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kvv77 [185]
3 years ago
13

The sum of two numbers is 85. twice one number plus four times the other is 218. find the numbers

Mathematics
1 answer:
Nina [5.8K]3 years ago
6 0
X + y = 85
2x + 4y = 218
x = 85 - y 
<span>2(85 - y) + 4y = 218 </span>
<span>170 - 2y + 4y = 218 </span>
<span>170 + 2y = 218 </span>
<span>2y = 48 </span>
<span>y = 24 </span>
<span>x = 61</span>
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Answer:

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Step-by-step explanation:

We are given the following in the question:

95% confidence interval for the population proportion

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Let x be the standard error, then, we can write

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Solving the two equations, we get,

2\hat{p} = 0.65 + 0.69\\\\\hat{p} = \dfrac{1.34}{2} = 0.67\\\\x = \dfrac{0.69 - 0.67}{1.96} \approx 0.01

99% Confidence interval:

p \pm z_{stat}(\text{Standard error})

z_{critical}\text{ at}~\alpha_{0.01} = 2.58

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0.67 \pm 2.58(0.01)\\=0.67 \pm 0.0258\\=(0.6442,0.6958)

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Step-by-step explanation:

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After years of maintaining a steady population of 32,000, the population of a town begins to grow exponentially. After 1 year an
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Answer:

The equation used to predict the number of people living in the town after x years is y = 32,000 (1.08)x

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

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  • <em>Growth per year: 8% </em>
  • <em>Years: x </em>

So, to obtain "y" (the number of people living in the town after x years), we have to multiply the initial population by 1+ 0.08 (the growth rate is 8%/100=0.08 and the original value) and the number of years (x).

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y = 32,000 (1+0.08) x

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The equation used to predict the number of people living in the town after x years is y = 32,000 (1.08)x

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