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3 years ago

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Ine segment AB has endpoints A(–4, –10) and B(–11, –7). To find the x-coordinate of the point that divides the directed line seg

ment in a 3:4 ratio, the formula x = (x2 – x1) + x1 was used to find that x = (–11 – (–4)) + (–4).
Therefore, the x-coordinate of the point that divides AB into a 3:4 ratio is

2 answers:

Ivenika [448]3 years ago

7 0

Answer:

-7

Step-by-step explanation:

The coordinates of the point wich divide the segment AB, where $A(x_A,y_A),\ B(x_B,y_B)$ in ratio $m:n$ can be calculated using formula

$C\left(\dfrac{nx_A+mx_B}{m+n},\dfrac{ny_A+my_B}{m+n}\right)$

In your case,

$A(-4,-10)\\ \\B(-11,-7)\\ \\m:n=3:4\Rightarrow m=3,\ n=4$

Hence,

$C\left(\dfrac{4\cdot (-4)+3\cdot (-11)}{3+4},\dfrac{4\cdot (-10)+3\cdot (-7)}{3+4}\right)\\ \\C\left(-\dfrac{49}{7},-\dfrac{61}{7}\right)\\ \\C\left(-7,-\dfrac{61}{7}\right)$

Therefore, x-coordinate of the point that divides AB into a 3:4 ratio is -7.

denpristay [2]3 years ago

7 0

Answer:

a) -7

Step-by-step explanation:

made 100%

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2 years ago

The area of a square garden is 36 square feet. What is the side length of the garden

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Answer:

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Step-by-step explanation:

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

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3 years ago

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2 years ago

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Artemon [7]

Answer:

0.2377 or about a 23.77% chance

Step-by-step explanation:

P(123<X<130) = normalcdf(123,130,130,11) = 0.2377303466 ≈ 0.2377

Therefore, the probability that the next game Victoria bowls, her score will be between 123 and 130 is 0.2377 or about a 23.77% chance

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3 years ago