Answer:
The probability that a call last between 4.2 and 4.9 minutes is 0.4599
Step-by-step explanation:
Let X be the length in minutes of a random phone call. X is a normal distribution with mean λ=4.2 and standard deviation σ=0.4. We want to know P(4.2 < X < 4.9). In order to make computations, we will use W, the standarization of X, given by the following formula

We will use
, the cummulative distribution function of W. The values of
are well known and the can be found in the attached file

We conclude that the probability that a call last between 4.2 and 4.9 minutes is 0.4599
Answer:
311.41 degrees
Step-by-step explanation:
If 4 sin Ф = -3 and Ф is between 0 and 360 degrees, then we conclude that Ф must be either in Quadrant III or Quadrant IV (because the sine is negative).
Let's assume we're in Quadrant IV. Then sin Ф = opp / hyp = -3/4; that is, the opp side is negative and has length 3, and the hypo is positive 4.
According to the Pythagorean Theorem, (-3)^2 + x^2 = 4^2, or,
x^2 = 16 - 9 = 7.
Then x is either √7 or -√7.
To find the angle Ф, use the inverse sine function:
Ф = arcsin (-3/4). Using a calculator we get the angle -40.59 degrees, which corresponds to (360 degrees - 40.59 degrees), or 311.41 degrees. We can check this by finding the sine of 311.41 degrees; the result is -0.75, which matches "If 4sintheta = -3."
Answer:
Joshua walked 48 feet in total.
Step-by-step explanation:
To find the total distance we need to sum every distance that he walked. We have:
- First: Joshua walked down the hall to the door = 14 feet
- Second: He continued in a straight line out the door and across the yard to the mailbox = 24 feet
- Third: He came straight back across the yard and stopped to pet his dog = 10 feet
Hence, the total distance is:

Therefore, Joshua walked 48 feet in total.
I hope it helps you!
<span>precision is after the decimal point.
</span>
This is a right angle triangle.
So, by Pythagoras theorem,
√(32^2+20^2) = x
or √(1024+400) = x
or √1424 = x
or <em>37.74 = x</em>