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dexar [7]
3 years ago
15

G(x) = x3 + 6x2 + 12x + 8 Determine the function’s value when x = −1.

Mathematics
1 answer:
salantis [7]3 years ago
5 0

Answer:

g(-1) = 1

Step-by-step explanation:

Synthetic division is by far the fastest way to evaluate this function at x = -1.  Set up synth. div. as follows:

-1   )   1    6    12    8

              -1    -5    -7

     ----------------------

         1     5     7     1                

since the remainder is 1, g(-1) = 1

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A company surveyed adult Americans about their consumer debt. They reported that 48% of Millennials (those born between 1980 and
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We reject H₀ at 95 % of CI the group of Gen Xers who do not pay their credit card each month, is greater than this proportion for Millennians

Step-by-step explanation:

Sample proportion 1: Born between 1980 and 1996

sample size    n₁  = 450

p₁  =  0,48        p₁ = 48 %

x₁ = 0,48 * 450        x₁ = 216

Sample proportion 2:  Born between 1965 and 1971

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p₂ =  0,60         p₂ = 60%

x₂  = 0,6* 300     x₂  = 180

Test Hypothesis:

Null Hypothesis                          H₀               p₂  =   p₁

Alternative Hypothesis              H                p₂  >  p₁

Samples both big enough to use the normal distribution as an approximation to the binomial distribution.

We assume  CI = 95 %   then significance level α   = 5 %  the alternative hypothesis tells us that we need to develop a one-tail test to the right.

z-score  is z(c)  for  α = 0,05       from z-table   z(c) = 1,64

To calculate z(s)

z(s)  =  ( p₂  -  p₁ ) / √ p*q ( 1 /n₁ + 1 / n₂)

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p₂ - p₁  =  0,12

p = ( x₁ + x₂ ) / n₁ + n₂

p = ( 216  + 300) / 450 + 300

p = 516 / 750     p = 0,688      then   q = 1 - p     q = 0,312

z(s) = 0,12 / √ 0,688*0,312* ( 1/450) + 1/ 300)

z(s) = 0,12 / √ 0,2146* ( 0,0022 + 0,0033)

z(s) = 0,12 / √ 0,001192

z(s) = 0,12/ 0,03452

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Comparing |z(c)|   and |z(s)|

z(s) > z(c)

Then z(s) is in the rejection region. We reject H₀.

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