Andrea brought $54.00 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was one-sixths as mu
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Answer:
Step-by-step explanation:
Component form of a vector is given by , where
represents change in x-value and
represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector
, the magnitude is
.
190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being , one leg being
, and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.
In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.
Therefore, we have:
To find the other leg, , we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:
Verify that
Therefore, the component form of this vector is
Let 
denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by 
, each independently and identically distributed with distribution 
.
You want to find
Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to
Recall that if
, then the sampling distribution 
with 
being the size of the sample.
Transforming to the standard normal distribution, you have
so that in this case,
and the probability is equivalent to
You want to find
Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to
Recall that if
Transforming to the standard normal distribution, you have
so that in this case,
and the probability is equivalent to