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)
</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
Remember the divisibility rule for 9. The sum of the digits of the number must be divisible by nine.
Let the digit be
. Then
has to be divisible by nine. Recalling that
, we note that
.
Answer:
109 degrees.
Step-by-step explanation:
m< AEB = 1/2 (98 + 120)
= 1/2 * 218
= 109 degrees.
the answer is c because it is a decimal
P is the principal amount, $12000.00.
r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.
t is the time involved, 3....month(s) time periods.
Since your interest rate is "per year" and you gave your time interval in "month(s)" we need to convert your time interval into "year" as well.
Do this by dividing your time, 3- month(s), by 12, since there's 12 months in 1 year.
So, t is 0.25....year time periods.
To find the simple interest, we multiply 12000 × 0.05 × 0.25 to get that:
The interest is: $150.00
Usually now, the interest is added onto the principal to figure some new amount after 3 month(s),
or 12000.00 + 150.00 = 12150.00. For example:
If you borrowed the $12000.00, you would now owe $12150.00
If you loaned someone $12000.00, you would now be due $12150.00
If owned something, like a $12000.00 bond, it would be worth $12150.00 now.
