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4 years ago

Are positive integers closed under subtraction?

Mathematics

2 answers:

Galina-37 [17]4 years ago

8 0

Do you remember the answer..? I need help as well.

Flura [38]4 years ago

6 0

#1 not closed
#2 closed
#3 not closed
#4 not closed

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In the united states, voters who are neither democrat nor republican are called independent. it is believed that 12% of voters a

Nitella [24]

Answer:

a) 0.0245 = 2.45%

b) 0.9483 = 94.83%

c) 0.6931 = 69.31%

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they are independent, or they are not. The probability of a person being independent is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

It is believed that 12% of voters are independent.

This means that $p = 0.12$

Survey of 29 people

This means that $n = 29$

a. what is the probability that none of the people are independent? probability =

This is P(X = 0). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{29,0}.(0.12)^{0}.(0.88)^{29} = 0.0245$

0.0245 = 2.45% probability that none of the people are independent

b. what is the probability that fewer than 7 are independent? probability =

$P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{29,0}.(0.12)^{0}.(0.88)^{29} = 0.0245$

$P(X = 1) = C_{29,1}.(0.12)^{1}.(0.88)^{28} = 0.0971$

$P(X = 2) = C_{29,2}.(0.12)^{2}.(0.88)^{27} = 0.1853$

$P(X = 3) = C_{29,3}.(0.12)^{3}.(0.88)^{26} = 0.2274$

$P(X = 4) = C_{29,4}.(0.12)^{4}.(0.88)^{25} = 0.2016$

$P(X = 5) = C_{29,5}.(0.12)^{5}.(0.88)^{24} = 0.1374$

$P(X = 6) = C_{29,6}.(0.12)^{6}.(0.88)^{23} = 0.0750$

$P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0245 + 0.0971 + 0.1853 + 0.2274 + 0.2016 + 0.1374 + 0.0750 = 0.9483$

0.9483 = 94.83% probability that fewer than 7 are independent

c. what is the probability that more than 2 people are independent? probability =

Either two or less are, or at least 3 are independent. The sum of the probabilities of these events is decimal 1. So

$P(X \leq 2) + P(X > 2) = 1$

We want P(X > 2). So

$P(X > 2) = 1 - P(X \leq 2)$

In which

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{29,0}.(0.12)^{0}.(0.88)^{29} = 0.0245$

$P(X = 1) = C_{29,1}.(0.12)^{1}.(0.88)^{28} = 0.0971$

$P(X = 2) = C_{29,2}.(0.12)^{2}.(0.88)^{27} = 0.1853$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0245 + 0.0971 + 0.1853 = 0.3069$

$P(X > 2) = 1 - P(X \leq 2) = 1 - 0.3069 = 0.6931$

0.6931 = 69.31% probability that more than 2 people are independent

3 0

3 years ago

Describe the nature of the roots for this equation, x^2-2x+1=0

zimovet [89]

Use the discrimant to determine the nature of the roots
Here's the formula of the discriminant from the equation ax²+bx+c = 0
D = b² - 4ac

If the discriminant is greater than 0, the quadratic equation has 2 real different roots
If the discriminant is equal to 0, the quadratic equation has only one real root.
If the discriminant is less than 0, the quadratic equation doesn't have real root.

Find the discriminant of the equation x² - 2x + 1 = 0
D = b² - 4ac
D = (-2)² - 4(1)(1)
D = 4 - 4
D = 0
The equation has only one real root.

5 0

4 years ago

The price of a watch was increased by 10% to £660. What was the price before the increase?

Bad White [126]

Answer:

£600

Step-by-step explanation:

First take if 110% equals to £660 what about 100%

100×660 =66000 ÷ 110 =£600

3 0

3 years ago

The answer to the problem

sergey [27]

Answer:

x = 100

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

52 + 28 + x = 180

80 + x = 180 ( subtract 80 from both sides )

x = 100

8 0

3 years ago

21. Consider the diagram below.

Anna [14]

Answer:

Step-by-step explanation:

the transversal across two parallel lines causes the consecutive internal angles to be congruent according to the consecutive internal angles theorem.

7 0

3 years ago

Read 2 more answers