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3 years ago

A 300-page book is 10 inches long, 8 inches wide, and 3 4 inches tall. What is the volume of 100 pages of the book?

Mathematics

2 answers:

jenyasd209 [6]3 years ago

6 0

Answer:

20 inches cubed

Step-by-step explanation:

The only thing that will change if we want to find the volume of 100 pages of the book will be the height. Previously for the 300 pages, the height was 3/4 inches. Now, however, it will be a third of that because 100 = 300/3. So, the new height will be: (3/4) / 3 = 1/4 inches.

The length of 10 inches and width of 8 inches will still be the same. The volume of a rectangular prism (the shape of the book) is: $V=lwh$ , where $l$ is the length, w is the width, and h is the height.

h = 1/4

w = 8

$l$ = 10

V = 10 * 8 * (1/4) = 80/4 = 20 inches cubed

The volume is thus 20 inches cubed.

Hope this helps!

katen-ka-za [31]3 years ago

5 0

Answer:

20 in³

Step-by-step explanation:

Volume of 300 pages:

10 × 8 × 3/4

When the no. of pages change, only the thickness of the book changes:

Volume = 10 × 8 × ¼

= 20 in³

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The volume of the pyramid is not equal to the volume of the cylinder.

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Now, the volume of a right cylinder is πr²h and that of a right circular cone is 1/3 πr²h.

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Use the formula for the probability of two dependent events P(A and B) to derive the conditional probability formula for P(B | A

gregori [183]

The conditional probability formula for P(B | A) has been derived from two dependent events P(A and B).

<h3>What is said to be dependent events?</h3>

When the outcome from one event influences the outcome of the other, two events are referred to as dependent.

Dependent events in probability are generally real-life events that depend on another event to occur.
Sam, for example, did well on his math test because he prepared; the gym class used to have a football session even though Adam brought a football from home.
When you look at these examples, you will realize that one occurrence is dependent on the other.

Derivation of conditional probability from two dependent events P(A and B) is-

The probability multiplication rule is used to derive the conditional probability formula, P(A and B) = P(A)×P(B|A).

This rule is also known as P(AB). The Union symbol (∪) represents "and," as in event A occurring and event B occurring.

Step 1: Write the multiplication rule down:

P(A and B) = P(A)*P(B|A)

Step 2: P(A) divides both sides of the equation:

P(A and B) / P(A) = P(A)*P(B|A) / / P(A)

Step 3: On the right side of the equation, cancel P(A):

P(A and B) / P(A) = P(B|A)

Step 4: Rewrite the equation as follows:

P(B|A) = P(A and B) / P(A)

Therefore, P(B | A) conditional probability formula is compiled from two dependent events P (A and B).

To know more about the conditional probability, here

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1 year ago

Calculate the annual interest for a $10,000 Treasury bond with a current yield of 3% that is quoted at 106 points.

Sergio [31]

Answer:

$318

Step-by-step explanation:

The treasury bond is $10,000

The current yield is 3%

= 3/100

=0.03

It is quoted at 106 points

The first step is to calculate the price of the bond

Price of the bond= $10,000×106/100

= $10,000×1.06

= $10,600

Therefore the annual interest can be calculated as follows

Annual interest= $10,600×0.03

= $318

Hence the annual interest is $318

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3 years ago