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kati45 [8]
2 years ago
8

Roberto wants to display his 18 sports cards in an album. Some pages hold 2 cards and others hold 3 cards. How many different wa

ys can Roberto display his figures ?
Mathematics
1 answer:
Ratling [72]2 years ago
7 0
<span>65 = number of different arrangements of 2 and 3 card pages such that the total number of card slots equals 18. 416,154,290,872,320,000 = number of different ways of arranging 18 cards on the above 65 different arrangements of page sizes. ===== This is a rather badly worded question in that some assumptions aren't mentioned. The assumptions being: 1. The card's are not interchangeable. So number of possible permutations of the 18 cards is 18!. 2. That all of the pages must be filled. Since the least common multiple of 2 and 3 is 6, that means that 2 pages of 3 cards can only be interchanged with 3 pages of 2 cards. So with that said, we have the following configurations. 6x3 card pages. Only 1 possible configuration. 4x3 cards and 3x2 cards. These pages can be arranged in 7!/4!3! = 35 different ways. 2x3 cards and 6x2 cards. These pages can be arranged in 8!/2!6! = 28 ways 9x2 card pages. These can only be arranged in 1 way. So the total number of possible pages and the orders in which that they can be arranged is 1+35+28+1 = 65 possible combinations. Now for each of those 65 possible ways of placing 2 and 3 card pages such that the total number of card spaces is 18 has to be multiplied by the number of possible ways to arrange 18 cards which is 18! = 6402373705728000. So the total amount of arranging those cards is 6402373705728000 * 65 = 416,154,290,872,320,000</span>
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Wouldnt it be four? id its 1/4

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2 years ago
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Give an example of a 2x2 matrix whose determinant is 13.
elixir [45]
<span>If all your entries are integers, the determinant is also an integer. 
</span>For this problem, 1        0
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For this question, you should just fix  3 values and make the 4th value an unknown and solve it.
I hope my answer helped you somehow.


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2 years ago
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The number f of miles a helicopter is from its destination x minutes after takeoff is given by f (x)=40-2x. The number f of mile
nevsk [136]

Answer:

Step-by-step explanation:

Function 'f' represents the number of miles (y-values) covered by the helicopter in 'x' (x-values) minutes.

f(x) = 40 - 2x

For x = 0,

f(x) = 40 miles

For f(x) = 0,

0 = 40 - 2x

x = 20 minutes

This shows that helicopter traveled 40 miles in 20 minutes.

Similarly, given graph shows distance covered by the jet on y-axis and duration of flight on x-axis.

For x = 0,

f(x) = 500 miles

For f(x) = 0,

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7 0
2 years ago
Complete the sentence. the roots of the equation x^2 - 8x - 48 = 0 are -4 and *blank*
prisoha [69]

Answer:

12 is the answer.

Step-by-step explanation:

The best way to get the roots of the equation is to factorize the equation but when the factors are not possible then we should apply the quadratic equations formula to get the value of x.

Now we will try to factorize

x² - 8x -48 = 0

Now we multiply coefficient of highest degree term and constant term

48×1 = 48 which may be factored in 12×4. 8×6, 24×2.

Now we will choose 12×4 out of three because the 12-4 = 8 which is the coefficient of x.

Now its simple.

x²-12x + 4x -48 = 0

x(x -12) + 4(x-12) = 0

(x +4)(x-12) = 0

Therefore roots are x + 4 = 0

x = -4

and x - 12 = 0

x = 12

So the answer is 12.

8 0
2 years ago
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Ms. Nina has 10 lbs of 25% sugar syrup. How much water does she need to add to make 10% sugar syrup
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10*0.25=2.5
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Nina need to add 15 lbs of water
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