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stealth61 [152]
3 years ago
5

Solve the system using the addition method. State your solution as an ordered pair.

Mathematics
1 answer:
vladimir1956 [14]3 years ago
6 0

Solution as ordered pair is:

(5,\frac{41}{2})

Step-by-step explanation:

Solving the system of equations:

3x+2y=56\,\,\,(1)\\9x-2y=4\,\,\,(2)

Adding equation(1) and equation(2)

3x+2y=56\\9x-2y=4\\--------\\12x=60\\x=\frac{60}{12}\\x=5

Putting value of x i.e x=5 in equation(1)

3x+2y=56\\3(5)+2y=56\\ 15+2y=56\\2y=56-15\\2y=41\\y=\frac{41}{2}\\y=\frac{41}{2}

So, value of x=5 and y=\frac{41}{2}

Solution as ordered pair is:

(5,\frac{41}{2})

Keywords:System of Equations

Learn more about System of Equations at:

  • brainly.com/question/6075514
  • brainly.com/question/7490805
  • brainly.com/question/13168205

#learnwithBrainly

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Use the given information to find the p-value. also use a0.05 significance level and state the conclusion about the null hypothe
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Answer:

(a) C: 0.0465 ; reject the null hypothesis

(b) B: 0.3409 ; fail to reject the null hypothesis

Step-by-step explanation:

Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;

  • If the P-value of test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.
  • If the P-value of test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.

(a) Now, we are given alternate hypothesis, H_1 : p < 3/5

Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;

             P-value = P(Z < -1.68) = 1 - P(Z \leq 1.68)

                           = 1 - 0.95352 = <u>0.0465</u>

Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which <u>we reject the null hypothesis.</u>

(b) Now, we are given alternate hypothesis, H_1 : p > 0.383

Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;

             P-value = P(Z > 0.41) = 1 - P(Z \leq 0.41)

                           = 1 - 0.6591 = <u>0.3409</u>

Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which <u>we fail to reject the null hypothesis.</u>

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Step-by-step explanation:

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The options Patel has to solve the quadratic equation 8x² + 16x + 3 = 0 is x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot.

<h3>Quadratic equation</h3>

8x² + 16x + 3 = 0

8x² + 16x = -3

8(x² + 2x) = -3

  • Using completing the square

8(x² + 2x + 1) = -3 + 8

  • factorization

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(x² + 1) = 5/8

  • Taking the square root of both sides

(x + 1) = ± √5/8

x = -1 ± √5/8

Therefore,

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