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devlian [24]
3 years ago
10

Form a polynomial function(x) with zeros: -2, multiplicity 1; 1, multiplicity 2; 5, multiplicity 3; and degree 6. Use 1 as the l

eading coefficient and leave the function in factored form.
Mathematics
1 answer:
Citrus2011 [14]3 years ago
8 0

Answer:

Remember, a number a is a zero of the polynomial p(x) if p(a)=0. And a has multiplicity n if the factor (x-a) appear n times in the factorization of p(x).

1. Since -2 is a zero with multiplicity 1, then (x+2) is a factor of the polynomial.

2. Since 1 is a zero with multiplicity 2, then (x-1) is a factor of the polynomial and appear 2 times.

3. Since 5 is a zero with multiplicity 3, then (x-5) is a factor of the polynomial and appear 3 times.

Then, the polynomial function with the zeros described above is

p(x)=(x+2)(x-1)^2(x-5)^3= x^6-15x^5+72x^4-78x^3-255x^2+525x-250

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Answer:

11+3z

Step-by-step explanation:

You would combine the like terms, 9+4-2 is 11 and 6z-3z=3z

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Evgen [1.6K]

Answer:

4 gallons.

Step-by-step explanation:

Reading the top point on the graph we see that 48 gallons of white paint mix with 12 gallons of black Paint.

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3 years ago
Which inequality represents all values of x for which the product below is defined
zavuch27 [327]

Answer:

(-∞, -2) ∪ (0, ∞)

Step-by-step explanation:

Multiply together the (7x) and the (x+2), obtaining 7x^2 + 14x.  This is the correct argument (input) to Answer A.

Since the domain of the square root function includes "all real numbers equal to or greater than 0," we set 7x^2 + 14x = to 0.  This factors to the original 7x*(x+2), set equal to 0.  The roots are 0 and -2.  

These two values create three intervals:  (-∞, -2), (-2, 0) and (0, ∞).

Choosing test numbers, one from each interval:  {-5, -1, 1}.

7x^2 + 14x is + at x = -5, - at x = -1, and + at x = 1.

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5 0
3 years ago
A company surveyed 2400 men where 1248 of the men identified themselves as the primary grocery shopper in their household. ​a) E
polet [3.4K]

Answer:

a) With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

b) The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

c) \alpha =1-0.98=0.02

Step-by-step explanation:

If np' and n(1-p') are higher than 5, a confidence interval for the proportion is calculated as:

p'-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }\leq  p\leq p'+z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }

Where p' is the proportion of the sample, n is the size of the sample, p is the proportion of the population and z_{\alpha/2} is the z-value that let a probability of \alpha/2 on the right tail.

Then, a 98% confidence interval for the percentage of all males who identify themselves as the primary grocery shopper can be calculated replacing p' by 0.52, n by 2400, \alpha by 0.02 and z_{\alpha/2} by 2.33

Where p' and \alpha are calculated as:

p' = \frac{1248}{2400}=0.52\\\alpha =1-0.98=0.02

So, replacing the values we get:

0.52-2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\leq  p\leq 0.52+2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\\0.52-0.0238\leq p\leq 0.52+0.0238\\0.4962\leq p\leq 0.5438

With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

Finally, the level of significance is the probability to reject the null hypothesis given that the null hypothesis is true. It is also the complement of the level of confidence. So, if we create a 98% confidence interval, the level of confidence 1-\alpha is equal to 98%

It means the the level of significance \alpha is:

\alpha =1-0.98=0.02

4 0
3 years ago
George is reading a book.On Monday he read 1/3 of the book. On Tuesday he reads three-tenths of the remaining pages. He has 35 p
solniwko [45]

Answer:

Step-by-step explanation:

m=p/3

t=(3/10)(1-1/3)

t=(3/10)(2/3)=p/5

p-p/3-p/5=35

(15p-5p-3p)/15=35

7p/15=35

7p=525

p=75

So the book has 75 pages.

3 0
2 years ago
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