a certain steel beam weighs 18.4 lbs per foot of length. If this beam is 26.5 feet long, how many lbs does it weigh?

Can you guys help me out for my math test <br> on usa test prep

Ber [7]

Answer:

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4 0

3 years ago

John wants to build a corral next to his barn. He has 300 feet of fencing to enclose three sides of his rectangular yard.

Mandarinka [93]

Let's first define the variables:
x = width
300 - 2x = long
The area will be:
A = (x) * (300 - 2x)
A = 300x - 2x²
We look for the maximum area, for this, we derive:
A '= 300 - 4x
We match zero:
0 = 300 - 4x
x = 300/4 = 75
Therefore, the width is:
x = 75 feet
The length is:
300 - 2x = 300 - 2 (75) = 300-150
150 feet
Answer:
Part A:
The maximum area will be:
A = (150) * (75) = 11250 square feet
Part B:
The dimensions are:
Length = 150 feet
width = 75 feet

3 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

What’s 6x-3y=18 in slope int? pls help lol

liraira [26]

Answer:

Using the Slope-intercept form, the slope is - 2.

8 0

3 years ago

You like math then here

Igoryamba

Answer:

-8b + 9 - 5k

Step-by-step explanation:

I am assuming the blue highlighted portion is your answer, and is not a part of the initial question

(-4b + 15 - 7k) - (6 + 4b - 2k)

Combine like terms

-4b - + 4b

Negative + Positive = Negative

-4b - 4b = -8b

15 - 6 = 9

-7k - - 2k

Negative + Negative = Positive

-7k + 2k = -5k

Put them all together:

0b + 9 - 5k

Simplify

-8b + 9 - 5k

I got the same answer as you (just in a different order)

5 0

3 years ago