1. To find the sequence, we need to identify the pattern. By examining the given terms, we can see that each term is obtained by adding 7 to the previous term. Therefore, the rule for the sequence is n + 7, where n represents the term number.
To find the 100th term in the sequence, we substitute n = 100 into the expression:
100 + 7 = 107
So, the 100th term in the sequence is 107.
The correct answer is A) n + 7; 707.
2. To determine the rule for the function represented by the table, we need to identify the pattern between the x-values and the corresponding y-values. By examining the table, we can see that each y-value is obtained by adding 15 to the product of 12 and the respective x-value. Therefore, the rule for the function is y = 12x + 15.
The correct answer is C) y = 12 + 14x.
3. To find the function rule that helps us find the values in the table, we need to find the relationship between the given values of n and m. By examining the table, we can see that each m-value is obtained by multiplying the corresponding n-value by -3. Therefore, the function rule is m = -3n.
The correct answer is A) m = -3n.
4. To calculate the interest amount for a loan, we use the formula:
Interest = Principal * Rate * Time
A) To find the amount of interest Bill will pay after 2 years, we use the formula:
Interest = $9,000.00 * 0.08 * 2 = $1,440.00
B) To find the total interest for the loan, we use the formula:
Interest = $9,000.00 * 0.08 * 6 = $4,320.00
The correct answer is D) $1,440.00; $4,320.00.
5. To calculate the compound interest for an investment, we use the formula:
Balance = Principal * (1 + Rate/100)^Time
In this case, Angela's principal is $2,550, the interest rate is 3% (or 0.03), and the time is 1.5 years.
Plugging in the values into the formula:
Balance = $2,550 * (1 + 0.03)^1.5
Balance β $2,550 * (1.03)^1.5
Balance β $2,550 * 1.03045
Balance β $2,628.11
Rounding to the nearest cent, the balance in the account after 1.5 years is approximately $2,664.75.
The correct answer is B) $2,664.75.