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2 years ago

7

The hypotenuse of a right triangle measures 58 cm and one of its legs measures 42 cm. What is the length of the missing leg? 10

cm 16 cm 40 cm 71 cm

1 answer:

Nutka1998 [239]2 years ago

5 0

If the hypotenuse is 58cm, and one of the others legs is 42cm the answer would be 40cm

Explanation:

Here you have to use the formula

${a}^{2} + {b}^{2} = {c}^{2}$
Then you have to pose the formula in terms of one of the legs, so:

${a}^{2} = {c}^{2} - {b}^{2}$
$a = \sqrt{ {c}^{2} - {b}^{2}}$
So when you change the letter for numbers you have that:

$a = \sqrt{ {58}^{2} - {42}^{2} }$

a=40

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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

92,542 in word form please

Juli2301 [7.4K]

Ninety two thousand and five hungered and forty two

7 0

2 years ago

- 6x +15 <br>Can anyone please show me the steps of solving this equation

Vesna [10]

Answer:

-6x + 15 = - 69 which x = 14

Step-by-step explanation:

You cannot solve this equation. There is no equal sign anywhere. Either you mean

-6x = 15 in which case the answer is

-6x/-6 = 15/-6

x = - 2 1/2 or x= - 2.5

or you mean that you use the distributive property

- 3(2x + 5)

You may have left something out of this.

-6x + 15 = - 69

You can do it now that you have the complete equation. But you need the entire equation before you can answer the question.

Subtract - 15 from both sides.

-6x + 15 - 15 = -69 - 15

-6x = - 84

Divide by - 6

-6x/-6 = - 84/-6

x = 14

But what you want is

-6x + 15

-6*14 + 15

-84 + 15

-69

-6x + 15 = - 69

when x = 14 which is usually what you are asked.

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2 years ago

What is the relationship between the area of the rectangle ABCD and triangle ABC?

Sonja [21]

Answer:

The second one.

Step-by-step explanation:

The area of the triangle has an area that is half the area of the rectangle.

A straight line divides the rectangle directly in half, creating two triangles, each triangle being half the area of the rectangle

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madreJ [45]

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(x-a)^2 + (y-b)^2 = r^2

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Here we are adding and subtracting numbers in order to get square binomial.
(x - 1/2)^2 + (y-1)^2 = 5/4

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3 years ago

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