Recall that the volume of a regular prism is given by the area of the base times the height.
Given that the base of the prism is a regular pentagon with an apothem of 2.8 centimeters.
The pentagon consist of 5 isosceles triangles with the apothem as the height and the side of the pentagon as the base.
Recall that the are of a triangle is given by 1/2 base times height.
Thus the area of of the pentagon base of the prism is given by
Therefore, the volume of the prism is given by
Answer:
x= -1 and x =0
Step-by-step explanation:
all work is shown and pictured
Answer:
0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the z-score of a measure X is given by:
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 p-value, we get the probability that the value of the measure is greater than X.
Mean 490 mg and variance of 400.
This means that 
What is the probability that a randomly selected pill contains at least 500 mg of minerals?
This is 1 subtracted by the p-value of Z when X = 500. So
has a p-value of 0.6915.
1 - 0.6915 = 0.3085
0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals
x= length, y=width
Both the length and width were increased by 60% so now they are:
1.6x and 1.6y
Then they were both reduced by 25% so now they are 75%(100-25) of their previous size so they are:
0.75(1.6x) and 0.75(1.6y)
Their area would be length * width so it would be:
0.75(1.6x) * 0.75(1.6y)
Simplified this would be:
1.2x * 1.2y
Simplified more it would be :
1.44xy which is also 144% of xy which is a 44% increase of the original area (xy)
So the answer is:
44%
Answer:
x = -9
Step-by-step explanation:
1.4 - 0.2x = 3.2
0.2x = 3.2 - 1.4
0.2x= 1.8
x= -9
