Mark invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest.How long was the money invested?

The value of the fraction is given by equation A = 6 7/12

What is a Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the simplified fraction be represented as A

Now , let the first fraction be p

The value of p = 12 1/4

Let the second fraction be q

The value of q = 5 2/3

On simplifying , we get

A = p - q

A = 12 1/4 - 5 2/3

A = ( 49/4 ) - ( 17/3 )

Taking the LCM of the denominators , we get

A = [ ( 49 x 3 ) - ( 17 x 4 ) ] / 12

A = ( 147 - 68 ) / 12

A = ( 79/12 )

On further simplification of the fraction , we get

A = 6 7/12

Therefore , the value of A is 6 7/12

Hence , the simplified fraction is A = 6 7/12

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Answer:

Options A, D

Step-by-step explanation:

The way that we will be checking if these 3 numbers can represent a triangle is by checking if a + b ≥ c.  That means that the first two sides have to be greater than or equal to the third side.

Step 1:  Determine if Option A is a triangle

10 + 16 = 26    <-    26 is less than 27 that means that it cannot form a triangle.

Step 2:  Determine if Option B is a triangle

14 + 28 = 42    <-    42 is greater than 39 which means that these three numbers can form a triangle.

Step 3:  Determine if Option C is a triangle

12 + 27 = 39    <-    39 is equal to 39 which means that these three numbers can form a right triangle.

Step 4:  Determine if Option D is a triangle

8 + 22 = 30    <-    30 is less than 31 meaning that these three numbers can't form a triangle.

Answer: Options A, D

Final answer:

To determine if a set of numbers can represent the sides of a triangle, we need to check if the sum of the lengths of any two sides is greater than the length of the third side. Two sets of numbers that could not represent the sides of a triangle are 1, 2, 3 and 4, 5, 9.

Explanation:

In order for three numbers to represent the sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side, which is known as triangle inequality. Let's consider the options:

• 1, 2, 3: The sum of the lengths of the two smaller sides is 1+2=3, which is equal to the length of the longest side. This does not satisfy the triangle inequality, so this set of numbers could not represent the sides of a triangle.
• 4, 5, 9: The sum of the lengths of the two smaller sides is 4+5=9, which is equal to the length of the longest side. This does not satisfy the triangle inequality, so this set of numbers could not represent the sides of a triangle.
• 6, 8, 10: The sum of the lengths of the two smaller sides is 6+8=14, which is greater than the length of the longest side (10). This satisfies the triangle inequality, so this set of numbers could represent the sides of a triangle.

Therefore, the sets of numbers that could not represent the sides of a triangle are 1, 2, 3 and 4, 5, 9.

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