Using the binomial distribution, it is found that the expected values are given by:
a) 120.
b) 150.
<h3>What is the binomial probability distribution?</h3>
It is the probability of <u>exactly x successes on n repeated trials, with p probability</u> of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
In this problem, for both items, we consider that the number cube is rolled 180 times, hence n = 180.
Item a:
4 of the 6 possible values are greater than 2, hence p = 4/6 = 2/3.
The expected value is given by:
E(X) = 180 x 2/3 = 120.
Item b:
5 of the 6 values are less than 6, hence p = 5/6.
The expected value is given by:
E(X) = 180 x 5/6 = 150.
More can be learned about the binomial distribution at brainly.com/question/24863377
The surface area of the right triangular prism is 270 sq ft
<h3>Total surface ara of the prism</h3>
The total surface area of the prism is the sum of all the area of its faces
For the two triangles
A = 2(0.5bh)
A = bh
A = 7 * 12 = 84 sq.ft
For the two rectangles
A = 2lw
A = 2(6*12)
A = 2 * 72 = 144 sq.ft
For the third triangle;
Area 6ft * 7ft
Area = 42 sq.feet
Taking the sum of the areas
TSA = 84 + 144 + 42
TSA = 270 sq ft
Hence the surface area of the right triangular prism is 270 sq ft
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If you simplify 256 you get 16 you have to square root it
An equation is formed of two equal expressions. The correct option is x+y=557 and Three-fifths(x)+five-sixths(y)=407.
<h3>What is an equation?</h3>
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the total number of pages in the shorter book be represented by x, and the total number of pages in the longer book be represented by y.
Given the total number of pages of the shorter book and the longer book is 557. Therefore, the equation can be written as,
x+y =557
Also, Scott reads Three-fifths of the shorter book and StartFraction 5 Over 6 EndFraction of the longer book, which is equal to 407 pages. Therefore,
(3/5)x + (5/6)y = 407
Hence, the correct option is x+y=557 and Three-fifths(x)+five-sixths(y)=407.
Learn more about Equation:
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