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3 years ago

Kim works 4 hours more each day than jill does, and jack works 2 hours less each day

Mathematics

2 answers:

Nadusha1986 [10]3 years ago

6 0

Where's the rest of the question

marusya05 [52]3 years ago

4 0

Answer:

The answer is 2(x+3)=3 * 2(x-1)-2x

Step-by-step explanation:

full question:

Kim works 3 hours more each day than Jill does, and Jack works 1 hour less each day than Jill does. Over 2 days, the number of hours Kim works is equal to the difference of 3 times the number of hours Jack works and the number of hours Jill works. How many hours does each person work each day? Let x be the number of hours Jill works in one day.

2(x+3)=3 * 2(x-1)-2x

2(x+3)=6(x-1)-2x

2x+6=4x-6

2x+6-6=4x-6-6

2x=4x-12

-2x=-12

-2x/-2=-12/-2

x=6

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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

Which three lengths could be the lengths of the sides of a triangle?

ZanzabumX [31]

Answer:

Step-by-step explanation:

5 0

3 years ago

Solve the following system using the substitution method.

Liono4ka [1.6K]

X = (15 - 8y)/9

-5[(15 - 8y)/9] + 12y = -107

(-75/9) + (40/9) + 12y = -107

y = -8.59

x = [15 - 8(-8.59)]/9

x = 9.3
(x,y) = (9.3, -8.59)

3 0

3 years ago

Boston, Massachusetts had a population of 617,594 people during January 1 2010, and 675,647 people on January 1 2020.

tigry1 [53]

Answer:

See below

Step-by-step explanation:

Exponential function is:

y = abˣ

If we consider the time difference in years as x and the initial population as a, then we get:

675647 = 617594*b¹⁰

Find the value of b:

b¹⁰ = 675647/617594
b¹⁰ = 1.09399864636
b = 1.09399864636^(1/10)
b = 1.009 (rounded)

The equation we got is:

y = 617594*1.009ˣ

Here we have y- population after x years since 2010, x - the number of years since 2010 and 1.009 is the population growth rate.

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1 year ago

The hourly cost of renting office space in Manhattan is shown by the graph below. The hourly cost of renting office space in Bro

Liula [17]

Answer:

Brooklyn is more expensive

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers