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An Earth scientist is testing how various soil mixtures affect plant growth. She begins with 10 soil types. For each mixture, she combines equal amounts of 2 soil types. How many soil mixtures must the scientist create in order to test all possible combinations of the 10 soil types?a. 20b. 45c. 55d. 90

Respuesta :

Oseni

Answer:

b

Explanation:

The correct answer would be 45.

Assuming that the 10 soils are each represented by A, B, C, D, E, F, G, H, I, J.

A can combine with 9 others as: AB AC AD AE A F AG AH AI AJ

B can combine as: BC BD BE BF BG BH BI BJ

C as: CD CE CF CG CH CI CJ

D as: DE DF DG DH DI DJ

E as: EF EG EH EI EJ

F as: FG FH FI FJ

G as: GH GI GJ

H as: HI HJ

I as: IJ

Adding all the combinations together = 45

In other words;

[tex]^{10}C_2[/tex] = [tex]\frac{10!}{(2!(10 - 2)!)}[/tex] = 45

Histrionicus

The soil mixtures must the scientist create in order to test all possible combinations of the 10 soil types- b. 45.

Given

soil samples = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

each mixture must have two sample

Solution

  • We have to mix 2 soils in equal amounts. Then, the total number of possible soil mixtures are:-
  • 1 and 2, 1 and 3, 1 and 4, 1 and 5, 1 and 6, 1 and 7, 1 and 8, 1 and 9, 1 and 10 = >9
  • 2 and 3, 2 and 4, 2 and 5, 2 and 6, 2 and 7, 2 and 8, 2 and 9, 2 and 10 => 8
  • 3 and 4, 3 and 5, 3 and 6, 3 and 7, 3 and 8, 3 and 9, 3 and 10 => 7
  • 4 and 5, 4 and 6, 4 and 7, 4 and 8, 4 and 9, 4 and 10 => 6
  • 5 and 6, 5 and 7, 5 and 8, 5 and 9, 5 and 10 => 5
  • 6 and 7, 6 and 8, 6 and 9, 6 and 10 => 4
  • 7 and 8, 7and 9, 7 and 10 => 3
  • 8 and 9, 8 and 10 => 2
  • 9 and 10 => 1

Then Total mixtures possible are =

9 + 8 + 7 + 6+ 5 + 4 + 3 + 2 + 1

= 45

Learn more:

https://brainly.com/question/13171394

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