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3 years ago

Find the area of the figure. Sides meet at right angles. No links please.

Mathematics

1 answer:

ss7ja [257]3 years ago

4 0

Answer:

40 ft²

Step-by-step explanation:

Divide the figure into 2 rectangles and find their areas.

The area of the smaller rectangle

= 3 × 4

= 12 ft²

The area of the larger rectangle

= (8-4) × 7

= 28 ft²

The area of the figure

= 12 + 28

= <u>40 ft²</u>

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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 plumber charges a $70 flat rate for all home repairs. His hourly rate is $15 per half hour. How much would a 2 hour and 26 m

Gnesinka [82]

The plumber's 2 hour and 26 min plumbing bill cost is $73

What is the plumber's per minute rate?

The plumber's per minute rate is the per half-hour rate divided by 30 minutes since the plumber charges $15 for every 30-minute job

per-minute rate=$15/30

per-minute rate=$0.50

Now, let us convert 2hours and 26 minutes to minutes, in other words, every 1 hour is 60 minutes, the two hours equal 120 minutes plus the 26 minutes gives a total of 146 minutes

Total minutes=120 min+26 min

total minutes=146 minutes

Total plumbing bill cost for 146 minutes is $0.50, the per-minute rate multiplied by the number of minutes the plumber needs to work in this case

2 hour and 26 min plumbing bill cost=146*$0.50

2 hour and 26 min plumbing bill cost=$73

Find out more about hourly rate on:brainly.com/question/4468523

#SPJ1

4 0

2 years ago

Which word best describes the degree of overlap between the two data sets? Low, High, None, Moderate

zlopas [31]

Answer:

In case of data set given with the question, the word that best describes the degree of overlap between the two data sets is low.

Step-by-step explanation:

Overlapping of two data sets means they contain common data or they have common elements in them.

In case of given data set, the elements are represented by 'x'.

If we compare both, the elements at line 30 and 35 overlap.

We conclude that out of 15 elements in each data set, only two of them overlaps. Hence the degree of overlap is low.

6 0

3 years ago

A snack tray at a party has cheese squares with 2 grams of protein apiece and turkey slices with 3 grams of protein apiece. Whic

Andreyy89

Answer:

The inequality equation is 12 ≤ 2x + 3y

Step-by-step explanation:

Protein in a cheese square = 2 grams

Protein in a turkey square = 3 grams

And She can eat 12 or more grams of proteins

Let x be the number of cheese squares and y be the number of turkey squares that she eats.

So, we can write an inequality equation, that describes the given situation in the problem.

i.e. 2x + 3y ≥ 12 or 12 ≤ 2x + 3y

So the inequality equation is 12 ≤ 2x + 3y

4 0

4 years ago

Read 2 more answers

The cost to repair linda's car is $500, including parts and labor. the cost of parts is $140. if the cost of labor is $40 per ho

Mkey [24]

500=140+40h
minus 140 both sides
360=40h
divide y 40
9=h
9 hours

5 0

3 years ago