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Nezavi [6.7K]
2 years ago
12

The areas of the squares adjacent to two sides of a right triangle are 32units^2 and 32 units^2

Mathematics
2 answers:
natima [27]2 years ago
8 0

Answer:

Step-by-step explanationmoo

adoni [48]2 years ago
4 0

Answer:

x = 8 units.

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

<em>The areas of the squares adjacent to two sides of a right triangle are 32 unit square and 32 units square. Find the length,x, of the third side of the triangle</em>

My answer:

  • Let a is the side length of the 1st square

The area of the 1st square is equal to 32 units square

<=> a^{2} = 32

<=> a = 4\sqrt{2} units

  • Let b is the length  of the 2nd  square

The area of the 2nd square is equal to 32 units square

<=> b^{2} = 32

<=> b = 4\sqrt{2} units

  • Find the value of x

Applying the Pythagoras Theorem, we have:

x^{2} = a^{2} + b^{2}

<=> x^{2}  = 32 + 32  

<=> x^{2} = 64

<=> x = 8 units

Hope it will find you well.

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Today’s cafeteria specials are a turkey sandwich and a pepperoni pizza. During 1st lunch, the cafeteria sold 70 turkey sandwiche
sveticcg [70]

Answer:

$4 and $3

Step-by-step explanation:

First, write out the equations as 70x + 29y = 367 and 70x + 45y = 415. Solve by using the elimination method by subtracting 70x from 70x. 45y minus 29y is equal to 16y. 415 minus 367 is 48. Divide 48 by 16, to get y is equal to get y is equal to three. Y represents pepperoni pizzas, so a pepperoni pizza costs $3. Plug a 3 into any equation for y and solve for x. 29 times 3 is 87. 367 minus 87 is 280. 280 divided by 70 is equal to 4, so x is equal to 4.

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2 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}

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