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2 years ago

How many oz of walnuts which cost $6/oz must be added to 2 oz of peanuts which cost $12/oz to make mixed nuts which cost $8/oz

Mathematics

1 answer:

Burka [1]2 years ago

4 0

Answer: 4 oz

<u>Step-by-step explanation:</u>

Create a table. Multiply across and add down (the middle column cannot be added). The Mixture line creates the equation that must be solved.

Let x represent the unknown quantity of walnuts.

$\begin{array}{c|c|c||c}&\underline{Quantity}&\underline{Cost}&\underline{Qty \times Cost}\\Walnuts&x&6&6x\\\underline{Peanuts}&\underline{\qquad 2\qquad}&\underline{\qquad 12\qquad}&\underline{\qquad 24\qquad }\\Mixture&x+2&8&6x+24\end{array}$

$.\qquad \qquad \qquad \qquad (x+2)(8) = 6x+24\\.\qquad \qquad \qquad \qquad 8x + 16 = 6x + 24\longrightarrow \text{distributed}\\.\qquad \qquad \qquad \qquad2x+16=24\qquad \longrightarrow \text{subtracted 6x}\\.\qquad \qquad \qquad \qquad 2x=8\qquad \qquad \ \longrightarrow \text{subtracted 16}\\.\qquad \qquad \qquad \qquad x=4\qquad \qquad \quad \longrightarrow \text{divided by 2}$

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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

What is the answer to (( 5 x 12)/3)+30-50

SpyIntel [72]

I believe the correct answer is 0

Step-by-step explanation:

To solve this question, we use an abbreviation formula called BODMAS which is:

B = Brackets

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

We solve each element that is available in the order of the abbreviated letter.

1. We solve the brackets:

$(5\times12) = 60$

2. We solve the second bracket:

$(60\div3) = 20$

The equation now is $20+30-50$

3. We now solve addition first:

$20+30=50$

4. Now we solve the subtraction:

$50-50=0$

The answer then = 0

8 0

3 years ago

Read 2 more answers

Can someone help meee

pickupchik [31]

Step-by-step explanation:

29+1/5r=

29+(1/5×-1/2)

29+1/10

291/10

=29.1

4 0

2 years ago

Read 2 more answers

Describe in words where the square root of twenty-four would be plotted on the number line.

Rzqust [24]

The square root of 24 would be plotted between 4 and 5, but closer to 5 on a number line.

<h3>What is a number line?</h3>

A number line is a horizontal line with evenly spaced numerical increments. The numbers on the line will dictate how you answer the number on the line.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, denoted by \mathbb {R}. Every point on a number line is assumed to be a real number, and every real number is assumed to be a point.

Number lines are extremely adaptable, that can be used to locate numbers, compare numbers, fractions and mixed numbers, decimals, integers, absolute value, addition, subtraction, inequalities, multiples, common denominators, and much more.

The square root of $\sqrt{24}=4.899$ , which is between 4 and 5, but closer to 5 on a number line.

To learn more about number lines, refer:

brainly.com/question/25230781

#SPJ4

5 0

1 year ago

Which of the following represents the inequality for the sum of 11 and y is greater than -33? O11-y> -33 O 11+ y -33 11 + y 2

laiz [17]

Answer:

11 + y > - 33

Step-by-step explanation:

To represent the expression :

Sum of 11 and y ; greater than - 33

Sum of 11 and y ; 11 + y

Greater Than - 33; > - 33

Hence ;

11 + y > - 33

5 0

3 years ago