Find the product of 23₅ and 21₅, leaving your answer in base

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

: Find the product of $23_5$ and $21_5$ , leaving your answer in base 5.

Convert the numbers from base 5 to base 10.
$23_5 = (2 \times 5^1) + (3 \times 5^0) = 10 + 3 = 13_{10}$ $21_5 = (2 \times 5^1) + (1 \times 5^0) = 10 + 1 = 11_{10}$
Multiply the base 10 numbers.
$13_{10} \times 11_{10} = 143_{10}$
Convert the product from base 10 back to base 5.
Divide 143 by 5 repeatedly and record the remainders:
$143 \div 5 = 28 \text{ remainder } 3$ $28 \div 5 = 5 \text{ remainder } 3$ $5 \div 5 = 1 \text{ remainder } 0$ $1 \div 5 = 0 \text{ remainder } 1$
Reading the remainders from bottom to top gives $1033_5$ .

The correct option is B.
$\boxed{\text{B. } 1033_5}$
: Simplify $16^{7/4} \times 2^{-3} \times 3^0$
Simplify each term using exponent rules.
$16^{7/4} = (2^4)^{7/4} = 2^{4 \times \frac{7}{4}} = 2^7 = 128$ $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$ $3^0 = 1 \quad (\text{Any non-zero number raised to the power of 0 is 1})$
Multiply the simplified terms.
$128 \times \frac{1}{8} \times 1$
Calculate the final product.
$128 \times \frac{1}{8} \times 1 = \frac{128}{8} = 16$
The correct option is C.
$\boxed{\text{C. } 16}$
: Evaluate $\frac{1.44}{(0.12)^2}$ , stating your answer in standard form.
Calculate the denominator.
$(0.12)^2 = 0.12 \times 0.12 = 0.0144$
Perform the division.
$\frac{1.44}{0.0144}$
To simplify, multiply the numerator and denominator by 10000 to remove decimals:
$\frac{1.44 \times 10000}{0.0144 \times 10000} = \frac{14400}{144} = 100$
Express the answer in standard form.
$100 = 1.00 \times 10^2$
The correct option is C.
$\boxed{\text{C. } 1.00 \times 10^2}$
: Find the rate per annum at which a sum of N52,200.00 gets to N58,000.00 in $1 \frac{1}{2}$ years.
Identify the given values for simple interest.
Principal ( $P$ ) = N52,200.00
Amount ( $A$ ) = N58,000.00
Time ( $T$ ) = $1 \frac{1}{2}$ years = 1.5 years
Calculate the simple interest ( $I$ ).
$I = A - P = \text{N}58,000.00 - \text{N}52,200.00 = \text{N}5,800.00$
Use the simple interest formula to find the rate ( $R$ ).
The formula for simple interest is $I = \frac{P \times R \times T}{100}$ .
Rearrange the formula to solve for $R$ :
$R = \frac{I \times 100}{P \times T}$
Substitute the values and calculate $R$ .
$R = \frac{5800 \times 100}{52200 \times 1.5}$ $R = \frac{580000}{78300}$ $R = \frac{5800}{783}$
As a percentage, the rate is approximately:
$R \approx 7.4074\%$
The rate per annum is $\boxed{\frac{5800}{783}\% \text{ or approximately } 7.41\%}$ .

Find the product of 23₅ and 21₅, leaving your answer in base

Answer

Step-by-step solution

Convert the numbers from base 5 to base 10.

Multiply the base 10 numbers.

Convert the product from base 10 back to base 5.

Simplify each term using exponent rules.

Multiply the simplified terms.

Calculate the final product.

Calculate the denominator.

Perform the division.

Express the answer in standard form.

Identify the given values for simple interest.

Calculate the simple interest ( $I$ ).

Use the simple interest formula to find the rate ( $R$ ).

Substitute the values and calculate $R$ .

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More Mathematics Questions

Find the product of 23₅ and 21₅, leaving your answer in base

Answer

Step-by-step solution

Convert the numbers from base 5 to base 10.

Multiply the base 10 numbers.

Convert the product from base 10 back to base 5.

Simplify each term using exponent rules.

Multiply the simplified terms.

Calculate the final product.

Calculate the denominator.

Perform the division.

Express the answer in standard form.

Identify the given values for simple interest.

Calculate the simple interest (III).

Use the simple interest formula to find the rate (RRR).

Substitute the values and calculate RRR.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Calculate the simple interest ( $I$ ).

Use the simple interest formula to find the rate ( $R$ ).

Substitute the values and calculate $R$ .