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3 years ago

Use the substitution method to solve the system of equations. Choose the correct ordered pair. 3x – y = 7 2x – 2y = 2

Mathematics

2 answers:

quester [9]3 years ago

5 0

Y=2, and x=3 so it is c

makkiz [27]3 years ago

3 0

Answer:

The solution set is (3,2)

C is correct

Step-by-step explanation:

Given: System of equation.

$3x-y=7$

$2x-2y=2$

We will solve x and y using substitution method.

$3x-y=7$

$y=3x-7------------------(1)$

Substitute into 2x-2y=2

$2x-2(3x-7)=2$

$2x-6x+14=2$

$-4x=-12$

$x=3$

Put x=3 into eq(1)

$y=3(3)-7$

$y=2$

Hence, The solution set is (3,2)

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3 years ago

A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.)

Maksim231197 [3]

Answer:

The 95% confidence interval is $0.0503 < p < 0.1297$

The sample proportion is $\r p = 0.09$

The critical value is $Z_{\frac{\alpha }{2} } = 1.96$

The standard error is $SE =0.020$

Step-by-step explanation:

From the question we are told that

The sample size is n = 200

The number of defective is k = 18

The null hypothesis is $H_o : p = 0.08$

The alternative hypothesis is $H_a : p > 0.08$

Generally the sample proportion is mathematically evaluated as

$\r p = \frac{18}{200}$

$\r p = 0.09$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the standard of error is mathematically represented as

$SE = \sqrt{\frac{\r p (1 - \r p)}{n} }$

substituting values

$SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }$

$SE =0.020$

The margin of error is

$E = Z_{\frac{ \alpha }{2} } * SE$

=> $E = 1.96 * 0.020$

=> $E = 0.0397$

The 95% confidence interval is mathematically represented as

$\r p - E < \mu < p < \r p + E$

=> $0.09 - 0.0397 < \mu < p < 0.09 + 0.0397$

=> $0.0503 < p < 0.1297$

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3 years ago