Answer:
I, II, and III are true.
Step-by-step explanation:
I. A correlation of -0.8 (negative) between weight and reliability means that the heavier the car, the less reliable it will be. Therefore, the statement is true.
II. A correlation of 0.6 (positive) between weight and maintenance means that the heavier the car, the higher the costs will be. Therefore, the statement is true.
III. Since the absolute value of the correlation between weight and reliability is higher than the absolute value of the correlation between weight and maintenance cost (0.8 > 0.6), weight is more strongly related to reliability than to maintenance cost. The statement is true.
Each year, it's value is 1.08 of the previous price, so the equation is
![x=32000*(1.08^6)](https://tex.z-dn.net/?f=x%3D32000%2A%281.08%5E6%29)
Using a calculator, you get that the answer is 50779.978. You must also round to the nearest hundredth because in our currency, cents are the smallest unit.
Therefore, an antique car that costs $32000 will be worth 50779.98 6 years after.
Step-by-step explanation:
We know that tan=sin/cos, so tan(x+π/2)=
![\frac{sin(x+pi/2)}{cos(x+pi/2)}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28x%2Bpi%2F2%29%7D%7Bcos%28x%2Bpi%2F2%29%7D)
Then, we know that sin(u+v)=sin(u)cos(v)+cos(u)sin(v),
so our equation is then
Then, cos(u+v)=cos(u)cos(v)-sin(u)sin(v), so our expression is then
![\frac{cos(x)}{cos(x)cos(\pi/2)-sin(x)sin(\pi/2)} = \frac{cos(x)}{-sin(x)} = -cot(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29%7D%7Bcos%28x%29cos%28%5Cpi%2F2%29-sin%28x%29sin%28%5Cpi%2F2%29%7D%20%3D%20%5Cfrac%7Bcos%28x%29%7D%7B-sin%28x%29%7D%20%3D%20-cot%28x%29)
Answer:
x=-3
Step-by-step explanation:
![- 5x + 2(x - 1) = 7](https://tex.z-dn.net/?f=%20-%205x%20%2B%202%28x%20-%201%29%20%3D%207)
![- 5x + 2x - 2 = 7](https://tex.z-dn.net/?f=%20-%205x%20%2B%202x%20-%202%20%3D%207)
![- 5x + 2x = 7 + 2](https://tex.z-dn.net/?f=%20-%205x%20%2B%202x%20%3D%207%20%2B%202)
![- 3x = 9](https://tex.z-dn.net/?f=%20-%203x%20%3D%209)
![\frac{ - 3x}{ - 3} = \frac{9}{ - 3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%203x%7D%7B%20-%203%7D%20%20%3D%20%20%20%5Cfrac%7B9%7D%7B%20-%203%7D%20)
![x = - 3](https://tex.z-dn.net/?f=x%20%3D%20%20-%203)