Answer:
c = 0.165
Step-by-step explanation:
Given:
f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,
f(x, y) = 0 otherwise.
Required:
The value of c
To find the value of c, we make use of the property of a joint probability distribution function which states that

where a and b represent -infinity to +infinity (in other words, the bound of the distribution)
By substituting cx y(1 + y) for f(x, y) and replacing a and b with their respective values, we have

Since c is a constant, we can bring it out of the integral sign; to give us

Open the bracket

Integrate with respect to y

Substitute 0 and 3 for y



Add fraction


Rewrite;

The
is a constant, so it can be removed from the integral sign to give


Integrate with respect to x

Substitute 0 and 3 for x




Multiply both sides by 


Using the normal distribution, it is found that 10.56% of the apples weigh less than Jermaine's apple.
--------------------
In a <em>normal distribution</em> with mean
and standard deviation
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure X is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X, that is, the proportion of measures that are less than X.
In this problem:
- Mean of 0.33 pounds, thus
. - Standard deviation of 0.06 pounds, thus
. - The proportion that is less than 0.25 pounds is the p-value of Z when X = 0.25, thus:



has a p-value of 0.1056.
0.1056 x 100% = 10.56%.
10.56% of the apples weigh less than Jermaine's apple.
A similar problem is given at brainly.com/question/13411796
Answer: 200 square units
Step-by-step explanation:
Given
Circumference of the circle is 
Suppose r is the radius of the circle
The biggest area of a quadrilateral that can fit in a circle is of square.
Deduce the radius of the circle

Suppose the side of the square is a
from the figure, we can write

Area of the quadrilateral is
