The system of equations is 
Step-by-step explanation:
We can answer this question as follows.
First of all, we call:
t = number of treadmills
b = number of stationary bikes
The two conditions that we have can be translated into equations as follows:
- The gym has a total of 25 treadmills and stationary bikes:
- There are seven more stationary bikes than treadmills:
So the system of equations to solve is
We now solve it in the following way: first, we rewrite the second equation by bringing t on the left side,
Now we add the 1st equation to the 2nd equation:
And therefore,
So, there are 16 stationary bikes and 9 treadmills.
Learn more about systems of equations:
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Answer:
This contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3
Step-by-step explanation:
The given function is
When we differentiate this function with respect to x, we get;
We want to find all values of c in (1,7) such that f(7) − f(1) = f '(c)(7 − 1)
This implies that;
![c-3=\sqrt[3]{63.15789}](https://tex.z-dn.net/?f=c-3%3D%5Csqrt%5B3%5D%7B63.15789%7D)
![c=3+\sqrt[3]{63.15789}](https://tex.z-dn.net/?f=c%3D3%2B%5Csqrt%5B3%5D%7B63.15789%7D)
If this function satisfies the Mean Value Theorem, then f must be continuous on [1,7] and differentiable on (1,7).
But f is not continuous at x=3, hence this hypothesis of the Mean Value Theorem is contradicted.
Answer:
The correct answer is:
r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.
This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).
Answer: possible values of Range will be values that are >=91 or <=998
Step-by-step explanation:
Given that :
Set Q contains 20 positive integer values. The smallest value in Set Q is a single digit value and the largest value in Set Q is a three digit value.
Therefore,
given that the smallest value in set Q is a one digit number :
Then lower unit = 1, upper unit = 9( this represents the lowest and highest one digit number)
Also, the largest value in Set Q is a three digit value:
Then lower unit = 100, upper unit = 999 ( this represents the lowest and highest 3 digit numbers).
Therefore, the possible values of the range in SET Q:
The maximum possible range of the values in set Q = (Highest possible three digit value - lowest possible one digit) = (999 - 1) = 998
The least possible range of values in set Q = (lowest possible three digit value - highest possible one digit value) = (100 - 9) = 91
