In circle Y, what is mArc T U?

Consider the product (x + y + z)2. If the expression is multiplied out and like terms collected, the result is: x2 + y2 + z2 + 2

VLD [36.1K]

Answer:

Part a: The coefficient of $v^9w^2x^5y^7z^2$ is $1.766 \times 10^{13}$

Part b: The number of terms are 23751.

Step-by-step explanation:

part a

From the given equation the

$(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx$

So the coefficient of any term $x^ny^nz^n$ is given as

$\dfrac{2!}{n!n!n!}$

Similarly for the generic equation of coefficient of the term $x_1^{r_1}x_2^{r_2}x_3^{r_3}......x_k^{r_k}$ in the equation of form $(x_1+x_2+x_3+x_4......x_k)^n$ is given as

$\dfrac{n!}{r_1!r_2!r_3!....r_k!}$

So now the coefficient of $v^9w^2x^5y^7z^2$ is given as

$=\dfrac{25!}{9!2!5!7!2!}\\=1.766 \times 10^{13}$

The coefficient of $v^9w^2x^5y^7z^2$ is $1.766 \times 10^{13}$

Part b:

The number of terms is given as $\left (\ {{m+n-1} \atop {n}} \right )$

where m is the number of variables which are 5 here

n is the power which is 25 so the number of variables is given as

$\left (\ {{5+25-1} \atop {25}} \right )\\\left (\ {{29} \atop {25}} \right )\\\dfrac{29!}{25!4!}=23751$

So the number of terms are 23751.

3 0

2 years ago

Every day, a lecture may be canceled due to inclement weather with probability 0.05. Class cancelations on different days are in

andrezito [222]

<h3>(a)Probability of cancelling at least 4 classes is 0.0055.</h3><h3>(b)Probability of 10th class is third class that gets cancelled = 0.0031</h3>

Step-by-step explanation:

Here, the question is<u> incomplete</u>.

Every day, a lecture may be canceled due to inclement weather with probability 0.05. Class cancellations on different days are independent.

(a) There are 15 classes left this semester. Compute the probability that at least 4 of them get canceled.

(b) Compute the probability that the tenth class this semester is the third class that gets canceled.

Now, here:

The probability of cancelling each class = 0.05

Now, probability of cancelling at least 4 classes

= 1 - P(Cancelling at max 3 classes)

= 1 - P(0 ≤ x ≤ 3) = 1 - Binomial (15,0.05,3)

= 0.0055

Hence, probability of cancelling at least 4 classes is 0.0055.

(b) As given, 10th class is third class that gets cancelled.

So, the first and second classes that get cancelled in between 1 - 9.

P(2 class cancelled in 1st 9) = Binomial (15,0.05,3) = 0.0629

Also, as given P(10th class cancelled) = 0.05

⇒ P(10th class is third class that gets cancelled ) = 0.0629 x 0.05 = 0.0031

5 0

2 years ago

The perimeter of a rectangle is represented by 4x2 + 5x − 2. The perimeter of a smaller rectangle is represented by x2 + 3x + 5.

REY [17]

<span>4x2 +5x - 2 -x2 +3x +5 Simplified: 3x2 + 8x +3 In order to determine the difference in size, you must subtract the perimeter of the smaller rectangle from the perimeter of the larger rectangle.</span>

6 0

2 years ago

Read 2 more answers

what is a correct first step in solving the inequality –4(3 – 5x)≥ –6x 9? –12 – 20x ≤ –6x 9 –12 – 20x ≥ –6x 9 –12 20x ≤ –6x 9 –1

DIA [1.3K]

<span>The answer is -12 + 20x ≥ –6x 9. The inequality is –4(3 – 5x)≥ –6x 9. The first step is to multiply factors on the left side. The intermediary steps are: (-4)*(3) - (-4)*(5x) ≥ –6x 9. -12 - (-20x) ≥ –6x 9. So, the first step will be: -12 + 20x ≥ –6x 9.</span>

3 0

2 years ago

Read 2 more answers

In a survey of 2,300 people who owned a certain type of car, 1,610 said they would buy that type of car again. What percent of t

trapecia [35]

Answer:

In a survey of 2,300 people who owned a certain type of car, 1,610 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?

1610/2300x100=

70%

Step-by-step explanation:

total number of people for the survey= 2300

those that wanted to buy the car= 1610

percentage= 1610/2300x 100=0.7x 100

percentage= 70%

3 0

2 years ago