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3 years ago

Solve the systems of equations 2x+2y+6z=8 5x+6y+5z =3 5x+6y+3z=3

Mathematics

1 answer:

vlabodo [156]3 years ago

4 0

Answer:

$x=21\\y=-17\\z=0$

Step-by-step explanation:

Multiply the second equation by -1:

$(-1)5x+6y+5z=3(-1)\\-5x-6y-5z=-3$

Add this equation and the third equation and solve for "z":

$\left \{ {{-5x-6y-5z=-3} \atop {5x+6y+3z=3}} \right.\\.........................\\-2z=0\\z=0$

Substitute $z=0$ into two original equations:

$2x+2y+6(0)=8$

$2x+2y=8$ [Equation A]

$5x+6y+5(0)=3$

$5x+6y=3$ [Equation B]

Multiply the Equation A by -3, add both equations and then solve for "x":

$\left \{ {{-6x-6y=-24} \atop {5x+6y=3}} \right.\\.....................\\-x=-21\\x=21$

Substitute $x=21$ into the Equation A or the Equation B and solve for "y":

$2(21)+2y=8\\\\42+2y=8\\\\2y=8-42\\\\2y=-34\\\\y=\frac{-34}{2}\\\\y=-17$

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13. Connie wants to paint one wall in her living room. Along the wall, she

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Answer: Approximately 96 square feet

======================================================

Work Shown:

1 ft = 30 cm

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1 ft = 5 board widths

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VikaD [51]

Answer:

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the binomial probability distribution.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$