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3 years ago

Factor the expression using the GCF 2r - 10

Mathematics

1 answer:

vovangra [49]3 years ago

5 0

Answer:2(r-5)

Step-by-step explanation: divide 2 on both sides which gives you 5 and then you write 2(r-5).

Hope it helps :)

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The formula for the surface area of a rectangular prism with a square base is SA=2s2+4shSA=2s2+4sh. What is the surface area of

Ivanshal [37]

This is the concept of algebra, given that the formula for the surface area of the prism is modeled by the expression SA=2s²+4sh , the surface area of the prism when s=3 and h=5 will be found by substituting the values in our expression as follows;
SA=2(3)²+4×3×5
SA=2(9)+60
SA=18+60
SA=78 sq. units
The answer is 78 sq. units

4 0

3 years ago

Read 2 more answers

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

4 0

3 years ago

During a sale at a bookstore, Joseph buys a book at full price. He is given a 50 percent discount on a second book of equal or l

NARA [144]

Total cost of books was 15 + 10 or 25. With the 50 % discount on the $10 book, the total is now $20. The total cost was reduced by (B) 20%.
$5 off the $25 price is a 20% discount.

5 0

3 years ago

Need some help on my precalculus homework

Pavlova-9 [17]

Answer:

#4 vertex form

and

vertex (h,k)

Step-by-step explanation:

vertex form

-2(x-3)^2+32

vertex

(h,k)

(3,32)

6 0

3 years ago

What is the standard form of 5.93-5

vredina [299]

Just subtract the whole numbers, 5.93-5 = 0.93.

4 0

3 years ago