Answer:
![\log_4 (x + 2) = \dfrac{\log (x + 2)}{\log 4}](https://tex.z-dn.net/?f=%20%5Clog_4%20%28x%20%2B%202%29%20%3D%20%5Cdfrac%7B%5Clog%20%28x%20%2B%202%29%7D%7B%5Clog%204%7D%20)
Step-by-step explanation:
Change of base formula:
![\log_a x = \dfrac{\log_b x}{\log_b a}](https://tex.z-dn.net/?f=%20%5Clog_a%20x%20%3D%20%5Cdfrac%7B%5Clog_b%20x%7D%7B%5Clog_b%20a%7D%20)
Changing to base 10:
![\log_4 (x + 2) = \dfrac{\log (x + 2)}{\log 4}](https://tex.z-dn.net/?f=%20%5Clog_4%20%28x%20%2B%202%29%20%3D%20%5Cdfrac%7B%5Clog%20%28x%20%2B%202%29%7D%7B%5Clog%204%7D%20)
Answer:
$0.25
Step-by-step explanation:
3.75/15 = 0.25
Answer:
4
Step-by-step explanation:
Let the number be x.
3 + 4x = 19
4x = 19 - 3
= 16
x = 16 ÷ 4
x = 4
The number is 4.
Answer:
18 times
Step-by-step explanation:
if you roll a number cube 54 times about how many times do you expect to roll a number less than 5? So you don't want a 5 or a 6. Then in your 54 tries, if the 5 or 6 can come up 18 times, what are you left with for the other possibility?
Answer:
0.6443 = 64.43% of the business travelers will have to stoop
Step-by-step explanation:
Problems of normally distributed samples are solved using 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 problem, we have that:
Each feet is 12 inches
So
5'9'' = 5*12 + 9 = 69
5'10'' = 5*12 + 10 = 70
![\mu = 70, \sigma = 2.7](https://tex.z-dn.net/?f=%5Cmu%20%3D%2070%2C%20%5Csigma%20%3D%202.7)
What percentage of the business travelers will have to stoop?
This is 1 subtracted by the pvalue of Z when X = 69. So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{69 - 70}{2.7}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B69%20-%2070%7D%7B2.7%7D)
![Z = -0.37](https://tex.z-dn.net/?f=Z%20%3D%20-0.37)
has a pvalue of 0.3557.
1 - 0.3557 = 0.6443
0.6443 = 64.43% of the business travelers will have to stoop