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julia-pushkina [17]
3 years ago
13

Which polynomial is in standard form? 2xy^3 +3x^3 y^4 -4x^4 y^5 +9x^5 y^6 Which polynomial is in standard form?

Mathematics
1 answer:
andrezito [222]3 years ago
5 0

Answer:

(D) 5x^7y^2+7x^6y^5-14x^3y^7+51x^2y^9

Step-by-step explanation:

A polynomial is said to be in standard form when it is arranged in descending powers of x.

When there are more than one variable, the alphabetical order is followed. For example, if there are variables x and y in the polynomial, x must be in descending order and y will be in ascending order.

From the given options, the polynomial which is in standard form is:

5x^7y^2+7x^6y^5-14x^3y^7+51x^2y^9

The correct option is D.

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A manufacturer of running shoes knows that the average lifetime for a particular model of shoes is 15 months. Someone in the res
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Answer:

The decision rule is  

Fail to reject the null hypothesis

 The conclusion is  

There is no sufficient evidence to show that  the  designer's claim of a better shoe is supported by the trial results.

Step-by-step explanation:

From the question we are told that

  The population mean is  \mu = 15 \ months

   The sample size is  n =  25

   The sample mean is  \= x  = 17 \ months

   The standard deviation is  s = 5.5 \ months

Let assume the level of significance of this test is  \alpha  = 0.05

    The null hypothesis is  H_o :  \mu = 15

     The alternative hypothesis is  H_a : \mu  > 17

Generally the degree of freedom is mathematically represented as  

         df = n -1

=>       df = 25 -1

=>       df = 24

Generally the test statistics is mathematically represented as

        t = \frac{\= x- \mu }{\frac{s}{\sqrt{n} } }

=>   t = \frac{ 17 - 15 }{\frac{5.5}{\sqrt{25} } }

=>   t =  1.8182

Generally from the student t distribution table the probability of obtaining   t =  1.8182 to the right of the curve at a degree of freedom of df = 24  is  

    p-value  = P(t > 0.18182 ) = 0.4286

From the value obtained we see that  p-value > \alpha hence

The decision rule is  

Fail to reject the null hypothesis

 The conclusion is  

There is no sufficient evidence to show that  the  designer's claim of a better shoe is  supported by the trial results.

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