Answer:
Let's call:
f = price of 1 cup of dried fruit
a = price of 1 cup of almonds
In order to build the linear system, you need to consider that the total price of a bag is given by the sum of the price of cups times the number of cups in each bag, therefore:
Solve for a in first equation:
a = (6 - 3f) / 4
Then substitute in the second equation:
41/2 f + 6 · (6 - 3f) / 4 = 9
41/2 f + 9 - 9/2 f = 9
16 f = 0
f = 0
Now, substitute this value in the formula found for a:
a = (6 - 3·0) / 4
= 3/2 = 1.5
Hence, the cups of dried fruit are free and 1 cup of almond costs 1.5$
Step-by-step explanation:
It's a trick question, you can't measure a dragon, being that they don't exist.
Answer:
7.57
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.
The height of sunflowers is Normally distributed with mean 50 inches and standard deviation 8 inches.
This means that ![\mu = 50, \sigma = 8](https://tex.z-dn.net/?f=%5Cmu%20%3D%2050%2C%20%5Csigma%20%3D%208)
Percent of all sunflowers that are between 35 and 40 inches tall.
As a proportion, this is the pvalue of Z when X = 40 subtracted by the pvalue of Z when X = 35. So
X = 40
![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{40 - 50}{8}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B40%20-%2050%7D%7B8%7D)
![Z = -1.25](https://tex.z-dn.net/?f=Z%20%3D%20-1.25)
has a pvalue of 0.1057
X = 35
![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{35 - 50}{8}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B35%20-%2050%7D%7B8%7D)
![Z = -1.88](https://tex.z-dn.net/?f=Z%20%3D%20-1.88)
has a pvalue of 0.03
0.1057 - 0.03 = 0.0757
As percent: 0.0757*100% = 7.57%