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Elena-2011 [213]
2 years ago
14

If n =270 and (p-hat) =0.43, find the margin of error at a 99% confidence level.. give answer to 3 decimals

Mathematics
1 answer:
Troyanec [42]2 years ago
7 0

Answer:

0.078

Step-by-step explanation:

Margin of error = z√(p(1-p)/n)

Given

p-hat = 0.43

n = 270

z at 99% confidence interval = 2.576

Substitute

MOE = 2.576√0.43(1-0.43)/270

MOE = 2.576√0.43*0.57/270

MOE = 2.576√0.2451/270

MOE = 2.576*0.030129

MOE = 0.078

Hence the margin og error is 0.078

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Step-by-step explanation:

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The area of trapezoid TRAP is 100 m squared
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Answer:  30 m ; (or, write as: "30 meters") .
______________________________________________
Explanation:
____________________

Area of a trapezoid, "A" = (1/2) ( b₁ + b₂) h ;
______________________________________________
or, write as:  A = ( b₁ + b₂) h  / 2 ;
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in which:  A = area;
              b₁ = length of "base 1" (choose either one of the 2 (two bases);
              b₂ = length of "base 2" (use the base that is remaining);
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From the information given: 
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A = 100 m² ; 
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Find "x", which is:  "b₂" ;
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      A = ( b₁ + b₂) h  / 2  ;
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Plug in our known values; and plug in "x" for "b₂" ; and solve for "x" ;
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  100 m² = [(10m + x) (5m)] / 2  ; Solve for "x" ;
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          (10m + x) (5m) = (2)* (100m²) ;
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             (5m) (10m + x) = 200 m² ;
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Note:  The distributive property of multiplication:
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    a(b+c) = ab + ac ;
 
    a(b−c) = ab <span>− ac ;
</span>____________________________________________

  We have:  (5m) (10m + x) = 200 m²  ;
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So:    (5m) (10m + x) =  (5m*10m) + (5m * x) ;
                           
                               =  50m² + (5m)x  ;
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     →  50m² + (5m)x = 200m²  ; 
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Divide the ENTIRE equation by "5m" ;
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     → { 50m² + (5m)x } / 5m = (200m² / 5m) ;
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     →  10m + x   = 40m ; 
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     →  10m + x  − 10m  =  40m − 10m ;

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Answer:  30 m ; (or, write as: "30 meters") .
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6 0
3 years ago
A student desired to invest $1,540 into an investment at 9% compounded semiannually for 6 years. With all else equal, what is th
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Answer:

The future value of this initial investment after the six year period is $2611.6552

Step-by-step explanation:

Consider the provided information.

A student desired to invest $1,540 into an investment at 9% compounded semiannually for 6 years.

Future value of an investment: FV=P(1+r)^n

Where Fv is the future value, p is the present value, r is the rate and n is the number of compounding periods.

9% compounded semiannually for 6 years.

Therefore, the value of r is: r=\frac{0.09}{2}=0.045

Number of periods are: 2 × 6 = 12

Now substitute the respective values in the above formula.

FV=1540(1+0.045)^{12}

FV=1540(1.045)^{12}

FV=1540(1.69588)

FV=2611.6552

Hence, the future value of this initial investment after the six year period is $2611.6552

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