The probability distribution histogram shows the number of days a book is checked out of the library. What is P(9≤X<18)?
1 answer:
Answer:
Step-by-step explanation:
- The probability distribution provides the probabilities of occurrence of different possible outcomes, in this case we want to know what is the probability that the variable X takes any value between 9 and 18.
- The probability of occurrence is shown in the vertical axis of the graph. We want to know what is the probability of finding values of X between 9 and 18, then we should add up the probabilities between these two values , which means adding
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Geometric shapes are mathematical shapes that include squares and triangles
<h3>How to prove the shape is a square</h3>The side lengths of a square are congruent, and the adjacent sides are perpendicular.
So, we start by calculating the side lengths using the following distance formula
Using the above formula, we have:
The above shows that the side lengths of the square are congruent.
Next, calculate the slope of the sides using:
So, we have:
Notice that the opposite slopes are congruent, and the adjacent slopes are opposite reciprocal.
The above highlight, and the equal side lengths show that the figure (1) is a square
<h3>How to prove the shape is a right isosceles triangle</h3>The legs of a right isosceles triangle are congruent, and the legs are perpendicular.
So, we start by calculating the lengths of the legs using the following distance formula
Using the above formula, we have:
The above shows that the legs of the right isosceles triangle are congruent.
Next, calculate the slope of the legs using:
So, we have:
Notice that the slopes are opposite reciprocal.
The above highlight, and the equal legs show that the figure (2) is a right isosceles triangle
Read more about geometric shapes at:
Answer:
The capacity of the mug = cups
Step-by-step explanation:
Given - A mug is 1/8 full. The mug contains 1/6 of a cup of water.
To find - Find the capacity of the mug. Write the answer as a fraction or mixed number
Proof -
Let the capacity of water = x
Given that,
A mug is full of water
⇒Total cups of water in the mug =
Now,
Given that, The mug contains of a cup of water.
∴ we get
=
⇒x = × 8
=
= =
⇒x =
∴ we get
The capacity of the mug = cups