A right triangle has one angle that measures 7°. What is the measure of the other acute angle?
2 answers:
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The question is missing the options and the the drawing of the prism. Here is the complete question and the drawing is in the attachment.
A prism is created using 2 regular pentagons as bases. The apothem of each pentagon is 2.8 centimeters.
Which expression represents the volume of the prism, in cubic centimeters?
a) 9x² + 7x
b) 14x² + 7x
c) 16x² + 14x
d) 28x² + 14x
Answer: b) 14x² + 7x
Step-by-step explanation: The formula to calculate the volume of a prism is:
V = Ab*h
Where
Ab is area of the base
h is the height of the prism
The base is a regular pentagon, which means that all the 5 sides of it is the same. The apothem of a pentagon is a line segment from the center of the pentagon to its side. The area is:
Ap =
where:
P is perimeter
a is apothem
Area of base:
Ab =
Ab =
Ab = 7x
h = 2x+1
Volume of the prism:
V = Ab.h
V = 7x.(2x+1)
V = 14x² + 7x
The expression that represents the volume of this prism is V = 14x² + 7x cubic inches.
Using the z-distribution, it is found that the correct option regarding the question in the problem is given by:
B. No, since the confidence interval includes values less than 50%, his opponent may get more votes.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
In this problem, we have a 95% confidence level, hence, z is the value of Z that has a p-value of
, so the critical value is z = 1.96.
In this problem, the parameters are given as follows:
Hence, the bounds are given by:
The lower bound is below 0.5, hence option B is correct.
More can be learned about the z-distribution at brainly.com/question/25890103
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