Lynette has a metal doorstop with the dimensions shown. Each cubic centimeter of the metal in the doorstop has a mass of about 8
.6 grams. Find the volume of the metal in the doorstop. Then find the mass of the doorstop.
(Picture is provided)
(Picture is provided)
2 answers:
Answer:
The answers are:
Volume: 75 cubic centimeters
Mass: 645 grams
Step-by-step explanation:
In order to determine both volume and mass of the doorstop, we have to know the formulas of a triangular prism.
I have attached an image that shows some formulas about triangular prism.
As we see in the image, a triangular prism consists basically in a triangular face and its projection.
So, using the variables and formula of the image:
B=10 cm
H=6 cm
L=2.5 cm
Then, we know the density of the metal that is:
δ=
So, the mass of the doorstop is:
m=δ*V
m=8.6 * 75
m=645 gr
Finally, the volume is 75 and the mass 645 gr
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Answer:
4.01% probability that the cable company will keep the shopping channel.
Step-by-step explanation:
For each subscriber, there are only two possible outcomes. Either they watch the shopping channel at least once a week, or they do not. This means that we can solve this problem using the binomial probability distribution.
However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
The cable company has decided to keep the shopping channel if the sample proportion is greater than 0.27. What is the approximate probability that the cable company will keep the shopping channel, even though the true proportion who watch it is only 0.20?
This probability is 1 subtracted by the pvalue of Z when . So
has a pvalue of 0.9599.
So there is a 1-0.9599 = 0.0401 = 4.01% probability that the cable company will keep the shopping channel.