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KATRIN_1 [288]
3 years ago
12

A quantity a varies inversely as a quantity b, if, when b changes a changes in the inverse ratio. What happens to the quantity a

if the quantity b doubts?
Mathematics
1 answer:
Julli [10]3 years ago
3 0

Answer:

quantity a is halfed

Corrected question;

A quantity a varies inversely as a quantity b, if, when b changes a changes in the inverse ratio. What happens to the quantity a if the quantity b doubles?

Step-by-step explanation:

Analysing the question;

A quantity a varies inversely as a quantity b,

a ∝ 1/b

a = k/b ......1

when b changes a changes in the inverse ratio;

Since the change at the same ratio but inversely, k = 1

So, equation 1 becomes;

a = 1/b

If the quantity b doubles,

ab = 1

a1b1 = a2b2

When b doubles, b2 = 2b1

a1b1 = a2(2b1)

Making a2 the subject of formula;

a2 = a1b1/(2b1)

a2 = a1/2

Therefore, when b doubles, a will be divided by 2, that means a is halfed.

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Answer:

(a) Margin of error ( E) = $2,000 , n = 54

(b)   Margin of error ( E) = $1,000 , n = 216

(c)   Margin of error ( E) = $500 , n= 864

Step-by-step explanation:

Given -

Standard deviation \sigma = $7,500

\alpha = 1 - confidence interval = 1 - .95 = .05

Z_{\frac{\alpha}{2}} =  Z_{\frac{.05}{2}} = 1.96

let sample size is n

(a) Margin of error ( E) = $2,000

Margin of error ( E)  = Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}

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Squaring both side

E^{2} = 1.96^{2}\times\frac{7500^{2}}{n}

n =\frac{1.96^{2}}{2000^{2}} \times 7500^{2}

n =  54.0225

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(b)   Margin of error ( E) = $1,000

          E     = Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}

         1000   =  Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}

Squaring both side

1000^{2} = 1.96^{2}\times\frac{7500^{2}}{n}

n =\frac{1.96^{2}}{1000^{2}} \times 7500^{2}

n = 216

(c)   Margin of error ( E) = $500

   E = Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}

  500 = Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}

Squaring both side

500^{2} = 1.96^{2}\times\frac{7500^{2}}{n}

n =\frac{1.96^{2}}{500^{2}} \times 7500^{2}

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Write the equation in slope intercept form as:

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Step-by-step explanation:

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kolezko [41]

Answer:

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Step-by-step explanation:

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Wewaii [24]

Answer:

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Step-by-step explanation:

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1. (10×14)×2 ←Because there are two rectanglular sides.

2. find the area of the triangles on the side. 1/2bh = area of triangle.

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3 years ago
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