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3 years ago

Factor the following trinomial, if possible 4x^2 + 4x - 3

1 answer:

6 0

$4x^2+\underbrace{4x}_{6x-2x}-3=2x\cdot2x+\underbrace{2x\cdot3}_{6x}-1\cdot2x-1\cdot3\\\\=2x(2x+3)-1(2x+3)=\boxed{\boxed{(2x+3)(2x-1)}}$

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Suppose calls are arriving at a telephone exchange at an average rate of one per second, according to a Poisson arrival process.

antoniya [11.8K]

Answer:

Explanation has been given below

Step-by-step explanation:

a) inter arrival times are exponentially distributed with mean 1/n , where n = rate = 1/sec.

probability distribution function is F(t)=n*exp(-n*t).

reference to any kth packet and the (k-1)th packet

the answer is = integration of F(t).dt with limits 0 to 2 = 1 - exp(-2*n) = 1 - exp(-2)

b) t=5 , P(q) = exp(-5)*(5)^q/factorial(q)

probability of fourth call within t=5 seconds is =

that is P(4) P(5) ...... = 1 - ( P(0) P(1) P(2) P(3) ) ; put the values and get the answer.

c) number of calls/rate = 4/n = 4 seconds

5 0

3 years ago

Debora [2.8K]

Use desmos hope that helps

4 0

3 years ago

An environment engineer measures the amount ( by weight) of particulate pollution in air samples ( of a certain volume ) collect

Serggg [28]

Answer:

$k = 1$

$P(x > 3y) = \frac{2}{3}$

Step-by-step explanation:

Given

$f \left(x,y \right) = \left{ \begin{array} { l l } { k , } & { 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x } & { \text 0, { elsewhere. } } \end{array} \right.$

Solving (a):

Find k

To solve for k, we use the definition of joint probability function:

$\int\limits^a_b \int\limits^a_b {f(x,y)} \, = 1$

Where

${ 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x }$

Substitute values for the interval of x and y respectively

So, we have:

$\int\limits^2_{0} \int\limits^{x/2}_{0} {k\ dy\ dx} \, = 1$

Isolate k

$k \int\limits^2_{0} \int\limits^{x/2}_{0} {dy\ dx} \, = 1$

Integrate y, leave x:

$k \int\limits^2_{0} y {dx} \, [0,x/2]= 1$

Substitute 0 and x/2 for y

$k \int\limits^2_{0} (x/2 - 0) {dx} \,= 1$

$k \int\limits^2_{0} \frac{x}{2} {dx} \,= 1$

Integrate x

$k * \frac{x^2}{2*2} [0,2]= 1$

$k * \frac{x^2}{4} [0,2]= 1$

Substitute 0 and 2 for x

$k *[ \frac{2^2}{4} - \frac{0^2}{4} ]= 1$

$k *[ \frac{4}{4} - \frac{0}{4} ]= 1$

$k *[ 1-0 ]= 1$

$k *[ 1]= 1$

$k = 1$

Solving (b): $P(x > 3y)$

We have:

$f(x,y) = k$

Where $k = 1$

$f(x,y) = 1$

To find $P(x > 3y)$ , we use:

$\int\limits^a_b \int\limits^a_b {f(x,y)}$

So, we have:

$P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {f(x,y)} dxdy$

$P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {1} dxdy$

$P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 dxdy$

Integrate x leave y

$P(x > 3y) = \int\limits^2_0 x [0,y/3]dy$

Substitute 0 and y/3 for x

$P(x > 3y) = \int\limits^2_0 [y/3 - 0]dy$

$P(x > 3y) = \int\limits^2_0 y/3\ dy$

Integrate

$P(x > 3y) = \frac{y^2}{2*3} [0,2]$

$P(x > 3y) = \frac{y^2}{6} [0,2]\\$

Substitute 0 and 2 for y

$P(x > 3y) = \frac{2^2}{6} -\frac{0^2}{6}$

$P(x > 3y) = \frac{4}{6} -\frac{0}{6}$

$P(x > 3y) = \frac{4}{6}$

$P(x > 3y) = \frac{2}{3}$

8 0

3 years ago

The price of an item has been reduced by 45% . The original price was $17

Artist 52 [7]

Price is reduced by 45%. Which means that the new price is 55% of the original.
Therefore, (55/100)*17 = $9.35 =new price

8 0

3 years ago

Can someone please help?

mel-nik [20]

Answer:

C. y = 2/3 x - 2.

Step-by-step explanation:

The general form of the slope-intercept equation of a line is y = mx + c where m = the slope and (0. c) is the y-intercept.

We are given that the slope = 2/3 and the y intercept is at (0,-2) so our equation is y = 2/3 x - 2.

4 0

3 years ago

Read 2 more answers