Answer:
<u>39.5 miles/gallon.</u>
Step-by-step explanation:
6 gallons of gas used to drive 237 miles
The rate of her car uses gas in miles per gallon =

Which mean the car will consume 1 gallon for each 39.5 miles.
We know that 1 yard equals 3 feet, therefore, we have:
65(3) + 2
= 195 + 2
= 197
therefore, 65 yards and 2 feet equals 197 feet
Answer:
the time taken for the radioactive element to decay to 1 g is 304.8 s.
Step-by-step explanation:
Given;
half-life of the given Dubnium = 34 s
initial mass of the given Dubnium, m₀ = 500 grams
final mass of the element, mf = 1 g
The time taken for the radioactive element to decay to its final mass is calculated as follows;
![1 = 500 (0.5)^{\frac{t}{34}} \\\\\frac{1}{500} = (0.5)^{\frac{t}{34}}\\\\log(\frac{1}{500}) = log [(0.5)^{\frac{t}{34}}]\\\\log(\frac{1}{500}) = \frac{t}{34} log(0.5)\\\\-2.699 = \frac{t}{34} (-0.301)\\\\t = \frac{2.699 \times 34}{0.301} \\\\t = 304.8 \ s](https://tex.z-dn.net/?f=1%20%3D%20500%20%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B34%7D%7D%20%5C%5C%5C%5C%5Cfrac%7B1%7D%7B500%7D%20%3D%20%20%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B34%7D%7D%5C%5C%5C%5Clog%28%5Cfrac%7B1%7D%7B500%7D%29%20%3D%20log%20%5B%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B34%7D%7D%5D%5C%5C%5C%5Clog%28%5Cfrac%7B1%7D%7B500%7D%29%20%20%3D%20%5Cfrac%7Bt%7D%7B34%7D%20log%280.5%29%5C%5C%5C%5C-2.699%20%3D%20%5Cfrac%7Bt%7D%7B34%7D%20%28-0.301%29%5C%5C%5C%5Ct%20%3D%20%5Cfrac%7B2.699%20%5Ctimes%2034%7D%7B0.301%7D%20%5C%5C%5C%5Ct%20%3D%20304.8%20%5C%20s)
Therefore, the time taken for the radioactive element to decay to 1 g is 304.8 s.
Answer:

Step-by-step explanation:

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You cannot add row 2 to column 3 because they have different dimensions. You can do any of the other operations, but the only one that makes any sort of sense is ...
Multiply row 2 by -1 and add it to row 3
_____
It makes no sense to multiply a row by zero. That makes the entire row zero and makes the matrix useless for finding any sort of solution.
You can switch columns, but that doesn't get you any closer to a solution here.
If I were trying to find a solution, I might
switch rows 1 and 2
multiply the new row 1 by -3 and add it to the new row 2
multiply the new row 1 by 2 and add it to row 3
This sequence of operations will make the first column [1 0 0], reducing the problem to 2×2 from 3×3.