The solution to a system of equations is the point that the 2 lines of the graph cross each other.
x = 1 and Y =4
Solution is (1,4)
Answer is C.
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4*d^(-3)*d^18 = 4*d^(18-3) = 4*d^(15). The trick here is to combine the exponents.
Another way to write this problem would be:
4*d^18
---------- . Here d^18 divided by d^3 results in d^15, so again the final
d^3 answer is 4*d^15.
Answer:
First blank - A)Total Number of Possible Outcomes
Second blank - B)Number of Winners
Step-by-step explanation:
The exact question is as follows :
We know that,
Probability of an event is equals to Total number of Favorable outcomes divided by Total number of outcomes
So,
P(event) = Number of favorable outcomes ÷ Total Number of Possible Outcomes
As we have to predict the Number of winners of a game
So,
P(Number of winner) = Number of winners ÷ Total number of Contestants
∴ we get
P(event) = Number of favorable outcomes ÷ Total Number of Possible Outcomes
= Number of winners ÷ Total number of Contestants
Answer: option a.
![f(x)=\frac{1}{3} (3)^x](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B3%7D%20%283%29%5Ex)
Explanation:
A <em>shrink</em> of a function is a <em>shrink</em> on the vertical direction. It means that for a certain value of x, the new function will have a lower value, in the intervals where the function is positive, or a higher value, in those intervals where the function is negative. This is, the image of the new function is shortened in the vertical direction.
That is the reason behind the rule:
- given f(x), the graph of the function a×f(x), when a > 1, represents a vertical stretch of f(x),
- given f(x), the graph of the function a×f(x), when a < 1, represents a vertical shrink of f(x).
So, we just must apply the rule: to find a shrink of an exponential growth function, multiply the original function by a scale factor less than 1.
Since it <em>is a shrink of</em> <em>an exponential growth function</em>, the base must be greater than 1. Among the options, the functions that meet that conditon are a and b:
![a. f(x)=\frac{1}{3} (3)^x \\ \\ b.f(x) = 3(3)^x](https://tex.z-dn.net/?f=a.%20f%28x%29%3D%5Cfrac%7B1%7D%7B3%7D%20%283%29%5Ex%20%5C%5C%20%5C%5C%20b.f%28x%29%20%3D%203%283%29%5Ex)
Now, following the rule it is the function with the fraction (1/3) in front of the exponential part which represents a <em>shrink of an exponential function</em>.