On the bottom right corner. I need help on that please! First to answer gets branliest and

Find a quadratic expression with integer coefficients whose roots are <img src="https://tex.z-dn.net/?f=5%2F2%2B%203i" id="TexFo

prohojiy [21]

Answer:

4x² -20x +61

Step-by-step explanation:

the quadratic equation can be written as (x-root1)(x-root2)

(x-(5/2) -3i) (x-(5/2)+3i), distribute

x² -(5/2)x +3xi -(5/2)x + 25/4 -(15/2)i -3xi +(15/2)i -9i², simplify

x² -(5/2)x -(5/2)x + 25/4 -9i², use the fact that i² =(√-1)² = -1 and substitute i²

x² -(5/2)x -(5/2)x + 25/4 +9, combine like terms and rewrite 9 as 36/4

x² -(10/2)x +25/4 + 36/4, combine like terms and simplify

x² -5x +61/4 is the quadratic expression yet it does not have integer coefficients so multiply by 4 to have all coefficients integers

4x² -20x +61

7 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

3 years ago

SHAYNA FREEL PLANS TO BUY $17.45 WORTH OF STATIONERY SUPPLIES. IF THE SALES TAX IS 13%, HOW MUCH WILL SHAYNA PAY?

Rainbow [258]

9514 1404 393

Answer:

$19.72

Step-by-step explanation:

The sales tax is 13% of $17.45:

0.13 × $17.45 = $2.27 . . . . . . rounded (up) to the nearest cent

Then the total Shayna will pay is ...

$17.45 +2.27 = $19.72

7 0

3 years ago

Wanna hear something funny I have been asking questions about math all day but none of them have been answered like this is the

scZoUnD [109]

Answer:

lollllllll

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Koto’s average velocity along her route was 4. 5 m/s. She started at her house and traveled 15,000 meters north, 5,000 meters ea

Lostsunrise [7]

The time taken for her trip is 3 hours.

<h3>Given that</h3>

Koto’s average velocity along her route was 4. 5 m/s.

She started at her house and traveled 15,000 meters north, 5,000 meters east, 20,000 meters south, and then 5,000 meters west.

<h3>We have to determine</h3>

What was the time of her trip?

<h3>According to the question</h3>

She started at her house and traveled 15,000 meters north, 5,000 meters east, 20,000 meters south, and then 5,000 meters west.

<h3 /><h3>The calculation of such a trip of Koto can be done by applying the known formula of Time when the Speed is multiplied by Distance to compute the actual time of the trip.</h3>

The formula to calculate the time for her trip is;

$\rm Speed = \dfrac{ Distance}{Time}\\
\\
Time = \dfrac{Distance}{Speed}\\
\\
$

Using the formula above, the commute in each direction is added as 45000 meters or 45 kilometers.

If Koto's average speed is 4.5 meters per second, then she travels roughly 270 meters in one minute.

Substitute all the values in the formula;

$\rm\ Time = \dfrac{Distance}{Speed}\\\\ Time = \dfrac{45000}{270}\\
\\
Time =166.7$

Converting minutes into hours,

$\rm Hours = \dfrac{Minute}{60}\\
\\
Hours = \dfrac{166.7}{60}\\
\\
Hours = 2.77 \\
\\
= 3\ hours$

Hence, the time taken for her trip is 3 hours.

To know more about Time and Distance click the link given below.

brainly.com/question/4433818

5 0

2 years ago