Answer:
![y=-3.2x+18.5](https://tex.z-dn.net/?f=y%3D-3.2x%2B18.5)
Step-by-step explanation:
Let
x ----> the number of days
y ----> the amount of money remaining in dollars
we have the points
(2,12.10) and (5,2.50)
step 1
Find the slope m
The formula to calculate the slope between two points is equal to
substitute the values
----> is negative because is a decreasing function
step 2
Find the equation of the line in slope intercept form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where
m is the slope
b is the y-intercept
with the slope m and the point (2,12.10) find the value of b
substitute
![12.10=-3.2(2)+b](https://tex.z-dn.net/?f=12.10%3D-3.2%282%29%2Bb)
solve for b
![12.10=-6.4+b](https://tex.z-dn.net/?f=12.10%3D-6.4%2Bb)
![b=12.10+6.4](https://tex.z-dn.net/?f=b%3D12.10%2B6.4)
![b=18.5](https://tex.z-dn.net/?f=b%3D18.5)
substitute
![y=-3.2x+18.5](https://tex.z-dn.net/?f=y%3D-3.2x%2B18.5)
She will need a minimum of 38 hours, at 38 hours she will make 456, plus the 300 she already has, so that in total is 756.
The odds against the event are 2/6
The odds for the event are 4/6
Answer:
x=1/5
Step-by-step explanation:
Answer:
You should expect to find the middle 98% of most head breadths between 3.34 in and 8.46 in.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
![\mu = 5.9, \sigma = 1.1](https://tex.z-dn.net/?f=%5Cmu%20%3D%205.9%2C%20%5Csigma%20%3D%201.1)
In what range would you expect to find the middle 98% of most head breadths?
From the: 50 - (98/2) = 1st percentile.
To the: 50 + (98/2) = 99th percentile.
1st percentile:
X when Z has a pvalue of 0.01. So X when Z = -2.327.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-2.327 = \frac{X - 5.9}{1.1}](https://tex.z-dn.net/?f=-2.327%20%3D%20%5Cfrac%7BX%20-%205.9%7D%7B1.1%7D)
![X - 5.9 = -2.327*1.1](https://tex.z-dn.net/?f=X%20-%205.9%20%3D%20-2.327%2A1.1)
![X = 3.34](https://tex.z-dn.net/?f=X%20%3D%203.34)
99th percentile:
X when Z has a pvalue of 0.99. So X when Z = 2.327.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![2.327 = \frac{X - 5.9}{1.1}](https://tex.z-dn.net/?f=2.327%20%3D%20%5Cfrac%7BX%20-%205.9%7D%7B1.1%7D)
![X - 5.9 = 2.327*1.1](https://tex.z-dn.net/?f=X%20-%205.9%20%3D%202.327%2A1.1)
![X = 8.46](https://tex.z-dn.net/?f=X%20%3D%208.46)
You should expect to find the middle 98% of most head breadths between 3.34 in and 8.46 in.