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adoni [48]
3 years ago
9

4.31(69)+4.31(31)solve

Mathematics
1 answer:
sesenic [268]3 years ago
7 0
4.31(69) = 297.39
4.31(31) = 133.61

297.39 + 133.61 = 431
You might be interested in
Person A can paint the neighbors house 2 times as fast as Person B. The year A and B worked together, it took them 2 days. How l
seraphim [82]

Answer:

A can paint in 3days and B in 6 days

Step-by-step explanation:

From the question we were told

Person A can paint the neighbors house 2 times as fast as Person B

Let A only paint the neighbors house in X days

Let B only paint the neighbors house in 2X days

If we express the given information from the question in terms of fraction we have,

1/X + 1/2X = 1/2

3/2X = 1/2

if we cross multiply we have

6= 2X

X= 6/2

X= 3

Then A can paint the house in 3 days and B in 2(3)= 6days.

5 0
3 years ago
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

4 0
3 years ago
Please help me this due soon
o-na [289]
Answer is 108 cause you will multiply 13.5 by 8 and get 108.

In short Answer is 108.
7 0
3 years ago
Twelve divided by the sum of x and 2 equals the quotient of 4 and the difference of x and 2. Find x.
Marizza181 [45]

Answer:

Step-by-step explanation:

12/(x+2) = 4/(x-2)

Cross-multiply to get:

12x-24 = 4x+8

8x = 32

x = 4

7 0
3 years ago
What is eight dozen in standard form?
Amiraneli [1.4K]
Assuming 8 dozen is 96 not 8000000000000 it would be 9.6x10¹. If it is 8000000000000 then it's 8x10¹²
8 0
3 years ago
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