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One table at a bake sale has 75 oatmeal cookies. Another table has 60 lemon cupcakes. Which table allows for more rectangular arrangements when all the cookies and cupcakes are displayed?

Respuesta :

sqdancefan

75 = 3·5², so has 6 divisors. 6 rectangles are possible if you make the distinction between 1×75 and 75×1.

60 = 2²·3·5, so has 12 divisors. 12 rectangles are possible under the same conditions.

The cupcake table can be arranged more ways.

_____

When 1 is added to each exponent of the prime factors, the product of those sums is the number of divisors. For 75: (1+1)(1+2) = 6; for 60: (1+2)(1+1)(1+1) = 12.

MrRoyal

Arrangement is simply the order, which items are displayed or presented.

The table of 60 lemon cupcakes allow more rectangular arrangements

The given parameters are:

[tex]\mathbf{Oatmeal = 75}[/tex]

[tex]\mathbf{Lemon = 60}[/tex]

The rectangular arrangement (R) is calculated as follows:

[tex]\mathbf{R = \frac{Area}{n}}[/tex]

Where n represents the number of items, and Area represents the area of the rectangular table

For the oatmeal, we have:

[tex]\mathbf{R_1 = \frac{Area}{75}}[/tex]

[tex]\mathbf{R_1 = 0.0133Area}[/tex]

For the lemon, we have:

[tex]\mathbf{R_2 = \frac{Area}{60}}[/tex]

[tex]\mathbf{R_2 = 0.0167Area}[/tex]

By comparison, 0.0167Area is greater than 0.0133Area

Hence, the table of 60 lemon cupcakes allow more rectangular arrangement

Read more about arrangements at:

https://brainly.com/question/1216161

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