Archive for August, 2015

Problem 1002

 

Determine whether the following statement is true or false.

{a} Є {a, b, c, d, e}

 

Solution:-

 

The symbol Є means “is an element of.”

For example, the statement b Є {a, b, c, d, e} is true because b is an element of {a, b, c ,d, e}.

The statement f Є {a, b, c, d, e} is false because f is not an element of {a, b, c, d, e}.

The statement {b} Є {a, b, c, d, e} is false because {b} refers to the set containing b as its only element. Although b is an element of {a, b, c, d, e} is not.

Therefore, {a} Є {a, b, c, d, e} is not a true statement.

 

 

Problem 1001

Express the following set in  set-builder notation.

B = {16,17,18,19,20,21,22,23}

 

Solution:-

 

When a set is named using set builder notation, specify the conditions under which a number is an element of the set.

To translate B = {16,17,18,19,20,21,22,23} into set-builder notation, first note that all of the number in B are natural that are less than or equal to 23 and greater than or equal to 16.

Set B includes all natural numbers that are greater than or equal to 16 and less than or equal to 23.

Therefore, B can be written in the following way in set- builder notation.

B = {x I x Є N and 16 ≤ x ≤ 23}

Note that another correct expression for B is B = {x I x  Є N and 15 < x < 24}.

 

Problem 1000

Determine whether the set is finite or infinite.

The set of odd numbers greater than 87.

 

Solution:-

 

If the number of elements in a set is a natural, the set is finite. If the element in a set cannot be counted, the set is infinite.

“The set of add numbers greater than 87” is the description of the set in question. The roster notation for the same set is {89,91,93,95,……}.

The element of the set cannot be counted be counted. An ellipsis in roster form indicates that the elements in the set continue in the same manner. An ellipsis followed by a last element indicates that the elements continue in the same manner up to and including the last element. In the roster form of this set, however, there is no last element, so the elements continue without stopping.

Thus, the set is infinite.

 

 

Problem 999

Determine whether the set is finite or infinite.

{12,16,20,24,…………}

 

Solution:-

 

If the number of elements in a set is natural number, the set is finite. If the elements in a set cannot be counted, the set is infinite.

{12,16,20,24,…………} is  the roster, or list notation of the set in question. The description of the same set is the set if multiples of 4 greater than 11.

The element of the set cannot be counted.

The set is infinite.

{12,16,20,24,…………}

So the set is finite.

 

Problem 998

Determine if the collection is not well defined and therefore is not a set.

The collection of the five best U.S governors

 

Solution:-

 

A set is a collection of objects whose content can be clearly determined. The objects in a set are called the elements, or members, of the set.

Since the five bet U.S. governors are left to our own interpretation, they cannot be clearly determined. The collection is not well defined and therefore it is not a set.

 

 

Problem 997

Determine if the collection is not well defined and therefore is not a set.

The collection of high schools in New York.

 

Solution:-

 

A set is a collection of objects whose contents can be clearly determined. The objects in a set are called the elements, or members, of the set.

Since high schools in New York are building that can be clearly determined, the collection is well defined. The collection forms a set.

 

 

 

Problem 996

Find the area of the rectangle.

1m

 

Solution:-

 

Recall how to find the area of a rectangle.

Area = Length* Width.

If A represents the area, L represent the length, and W represents the width, we  have

A = L . W.

Let the length be 8 and the width be 5y.

A = L * W

= 8 *5y

= 40y

Finally , the area is 40y sq in.

 

 

Problem 995

 

Fill in the blank below.

18y2 + 8x – 26 is called a(n) ………………while 18y2, 8x, and -26 are each called a(n)……………………

 

Solution:-

 

Expression

 

Term.

 

 

Problem 994

Identify the terms as like or unlike,

8r , 8r2

 

Solution:-

 

To determine if terms are like or unlike, you can begin by writing each term as the product of its numerical coefficient and its variable portion.

8r = 8* r

8r2 = 8*r2

Now look at the variable parts, r and r2. If they are identical including the powers on the variable, then the terms 8r and 8r2  are like terms. Otherwise, they are unlike terms.

The variable parts are not identical because one has an exponent of 2 and the other doesn’t.

Thus, the terms are unlike terms.

 

Problem 993

Anthony Tedesco sold his used mountain bike and accessories for $308. If he receive six times as much money for the bike as he did for the accessories, find how much money he receive for the bike.

 

Solution:-

 

He received $264 for the bike.