What is the value of x. 3x

A deck of ordinary cards is shuffled and 13 cards are dealt. What is the probability that the last card dealt is an ace?

alexandr1967 [171]

Answer:

The probability that the last card dealt is an ace is $\frac{1}{13}$ .

Step-by-step explanation:

Given : A deck of ordinary cards is shuffled and 13 cards are dealt.

To find : What is the probability that the last card dealt is an ace?

Solution :

There are total 52 cards.

The total arrangement of cards is 52!.

There is 4 ace cards in total.

Arrangement for containing ace as the 13th card is $4\times 51!$ .

The probability that the last card dealt is an ace is

$P=\frac{4\times 51!}{52!}$

$P=\frac{4\times 51!}{52\times 51!}$

$P=\frac{4}{52}$

$P=\frac{1}{13}$

Therefore, the probability that the last card dealt is an ace is $\frac{1}{13}$ .

4 0

3 years ago

How to simplify 24/1

earnstyle [38]

since its over 1 it just makes it 24

6 0

3 years ago

Read 2 more answers

Find two consecutive even integers such that the smaller added to three times the larger gives a sum of 54

REY [17]

Let n be the first even integer, and n+2 will be the second even integer. (Why? Think 2 and 4, 2+2=4. This is the case for every consecutive even integers).

n + 3(n+2) = 54
n + 3n + 6 = 54
4n = 48
n = 12, n+2 = 14

7 0

3 years ago

Read 2 more answers

A survey of 76 commercial airline flights of under 2 hours resulted in a sample average late time for a flight of 2.55 minutes.

nika2105 [10]

Answer:

The best point of estimate for the true mean is:

$\hat \mu = \bar X = 2.55$

$2.55-1.96\frac{12}{\sqrt{76}}=-0.148$

$2.55+1.96\frac{12}{\sqrt{76}}=5.248$

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

Step-by-step explanation:

Information given

$\bar X=2.55$ represent the sample mean for the late time for a flight

$\mu$ population mean

$\sigma=12$ represent the population deviation

n=76 represent the sample size

Confidence interval

The best point of estimate for the true mean is:

$\hat \mu = \bar X = 2.55$

The confidence interval for the true mean is given by:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The Confidence level given is 0.95 or 95%, th significance would be $\alpha=0.05$ and $\alpha/2 =0.025$ . If we look in the normal distribution a quantile that accumulates 0.025 of the area on each tail we got $z_{\alpha/2}=1.96$

Replacing we got:

$2.55-1.96\frac{12}{\sqrt{76}}=-0.148$

$2.55+1.96\frac{12}{\sqrt{76}}=5.248$

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

7 0

3 years ago

adrian began riding his scooter at 7:00am. He stopped riding it at 8:10am. How long did adrian ride his scooter for?

Alenkinab [10]

Answer:

Adrian rode his scooter for a total of 70 minutes, or an hour and ten minutes.

Step-by-step explanation:

There are 60 minutes in an hour, so if Adrian started riding his scooter at 7:00AM, to get to 8:10AM he needs to add 70. Again, since there are 60 minutes in an hour, 70 minutes converts to one hour and 10 minutes. Adrian rode his scooter for 70 minutes, or an hour and ten minutes.

7:00 + :70 = 8:10

8 0

3 years ago

What is the value of x. 3x – 3 = 3