(19-2)!} \\ \\ = \frac{19!}{17!} =19\times18 \\ \\ =342\ ways$


Part C:

Given that at a gymnastics meet, twenty gymnasts compete for first, second, and third place. If the third and second places have been announced the number of ways that the first place can be assigned is given by :

$^{18}P_1= \frac{18!}{(18-1)!} \\ \\ = \frac{18!}{17!} =18\ ways$

7 0

3 years ago

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What is 9+6(2^2+4) and why?

Dmitry [639]

Answer:

first : (2^2+4)=(4+4)=8

second : 9+6×8=57

5 0

3 years ago

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How many chlorine (Cl) atoms would be in 4 molecules of salt (4 NaCl)?

Sholpan [36]

The answer is A,because the way your question is written,there would be 4 molecules of salt (NA) and one molecule of CL (Chlorine)

3 0

3 years ago

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To decrease the impact on the environment, factory chimneys must be high enough to allow pollutants to dissipate over a larger a

Komok [63]

Answer:

The probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.

Step-by-step explanation:

Let the random variable X be defined as the height of chimneys in factories.

The mean height is, μ = 100 meters.

The standard deviation of heights is, σ = 12 meters.

It is provided that a random sample of n = 40 chimney heights is obtained.

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample means is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the distribution of sample means is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

Since the sample selected is quite large, i.e. n = 40 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean heights of chimneys.

$\bar X\sim N(\mu_{\bar x},\ \sigma^{2}_{\bar x})$