Since only one person can finish in first place, one in second, etc., the total number of placers is 12x11x10, or 1320 different ways the 12 racers can finish 1st, 2nd and 3rd....
☺☺☺☺
Answer: ![\bold{y=7cos\bigg(\dfrac{2\pi}{7}x\bigg)}](https://tex.z-dn.net/?f=%5Cbold%7By%3D7cos%5Cbigg%28%5Cdfrac%7B2%5Cpi%7D%7B7%7Dx%5Cbigg%29%7D)
<u>Step-by-step explanation:</u>
y = A cos (Bx - C) + D
- A = amplitude (vertical stretch)
- Period = 2π/B
- C/B = phase shift
- D = vertical shift
The minimum is -7 and the max is 7 so A = 7 and D = 0
Period is 7. Since P = 2π/B then 7 = 2π/B --> B = 2π/7
Nothing was stated about a phase shift so you can use any value for C. I chose C = 0.
Now, input A = 7, B = 2π/7, C = 0, & D = 0 into the equation
![y=7\cos\bigg(\dfrac{2\pi}{7}x-0\bigg)+0\\\\\\\text{Simplify}:\\y=7\cos\bigg(\dfrac{2\pi}{7}x\bigg)](https://tex.z-dn.net/?f=y%3D7%5Ccos%5Cbigg%28%5Cdfrac%7B2%5Cpi%7D%7B7%7Dx-0%5Cbigg%29%2B0%5C%5C%5C%5C%5C%5C%5Ctext%7BSimplify%7D%3A%5C%5Cy%3D7%5Ccos%5Cbigg%28%5Cdfrac%7B2%5Cpi%7D%7B7%7Dx%5Cbigg%29)
= cos(x-π/2)/sin(x-π/2)
= (cos(x)cos(π/2) + sin((x)sin(π/2)) / (sin(x)cos(π/2) - cos(x)sin(π/2)
= sin(x)/ (-cos(x)) .... cos(π/2) = 0; sin(π/2) = 1
= -tan(x)
idk if this is right but i tried
The smallest number would be 2,478
The correct answer is choice A. Qualitative data is data that is collected based on a quality or a characteristic. These type of data will not involve numbers or measurements, but descriptive words.