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True [87]
3 years ago
8

Which expression is equivalent to 2(x -1)+x

Mathematics
2 answers:
gayaneshka [121]3 years ago
8 0

Answer:

  • Option B

Step-by-step explanation:

<u>First, let's simplify the given expression.</u>

  • => 2(x - 1) + x
  • => 2x - 2 + x
  • => (2x + x) - 2
  • => 3x - 2

Looking at all the options, we can say that Option B is correct.

olchik [2.2K]3 years ago
5 0

\huge\text{Hey there!}

\huge\textbf{Question reads....}

\large\text{Which expression is equivalent to 2(x - 1) + x?}

\huge\textbf{Step by step to find your result}

\large\textbf{First you have to DISTRIBUTE 2 WITHIN the}\\\large\textbf{PARENTHESES}

\large\text{2(x - 1) + x}\\\rightarrow\large\text{2(x) + 2(-1) + x}\\\rightarrow\large\text{2x - 2 + x}\\\rightarrow\large\text{2x - 2 + 1x}\\\rightarrow\large\textbf{COMBINE the LIKE TERMS}\leftarrow\\\rightarrow\large\text{(2x + 1x) - (2)}\\\rightarrow\large\text{3x - 2}

\huge\textbf{FINALLY WE HAVE YOUR RESULT}

\huge\boxed{\textsf{Therefore, your answer is: }}}\\\huge\boxed{\mathsf{Option\ B. \ 3x - 2}}\huge\checkmark

\huge\text{Good luck on your assignment \& enjoy }\\\huge\text{your day!}

<h2>~\frak{Amphitrite1040:)}</h2>
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Step-by-step explanation:

So there are 36 different ways

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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

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Step-by-step explanation: Used my sheet.

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