Step-by-step explanation:
x²+4x=8
rearrange
x² + 4x - 8 = 0
half of 4 is 2
so
x² + 4x + 2² - 2² - 8 = 0
do x² + 4x + 2²
multiplies to give 4 adds to give 4
2+ 2
(x + 2)²
(x + 2)² - 2² - 8
(x + 2)² - 4 - 8
(x + 2)² - 12
(x + 2 + √12) (x + 2 - √12)
√12 = √4 * √3 = 2 √3
(x + 2 + 2√3) (x + 2 - 2√3)
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)
</span>
<span>Answer: 2/13 ≈ 0.12
</span>
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
<span>
2.P(red or black)
</span>
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
<span>
3.P(queen or club)
</span>
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
<span>
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
<span>
5.P(diamond or black)
</span><span>
</span>
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
Answer: $0
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 1 year
P = $450
R = 4.5%
Therefore
I = (450 × 4.5 × 1)/100
I = 2025/100
I = 20.25
For compound interest,
Initial amount deposited into the account is $450 This means that the principal,
P = 450
It was compounded annually. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 4.5%. So
r = 4.5/100 = 0.045
It was compounded for just a year. So
t = 1
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 450 (1+0.045/1)^1×1
A = 450(1.045) = $470.25
Compound interest = 470.25 - 450 = 20.25
The difference is 20.25 - 20.25 = 0
Answer:
x ≥ 1/2
Step-by-step explanation:
6x + 21 ≥ 24
6x ≥ 3
x ≥ 1/2
check: (1/2 x 6) + 21 = 24
