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yarga [219]
2 years ago
5

CL 6-131. Solve each system using the method of your choice.

Mathematics
1 answer:
shepuryov [24]2 years ago
4 0

System 1: The solution is (x, y) = (-4, 5)

System 2:  The solution is (x, y) = (\frac{11}{3}, -3)

<em><u>Solution:</u></em>

<em><u>Given system of equations are:</u></em>

2x + 3y = 7 ------ eqn 1

-3x - 5y = -13 --------- eqn 2

We can solve by elimination method

Multiply eqn 1 by 3

6x + 9y = 21 ------ eqn 3

Multiply eqn 2 by 2

-6x - 10y = -26 ------- eqn 4

Add eqn 3 and eqn 4

6x + 9y -6x - 10y = 21 - 26

-y = -5

y = 5

Substitute y = 5 in eqn 1

2x + 3(5) = 7

2x + 15 = 7

2x = -8

x = -4

Thus the solution is (x, y) = (-4, 5)

<h3><em><u>Second system of equation is:</u></em></h3>

8 - y = 3x ------ eqn 1

2y + 3x = 5 ----- eqn 2

We can solve by susbtitution method

From given,

y = 8 - 3x ----- eqn 3

Substitute eqn 3 in eqn 2

2(8 - 3x) + 3x = 5

16 - 6x + 3x = 5

3x = 16 - 5

3x = 11

x = \frac{11}{3}

Substitute the above value of x in eqn 3

y = 8 - 3x

y = 8 - 3 \times \frac{11}{3}\\\\y = 8 - 11\\\\y = -3

Thus the solution is (x, y) = (\frac{11}{3}, -3)

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Of 560 samples of seafood purchased from various kinds of food stores in different regions of a country and genetically compared
frutty [35]

Answer:

a) (0.5256,0.5944)  

c) Criticism is invalid

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 560

Proportion of mislabeled = 56%

\hat{p} = 0.56

a) 90% Confidence interval:

\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.64

Putting the values, we get:

0.56\pm 1.64(\sqrt{\dfrac{0.56(1-0.56)}{560}}) = 0.56\pm 0.0344\\\\=(0.5256,0.5944)

b) Interpretation of confidence interval:

We are 90% confident that the true proportion of all seafood in the country that is mislabeled or misidentified is between 0.5256 and 0.5944 that is 52.56% and 59.44%.

c) Validity of criticism

Conditions for validity:

np > 10\\n(1-p)>10

Verification:

560\times 0.56 = 313.6>10\\560(1-0.56) = 246.4>10

Both the conditions are satisfied. This, the criticism is invalid.

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If p → q is true, then ~ p → ~ q is __________ true. always sometimes never
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The correct answer is Never

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