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3 years ago

What is the converse of a theorem

Mathematics

2 answers:

fiasKO [112]3 years ago

6 0

Step-by-step explanation:

The converse of a theorem happens when the conclusion and hypothesis of a theorem are switched.

Illusion [34]3 years ago

3 0

Answer:

equivalent to the opposite of the direct theorem

Step-by-step explanation:

the theorem in which the premise and conclusion of the direct theorem are replaced by their negations.

You might be interested in

Suppose the number of children in a household has a binomial distribution with parameters n=12n=12 and p=50p=50%. Find the proba

nadya68 [22]

Answer:

a) 20.95% probability of a household having 2 or 5 children.

b) 7.29% probability of a household having 3 or fewer children.

c) 19.37% probability of a household having 8 or more children.

d) 19.37% probability of a household having fewer than 5 children.

e) 92.71% probability of a household having more than 3 children.

Step-by-step explanation:

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.

In this problem, we have that:

$n = 12, p = 0.5$

(a) 2 or 5 children

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

$P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161$

$P(X = 5) = C_{12,5}.(0.5)^{5}.(0.5)^{7} = 0.1934$

$p = P(X = 2) + P(X = 5) = 0.0161 + 0.1934 = 0.2095$

20.95% probability of a household having 2 or 5 children.

(b) 3 or fewer children

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

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

$P(X = 0) = C_{12,0}.(0.5)^{0}.(0.5)^{12} = 0.0002$

$P(X = 1) = C_{12,1}.(0.5)^{1}.(0.5)^{11} = 0.0029$

$P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161$

$P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.0537$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0002 + 0.0029 + 0.0161 + 0.0537 = 0.0729$

7.29% probability of a household having 3 or fewer children.

(c) 8 or more children

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

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

$P(X = 8) = C_{12,8}.(0.5)^{8}.(0.5)^{4} = 0.1208$

$P(X = 9) = C_{12,9}.(0.5)^{9}.(0.5)^{3} = 0.0537$

$P(X = 10) = C_{12,10}.(0.5)^{10}.(0.5)^{2} = 0.0161$

$P(X = 11) = C_{12,11}.(0.5)^{11}.(0.5)^{1} = 0.0029$

$P(X = 12) = C_{12,12}.(0.5)^{12}.(0.5)^{0} = 0.0002$

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.1208 + 0.0537 + 0.0161 + 0.0029 + 0.0002 = 0.1937$

19.37% probability of a household having 8 or more children.

(d) fewer than 5 children

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

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

$P(X = 0) = C_{12,0}.(0.5)^{0}.(0.5)^{12} = 0.0002$

$P(X = 1) = C_{12,1}.(0.5)^{1}.(0.5)^{11} = 0.0029$

$P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161$

$P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.0537$

$P(X = 4) = C_{12,4}.(0.5)^{4}.(0.5)^{8} = 0.1208$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0002 + 0.0029 + 0.0161 + 0.0537 + 0.1208 = 0.1937$

19.37% probability of a household having fewer than 5 children.

(e) more than 3 children

Either a household has 3 or fewer children, or it has more than 3. The sum of these probabilities is 100%.

From b)

7.29% probability of a household having 3 or fewer children.

p + 7.29 = 100

p = 92.71

92.71% probability of a household having more than 3 children.

5 0

3 years ago

Solve 4x - 5 = 19. O A. x = 8 O B. x = 10 C. x = 6 O D. x = 3.5

Basile [38]

Answer:

C x=6

Step-by-step explanation:

4x-5=19

+5 on both sides

4x=24

divide both sides by 4

x=6

6 0

2 years ago

chris has 3 1/2 boxes of tomatoes at his restaurant he uses 1 3/4 boxes to make tomato sauce for tonight's dinner. How many boxe

Sladkaya [172]

Answer:

1 3/4

Step-by-step explanation:

3 1/2 boxes of tomatoes currently. uses 1 3/4, taking it away basically.

3 1/2 - 1 3/4

3 2/4 - 1 3/4 ;; i did this with finding a common denominator for it to be easier for me to solve.

3 - 1 = 2

2/4 - 3/4 = -1/4

2 + -1/4 = 1 3/4

correct me if wrong.

5 0

3 years ago

Read 2 more answers

Write the following comparison as a ratio reduced to lowest terms 70 days to 3 weeks

aliya0001 [1]

Answer:

I think that it is already in lowest terms

Step-by-step explanation:

8 0

3 years ago

Can anyone help? Will give Brainly + 20 pts .

katen-ka-za [31]

Answer:

She invested 1600 at 8% (to get the shown $160 interest)

and $7400 at 10% (to get the shown 640 interest)

If x = 4000 then $80 interest is x2 again = $160

and so forth $320 interest x 2 again = $640

Step-by-step explanation:

The format would always be for x and then where

investment - x = interest we can work out totals this way and find x.

9000-x = 800 is first equation and substituted into 2nd equation;

0.10x+0.08(9000−x)=800

Use the distributive property to multiply 0.08 by 9000−x.

0.10x+720−0.08x=800

Combine 0.10x and -0.08x to get 0.02x.

0.02x + 720 = 800

Subtract 720 from both sides.

0.02x=800−720

Subtract 720 from 800 to get 80.

0.02x=80

Divide both sides by 0.02.

x= 80 / 0.02

Make decimals numbers = 1 or above.

80 / 0.02 x 100

x= 8000 / 2

x = 4000

3 0

3 years ago