A bacteria colony increases exponentially every day. There are 24 bacteria on the third day. The bacteria started with only three individuals. How By how much does the bacteria multiply each day?
We know that y=3 when x = 0, and that the bacteria increase exponentially each day. We want to find the base, using our info for day 3 and day 0.
Equation:
24 = 3 * b^3 Divide both sides by 3
8 = b^3 Take the cubed root of each side
2 = b
The bacteria double each day.
Formula:
y = 3* 2^x
The equation we use here is:
![(0.85)x +(1.00)y = (0.94)(x + y)](https://tex.z-dn.net/?f=%280.85%29x%20%2B%281.00%29y%20%3D%20%280.94%29%28x%20%2B%20y%29)
x is for the number of games he played on first day, y is the games on second day. The coefficients are the decimal form of percentages.
Simplify:
![0.85x + y = 0.94x + 0.94y \\ \\ 0.06y = 0.09x \\ \\ \frac{6y}{100} = \frac{9x}{100} \\ \\ 6y = 9x \\ \\ 2y = 3x](https://tex.z-dn.net/?f=0.85x%20%2B%20y%20%3D%200.94x%20%2B%200.94y%20%5C%5C%20%5C%5C%200.06y%20%3D%200.09x%20%5C%5C%20%5C%5C%20%5Cfrac%7B6y%7D%7B100%7D%20%3D%20%5Cfrac%7B9x%7D%7B100%7D%20%5C%5C%20%5C%5C%206y%20%3D%209x%20%5C%5C%20%5C%5C%202y%20%3D%203x)
To find x we need to use the ratio. We have 85/100 as the first day's ratio and because the games needs to be whole, we can simplify this as 17/20. So in first day, he played at least 20 games and won 17 of them.
When we plug the 20 into the equation as x:
![2y = 3 \times 20 \\ \\ 2y = 60 \\ \\ y = 30](https://tex.z-dn.net/?f=2y%20%3D%203%20%5Ctimes%2020%20%5C%5C%20%5C%5C%202y%20%3D%2060%20%5C%5C%20%5C%5C%20y%20%3D%2030)
So he needs to play at least 30 games in order to get his score to 94%.
Answer:
b. II and III
Step-by-step explanation:
A graph is a data presentation that has two axis - x and y, divided into appropriate scales.
A scale is used to divide given units into equal parts. It is crucial to and used to create uniformity in drawing of graphs. Choosing a good scale to represent an information on a graph is vital to avoid confusion. This can be done by considering the variations in the values forming the data.
In the question, the single graph shows an information about the bear population in two national parks. Thus, the scale of the y-axis must be adjusted and the identity of the two parks be more differentiated so as to make the graph less misleading.
9514 1404 393
Answer:
- n = (s/m) -r
- n = (s -mr)/m
Step-by-step explanation:
1. Undo the operations done to n, in reverse order. Here, n has r added and the sum is multiplied by m. First we divide by m, then we subtract r.
m(n+r) = s . . . given
n +r = s/m . . . divide by m
n = (s/m) -r . . . subtract r
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2. Eliminate the parentheses, then proceed as above. Subtract the added term, then divide by the coefficient of n.
m(n+r) = s
mn +mr = s . . . eliminate parentheses
mn = s -mr . . . subtract the added term
n = (s -mr)/m . . . divide by the coefficient of n