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Whitepunk [10]
3 years ago
5

How many solutions does the equation 3x + 6 = − 1 − 3 + 4x have?

Mathematics
1 answer:
marissa [1.9K]3 years ago
8 0

Answer:

  • one solution: x=10

Step-by-step explanation:

The coefficients of x on each side of the equal sign are different, so the equation is <em>not a tautology</em>. It must have exactly one solution.

You might be interested in
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
Can someone help me please? I don't nderstand this
musickatia [10]

Answer:

perpendicular(p)=5

base(b)=12

hypotenuese(h)=?

using pytha goras theorem,

h^2=P^2+b^2

h^2=(5)^2+(12)^2

h^2=25+144

h^2=169

h^2=13^2

h=13.

6 0
3 years ago
3x^2+48=0, solve the equation
MAXImum [283]

Answer:

16 + x2 = 0     (16)

I THINK

Step-by-step explanation: Simplifying

3x2 + 48 = 0

Reorder the terms:

48 + 3x2 = 0

Solving

48 + 3x2 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-48' to each side of the equation.

48 + -48 + 3x2 = 0 + -48

Combine like terms: 48 + -48 = 0

0 + 3x2 = 0 + -48

3x2 = 0 + -48

Combine like terms: 0 + -48 = -48

3x2 = -48

Divide each side by '3'.

x2 = -16

Simplifying

x2 = -16

Reorder the terms:

16 + x2 = -16 + 16

Combine like terms: -16 + 16 = 0

16 + x2 = 0

The solution to this equation could not be determined.

8 0
3 years ago
The midpoint of a line segment is (−1,6) . One endpoint of the line segment is (4,−7) .
pogonyaev

Answer:

The other coordinate is (-6,19)

Step-by-step explanation:

m = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )

(4,-7)

(x,y)

[(4+x)/2 , (-7+y)/2] = (-1,6)

(4 + x)/2 = -1

4 + x = -2

× = -6

(-7 + y)/2 = 6

-7 + y = 12

y = 19

(Correct me if i am wrong)

5 0
3 years ago
Please answer this correctly
Klio2033 [76]

Answer:

x =1

Step-by-step explanation:

Assuming the figures are similar, we can use ratios to solve

x        2

---- = -----

4         8

Using cross products

8x = 2*4

8x = 8

Divide by 8

8x/8 = 8/8

x=1

6 0
2 years ago
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