Answer: a = 18
explanation:
2(a + 10) = 56 -> distribute the 2
2a + 20 = 56 -> subtract 20 from both sides
2a = 56 - 20
2a = 36 -> divide both sides by 2
a = 18
Answer:
The actress has the more extreme age because
Step-by-step explanation:
Given
Male Athletes:
![x = 35](https://tex.z-dn.net/?f=x%20%3D%2035)
![\=x = 42.1](https://tex.z-dn.net/?f=%5C%3Dx%20%3D%2042.1)
![SD = 6.6](https://tex.z-dn.net/?f=SD%20%3D%206.6)
Female Athletes
![x = 54](https://tex.z-dn.net/?f=x%20%3D%2054)
![\=x = 34.3](https://tex.z-dn.net/?f=%5C%3Dx%20%3D%2034.3)
![SD = 10.1](https://tex.z-dn.net/?f=SD%20%3D%2010.1)
Required
Determine which athlete had more extreme age
To do this, we simply calculate the standard z score using
![z = \frac{x - \=x}{SD}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7Bx%20-%20%5C%3Dx%7D%7BSD%7D)
For the actor:
![z = \frac{35 - 42.1}{6.6}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B35%20-%2042.1%7D%7B6.6%7D)
![z = \frac{-7.1}{6.6}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B-7.1%7D%7B6.6%7D)
![z = 1.0758](https://tex.z-dn.net/?f=z%20%3D%201.0758)
For the actress:
![z = \frac{54 - 34.3}{10.1}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B54%20-%2034.3%7D%7B10.1%7D)
![z = \frac{19.7}{10.1}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B19.7%7D%7B10.1%7D)
![z = 1.950](https://tex.z-dn.net/?f=z%20%3D%201.950)
Comparing both z values;
The actress has the more extreme age because
- <em>It has a positive z value</em>
- <em>Its z value is greater than that of the actor</em>
<em></em>
The number of units produced by the worker during t hours of work can be modelled by the following function:
![N(t)=100t e^{(-0.5t)}](https://tex.z-dn.net/?f=N%28t%29%3D100t%20e%5E%7B%28-0.5t%29%7D%20)
To find the number of units produced during first 3 hours, we can substitute 3 for t. This will give us the number of units produced by the worker during first 3 hours.
![N(3)=100(3) e^{-0.5(3)} = 67](https://tex.z-dn.net/?f=N%283%29%3D100%283%29%20e%5E%7B-0.5%283%29%7D%20%3D%2067)
Thus the worker will produce 67 units during the first 3 hours of the work.
Answer:
Step-by-step explanation:
1) a variable term contains a variable. If x is a variable
5x is an example of a variable therm
2) a constant therm is not a variable
3 is an example
3) for example when a number multiply a sum or a difference between a constant and a variable
Example:
2(x-3) = 5(x+4)
4) one solution: only if x is equal to 0 the equation is true
5) no solution: the equation can’t be true for ever value of the variable
6) infinite solutions: the equation is ever true for every value of the variable