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3 years ago

Factor completely 3x2 + y. x(3x + y) y(3x2) xy(3x + 1) Prime

Mathematics

2 answers:

creativ13 [48]3 years ago

6 0

Answer: PRIME (OPTION D)

Rainbow [258]3 years ago

5 0

Answer:

Option (d) is correct.

The given polynomial $3x^2+y$ is a prime polynomial.

Step-by-step explanation:

Given : $3x^2+y$

We have to factorize it completely.

Since , factorization is the process of reducing a given polynomial into a lower degree polynomial by taking common factors out into the simplest form.

Consider the given polynomial $3x^2+y$

Since the given polynomial do not have any term common in both terms .

So we cannot factorized it further.

So, the given polynomial $3x^2+y$ is a prime polynomial.

Thus, Option (d) is correct.

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In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal p

skelet666 [1.2K]

Answer:

$\mathbf{P(X=5) =0.0888}$

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

$\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}$

$\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}$

where;

n = 8 and π = 0.36

For x = 5

The probability $\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}$

$\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =0.0887645}$

$\mathbf{P(X=5) =0.0888}$ to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5) $\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})$

${P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +$ $\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )$

P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888

P(x ≤ 5 ) = 0.9707

c. x ≥ 6

The probability of P ( x ≥ 6) = 1 - P( x ≤ 5 )

P ( x ≥ 6) = 1 - 0.9707

P ( x ≥ 6) = 0.0293

4 0

3 years ago

Find the domain of the function algebraically q(r)=3square root r^2 -16

lawyer [7]

Hello :
q(r)=3√(r²-16)
q exist : r² - 16 ≥ 0
r² ≥ 16
√r² ≥ √16
but : √16 = 4 and √r² = |r |
|r | ≥ 4
r ≤ 4 or r ≥ 4
the domain is : ] -∞, 4] ∪ [,4 , + ∞ [

4 0

4 years ago

Math question (working too, if possible)

inessss [21]

4/15 of the Primary School chose chicken nuggets.

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4 years ago

Read 2 more answers

Sin(x+pi/4)-sin(x-pi/4)=1 solve the equation

evablogger [386]

Sin(α+β)=sin(α)cos(β)+cos(α)sin(β)
sin(α-β)=sin(α)cos(β)-cos(α)sin(β)

$sin(x+ \frac{ \pi }{4} )=sin(x)cos\frac{ \pi }{4} +cos(x)sin\frac{ \pi }{4} \\ sin(x- \frac{ \pi }{4} )=sin(x)cos\frac{ \pi }{4} -cos(x)sin\frac{ \pi }{4} \\ \\ \\sin(x+ \frac{ \pi }{4} )-sin(x- \frac{ \pi }{4} ) =1 \\ sin(x)cos\frac{ \pi }{4} +cos(x)sin\frac{ \pi }{4} -(sin(x)cos\frac{ \pi }{4} -cos(x)sin\frac{ \pi }{4} )=1 \\ sin(x)cos\frac{ \pi }{4} +cos(x)sin\frac{ \pi }{4} -sin(x)cos\frac{ \pi }{4} +cos(x)sin\frac{ \pi }{4} =1 \\ cos(x)sin\frac{ \pi }{4} +cos(x)sin\frac{ \pi }{4} =1 \\$
$2cos(x)sin\frac{ \pi }{4} =1 \\ sin\frac{ \pi }{4} = \frac{ \sqrt{2} }{2} \\ 2cos(x) \frac{ \sqrt{2} }{2} =1 \\ 2 \cdot \frac{ \sqrt{2} }{2}cos(x) =1 \\ \sqrt{2} cos(x)=1 \\$
$cos(x)= \frac{1}{ \sqrt{2} } \\ x=\pm arccos \frac{1}{ \sqrt{2} }+2 \pi k , k \in Z \\ x=\pm \frac{ \pi }{4} +2 \pi k , k \in Z$

6 0

3 years ago

Britney is going to the candy store to buy 20 pieces of candy. She is going to buy chocolate candy and caramel candy. Each piece

igomit [66]

To start off, you want to make the equations. first, we will make x = chocolate candy and y=caramel candy since thats the order they come in the problem. we know she bought 20 pieces of candy, so we now know our first equation, x+y=20. next, if each chocolate candy costs $.50, that now makes x in our second equation .5x. the y will then be .1y. they then total up to equal $6.80, so our second equation is .5x+.1y=6.8. to then find x, subtract the y from the first equation to get x=20-y. then in the second equation, replace x with y and solve. you then get y=8, so we know britney has 8 caramels. now in the first equation, replace the y to get x+8=20. and now x=12

7 0

3 years ago