You put $500 in your bank account. With an interest rate of 5%, how long will it take the account to reach $600? Use the formula

Answer:

1. Addition Property of Equality

2. Segment addition

3. Substitution Property of Equality.

4. Transitive Property of Equality.

Step-by-step explanation:

Given: CD = EF and AB = CE

To Show: AB = DF

Following the steps outlined:

1. CD + DE = EF + DE by the (addition) Property of Equality.

This shows that the same value has been added to both sides of the equation.

2. CE = CD + DE and DF = EF + DE through (segment addition).

This indicates that CE and DF are segments, and the length of any segment equals the total of its parts.

3. CE = DF according to the (Addition, subtraction, substitution, transitive) Property of Equality. Recognizing that CE = CD + DE and using the fact that CD = EF allows us to replace CD with EF.

So, CE = EF + ED = FD (via substitution) Property of Equality.

4. Since AB = CE and CE = DF, we can conclude AB = DF by the (transitive) Property of Equality.

This follows the rule that if x = y and y = z, then x = z.

Events A and B are termed independent when

if not, events A and B are classified as dependent.

The events A, B and A∩B are:

• A - Jane plans to attend a ballgame on Monday;
• B - Kate intends to go to a ballgame on Monday;
• A∩B - Both Kate and Jane will be at the ballgame on Monday.

Answer: events A and B are dependent

The dimensions are 58 ft × 58 ft. Step-by-step explanation: Let the length of the region be represented as x feet, and the width as y feet. Given a perimeter of 234 feet, the area A can be represented as xy. By differentiating the equation with regards to x, we can determine the point of maximum area, revealing that for x = 58.5 feet, the area's maximum occurs when both dimensions are 58.5 ft.

In 1980, if there were N individuals aged 100 or older, then by 2010, the number grew to N*1.66 for those 100 and above. A straightforward conditional expression can be framed as: If P, then Q, where P represents the hypothesis and Q is the conclusion. We understand that "The count of individuals aged 100 years or older increased by about 66% from 1980 to 2010," meaning that if we had N individuals aged 100 or older in 1980, we will have N*(166%/100%) = N*1.66 in 2010, allowing us to write a conditional statement: If there were N individuals aged 100 years old in 1980, then by 2010, we had N*1.66 individuals who were at least 100 years old.

Wages expenses. 5000
To wages payable. 5000