In 1414 hours it covered 700 miles
In 1 hour it would have covered (700/1414) mile
In 33 hours it will then cover : 700/1414 * 33 = 16.34
So in 33 hours it will cover ≈ 16.34 miles.
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)
</span>
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)
</span><span>
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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
A fraction. I.E. : 6 has 36 parts (6 parts per one) If you took 2 out of the six parts away you would get 32/6 or 5 2/6 (2/6 could be simplified to 1/3)
Answer:
19.) r = -4 20.) r = 1
Step-by-step explanation:
19.) Because we know the slope and have some points, we can use point-slope form to find the equation.
Point-slope form is:
y - y1 = m(x - x1)
Substitute the numbers into the equation:
y - 3 = 7/6(x - 1)
y - 3 = 7/6x -7/6
y = 7/6x + 11/6
Now that we know the equation, we can put in the x value to find the y (In this case, y = r):
r = 7/6(-5) + 11/6
r = -35/6 + 11/6
r = -4
20.) Because the slope is undefined, that means on the graph, the line will appear straight and vertical. This means the equation will be something like x = a number.
We have the point (1,4). Since we know that the x value will never change, we know that r will have to equal 1 as well.
r = 1
