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xxTIMURxx [149]
3 years ago
6

2. Solve the following system of equations

Mathematics
1 answer:
notsponge [240]3 years ago
6 0

Answer:

The answer to your question is x = 2, y = -1, z = 3

Step-by-step explanation:

Data

          x  +  y  +  z =  4

          x  - 2y  -  z =   1

         2x  -  y  - 2z = -1

Solve the system of equations

          |  1   1   1  |

          |   1 -2 - 1 |

Δ =     |  2  -1  -2|    = (4 - 1 -2) - (-2 + 1 -4) = 1 + 5 = 6

          |  1    1   1  |

          |  1  -2  -1 |  

         | 4   1   1 |

         | 1   -2  -1 |

Δx =   |-1   -1   -2|   = (16 - 1 + 1) - (-2 + 4 + 2) = 16 + 4 = 12

         | 4   1    1 |

         |  1  -2  -1 |

         | 1   4   1  |

         | 1    1  -1  |

Δy =  | 2 - 1  -2 | = (-2 -1 -8) - (-8 + 1 + 2) = -11 - 5 = -6

         | 1   4    1 |

         | 1    1    -1|

         | 1   1   4|

         | 1 -2   1|

Δz =  | 2 -1   -1|   = (2 - 4 + 2) - (-1 -1 -16) = 0 + 18

         | 1   1    4|

         | 1  -2   1|

Find x, y and z

x = Δx/ Δ = 12/6 = 2

y = Δy/Δ = -6/6 = -1

z = Δz/Δ = 18/6 = 3

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Answer:

Option B - =8.4672\times 10^{13}

Step-by-step explanation:

Given : Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5,880,000,000,000 miles.Suppose a star is 14.4 light years from earth.

To find : In scientific notation, how many miles away a star is from earth?

Solution :

One light-year is the distance that light can travel in one year is = 5,880,000,000,000 miles.

In scientific notation, 5.88\times 10^{12} miles.

In 14.4 lights year the distance is  =14.4\times5.88\times 10^{12}

In 14.4 lights year the distance is  =84.672\times 10^{12}

                                                  or  =8.4672\times 10^{13}

Therefore, Option B is correct.

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Convert this rational number to its decimal form and round to the nearest thousandth 5/7
Ksju [112]

The rational number, 5/7 converted to a decimal is 0.714.

<h3>What is the decimal?</h3>

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A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide i
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Answer:

The probability that exactly 10 insects will die

                     P( X = 10 ) = 0.06385        

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given a certain insecticide kills 60% of all insects in laboratory experiments

Given proportion  p = 0.60

                           q = 1 - 0.60 = 0.40

Given sample size 'n' = 12

<u><em>Step(ii):</em></u>-

Let "X' be the random variable of binomial distribution

                              P(X=r) = n_{C_{r} } p^{r} q^{n-r}

The probability that exactly 10 insects will die

                              P(X=10) = 12_{C_{10} } (0.60)^{10} (0.40)^{12-10}

                           

                          n_{C_{r} } = \frac{n!}{(n-r)!r!} = \frac{12!}{(12-10)!10!} = 66

                          P(X=10) = 66 X (0.60)^{10} (0.40)^{2} = 0.06385

<u><em>Final answer:</em></u>-

The probability that exactly 10 insects will die

                     P( X = 10 ) = 0.06385        

4 0
3 years ago
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