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2 years ago

Solve using addition method 3x-3y+2z=7 3x+y-3z=-5 7x-y-2z=0

1 answer:

6 0

3x - 3y + 2z = 7
3x + 1y - 3z = -5 ⇒ 6x - 2y - 1z = 2 ⇒ 42x - 14y - 7z = 14
7x - 1y - 2z = 0 ⇒ 7x - 1y - 2z = 0 ⇒ 42x - 6y - 12z = 0 
 -20y - 19z = 14
 -20y + 20y - 19z = 14 + 20y
 -19z = 14 + 20y
 -19 -19
 z = -14/19 - 1 1/19y
 3x - 3y + 2(-14/19 - 1 1/19y) = 7
 3x - 3y - 1 9/19 - 2 2/19y = 7
 3x - 5 2/19y - 1 9/19 = 7
 +1 9/19 +1 9/19 
 3x - 5 2/19y = 8 9/19
 3x - 3x - 5 2/19y = 8 9/19 - 3x
 -5 2/19y = 8 9/19 - 3x
 -5 2/19 -5 2/19
 y = -1 64/97 + 57/97x
 3x - 3(-1 64/97 + 57/97x) + 2(-14/19 - 1 1/19y) = 7
 3x + 4 95/97 + 1 74/97x - 1 9/19 - 2 2/19y = 7
 4 74/97x - 2 2/19y + 3.5056972328 = 7
 -3.5056972328 -3.5056972328
 4 74/97x - 2 2/19y = 3.494302767
 4 74/97x + 2 2/19y - 2 2/19y = 3.494302767 + 22/19y
 4 74/97x = 3.494302767 + 2 2/19
 4 74/97 4 74/97
 x = 0.7336523126 + 0.4420141262y
3(0.733652316 + 0.4420141262y) - 3(-1 64/97 + 57/97x) + 2(-14/19 - 1 1/19y)=7
 2.200956948 + 1.326042379y + 4 95/97 - 1 74/97x - 1 9/19 - 2 2/19y = 7 -1 74/97x - 0.7792207789y + 5.706654181 = 7
 -5.706654181 -5.70665418
 -1 74/97x - 0.7792207789y = 1.293345820
(x, y, z) = (0.733652316 + 0.4420141262, -1 64/97 + 57/97x, -14/19 - 1 1/19y)

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-7x + 6= 27 what does x stand for ?

ivolga24 [154]

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x = -3 (Divide -7 from both sides)

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3 years ago

In 2016, the top 1 percent of taxpayers accounted for more income taxes paid than the bottom 90 percent combined. The top 1 perc

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Answer:

$464Billion

Step-by-step explanation:

If 37.3%=$538B

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3 years ago

Can you please help me with this problem

vagabundo [1.1K]

$\bf \begin{cases}
\textit{area of a circle}=\pi r^2
\\ \quad \\
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\end{cases}
\\ \quad \\

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8 0

3 years ago

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true

IgorLugansk [536]

Answer:

(a) 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].

(b) 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].

Step-by-step explanation:

We are given that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.75.

(a) Also, the average porosity for 20 specimens from the seam was 4.85.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average porosity = 4.85

$\sigma$ = population standard deviation = 0.75

n = sample of specimens = 20

$\mu$ = true average porosity

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 95% confidence interval for the true mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $4.85-1.96 \times {\frac{0.75}{\sqrt{20} } }$ , $4.85+1.96 \times {\frac{0.75}{\sqrt{20} } }$ ]

= [4.52 , 5.18]

Therefore, 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].

(b) Now, there is another seam based on 16 specimens with a sample average porosity of 4.56.

The pivotal quantity for 98% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average porosity = 4.56

$\sigma$ = population standard deviation = 0.75

n = sample of specimens = 16

$\mu$ = true average porosity

Here for constructing 98% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 98% confidence interval for the true mean, $\mu$ is ;

P(-2.3263 < N(0,1) < 2.3263) = 0.98 {As the critical value of z at 1% level

of significance are -2.3263 & 2.3263}

P(-2.3263 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.3263) = 0.98

P( $-2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.3263$ ) = 0.98

P( $\bar X-2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.98

98% confidence interval for $\mu$ = [ $\bar X-2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.3263 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $4.56-2.3263 \times {\frac{0.75}{\sqrt{16} } }$ , $4.56+2.3263 \times {\frac{0.75}{\sqrt{16} } }$ ]

= [4.12 , 4.99]

Therefore, 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].

7 0

3 years ago

Simplify the following using PEMDAS: [3−(3⋅3)+33÷3] × 4⋅5/10−2⋅3

kompoz [17]

Answer: 34

Step-by-step explanation:

Given expression

[3 - (3 · 3) + 33 ÷ 3] × 4 · 5 / 10 - 2 · 3

Simplify by parentheses in the bracket

=[3 - 9 + 33 ÷ 3] × 4 · 5 / 10 - 2 · 3

Simplify by multiplication

=[3 - 9 + 33 ÷ 3] × 20 / 10 - 6

Simplify by division

=[3 - 9 + 11] × 10 - 6

Simplify by bracket (addition/subtraction)

=[-6 + 11] × 10 - 6

=[4] × 10 - 6

Simplify by multiplication

=40 - 6

Simplify by subtraction

= $\boxed{34}$

Hope this helps!! :)

Please let me know if you have any questions

8 0

2 years ago