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3 years ago

The root x = 1 has multiplicity 3 for the function f(x)=x^3-x^2-x+1. True or false

1 answer:

7 0

X^3 - x^2 - x + 1 = 0
Plug in x = 1:-
1 -1 - 1 + 1 = 2 - 2 = 0 so x =1 is a root.

If it has multiplicity 3 then the function will factor to (x - 1)^3:-

(x - 1)^3 = (x - 1)(x^2 - 2x + 1) = x^3 - 2x^2 + x - x^2 + 2x - 1

= x^3 - 3x^2 + 3x - 1 so it is FALSE

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masha68 [24]

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Step-by-step explanation:

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3 years ago

A study of the US clinical population found that 24.1% are diagnosed with a mental disorder, 14.9% are diagnosed with an alcohol

jeka57 [31]

Answer:

a) 0.336

b) 0.207

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a person from the clinical population is diagnosed with mental disorder.

B is the probability that a person from the clinical population is diagnosed with alcohol related disorder.

We have that:

$A = a + (A \cap B)$

In which a is the probability that a person is diagnosed with mental disorder but not alcohol related disorder and $A \cap B$ is the probability that a person is diagnosed with both of these disorders.

By the same logic, we have that:

$B = b + (A \cap B)$

We find the values of a,b and the intersection, starting from the intersection.

5% are diagnosed with both disorders.

This means that $A \cap B = 0.05$

14.9% are diagnosed with an alcohol-related disorder

This means that $B = 0.149$

$B = b + (A \cap B)$

$0.149 = b + 0.05$

$b = 0.099$

24.1% are diagnosed with a mental disorder

This means that $A = 0.241$

$A = a + (A \cap B)$

$0.241 = a + 0.05$

$a = 0.203$

(a) What is the probability that someone from the clinical population is diagnosed with a mental disorder, knowing that the person is diagnosed with an alcohol-related disorder?

Desired outcomes:

Mental and alcohol-related disorders, which $A \cap B$ . So $D = 0.05$

Total outcomes:

Alcohol-related disorder, which is B. So $T = 0.149$

Probability:

$P = \frac{0.05}{0.149} = 0.336$

(b) What is the probability that someone from the clinical population is diagnosed with an alcohol-related disorder, knowing that the person is diagnosed with a mental disorder?

Desired outcomes:

Mental and alcohol-related disorders, which $A \cap B$ . So $D = 0.05$

Total outcomes:

Mental disorder, which is B. So $T = 0.241$

Probability:

$P = \frac{0.05}{0.241} = 0.207$

4 0

3 years ago

My brother is 5 years older than me. My sister is 3 years younger than me.

Ad libitum [116K]

Answer:

A) You would be 5

B) She would be 21

C) (Im guessing n in 9?) She would be 6 then

D) (idk what k is)

E)7 Years apart

Hope this helps

7 0

2 years ago

Read 2 more answers

A machine is set to fill the small-size packages of m&m candies with 56 candies per bag. a sample revealed: three bags of 56

luda_lava [24]

In statistics, the amount of degrees of freedom is the quantity of values in the final computation of a statistic that are free to differ. In this case, you can get the answer by adding the number of bags and subtracting 1.

So in computation, this would look like: 3 + 2 + 1 + 2 - 1 = 7

Therefore, 7 is the degrees of freedom.

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3 years ago