Answer:
![P(38.6](https://tex.z-dn.net/?f=%20P%2838.6%20%3CX%20%3C57.8%29)
And we can assume a normal distribution and then we can solve the problem with the z score formula given by:
![z=\frac{X -\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7BX%20-%5Cmu%7D%7B%5Csigma%7D)
And replacing we got:
![z=\frac{38.6- 45}{16}= -0.4](https://tex.z-dn.net/?f=%20z%3D%5Cfrac%7B38.6-%2045%7D%7B16%7D%3D%20-0.4)
![z=\frac{57.8- 45}{16}= 0.8](https://tex.z-dn.net/?f=%20z%3D%5Cfrac%7B57.8-%2045%7D%7B16%7D%3D%200.8)
We can find the probability of interest using the normal standard table and with the following difference:
![P(-0.4](https://tex.z-dn.net/?f=%20P%28-0.4%20%3Cz%3C0.8%29%3D%20P%28z%3C0.8%29%20-P%28z%3C-0.4%29%20%3D%200.788-0.345%3D%200.443)
Step-by-step explanation:
Let X the random variable who represent the expense and we assume the following parameters:
![\mu = 45, \sigma 16](https://tex.z-dn.net/?f=%5Cmu%20%3D%2045%2C%20%5Csigma%2016)
And for this case we want to find the percent of his expense between 38.6 and 57.8 so we want this probability:
![P(38.6](https://tex.z-dn.net/?f=%20P%2838.6%20%3CX%20%3C57.8%29)
And we can assume a normal distribution and then we can solve the problem with the z score formula given by:
![z=\frac{X -\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7BX%20-%5Cmu%7D%7B%5Csigma%7D)
And replacing we got:
![z=\frac{38.6- 45}{16}= -0.4](https://tex.z-dn.net/?f=%20z%3D%5Cfrac%7B38.6-%2045%7D%7B16%7D%3D%20-0.4)
![z=\frac{57.8- 45}{16}= 0.8](https://tex.z-dn.net/?f=%20z%3D%5Cfrac%7B57.8-%2045%7D%7B16%7D%3D%200.8)
We can find the probability of interest using the normal standard table and with the following difference:
![P(-0.4](https://tex.z-dn.net/?f=%20P%28-0.4%20%3Cz%3C0.8%29%3D%20P%28z%3C0.8%29%20-P%28z%3C-0.4%29%20%3D%200.788-0.345%3D%200.443)
To solve, set an equation:
472=0.8x
Divide both sides by 0.8
472/0.8=0.8x/0.8
x=590
Answer: The original price was $590
Answer:
C(t)=5000 -10t
Step-by-step explanation:
There are many examples in the real world of relationships that are functions.
For example, imagine a tank full of water with a capacity of 5000 liters, this tank has a small hole, by which 10 liters of water are lost every hour.
If we call C the amount of water in the tank as a function of time, then we can write the following equation for C:
![C(t)=C_{0}-at\\](https://tex.z-dn.net/?f=C%28t%29%3DC_%7B0%7D-at%5C%5C)
Where:
C (t): Amount of water in the tank as a function of time
: Initial amount of water in the tank at time t = 0
a: amount of water lost per hour
t: time in hours
Then the equation is:
The graph of C (t) is a line of negative slope. This relation is a function since for each value of t there is a single value of C.
Its domain is the set of all positive real numbers t between [0,500]
Because the time count starts at t = 0 when the tank is full and ends at t = 500 when empty
Its Range is the set of all positive real numbers C between [0,5000] Because the amount of water in the tank can never be less than zero or greater than 5000Litres
Answer:
3
Step-by-step explanation:
by question
5x+2=17
5×=15
×=3
The probability that the first two votes drawn are both for candidate a is given by:
3C2/5C2 = 3/10
Having drawn two votes for candidate a on the first two draws, there are 2 votes for candidate b and one vote for candidate a remaining. The probability that a vote for candidate b will be drawn on the third draw is:
2/3.
After the first three draws, there reains one vote for candidate a and one vote for candidate b. The probability that a vote for candidate a will be drawn on the fourth draw is:
1/2.
The probability of the ordering aabab is therefore given by:
![\frac{3}{10}\times\frac{2}{3}\times\frac{1}{2}=\frac{6}{60}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B10%7D%5Ctimes%5Cfrac%7B2%7D%7B3%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B6%7D%7B60%7D)
The answer is: 0.1.