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FinnZ [79.3K]
2 years ago
5

In the game of blackjack played with one​ deck, a player is initially dealt 2 different cards from the 52 different cards in the

deck. a winning​ "blackjack" hand is won by getting 1 of the 4 aces and 1 of 16 other cards worth 10 points. the two cards can be in any order. find the probability of being dealt a blackjack hand. what approximate percentage of hands are winning blackjack​ hands?
Mathematics
1 answer:
Tpy6a [65]2 years ago
6 0

We are given here that a blackjack hand consists of:

1 of the 4 aces = 4 / 52

1 of the 16 cards worth 10 points (10, jack, queen, king) = 16 / 52

 

So assuming that cards are dealt without replacement, therefore the probability of getting a blackjack hand is:

<span>P = 1st is ace * 2nd is 10 pt card + 1st is 10 pt card * 2nd is ace</span>

P = (4 / 52) * (16 / 51) + (16 / 52) * (4 / 51)

P = 0.04827 = 4.83%

 

Therefore there is a 4.83% probability to get a blackjack hand.

<span> </span>

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3 1/2

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A worker has a base pay of $20 per hour, gets $3 more per hour after 8 hours, and gets $4 more
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177 $

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20 x8 = 160

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You plan to rent a car from XYZ Car Rental Company for a flat rate of $35 a
vagabundo [1.1K]

Answer:

The piece-wise function is;

f\left (x  \right ) = \begin{cases} \$ 45 \times  x & \text{ if } x \leq 3  \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}

Step-by-step explanation:

The flat rate for renting the car = $35 per day

The amount charged as insurance fee per day for renting the car for 3 days or less = $10

The insurance fee charged per day when the car is rented for more than 3 days = $5

Let the number of days = x

Therefore, we have;

For x ≤ 3, f(x) = 35 × x + 10 × x = x × (35+10) = 45·x

For x > 3, f(x) = 35 × x + 5 × x = x × (35+5) = 40·x

Therefore;

The charge rate for renting the car for less than or equal to 3 days = 45·x

The charge rate for renting the car for more than 3 days = 40·x

The piece-wise function can be presented as follows;

f\left (x  \right ) = \begin{cases} \$ 45 \times  x & \text{ if } x \leq 3  \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}

3 0
2 years ago
A ketchup company regularly receives large shipments of tomatoes. For each shipment that is received, a supervisor takes a rando
fredd [130]

Answer:

H_o:p=0.1\\\\H_a:p\neq 0.1

Step-by-step explanation:

-A hypothesis is a claim of evidence and is used in making statistical decisions during experiments/ research.

-Given that 10% of the entire shipment is bruised.

-the null hypothesis states that the proportion is equal to the stated value:

H_o:p=0.1

-The alternative  states that the null hypothesis is not correct:

H_a:p\neq 0.1

8 0
2 years ago
Of the coffee makers sold in an appliance​ store, 4.0% have either a faulty switch or a defective​ cord, 2.5% have a faulty​ swi
lukranit [14]

Answer: Hence, Probability that a coffee maker will have a defective cord is 0.376=37.6%.

Step-by-step explanation:

Since we have given that

Let A be the event of getting a faulty switch.

Let B be the event of getting a defective cord.

Here, P(A∪B) = 4% = 0.04

P(A∩B) = 0.1% = 0.001

P(A) = 2.5% = 0.025

We need to find P(B):

As we know that

P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\0.04=P(A)+0.025-0.001\\\\0.04=P(A)+0.024\\\\P(A)=0.04-0.024=0.376

Hence, Probability that a coffee maker will have a defective cord is 0.376=37.6%.

6 0
2 years ago
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