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olga nikolaevna [1]
3 years ago
13

Third-degree, with zeros of −3 , − 2 , and 1 , and passes through the point ( 3 , 11 ) .

Mathematics
1 answer:
Masja [62]3 years ago
8 0

Answer:

y  =   ( x + 3 ) *  ( x +  2 ) * ( x - 1 )* 11/60

Step-by-step explanation:

Lets   y  =  f(x)   in a cartesian coordinates

Having three zeros:

x = -3       ⇒   x  = -2      ⇒   and   x = 1  

That meas that if   x  takes the above mentioned  values " y " must be zero

therefore  y  must be of the form

f (x)  =  y  =  ( x + 3 ) *  ( x +  2 ) * ( x - 1 )     (1)

In that case for y to be zero one of the factors should be zero or

y  =  0        x  + 3 = 0    and  x = - 3  is a zero of the function y .

The same reasoning applies for the other two roots

Now we have to evaluate the other condition.

According to problem statement the function passes through the point ( 3, 11 ) , that means that when x =  3 ,  y have to be 11, therefore we plug in equation (1)  that value to see what happens

y  =   ( x + 3 ) *  ( x +  2 ) * ( x - 1 )

11  =  ( 3 + 3 ) * ( 3 + 2 ) + ( 3 - 1)   =  6*5*2  = 60

Then we adjust the expression (1) to meet the condition of the function passing through point  ( 3 , 11) as:

y  =  ( 3 + 3 ) * ( 3 + 2 ) + ( 3 - 1) * 11/60    (2)

and check to see if we did right

for y to be zero      x   can be    x = - 3    x  =  -2   and  x = 1 in all these cases y = 0.  And if  x  =  3   in equation (2)  y = 11. And that what we want to shown. Then the solution is:

y  =   ( x + 3 ) *  ( x +  2 ) * ( x - 1 )* 11/60

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I think -2 is the answer
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Find the length of BC
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Answer:

13.3650978628

Step-by-step explanation:

Angle A=180-(Angle B+C)=180-117=63

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b=BC, p=AC & AB=12

Using the relation of cos,

cosx=b/h

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BC=13.3650978628

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2 years ago
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Masja [62]
The correct answer is c.
6 0
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Read 2 more answers
Expand the polynomial and simplify: (4xy− 1 8 y^2)^2
Vinvika [58]

Answer: 4y^{2}(2x-9y)^{2}

Step-by-step explanation:

We have the following polynomial:

(4xy-18y^{2})^{2}

This is a polynomial of the form (a-b)^{2}=a^{2}-2ab+b^{2}. Following this rule to expand it, we have:

(4xy)^{2}-2(4xy)(18y^{2})+(18y^{2})^{2}

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Applying common factor 4y^{2}:

4y^{2}(4x^{2}-36xy+81y^{2})

Note the polynomial inside the parenthesis is a perfect square trinomial, which can be factored to(2x-9y)^{2}. Hence, the final simplification is:

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3 0
3 years ago
4.One attorney claims that more than 25% of all the lawyers in Boston advertise for their business. A sample of 200 lawyers in B
AleksAgata [21]

Answer:

z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123  

p_v =P(Z>2.123)=0.0169  

The p value obtained was a very low value and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .  

Step-by-step explanation:

1) Data given and notation  

n=200 represent the random sample taken

X=63 represent the lawyers had used some form of advertising for their business

\hat p=\frac{63}{200}=0.315 estimated proportion of lawyers had used some form of advertising for their business

p_o=0.25 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that more than 25% of all the lawyers in Boston advertise for their business:  

Null hypothesis:p\leq 0.25  

Alternative hypothesis:p > 0.25  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

p_v =P(Z>2.123)=0.0169  

The p value obtained was a very low value and using the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .  

8 0
3 years ago
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