HELP!!!!? ASP! PLSSSS #14

What number must be added to the expression below to complete the square

EastWind [94]

Where is it? In order to help you I need to see what the problem is.

3 0

4 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

3 years ago

The measure of angle x is 25 more than 4 times the measure of its complement. Find the measure of x.

topjm [15]

- Two angles that are complements of each other add to equal 90 degrees (they are complementary angles).
- One angle measures x degrees.
- The other angle measures 25 more than 4 times the angle that measures x degrees; it measures 4x + 25 degrees.

To find x, set the sum of these expressions (x and 4x + 25) equal to 90 and solve algebraically for x.

90 = x + (4x + 25)
90 = x + 4x + 25
90 = 5x + 25
65 = 5x
13 = x

If you wanted to find the measure of angle x, you'd substitute 13 for x in its expression, 4x + 25.

4x + 25
4(13) + 25
52 + 25
77

Answer:
x = 13
m∠x = 77°

4 0

3 years ago

Charlie bought 16 cartons of ice cream and 7 cartons of yogurt. Each carton of ice cream cost $6 and each carton of yogurt cost

lys-0071 [83]

Charlie spent $89 more dollars on ice cream than on yogurt. He spent a total of $96 on ice cream and $7 on yogurt. If you subtract 7 from 96 you get 89.
$96- $7= $89

4 0

3 years ago

Read 2 more answers

Help me please.........

Rama09 [41]

Answer:

1. true 2. true 3.true 4. false 5. false

Step-by-step explanation: 4/4-3/4 is 1/5. You multiply the top first (4-3=1) and the bottom isn't supposed to change. so the answer is 1/4

5 0

3 years ago