The formula for conditional probablity states that

Since we know both numerator and denominator, we only need to plug in the values:

Answer:
<em>The angle between their paths when they started is 93°.</em>
Step-by-step explanation:
<u>The Law of Cosines</u>
It relates the length of the sides of a triangle with one of its internal angles.
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:

When the two ships travel in different directions from the same point in the plane, they form an angle we called x in the image below.
Tyler's ship sails a=35 miles and Noah's ship sails for b=42 miles. At some time they are c=56 miles apart.
Since we know the values of all three side lengths, we solve the equation for x:

Substituting values:

Calculating:

Computing the inverse cosine:


The angle between their paths when they started is 93°.
Answer:
47.3 m³
Step-by-step explanation:
The garden shed is made up of a rectangular prism and a pyramid.
<h3><u>Volume of a rectangular prism</u></h3>

<h3><u>Volume of a pyramid</u></h3>
<u />
From inspection of the given diagram, the slant height of the pyramid is 3.5 m.
Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

Therefore:

<h3><u>Volume of the garden shed</u></h3>

Answer:

Step-by-step explanation:






