Assuming the volume of a trigonal prism, who has a side of 10cm and a length of 20 cm, is 866cm^3, what is its surface area?
1 answer:
The surface area of the triangular prism is 686.6 cm².
Step-by-step explanation:
Step 1:
The volume of a triangular prism can be determined by multiplying its area of the triangular base with the length of the prism.
The base triangle has a base length of 10 cm and assume it has a height of h m.
The volume of the prism
The height of the triangle is 8.66 cm.
Step 2:
The surface area of the triangle is obtained by adding all the areas of the shapes in the prism. There are 2 triangles and 3 rectangles in a triangular prism.
The triangles have a base length of 10 cm and a height of 8.66 cm. A triangles area is half the product of its base length and height.
The rectangles all have a length of 20 cm and a width of 10 cm. The area of a rectangle is the product of its length and width.
The area of the 2 triangles
The area of the 3 rectangle
Step 3:
The surface area of the triangular prism
The surface area of the prism is 686.6 cm².
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Answer:
a) We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:
Null hypothesis:
Alternative hypothesis:
Right tailed test
b)
c) So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3
Step-by-step explanation:
Part a: Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:
Null hypothesis:
Alternative hypothesis:
Right tailed test
When we conduct a proportion test we need to use the z statisitc, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
For this case the statistic is given by
Part b: Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
Part c
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3