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2 years ago

How many cubes with side lengths of 1/3 does it take to fill the prism?

Mathematics

1 answer:

Ugo [173]2 years ago

8 0

Answer:

180 cubes

Step-by-step explanation:

little cubes:

$v=(\frac{1}{3} )^{3} =\frac{1}{27}$

The prism:

$v=(\frac{5}{3})(\frac{4}{3} )(2)=\frac{40}{9} =\frac{20}{3}$

the number of cubes that fill the prism:

$cubes=\frac{\frac{20}{3} }{\frac{1}{27} } =\frac{(20)(27)}{(3)(1)}= \frac{540}{3} =180$

Hope this helps

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5.2.14. For the negative binomial pdf p (k; p, r) = k+r−1 (1 − p)kpr, find the maximum likelihood k estimator for p if r is know

Volgvan

Answer:

$\hat p = \frac{r}{\bar x +r}$

Step-by-step explanation:

A negative binomial random variable "is the number X of repeated trials to produce r successes in a negative binomial experiment. The probability distribution of a negative binomial random variable is called a negative binomial distribution, this distribution is known as the Pascal distribution".

And the probability mass function is given by:

$P(X=x) = (x+r-1 C k)p^r (1-p)^{x}$

Where r represent the number successes after the k failures and p is the probability of a success on any given trial.

Solution to the problem

For this case the likehoof function is given by:

$L(\theta , x_i) = \prod_{i=1}^n f(\theta ,x_i)$

If we replace the mass function we got:

$L(p, x_i) = \prod_{i=1}^n (x_i +r-1 C k) p^r (1-p)^{x_i}$

When we take the derivate of the likehood function we got:

$l(p,x_i) = \sum_{i=1}^n [log (x_i +r-1 C k) + r log(p) + x_i log(1-p)]$

And in order to estimate the likehood estimator for p we need to take the derivate from the last expression and we got:

$\frac{dl(p,x_i)}{dp} = \sum_{i=1}^n \frac{r}{p} -\frac{x_i}{1-p}$

And we can separete the sum and we got:

$\frac{dl(p,x_i)}{dp} = \sum_{i=1}^n \frac{r}{p} -\sum_{i=1}^n \frac{x_i}{1-p}$

Now we need to find the critical point setting equal to zero this derivate and we got:

$\frac{dl(p,x_i)}{dp} = \sum_{i=1}^n \frac{r}{p} -\sum_{i=1}^n \frac{x_i}{1-p}=0$

$\sum_{i=1}^n \frac{r}{p} =\sum_{i=1}^n \frac{x_i}{1-p}$

For the left and right part of the expression we just have this using the properties for a sum and taking in count that p is a fixed value:

$\frac{nr}{p}= \frac{\sum_{i=1}^n x_i}{1-p}$

Now we need to solve the value of $\hat p$ from the last equation like this:

$nr(1-p) = p \sum_{i=1}^n x_i$

$nr -nrp =p \sum_{i=1}^n x_i$

$p \sum_{i=1}^n x_i +nrp = nr$

$p[\sum_{i=1}^n x_i +nr]= nr$

And if we solve for $\hat p$ we got:

$\hat p = \frac{nr}{\sum_{i=1}^n x_i +nr}$

And if we divide numerator and denominator by n we got:

$\hat p = \frac{r}{\bar x +r}$

Since $\bar x = \frac{\sum_{i=1}^n x_i}{n}$

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3 years ago

WORTH 20 POINTS!!!!!!

Georgia [21]

Step-by-step explanation:

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3 years ago

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Evgen [1.6K]

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3 years ago

C and d are complementary. The measure of c is 4x and the measure of d is 26. What is the value of x

const2013 [10]

Answer:

The value of x is 16.

Step-by-step explanation:

We are given the following in the question:

c and d are complementary angles.

Measure of c = $4x$

Measure of d = 26

Since c and d are complementary, we can write from property of complementary:

$c + d = 90$

Putting values, we get,

$4x + 26 =90\\4x = 90-26 = 64\\\\\Rightarrow x = \dfrac{64}{4} = 16$

Thus, value of x is 16.

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3 years ago

Five less then 3 times a number is 3 let x be unknown <br> number

azamat

Answer:

3x-5=3

Step-by-step explanation:

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3 years ago

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