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zepelin [54]
3 years ago
13

In a two-digit number, the units digit is twice the tens digit. If the number is doubled, it will be 9 more than the number reve

rsed. Find the number. :) Thanks!
Mathematics
2 answers:
snow_lady [41]3 years ago
6 0
We know that the ones digit is 2x the tens digit. The number has to be two digits, so this leaves the options of 12, 24, 36, and 48.

Next, we double each number.
12 x 2 is 24
24 x 2 is 48
36 x 2 is 72
48 x 2 is 96

And subtract 9 from each of those. 15, 39, 63, and 87.

63 backwards is 36. The number you are looking for is 36. :)
taurus [48]3 years ago
5 0
10(2x)+x 
21x is the original number

12x is the reversed number
24x is the reversed then doubled number

Set up an equation:
24x=21x+9
3x=9
x=3

The original number is 63 and the reversed number is 36, which then is 72 when doubled.
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A 52-card deck is thoroughly shuffled and you are dealt a hand of 13 cards. (a) If you have at least one ace, what is the probab
jasenka [17]

Answer:

a) 0.371

b) 0.561

Step-by-step explanation:

We can answer both questions using conditional probability.

(a) We need to calculate the probability of obtaining two aces given that you obtained at least one. Let's call <em>A</em> the random variable that determines how many Aces you have. A is a discrete variable that can take any integer value from 0 to 4. We need to calculate

P(A \geq 2 | A \geq 1) = P(A\geq 2 \cap A \geq 1) / P(A \geq 1)

Since having 2 or more aces implies having at least one, the event A \geq 2 \cap A \geq 1 is equal to the event A \geq 2. Therefore, we can rewrite the previous expression as follows

P(A \geq 2) / P(A \geq 1)

We can calculate each of the probabilities by substracting from one the probability of its complementary event, which  are easier to compute

P(A \geq 2) = 1 - P((A \geq 2)^c) = 1 - P((A = 0) \bigsqcup (A = 1)) = 1 - P(A = 0) - P (A = 1)

P (A \geq 1) = 1 - P ((A \geq 1)^c) = 1 - P(A = 0)

We have now to calculate P(A = 0) and P(A = 1).

For the event A = 0, we have to pick 13 cards and obtain no ace at all. Since there are 4 aces on the deck, we need to pick 13 cards from a specific group of 48. The total of favourable cases is equivalent to the ammount of subsets of 13 elements of a set of 48, in other words it is 48 \choose 13. The total of cases is 52 \choose 13. We obtain

P(A = 0) = {48 \choose 13}/{52 \choose 13} = \frac{48! * 39!}{52!*35!} \simeq 0.303  

For the event A = 1, we pick an Ace first, then we pick 12 cards that are no aces. Since we can pick from 4 aces, that would multiply the favourable cases by 4, so we conclude

P(A=1) = 4*{48 \choose 12}/{52 \choose 13} = \frac{4*13*48! * 39!}{52!*36!} \simeq 0.438      

Hence,  

1 - P(A = 1)-P(A=0) /1-P(A=1) = 1 - 0.438 - 0.303/1-0.303 = 0.371

We conclude that the probability of having two aces provided we have one is 0.371

b) For this problem, since we are guaranteed to obtain the ace of spades, we can concentrate on the other 12 cards instead. Those 12 cards have to contain at least one ace (other that the ace of spades).

We can interpret this problem as if we would have removed the ace of spades from the deck and we are dealt 12 cards instead of 13. We need at least one of the 3 remaining aces. We will use the random variable B defined by the amount of aces we have other that the ace of spades. We have to calculate the probability of B being greater or equal than 1. In order to calculate that we can compute the probability of the <em>complementary set</em> and substract that number from 1.

P(B \geq 1) = 1-P(B=0)

In order to calculate P(B=0), we consider the number of favourable cases in which we dont have aces. That number is equal to the amount of subsets of 12 elements from a set with 48 (the deck without aces). Then, the amount of favourable cases is 48 \choose 12. Without the ace of spades, we have 51 cards on the deck, therefore

P(B = 0) = {48 \choose 12} / {51 \choose 12} = \frac{48!*39!}{51!*36!} = 0.438

We can conclude

P(B \geq 1) = 1- 0.438 = 0.561

The probability to obtain at least 2 aces if we have the ace of spades is 0.561

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kenny6666 [7]

Answer:

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Step-by-step explanation:

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Novay_Z [31]

Answer:

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Step-by-step explanation:

To find the distance use a trigonometric ratio. Since we are looking for the hypotenuse and we are given the opposite side we will be using the ration of sine. We can set up the equation like this by using x as the measure we are looking for.

Sin of x=Opposite leg/Hypotnuse

Sin of 30= 15/x

Multiply by x and then divide by Sin of 30 to isolate the x.

x=15/Sin of 30

Plug it in to a calculator.

x=30

4 0
3 years ago
ellen buys 24 ounces of green beans at the grocery store. the green beans cost $1.90 per pound. how much does she pay for the gr
RideAnS [48]

Answer:

  $2.85

Step-by-step explanation:

The price Ellen pays can be found using the proportion ...

  price/(24 oz) = $1.90/(16 oz)

Multiplying by 24 oz, we get ...

  price = $1.90(24/16) = $2.85

Ellen pays $2.85 for the beans.

7 0
2 years ago
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