Mathematics, 25.01.2020 06:31 krazziekidd2p845ri

Adigital scale that provides weights to the nearest gram is used. a. what is the sample space for this experiment? let a denote the event that a weight exceeds 11 grams, let b denote the event that a weight is less than or equal to 15 grams, and let c denote the event that a weight is greater than or equal to 8 grams and less than 12 grams. describe the following events. b. a ∪ b c. a ∩ b d. a' e. a ∪ b ∪ c f. (a ∪ c)' g. a ∩ b ∩ c h. b' ∩ c i. a ∪ (b ∩ c)

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Answer from: ernest214

a) $S= [x \in x \geq 0]$

Because the weigth can't be negative.

b) AUB = "a weight exceeds 11 grams OR is less than or equal to 15 grams" and that is represent by all the sample space S.

c) A ∩ B ="a weight exceeds 11 grams AND is less than or equal to 15 grams" and that is represent by $11 < X \leq 15$ who is the same as $12 \leq X \leq 15$ .

d) A' = "a weight NOT exceeds 11 grams" $X \leq 11$ that's the complement of the event A

e) A ∪ B ∪ C = "represent all the possib;e values for the sample space or S"

f) (A ∪ C)'="for this case (AUC) represent the weigths that exceeds 11 gr OR are between 8 and less than 11, so on this case values $X \geq 8$ , so then the complement (AUC)' woudl be all the values "

g) A ∩ B ∩ C = $\emptyset$ since we don't have a common interval for the 3 events at the same time

h) B' ∩ C = The complement of B are the X15 and for C we have values $8 \leq X$ and the intersection between these two events is the $\emptyset$ .

i) A ∪ (B ∩ C) = For this case (B ∩ C) represent the values between $8\leq X$ and if we do the union A ∪ (B ∩ C) we got $X \geq 8$

Step-by-step explanation:

For this case we have defined the following events, assuming that X represent the weight:

A= "a weight exceeds 11 grams" X11

B= " a weight is less than or equal to 15 grams" $X \leq 15$

C= "a weight is greater than or equal to 8 grams and less than 12 grams" $8 \leq X < 12$

Part a

The sample space is given by:

$S= [x \in x \geq 0]$

Because the weigth can't be negative.

Part b

AUB = "a weight exceeds 11 grams OR is less than or equal to 15 grams" and that is represent by all the sample space S.

Part c

A ∩ B ="a weight exceeds 11 grams AND is less than or equal to 15 grams" and that is represent by $11 < X \leq 15$ who is the same as $12 \leq X \leq 15$ .

Part d

A' = "a weight NOT exceeds 11 grams" $X \leq 11$ that's the complement of the event A

Part e

A ∪ B ∪ C = "represent all the possib;e values for the sample space or S"

Part f

(A ∪ C)'="for this case (AUC) represent the weigths that exceeds 11 gr OR are between 8 and less than 11, so on this case values $X \geq 8$ , so then the complement (AUC)' woudl be all the values "

Part g

A ∩ B ∩ C = $\emptyset$ since we don't have a common interval for the 3 events at the same time

Part h

B' ∩ C = The complement of B are the values in X15 and for C we have values $8 \leq X$ and the intersection between these two events is the $\emptyset$ .

Part i

A ∪ (B ∩ C) = For this case (B ∩ C) represent the values between $8\leq X$ and if we do the union A ∪ (B ∩ C) we got $X \geq 8$

Answer from: Quest

There was 504 pages in that chunk

Answer from: Quest

∠cbe and ∠deb are same-side interior angles.

i took the test

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