Answer:
Gay Lussac's Law - states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature. If you heat a gas you give the molecules more energy so they move faster. This means more impacts on the walls of the container and an increase in the pressure.
Step-by-step explanation: An increase in the number of gas molecules in the same volume container increases pressure. A decrease in container volume increases gas pressure. An increase in temperature of a gas in a rigid container increases the pressure
Let x be the cost of 1 pen
then cost of 1 notebook = x + 8.20
Let y be the number of pens Tan buys
then number of notebooks Tan buys = y/4
She spent $26 more on books than on pens which means
Cost of notebooks - Cost of pens = 26
(x + 8.20) * y/4 - xy = 26
Sinplifying it
(xy + 8.20y)/4 - xy = 26
(xy + 8.20y - 4xy)/4 = 26
8.20y - 3xy = 104
She spent $394 which means
Cost of notebooks + Cost of pens = 394
(x + 8.20) * y/4 + xy = 394
Simplifying it
(xy + 8.20y)/4 + xy = 394
(xy + 8.20y + 4xy)/4 = 394
8.20y + 5xy = 1576
Now, we have two equations,
(1) 8.20y - 3xy = 104
(2) 8.20y + 5xy = 1576
Now we need to find a third equation with either x or y as the subject of any of both the previous equations.
Let's make y the subject of (2) equation
8.20y + 5xy = 1576
y(8.20 + 5X) = 1576
(3) y = 1576/(8.20 + 5x)
Let's substitute the new value of y from (3) into (1) because we rearranged (2) to from (3)
8.20y - 3xy = 104
y(8.20 - 3x) = 104
y = 104/(8.20 - 3x)
1576/(8.20 + 5x) = 104/(8.20 - 3x)
1576 * (8.20 - 3x) = 104 * (8.20 + 5x)
12923.2 - 4728x = 852.8 + 520x
12923.2 - 852.8 = 4728x + 520x
12070.4 = 5248x
12070.4/5248 = x
x = 2.3
Now find the value of y by substituting the value of x in either equation, preferably (3)
y = 1576/(8.20 + 5x)
y = 1576/(8.20 + 5 * (2.3))
y = 80
Therefore cost of 1 notebook = x + 8.20 = 2.3 + 8.20 = $10.50
Answer:
482
Step-by-step explanation:
We can see that the numbers shown resemble an arithmetic sequence because they have a common difference. The formula for the nth term of an arithmetic sequence is:

Where
is the first term,
is the nth term, and
is the common difference. To find the 61st term, all we need is the first term and the common difference. By looking at what given, we can say the first term is 2. Now, to find the common difference, we find the difference of a term from the term before it. In this case we can do
, which is
, or the common difference. Since we have everything we need, it can be plugged into the equation:

So, the 61st term is 482.
Answer:
The second option
Step-by-step explanation:
This is because the more samples she has, the closer her experimental probability will be to the real value.