Question

PLEASE HELP ASAP!!!!

Answer 1

Answer:

Given: Data for 5 Days

Part A:-

No. of creatures on 6th day = Average/Mean of the Given Data

$\text{Mean = }\frac{\text{Sum of all the observation}}{\text{Total No. of observation}}$

⇒ $\text{Mean = }\frac{42+26+61+65+56}{5}$

⇒ Mean = 50

∴She collect 50 creatures on day 6.

Part B:-

As we Predicted she collected 50 pokenmon on day 6. So her Average is 50.

if She collected 53 creatures, then the average will be-

$\text{Average = }\frac{42+26+61+65+56+53}{6}$

⇒ Average = 50.5

Therefore, her new average become 50.5

Part C:-

There is no fixed no of creature collected on day 6,7,8. It can be increased or Decreased but her average will always be around 50.

Answer 2

Let us model this problem with a polynomial function.

Let x =  day number (1,2,3,4, ...)
Let y = number of creatures colled on day x.

Because we have 5 data points, we shall use a 4th order polynomial of the form
y = a₁x⁴ + a₂x³ + a₃x² + a₄x + a₅

Substitute x=1,2, ..., 5 into y(x) to obtain the matrix equation
|   1     1    1    1    1  |  | a₁ |      | 42 |
| 2⁴  2³  2²  2¹  2⁰  |  | a₂ |      | 26 |
| 3⁴  3³  3²  3¹  3⁰   |  | a₃ |  =  | 61 |
| 4⁴  4³  4²  4¹  4⁰   |  | a₄ |      | 65 |
| 5⁴  5³  5²  5¹  5⁰  |  | a₅ |      | 56 |

When this matrix equation is solved in the calculator, we obtain
a₁ =      4.1667
a₂ =  -55.3333
a₃ =  253.3333
a₄ =  -451.1667
a₅ =   291.0000

Test the solution.
y(1) = 42  
y(2) = 26
y(3) = 61
y(4) = 65
y(5) = 56

The average for 5 days is (42+26+61+65+56)/5 = 50.
If Kathy collected 53 creatures instead of 56 on day 5, the average becomes
(42+26+61+65+53)/5 = 49.4.

Now predict values for days 5,7,8.
y(6) = 152
y(7) = 571
y(8) = 1631