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alexira [117]
3 years ago
5

Find a third degree polynomial function with real coefficients and with zeros 4 and 3+i

Mathematics
1 answer:
Anvisha [2.4K]3 years ago
3 0
X = 4 ; x = 3 + i ; x = 3 - i

(If you get a zero that is adding or subtracting, you always need to write it twice but change the sign do they cancel out)

f(x) = (x-4)(x-3-i)(x-3+i)

Distributing the last two parenthesis first is always the best way to start off

(x-3-i)(x-3+i) has (x-3) in common so it can be separated to

(x-3)^2 + (-i)(+i)

(x^2 - 6x + 9) ; (-i)(+i) is always +1
(x^2 - 6x + 9) + 1
(x^2 - 6x + 10)

Now multiply this with (x-4)
x^3 - 6x^2 + 10x
- 4x^2 + 24x - 40

x^3 - 10x^2 + 34x - 40 = f(x)

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An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had
Stolb23 [73]

Answer:

Q1 z(s) is in the rejection region for H₀ ; we reject H₀. We can´t support the that means have no difference

Q2  CI 95 %  =  (  0,056 ;  0,164 )

Step-by-step explanation:

Sample information for people under 18

n₁  =  500

x₁ =  180

p₁  =  180/ 500    p₁  =  0,36    then  q₁  =  1 -  p₁     q₁ =  0,64

Sample information for people over 18

n₂  =  600

x₂  =  150

p₂  =  150 / 600   p₂ =  0,25   then   q₂  =  1 - p₂   q₂ =  1 - 0,25   q₂ = 0,75

Hypothesis Test

Null hypothesis                        H₀              p₁  =  p₂

Alternative Hypothesis           Hₐ              p₁  ≠  p₂

The alternative hypothesis indicates that the test is a two-tail test.

We will use the approximation to normal distribution of the binomial distribution according to the sizes of both samples.

Testin at CI =  95 %    significance level is  α = 5 %   α  =  0,05  and

α/ 2  =  0,025   z (c) for that α  is from z-table:

z(c) = 1,96

To calculate   z(s)

z(s)  =  ( p₁  -   p₂ ) / EED

EED = √(p₁*q₁)n₁  +  (p₂*q₂)/n₂

EED = √( 0,36*0.64)/500  +  (0,25*0,75)/600

EED = √0,00046  +  0,0003125

EED = 0,028

( p₁  -  p₂  )  =  0,36  -  0,25  = 0,11

Then

z(s)  =  0,11 / 0,028

z(s) = 3,93

Comparing  z(s) and  z (c)    z(s) > z(c)

z(s) is in the rejection region for H₀ ; we reject H₀. We can´t support the idea of equals means

Q2  CI  95 %   =  (  p₁  -  p₂  ) ±  z(c) * EED

CI 95%  =  ( 0,11   ±  1,96 * 0,028 )

CI 95%  = (  0,11  ±  0,054 )

CI 95 %  =  (  0,056 ;  0,164 )

8 0
3 years ago
There are 205 total students in a school. 20% of the students are 5th
Slav-nsk [51]

Answer:

41 students

Step-by-step explanation:

20% of 205 is 41

7 0
3 years ago
Read 2 more answers
A number is selected, at random, from the set {1,2,3,4,5,6,7,8}.
Olegator [25]

Applying the formula, you have:

A = the number is prime

B = the number is odd

I assume that with "random" you imply that all numbers can be chosen with the same probability. So, we have

P(A) = \dfrac{4}{8} = \dfrac{1}{2}

because 4 out of 8 numbers are prime: 2, 3, 5 and 7.

Similarly, we have

P(B) = \dfrac{4}{8} = \dfrac{1}{2}

because 4 out of 8 numbers are odd: 1, 3, 5 and 7.

Finally,

P(A \land B) = \dfrac{3}{8}

because 3 out of 8 numbers are prime and odd: 3, 5 and 7.

So, applying the formula, we have

P(\text{prime } | \text{ odd}) = \dfrac{P(\text{prime and odd})}{P(\text{odd})} = \dfrac{\frac{3}{8}}{\frac{1}{2}} = \dfrac{3}{8}\cdot 2 = \dfrac{3}{4}

Note:

I think that it is important to have a clear understanding of what's happening from a conceptual point of you: conditional probability simply changes the space you're working with: you are not asking "what is the probability that a random number, taken from 1 to 8, is prime?"

Rather, you are adding a bit of information, because you are asking "what is the probability that a random number, taken from 1 to 8, is prime, knowing that it's odd?"

So, we're not working anymore with the space {1,2,3,4,5,6,7,8}, but rather with {1,3,5,7} (we already know that our number is odd).

Out of these 4 odd numbers, 3 are primes. This is why the probability of picking a prime number among the odd numbers in {1,2,3,4,5,6,7,8} is 3/4: they are literally 3 out of 4.

5 0
3 years ago
The drawing I don’t quite understand please could someone explain but don’t do it
kifflom [539]

Answer:

?idk maybe it's supposed to be how long it's on the top but I know that not right sorry I dont get it

5 0
3 years ago
Which equation is equivalent to square root x+11=15?
Vera_Pavlovna [14]
The answer is x= 214
3 0
3 years ago
Read 2 more answers
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