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2 years ago

Use multiplication to write 2 + 2 + 2 + 2+2.

Mathematics

2 answers:

Katena32 [7]2 years ago

8 0

2 x 5
2+2+2+2+2= 10
2 x 5= 10

Elina [12.6K]2 years ago

4 0

Answer:

5 × 2

Step-by-step explanation:

Multiplication is a simpler way of writing 'adding the same number multiple times'

Here you have added 5 2s together

So the answer is 5 times 2

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

4 0

3 years ago

A rectangular jewelry box costs $125 to gold plate. Calculate the cost of gold plating a box which is similar in shape and that

Alja [10]

To determine the amount of gold plating necessary for the similar box, you will use the fact that it is 8 times larger in volume to determine how many times larger the area is. This would be what you will multiply $125 by.

Volume is a three dimensional measurement, so the fact that it is 8 times larger tells us each dimension was 2 times larger (2 x 2 x 2=8).

Area is a two dimensional measurement, so the area would have been 2 x 2 or 4 times larger. This means the price would be 4 times as much.
$125 x 4 = $500.

It will cost $500 to gold plate the similar jewelry box.

7 0

3 years ago

If f(x)=3x^2-2 and g(x)=4x+2 what is the value of f+g 2

Papessa [141]

Answer:

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = 3x² - 2 + 4x + 2 = 3x² + 4x

Substitute x = 2 into f(x) + g(x)

(f + g)(2) = 3(2)² + 4(2) = (3 × 4) + 8 = 12 + 8 = 20

5 0

2 years ago

Which rational number is one tick mark to the left of -3/4

Zolol [24]

I'm assuming each tickmark is 1/4 = 0.25

If that assumption is correct, then going one tickmark to the left of -3/4 lands you on -4/4 which simplifies to -1.

So -1 is one tickmark to the left of -3/4

Again, this all hinges on the assumption that each tickmark is 1/4 a unit away from its neighbor.

5 0

3 years ago

What is equivalent to y=(x+3)2+53

viva [34]

The answer is y=2x+59

8 0

3 years ago

Read 2 more answers