The Area of Shaded region is equal to the difference in Area of rectangle and Area of triangle .
let's solve for area of rectangle :
Now, Area of Triangle :
So, the area of the shaded region in terms of x :
And since, Area of Shaded region = 44 cm²
By equating the area, we get
Value of x = 2
Answer:
(a)There are 500 integers from 1 through 1,000 are multiples of 2.
There are 111 integers from 1 through 1,000 are multiples of 9.
(b)0.611
Step-by-step explanation:
Given the set of Integers from 1 through 1000
The least multiple of 2 is 2 and the highest multiple of 2 in the interval is 1000.
To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 2,4,6,... is an Arithmetic Progression,
where first term, a =2, common difference, d =2
Nth term of an A.P,
Similarly,
Given the set of Integers from 1 through 1000
The least multiple of 9 is 9 and the highest multiple of 9 in the interval is 999.
To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 9,18,27,... is an Arithmetic Progression,
where first term, a =9, common difference, d =9
Nth term of an A.P,
(b)Probability that an integer selected at random is a multiple of 2 or a multiple of 9.
There are a total of 1000 numbers between from 1 through 1,000
n(S)=1000
n(Multiples of 2)=500
n(Multiples of 9)=111
Therefore: