Answer:
So, the number of combinations is 57600.
Step-by-step explanation:
From Exercise we have
5 different history textbooks
4 different science textbooks
For the place in the middle we have 4 books so the number of combinations for that place is 4.
For the places at the end of the shelf I have 5 books, I need 2, so the number is a combination:
2· \frac{5!}{(5-2)!·2!}=2·10=20
For the 6 places on the shelf I have 6 books so the number is a combination 6!=720
So, the number of combinations is:
4·20·720=57600.
9 student because if each row holds nine then the last row must hold nine
Answer:
Henry's balloon was farther from the town at the beginning and Henry's balloon traveled more quickly.
Step-by-step explanation:
The distance of Tasha's balloon from the town is represented by the function y = 8x+ 20 ............. (1)
Where y is the distance in miles from the town and x represents the time of fly in hours.
So, at the start of the journey i.e. at x = 0, y = 20 miles {From equation (1)} from the town.
Again, Tasha's balloon is traveling at a rate of 8 miles per hour.
Now, Henry's balloon begins 30 miles from the town and is 48 miles from the town after 2 hours.
So, Henry's balloon traveling with the speed of miles per hour.
Therefore, Henry's balloon was farther from the town at the beginning i.e. 30 miles from the town. And Henry's balloon traveled more quickly i.e at the rate of 9 miles per hour. (Answer)
Answer:
17.11%
Step-by-step explanation:
since 43.2 months is the mean, and the standard deviation is 7.7 months
that means if we take the z score:
z=(36-43.2)/7.7
now that we know how many standard deviations you are away from the mean: -0.9351
using the zscore table you can find the proportion, or you can use the calculator if you have one that can do that.
you get 0.1711 which in percentages is 17.11%
Answer:
0.0062 = 0.62% probability of this occurring
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, we have that:
![\mu = 2000, \sigma = 20](https://tex.z-dn.net/?f=%5Cmu%20%3D%202000%2C%20%5Csigma%20%3D%2020)
a. If the process overfills the bottle by more than 50 milliliters, the overflow will cause a machine malfunction. What is the probability of this occurring
Probability of filling the bottle with more than 2000 + 50 = 2050 milliliters, which is 1 subtracted by the pvalue of Z when X = 2050. 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{2050 - 2000}{20}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B2050%20-%202000%7D%7B20%7D)
![Z = 2.5](https://tex.z-dn.net/?f=Z%20%3D%202.5)
has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability of this occurring