Determine if 0.669429565254154 is rational or irrational and give a reason for your answer

Mathematics

1 answer:

raketka [301]1 year ago

7 0

Answer:

Rational

Step-by-step explanation:

The reason why this number is rational is because this number terminates.

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Luther owns a farm where he grows red and green tomatoes. He sells both types of tomatoes for $1.70 per pound. One customer boug

pashok25 [27]

Answer:

Total revenue= $32.13

Step-by-step explanation:

Giving the following information:

He sells both types of tomatoes for $1.70 per pound. One customer bought 10.6 pounds of red tomatoes and 8.3 pounds of green tomatoes.

We need to calculate the total revenue:

Total revenue= 1.7*10.6 + 1.7*8.3

Total revenue= $32.13

6 0

2 years ago

a movie theater has 14 different movies showing. If you want to attend no more than 3 of the movies, how many different combinat

zvonat [6]

14C3 = 14! / 11!3!

= 14 x13 x12 / 3x2x1 
= 2184 / 6 
= 364 different combinations 

The first movie can be any of 14 
As you have already seen one the second movie can be any of the 13 remaining 
As you have already seen two the third movie can be any of the 12 remaining. 

Therefore there are 14 x 13 x 12 = 2184 PERMUTATIONS of movies you can see. 
However among those 2184 different permutations will be instances where you have watched the same three movies but just in a different order. 
eg ET, The Piano, Harry Potter = ET Harry Potter The Piano = The Piano, ET, Harry Potter = The Piano Harry Potter ET = Harry Potter ET The Piano = Harry Potter The Piano ET. 
For each set of three films there are 3! or 3x2x1 or SIX different ways they can be arranged in. 
Therefore we need to DIVIDE the above 2184 permutations by 6 to get the number of COMBINATIONS of different films that can be watched. 
2184 / 6 = 364

5 0

1 year ago

Choose the option that best completes the statement below. In finding the number of permutations for a given number of items, __

vodomira [7]

Let’s look at the permutations of the letters “ABC.” We can write the letters in any of the following ways:
ABC
ACB
BAC
BCA
CBA
CAB
Since there are 3 choices for the first spot, two for the next and 1 for the last we end up with (3)(2)(1) = 6 permutations. Using the symbolism of permutations we have: $3 P_{3}=(3)(2)(1)=6$ . Note that the first 3 should also be small and low like the second one but I couldn’t get that to look right.

Now let’s see how this changes if the letters are AAB. Since the two As are identical, we end up with fewer permutations.
AAB
ABA
BAA
To make the point a bit better let’s think of one A are regular and one as bold A.
ABA and ABA look different now because we used bold for one of the As but if we don’t do this we see that these are actual the same. If they represented a word they would be the same exact word.

So in this case the formula would be $\frac{3 P_{3} }{2!}= \frac{(3)(2)(1)}{(2)(1)}= \frac{6}{2}=3$ . We use 2! In the denominator because there are 2 repeating letters. If there were three we would use 3!

Hopefully, this is enough to let you see that the answer is A. The number of permutations is limited by the number of items that are identical.

7 0

2 years ago

The crew of apollo 17 consisted of 2 pilots and a geologist. Suppose that nasa had actually trained 9 pilots and 4 geologists as

Troyanec [42]

They could have assembled total 336 different possible crews.

Explanation

Total number of trained pilots is 9 and geologists is 4.

The crew should be consisted of 2 pilots and 1 geologist. That means, 2 pilots are chosen from total 9 and 1 geologist is chosen from total 4.

Number of ways for choosing 2 pilots from 9 $= ^9C_{3} =84$ and