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-Dominant- [34]
3 years ago
7

Evaluate the expression \dfrac{7^2}{x^2-2} x 2 −2 7 2 ​ start fraction, 7, squared, divided by, x, squared, minus, 2, end fracti

on for x=3x=3x, equals, 3
Mathematics
1 answer:
sertanlavr [38]3 years ago
3 0

Answer:

7

Step-by-step explanation:

We want to evaluate the fraction below for x = 3. We will put the value of x to be 3:

\dfrac{7^2}{x^2-2}\\\\= \dfrac{7^2}{3^2-2}\\\\= \dfrac{49}{9-2}\\\\= \dfrac{49}{7} = 7

The answer is 7.

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Gloria is an artist. She sets a goal to paint 2 paintings every month. The number of paintings Gloria creates depends on the num
BartSMP [9]

Answer:

we get the all equation of given condition  M = 2P+1   &   P=2M+1Step-by-step explanation:

Given that,

Number of painting made by Gloria every month is 2.

Gloria creates depends on the number of paintings p, Gloria paints over m months if she meet her goal.

we have to check all the apply.

According to question,

M is the independent variable and P is dependent variable.

So,   Relation formed by given statement is  M =2P

Case(1):  P is increased by 2 as M is increased by 1.

    Then,                   M+1= 2\times (P+2)

                                  M+1= 2P+2

                                       M = 2P+1

This is Equation of the given case(1).

Again, P is the independent variable and M is dependent variable.

      ∴                         P=2M

Case (2) M is increased by 2 as P increased by 1.

  Then,                P+1=2\times(M+2)

                             P+1=2M+2

                               P=2M+1

Hence,

we get the all equation of given condition  M = 2P+1   &   P=2M+1

4 0
3 years ago
A textile mill wishes to establish a control procedure on flaws in towels it manufactures. Using an inspection unit of 50 units,
Natasha_Volkova [10]

Answer:

•A c-chart is the appropriate control chart

• c' = 8.5

• Control limits, CL = 8.5

Lower control limits, LCL = 0

Upper control limits, UCL = 17.25

Step-by-step explanation:

A c chart is a quality control chart used for the number of flaws per unit.

Given:

Past inspection data:

Number of units= 100

Total flaws = 850

We now have:

c' = 850/100

= 8.5

Where CL = c' = 8.5

For control limits, we have:

CL = c'

UCL = c' + 3√c'

LCL = c' - 3√c'

The CL stands for the normal control limit, while the UCL and LCL are the upper and lower control limits respectively

Calculating the various control limits we have:

CL = c'

CL = 8.5

UCL = 8.5 + 3√8.5

= 17.25

LCL = 8.5 - 3√8.5

= -0.25

A negative LCL tend to be 0. Therefore,

LCL = 0

4 0
3 years ago
Let the number of chocolate chips in a certain type of cookie have a Poisson distribution. We want the probability that a cookie
ludmilkaskok [199]

Answer:

\lambda \geq 6.63835

Step-by-step explanation:

The Poisson Distribution is "a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event".

Let X the random variable that represent the number of chocolate chips in a certain type of cookie. We know that X \sim Poisson(\lambda)

The probability mass function for the random variable is given by:

f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...

And f(x)=0 for other case.

For this distribution the expected value is the same parameter \lambda

E(X)=\mu =\lambda

On this case we are interested on the probability of having at least two chocolate chips, and using the complement rule we have this:

P(X\geq 2)=1-P(X

Using the pmf we can find the individual probabilities like this:

P(X=0)=\frac{e^{-\lambda} \lambda^0}{0!}=e^{-\lambda}

P(X=1)=\frac{e^{-\lambda} \lambda^1}{1!}=\lambda e^{-\lambda}

And replacing we have this:

P(X\geq 2)=1-[P(X=0)+P(X=1)]=1-[e^{-\lambda} +\lambda e^{-\lambda}[]

P(X\geq 2)=1-e^{-\lambda}(1+\lambda)

And we want this probability that at least of 99%, so we can set upt the following inequality:

P(X\geq 2)=1-e^{-\lambda}(1+\lambda)\geq 0.99

And now we can solve for \lambda

0.01 \geq e^{-\lambda}(1+\lambda)

Applying natural log on both sides we have:

ln(0.01) \geq ln(e^{-\lambda}+ln(1+\lambda)

ln(0.01) \geq -\lambda+ln(1+\lambda)

\lambda-ln(1+\lambda)+ln(0.01) \geq 0

Thats a no linear equation but if we use a numerical method like the Newthon raphson Method or the Jacobi method we find a good point of estimate for the solution.

Using the Newthon Raphson method, we apply this formula:

x_{n+1}=x_n -\frac{f(x_n)}{f'(x_n)}

Where :

f(x_n)=\lambda -ln(1+\lambda)+ln(0.01)

f'(x_n)=1-\frac{1}{1+\lambda}

Iterating as shown on the figure attached we find a final solution given by:

\lambda \geq 6.63835

4 0
2 years ago
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7 0
2 years ago
Find the Quadratic Formula: m2 - 5m - 14 = 0
anastassius [24]

Answer: Do want to solve it using the quadratic formula because if so the answer is m=7,-2

Step-by-step explanation:

6 0
2 years ago
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