Answer:
7.2 units
Step-by-step explanation:
Coordinates of city A = (0, 0)
Coordinates of city B = (6, 4)
Use the distance formula to find the distance between the two cities as follows:
![AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=%20AB%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%20)
Let,
![A(0, 0) = (x_1, y_1)](https://tex.z-dn.net/?f=%20A%280%2C%200%29%20%3D%20%28x_1%2C%20y_1%29%20)
![B(6, 4) = (x_2, y_2)](https://tex.z-dn.net/?f=%20B%286%2C%204%29%20%3D%20%28x_2%2C%20y_2%29%20)
Plug in the values into the formula
![AB = \sqrt{(6 - 0)^2 + (4 - 0)^2}](https://tex.z-dn.net/?f=%20AB%20%3D%20%5Csqrt%7B%286%20-%200%29%5E2%20%2B%20%284%20-%200%29%5E2%7D%20)
![AB = \sqrt{(6)^2 + (4)^2}](https://tex.z-dn.net/?f=%20AB%20%3D%20%5Csqrt%7B%286%29%5E2%20%2B%20%284%29%5E2%7D%20)
![AB = \sqrt{36 + 16} = \sqrt{52}](https://tex.z-dn.net/?f=%20AB%20%3D%20%5Csqrt%7B36%20%2B%2016%7D%20%3D%20%5Csqrt%7B52%7D%20)
(nearest tenth)
Leonard method is likely to to give an accurate estimate of the mean since his sample was randomly selected from campers at his camp.
hope this helped
Answer:
40%
Step-by-step explanation:
The whole rectangle is split into 5 parts. Two out of 5 parts are shaded.
Set up a fraction:
![\frac{\text{Shaded}}{\text{Whole}}=\frac{2}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BShaded%7D%7D%7B%5Ctext%7BWhole%7D%7D%3D%5Cfrac%7B2%7D%7B5%7D)
Convert into a decimal:
![\frac{2}{5}= 0.4](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%3D%200.4)
Multiply the decimal by 100 to get the percent:
![0.4*100=40](https://tex.z-dn.net/?f=0.4%2A100%3D40)
So, forty percent of the rectangle is shaded.
Hope this helps.
Answer:
![t= \frac{125}{38} s](https://tex.z-dn.net/?f=t%3D%20%5Cfrac%7B125%7D%7B38%7D%20s)
Step-by-step explanation:
We are given the temperature inside the machine from startup until 10 seconds later, the formula is:
![h(t)= 42 \cdot t +1 - 4\cdot t +2 (degrees \, C)](https://tex.z-dn.net/?f=h%28t%29%3D%2042%20%5Ccdot%20t%20%2B1%20-%204%5Ccdot%20t%20%2B2%20%20%28degrees%20%5C%2C%20C%29)
We want to know at what time t the temperature inside the machine will be equal to 128 °C.
So we set:
![h(t)=128](https://tex.z-dn.net/?f=h%28t%29%3D128)
![42\cdot t+1-4\cdot t+2=128](https://tex.z-dn.net/?f=42%5Ccdot%20t%2B1-4%5Ccdot%20t%2B2%3D128)
Now, we rearrange the equation to keep terms with t on the left hand side and terms without t on the right hand side
![42\cdot t-4\cdot t=128-1-2](https://tex.z-dn.net/?f=42%5Ccdot%20t-4%5Ccdot%20t%3D128-1-2)
and we simplify:
![(42-4)\cdot t= 128-2-1= 125](https://tex.z-dn.net/?f=%2842-4%29%5Ccdot%20t%3D%20128-2-1%3D%20125)
![38 \cdot t = 125](https://tex.z-dn.net/?f=38%20%5Ccdot%20t%20%3D%20125)
now it's easy to solve for t:
![t=\frac{125}{38}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B125%7D%7B38%7D)
And thus we arrive to the solution.