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Mandarinka [93]
3 years ago
11

I need help with elimination with substitution. The equations are 3x+4y=19 and 3x+6y=33

Mathematics
1 answer:
olganol [36]3 years ago
4 0
For elimination, multiply one whole equation by negative one (-1), then add or subtract according to your signs. After that, it will be a one-step equation.

3x + 4y = 19          3x + 4y = 19             3x + 4y = 19          -2y = -14        y = 7
3x + 6y = 33     -1 (3x + 6y = 33)          -3x - 6y = -33          -14 / -2

Then you would go back and substitute the value of (y) back into either equation and then solve for the remaining variable (x). Finally, use both values to make an ordered pair.

3x + 4y = 19          3x = -9          x = -3          (-3 , 7)
3x + 4(7) = 19       (-9 / 3)
3x + 28 = 19          

Good Luck

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p = 0.03

q = 1 - 0.03 = 0.97

The mean is

\mu  = np

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The standard deviation is

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We want to find the probability that exactly 24 patients will gain weight as side effect.

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We apply the Continuity Correction Factor(CCF)

P(24-0.5<X<24+0.5)=P(23.5<X<24.5)

We convert to z-scores.

P(23.5 \: < \: X \: < \: 24.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \:  \frac{24.5 - 19.29}{4.33} ) \\  = P( 0.97\: < \: z \: < \:  1.20) \\  = 0.051

Part b) We want to find the probability that 24 or fewer patients will gain weight as a side effect.

P(X≤24)

We apply the continuity correction factor to get;

P(X<24+0.5)=P(X<24.5)

We convert to z-scores to get:

P(X \: < \: 24.5) = P(z \: < \:  \frac{24.5 - 19.29}{4.33} )  \\ =   P(z \: < \: 1.20)  \\  = 0.8849

Part c)

We want to find the probability that

11 or more patients will gain weight as a side effect.

P(X≥11)

Apply correction factor to get:

P(X>11-0.5)=P(X>10.5)

We convert to z-scores:

P(X \: > \: 10.5) = P(z \: > \:  \frac{10.5 - 19.29}{4.33} )  \\ = P(z \: > \:  - 2.03)

= 0.9788

Part d)

We want to find the probability that:

between 24 and 28, inclusive, will gain weight as a side effect.

P(24≤X≤28)=

P(23.5≤X≤28.5)

Convert to z-scores:

P(23.5  \:  <  \: X \:  <  \: 28.5) = P( \frac{23.5 - 19.29}{4.33}   \:  <  \: z \:  <  \:  \frac{28.5 - 19.29}{4.33} ) \\  = P( 0.97\:  <  \: z \:  <  \: 2.13) \\  = 0.1494

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