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
Answer:
![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
Step-by-step explanation:
Total number of red disk=6
Total number of yellow disk=2
Total disk=6+2=8
Odd number=1,3,5,7=4
Odd number on red disk=1,3,5=3
Probability,![P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}](https://tex.z-dn.net/?f=P%28E%29%3D%5Cfrac%7Bfavorable%5C%3Bcases%7D%7Btotal%5C%3Bnumber%5C%3Bof%5C%3Bcases%7D)
Using the formula
The probability of getting odd number disk=![\frac{4}{8}=\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B8%7D%3D%5Cfrac%7B1%7D%7B2%7D)
The probability of getting odd numbered red disk=![\frac{3}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B8%7D)
The probability of selecting a red disk,given that an odd numbered disk is selected=![\frac{\frac{3}{8}}{\frac{1}{2}}=\frac{3}{8}\times 2=\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B3%7D%7B8%7D%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cfrac%7B3%7D%7B8%7D%5Ctimes%202%3D%5Cfrac%7B3%7D%7B4%7D)
Using conditional probability
![P(A/B)=\frac{P(A\cap B)}{P(B)}](https://tex.z-dn.net/?f=P%28A%2FB%29%3D%5Cfrac%7BP%28A%5Ccap%20B%29%7D%7BP%28B%29%7D)
Answer:
121.53% as we do the following
23=4w-13
First add 13 to both sides.
36=4w
w=9
Hope this helps!