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The number of ways to choose 2 pens from 4 pens can be calculated using the combination formula ( \binom{n}{r} ), where ( n ) is the total number of items and ( r ) is the number of items to choose. Here, ( n = 4 ) and ( r = 2 ). Thus, the calculation is ( \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 ). Therefore, there are 6 ways to choose 2 pens from 4.

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Suppose you buy several pens at a discount store. All the pens are the same price and you buy as many pens as the cost (in cents) of each pen. The pens cost a total of 1.44. How many pens did you buy?

Let the cost of each pen be ( x ) cents. Since you buy ( x ) pens, the total cost can be expressed as ( x \times x = x^2 ) cents. Given that the total cost is 1.44 dollars, which is 144 cents, we have the equation ( x^2 = 144 ). Solving for ( x ), we find ( x = 12 ). Therefore, you bought 12 pens.


There are p pens in a pack 2 of them don't work. write an expression for the number of working pens in a pack?

If there are ( p ) pens in a pack and 2 of them don't work, the expression for the number of working pens in the pack is ( p - 2 ). This represents the total number of pens minus the non-functioning ones.


How many different ways can you write a fraction that has a numerator of 2 as a sum of fractions?

Infinitely many ways, since if you have found one way then take one of the fractions and replace it by an equivalent fraction. Repeat for ever.


How many different ways can 40 be written as a sum of 2 positive prime numbers?

Three ways. 3 + 37 11 + 29 17 + 23


How many backpacks out of 38 contained none of the three writing instruments?

First, I would like to say that the whole question is not here. The question states: upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil and 10 contained all three items. How many backpacks contained none of the three writing instruments? OK I will explain this the best I can! Starting out, their are 10 backpacks that contain all the items. 12 contained both a black and blue pen. You would subtract 10 from 12; therefore there are 2 backpacks that contain only black and blue pens. 18 contain both a blue pen and a pencil. subtract 10 from 18 and you get 8. 15 contained both a black pen and a blue pen. You would subtract 10 from 15 and you get 5. There are 23 with black pens. So you would do 23 - (5+10+2)= 6. There are 6 backpacks that contain only black pens. There are 27 that contain blue pens. So you would do 27 - (5+10+8) = 4. There are 4 backpacks that contain only blue pens. There are 21 backpacks that contain a pencil. You would do 21 - (2+10+8) = 1. All together, there a 6 that contain only black pens, 5 that contain only black and blue pens, 4 that contain only blue pens, 10 that contain all three items, 2 that contain only black pens and pencils, 8 that contains only blue pens and pencils, and 1 that contains only 1 pencil. So you would add 6+5+4+10+8+2+1= 36. There are 38 backpacks, so you would subtract 36 from 38. There are 2 backpacks that contain none of the three writing instruments. Ashfords quiz says this is right.

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There are p pens in a pack 2 of them don't work. write an expression for the number of working pens in a pack?

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