The derivative of a function is used to determine whether the function is increasing or decreasing on any intervals in its domain.
Derivative of function f is increasing in interval (-2 , 1) and (3 , 6)
Derivative of function f is decreasing in interval (1 , 3) and (6 , 9)
If f′(x) > 0 at each point in an interval , then the function is said to be increasing in that interval.
If f′(x) < 0 at each point in an interval , then the function is said to be decreasing on that interval.
By observing graph, it is observed that slope of function f is positive in interval (-2 , 1) and (3 , 6) . Hence, derivative of function f is increasing in interval (-2 , 1) and (3 , 6)
By observing graph, it is observed that slope of function f is negative in interval (1 , 3) and (6 , 9) . Hence, derivative of function f is decreasing in interval (1 , 3) and (6 , 9).
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These are 6 questions and 6 answers.
To find each probability we will use the definition of probability:
Probability = number of positive outcomes / number of total possible outcomes
1) <span>P(Jack or ten)
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<span>Answer: 2/13 ≈ 0.12
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Justification:
i) Positive outcomes: A standard deck of cards has 4 jacks and 4 tens, then those are 4 + 4 = 8 different positive outcomes.
ii) Possible outcomes: a standard deck of cards has 52 different cards, so, that is a total of 52 different possible outcomes
iii) Probability, P
P = number of positive outcomes / number of total possible outcomes
P = 8 / 52 = 2/13 ≈ 0.15
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2.P(red or black)
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Answer: 1
Justification:
i) Positive outcomes
Half of the cards are red and half of the cards are black, so they both add for the total of the cards = 52
ii) Possible outcomes: 52 cards
iii) Probaility, P
P = number of positive outcomes / number of total possible outcomes
P = 52 / 52 = 1
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3.P(queen or club)
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Answer: 4/13 ≈ 0.31
Justification:
i) Positive outcomes
There are 4 Queens.
There are 1/4 of 52 clubs = 1/4 × 52 = 13 clubs.
But you cannot add all of them, because one club is the Quenn of Clubs.
Then, the total number of different Queens and clubs is 4 + 13 - 1 = 16
ii) Possible outcomes: 52 different cards
iii) Probaility, P
P = number of positive outcomes / number of total possible outcomes
P = 16 /52 = 4 / 13 ≈ 0.31
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4.P(red or ace)
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Answer: 7 / 13 ≈ 0.54
Justification:
i) Positive outcomes
Half of the cards are red: 26
There are 4 aces.
Since 2 aces are red, the number of different red and aces cards is: 26 + 4 - 2 = 28
ii) Possible outcomes: 52 different outcomes
iii) Probaility, P
P = number of positive outcomes / number of total possible outcomes
P = 28 / 52 = 7 / 13 ≈ 0.54
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5.P(diamond or black)
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Answer: 1/2 = 0.5
Justification:
i) Positive outcomes
There are 52 / 4 = 13 diamonds
There are 26 black cards.
All the diamonds are black cards.
Then, the number of different diamond or black cards is 13 + 26 - 13 = 26
ii) Possible outcomes: 52 different cards.
iii) Probaility, P
P = number of positive outcomes / number of total possible outcomes
P = 26 / 52 = 1/2 = 0.5
6.P(face card or spade)
Answer: 11/26 ≈ 0.42
Justification:
i) Positive outcomes
Face cards are jacks, queens and kings. That is 3 × 4 = 12 different cards.
The spades are 13 cards.
Since, 3 of the faces are spade cards, the number of different cards of those types are 12 + 13 - 3 = 22
ii) Possible outcomes: 52 different cards
iii) Probaility, P
P = number of positive outcomes / number of total possible outcomes
P = 22 / 52 = 11 / 26 ≈ 0.42
You put the values of x into the equation to work out y, so the y column would be -5, -1, 3, 7 (for question 6)
For question 7, the y column would be 2,2,0,-2
Use these values to draw the graphs :)
Answer:
b
Step-by-step explanation:
