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Rama09 [41]
2 years ago
7

Find the ordered pair of x=5y-7 and x+5y=8

Mathematics
1 answer:
zepelin [54]2 years ago
3 0

Answer:

The desired ordered pair is (1/2, 3/2).

Step-by-step explanation:

Let's use the substitution method here to determine either x or y first:

x = 5y - 7 (given).  Then 5y - 7 can be substituted for x in x + 5y = 8:

5y - 7 + 5y = 8.

Combining like terms, we get 10y = 15, so that y = 3/2.

Find x by substituting 3/2 for y in x = 5y - 7:  x = 5(3/2) - 7 = 15/2 - 14/2 = 1/2

The desired ordered pair is (1/2, 3/2).

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The manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour. (a-1) At α = .05 i
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Answer:

The calculated value t = 1.76 < 2.131 at 0.05 level of significance

Null hypothesis is accepted

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Step-by-step explanation:

<u><em>Explanation</em></u>:-

Given sample size 'n' =16

Given the manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour.

mean of the Population 'μ' = 560

Mean of the sample Χ⁻ = 538

sample standard deviation' S' = 50

<em><u>Null hypothesis</u></em><em>:H₀:μ > 560</em>

<em><u>Alternative Hypothesis</u></em><em>:H₁ : :μ < 560 (left tailed test)</em>

<em>Test statistic</em>

   t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }

  t = \frac{538-560 }{\frac{50}{\sqrt{16} } } = -1.76

|t| = |-1.76| = 1.76

<em>Degrees of freedom </em>

<em>γ = n-1 =16-1 =15</em>

t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } =t_{0.025} =2.131

<em><u>Conclusion</u></em>:-

The calculated value t = 1.76 < 2.131 at 0.05 level of significance

Null hypothesis is accepted

The manufacturer’s claim is greater than 560 bags per hour

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