If Johnny had 20 complete living room outfits, disregard color scheme, how many different sets of five complete outfits could be
1 answer:
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Answer:
Step-by-step explanation:
Given
close
fail to close
First, calculate the value of q
Using complement rule
So, we have:
and
Solving (a): Fails to close on the 4th attempt
This means that he closes the first three attempts. The event is represented as: p p p q
So, we have:
Solving (b): He closes for the first time on the 3rd attempt
This means that he fails to close the first two attempts. The event is represented as: q q p
So, we have:
Solving (c): First he closes is his 2nd attempt
This means that he fails to close the first. The event is represented as: q p
So, we have:
Solving (d): The first he close is one of his 3 attempts
To do this, we make use of complement rule
The event that he does not close any of his first three attempts is: q q q
The probability is:
The opposite is that the first he closes is one of the first three
So, we have:
--- complement rule
Answer:
distance: 320.624 miles
direction: 43.576°
Step-by-step explanation:
The speed and direction can be found by adding the given vectors.
... 320∠40° + 20∠130°
... = (320·cos(40°), 320·sin(40°)) + (20·cos(130°), 20·sin(130°))
... = (245.134, 205.692) +(-12.856, 15.321) = (232.278, 221.013)
The magnitude of the vector with these components is found using the Pythagorean theorem. The direction is found using the arctangent function.
... = √(232.278² +221.013²)∠arctan(221.013/232.278)
... = 320.624∠43.576°
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A suitable vector or graphing calculator can do this easily. In the screenshot of a TI-84 app below, the variable D has the value π/180. The display mode is set to degrees.
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<em>Comment on coordinate systems</em>
Navigation directions are generally measured clockwise from North. Angles in the usual x-y coordinate plane are measured counterclockwise from +x (effectively, East). You can consider the geometry of the navigation coordinate system to be a reflection across the line y=x of the geometry of the usual x-y coordinate system.
Reflection does not change lengths or angles within a given geometry. Hence, we can use all the usual tools of vector calculation using navigation coordinates, without bothering to translate them back and forth to x-y coordinates.
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Problems like this generally can be worked using the Law of Cosines and the Law of Sines, too. It generally helps to draw a diagram so you can find the values of the angles betwee the various vectors more easily.
