20 possibilities based on this as a combination not a permutation, 6 nCr 3 = 20
I suppose you just have to simplify this expression.
(2ˣ⁺² - 2ˣ⁺³) / (2ˣ⁺¹ - 2ˣ⁺²)
Divide through every term by the lowest power of 2, which would be <em>x</em> + 1 :
… = (2ˣ⁺²/2ˣ⁺¹ - 2ˣ⁺³/2ˣ⁺¹) / (2ˣ⁺¹/2ˣ⁺¹ - 2ˣ⁺²/2ˣ⁺¹)
Recall that <em>n</em>ª / <em>n</em>ᵇ = <em>n</em>ª⁻ᵇ, so that we have
… = (2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺³⁾ ⁻ ⁽ˣ⁺¹⁾) / (2⁽ˣ⁺¹⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾)
… = (2¹ - 2²) / (2⁰ - 2¹)
… = (2 - 4) / (1 - 2)
… = (-2) / (-1)
… = 2
Another way to get the same result: rewrite every term as a multiple of <em>y</em> = 2ˣ :
… = (2²×2ˣ - 2³×2ˣ) / (2×2ˣ - 2²×2ˣ)
… = (4×2ˣ - 8×2ˣ) / (2×2ˣ - 4×2ˣ)
… = (4<em>y</em> - 8<em>y</em>) / (2<em>y</em> - 4<em>y</em>)
… = (-4<em>y</em>) / (-2<em>y</em>)
… = 2
Answer :
(a) Amount paid after using the coupon = $b - $5 = $(b-5)
(b) Amount paid = $23.45 - $5 = $(23.45-5) = $18.45
Amount paid = $54.83- $5 = $(54.83-5) = $49.83
Step-by-step explanation :
As we are given that:
Amount of coupon = $5
If amount of total bill = $b
Now we have to calculate the amount paid after using the coupon.
Amount paid after using the coupon = Total amount of bill - Amount of coupon
Amount paid after using the coupon = $b - $5 = $(b-5)
Now we have to calculate the amount paid if bill was $23.45.
Amount paid after using the coupon = Total amount of bill - Amount of coupon
Amount paid = $23.45 - $5 = $(23.45-5) = $18.45
Now we have to calculate the amount paid if bill was $54.83.
Amount paid after using the coupon = Total amount of bill - Amount of coupon
Amount paid = $54.83- $5 = $(54.83-5) = $49.83
Answer:
The probability that Katie will draw a face card on her next turn is 3/13, or approximately 23%.
Step-by-step explanation:
In a regular deck, there are four suits (clubs, spades, hearts and diamonds). Each suit has 13 cards that go from 2 - 10 plus the Ace, King, Queen and Jack. Since Katie is playing using a 26-card deck of only two suits, then there are only two kings, two queens and two jacks in the entire deck. In order to find probability, we form a fraction where the denominator is the total number of outcomes, in this case 26, and the numerator is the number of desired outcomes, in this case the total number of face cards in the deck - 6. So, the probability that Katie will choose a face card on the next turn is 6/26, which simplifies to 3/13 in lowest terms.
