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3 years ago

What is 3х? ?????????????????????????????

Mathematics

1 answer:

Helen [10]3 years ago

7 0

Answer:

3x means you have three x's. Then 3x - x means you have three x's and you take away (subtract) one x. This would leave you with two x's.

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At NC State University, 16.4% of the undergraduate classes have more than 50 students. If a random sample of 200 undergraduate c

Lena [83]

Answer:

We need to check the conditions in order to use the normal approximation.

$np=200*0.164=32.8 \geq 10$

$n(1-p)=200*(1-0.164)=167.2 \geq 10$

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The mean is given by:

$p =0.164$

And the deviation is given by:

$\sigma_{p}= \sqrt{\frac{0.164*(1-0.164)}{200}}= 0.0262$

So then the correct options for this case are:

The sampling distribution will be approximately normal.

The mean of the sampling distribution will be 16.4%.

The standard deviation of the sampling distribution will be 0.0262.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=200, p=0.164)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=200*0.164=32.8 \geq 10$

$n(1-p)=200*(1-0.164)=167.2 \geq 10$

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The mean is given by:

$p =0.164$

And the deviation is given by:

$\sigma_{p}= \sqrt{\frac{0.164*(1-0.164)}{200}}= 0.0262$

So then the correct options for this case are:

The sampling distribution will be approximately normal.

The mean of the sampling distribution will be 16.4%.

The standard deviation of the sampling distribution will be 0.0262.

6 0

3 years ago

Describe what probability is and how it is used in the real world. Explain how to calculate probability of an event. Explain the

slavikrds [6]

Answer:

Nearly every day you use probability to plan around the weather. Meteorologists can't predict exactly what the weather will be. So they use tools and instruments to determine the likelihood that it will rain, snow or hail.

Step-by-step explanation:

6 0

3 years ago

g Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that it forms a pile in the sh

Maslowich

Answer:

0.3537 feet per minute.

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=10$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

If the Base Diameter = Height of the Cone

The radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10$

We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.

$When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute$