To represent the change in points, you can think of it in two ways:
1. You will go down 25 points for every wrong answer, so -25 + -25 + -25 would represent what is happening. They are all negative, so you keeping moving down in value.
2. You can also think of this as 3 groups of -25.
Both answers are -75. The answer is negative because the change was down in points.
-75 is the integer that represents this situation.
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
Therefore, the answer is b < 7.
Answer: standard deviation = 8
This is because mu = 75 is the mean, which is at the very exact center of this distribution. One space to the right is 83, which is 83-75 = 8 units away from the center. This distance is exactly one standard deviation. We can say "83 is one standard deviation larger than 75".
Or you could note the distance from 67 to 75 is also 8, because 75-67 = 8. Each tickmark represents stepping one standard deviation in distance.
Answer:
The answer would be 60 cubic centimeters.
Step-by-step explanation:
