These are the completed prime factor trees for 30 and 42. A) What two prime numbers are in both trees? B) Write down the hcf of 30 and 42 as the product of its prime factors C) Hence, work out the HCF of 30 and 42

The difference of a number q and 8 is q-8.

It is required to write thedifference of a number q and 8.

What is algebra?

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given that:

considering the word "difference" means subtraction, so to  subtract 8 from q.

the difference of a number q and 8 is

q-8.

Therefore, the difference of a number q and 8 is q-8.

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Answer: 9 minutes.

Step-by-step explanation: 12-3=9.

3 x 4 = 12, 3 x 3 x 3=9, 3 x 3 x 3 x 3=12, 4+4+4=12. So if you think about it, three goes into twelve four times, just like a quarter goes into a dollar four times, or 25 goes into 100 four times. So, if you take twelve minus three and equal it, it is nine.

In system A, the first equation multiply by 4

8x - 4y = 12 (1st)

3x + 4y = 10 (2nd)

--------------------add

11x = 22

So answer is B.

Answer:

A = $ 7,449.23

A = P + I where

P (principal) = $ 5,000.00

I (interest) = $ 2,449.23

Step-by-step explanation:

Compound Interest Equation

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Compound Interest Formulas and Calculations:

Calculate Accrued Amount (Principal + Interest)

A = P(1 + r/n)^nt

Calculate Principal Amount, solve for P

P = A / (1 + r/n)^nt

Calculate rate of interest in decimal, solve for r

r = n[(A/P)(^1/nt) - 1]

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / n[ln(1 + r/n)] = [ ln(A) - ln(P) ] / n[ln(1 + r/n)]

Formulas where n = 1 (compounded once per period or unit t)

Calculate Accrued Amount (Principal + Interest)

A = P(1 + r)^t

Calculate Principal Amount, solve for P

P = A / (1 + r)^t

Calculate rate of interest in decimal, solve for r

r = (A/P)1/t - 1

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = t = ln(A/P) / ln(1 + r) = [ ln(A) - ln(P) ] / ln(1 + r)

Continuous Compounding Formulas (n → ∞)

Calculate Accrued Amount (Principal + Interest)

A = Pe^rt

Calculate Principal Amount, solve for P

P = A / ert

Calculate rate of interest in decimal, solve for r

r = ln(A/P) / t

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / r

Final answer:

To calculate the future amount in the account after 5 years with compound interest, you can use the formula A = P(1 + r/n)^(nt). Plugging in the values, the amount in the account would be $6,803.85.

Explanation:

To calculate the future amount in the account, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the future amount
• P is the principal amount ($5000 in this case)
• r is the annual interest rate (8% in this case)
• n is the number of times the interest is compounded per year (12, since it is compounded monthly)
• t is the number of years

Plugging in the values, we get:

A = 5000(1 + 0.08/12)^(12*5)

Calculating this, we find that the amount in the account after 5 years would be $6,803.85.

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