a. A proper joint density function is established if, within its support, it remains non-negative and its integral totals 1. The first requirement is satisfied provided that
. Meeting the second stipulation necessitates integrating over
. b. To derive the marginal joint density of
and
, integrate the joint density concerning
. Next, you can obtain the desired probability by integrating the joint density.
Answer:
Step-by-step explanation:
There are two distinct issues to address, correct?
1, The overall duration T required to fly from New York to Los Angeles:
Time = Distance/average speed
2, The problem related to the race:
A) The total duration of the race would be:
B) For swimming at an average pace of 2 miles per hour, this means r=2.
Substituting r=2 allows us to calculate the total time needed as follows:
When rounding the result: 1.84047 hours rounds to 110 minutes
I have included a screenshot of the entire question along with its accompanying diagram.
Answer:∠1 = 163°
Explanation:1- finding angle 2:Given that ∠2 together with 17° creates a straight angle, their total is 180°.
Thus:
180 = 17 + ∠2
Solving for ∠2 gives us:
∠2 = 180 - 17
∠2 = 163°
2- finding angle 1:Since lines a and b are parallel, ∠1 and ∠2 are alternate angles and therefore equal.
We determined that ∠2 = 163°, leading to:
∠1 = 163°
I hope this clarifies things!:)
Answer:
60.36 steps West from center
85.36 steps North from center
Step-by-step explanation:
Refer to the attached
Musah's starting point and movement are depicted in the image.
- 1. He moves 50 steps towards the North,
- 2. Next, he moves 25 steps towards the West,
- 3. Then he proceeds 50 steps on a bearing of 315°. We now recognize that North is measured at 0°
or 360°, so a bearing of 315° corresponds to North-West 45°.
Note: According to the Pythagorean theorem, a right triangle at 45° with hypotenuse 'a' will have legs equal to a/√2.
What is the distance West of Musah's final position from the center?
25 + 50/√2 ≈ 60.36 steps
What is the distance North of Musah's final position from the center?
z = -1.66. The Z-statistic is calculated as follows. Here X signifies the obtained proportion. p stands for the mean proportion. The formula includes the standard error for the sample. From a total of 593 surveyed students, 64 met the criteria described. Thus, if the national percentage of binge drinkers is 13.1%, she has found the proportion in her data. The resulting z statistic for the dataset is derived accordingly.
