All categories

3 years ago

A comic book costs $3.99, including tax. It is marked up 45%.

Mathematics

1 answer:

o-na [289]3 years ago

6 0

Take 3.99 x 45/100 and then add that to the original 3.99

3.99 x 45/100 = 1.80

1.80 + 3.99 = 5.79

$5.79

You might be interested in

Graph the solution set 2(x-y)>6-y

Greeley [361]

Answer:

The area right side to the line

Step-by-step explanation:

2 (X-Y) > 6-Y

2X - 2Y > 6 - Y

2X -6 > Y

Y < 2X - 6

8 0

3 years ago

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 store owner sold 4 paint brushes for $12.00 and 8 pens for $3 20. What is the difference between the unit price of a paint bru

DaniilM [7]

Answer:

$2.6

Step-by-step explanation:

12/4=3 that means each paintbrush cost $3

3.20/8=0.4 that means each pen cost $0.40

3-0.4=2.6

3 0

3 years ago

Read 2 more answers

The width of a rectangle is 1.9 feet. The perimeter is 7.4 feet. What is the length?

dimaraw [331]

Answer:2.8 feet

Step-by-step explanation:

length(l)=?

breadth(b)= 1.9 feet

perimeter(p)=7.4 feet

we know,

p=2(l+b)

7.4=2(l+1.9)

7.4=2l+3.8

2l=7.4-3.8 (changing side and bringing 3.8 to 7.4 it gets -3.8)

l=3.6/2

l=2.8 feet

Hence,length is 2.8 feet

7 0

3 years ago

When Emily arrived home from school, she spent 8 minutes eating a snack. Then, she spent 15 minutes playing

OleMash [197]

Answer:

8+15+32+45= 100 minutes, or an hour and 40 minutes

6 0

3 years ago