Number

Evaluate $\sqrt{225} - \sqrt{100}$.

If $a = \sqrt{2}$ and $b = \sqrt{18}$, find the product $ab$.

Calculate $\frac{1}{2} + \frac{1}{4}$ and classify the result.

Find the value of $\sqrt{625}$.

Simplify the expression $\frac{1}{1+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{3}} + \frac{1}{\sqrt{3}+\sqrt{4}}$.

Given that $x = 3 - \sqrt{2}$, find the value of the expression $x^2 - 6x + 7$.

Express the recurring decimal $0.\dot{1}0\dot{8}$ as a fraction in its simplest form.

How many positive integers $n$ in the range $1 \leq n \leq 100$ are there such that the expression $\sqrt{n + \sqrt{n}}$ is a rational number?

Simplify the expression $\sqrt{50} - \sqrt{18}$.

If $a$ is rational and $b$ is rational, which of the following is not necessarily rational?

What is $1.0 \times 10^6$ expressed as an ordinary number?

Express $0.00000000123$ in standard form.

Subtract $(5 \times 10^3) - (1 \times 10^3)$ and express in standard form.

Find $(1 \times 10^2) + (1 \times 10^1)$ and write in standard form.

Work out the value of $P^2$ if $P = 3 \times 10^{-5}$, in standard form.

Light travels at $3 \times 10^5$ km/s. How many kilometers are in one light-minute?

Find the value of $(2.5 \times 10^{-2})^{-1}$ in standard form.

The probability of a specific mutation is $1.2 \times 10^{-7}$ per cell division. If there are $5 \times 10^9$ cell divisions, what is the expected number of mutations?

If the density of a gas is $1.25 \times 10^{-3} \text{ g/cm}^3$, find the volume in $\text{cm}^3$ occupied by $5 \times 10^{-2}$ kg of the gas.

Evaluate $(0.00004)^3$ and write the result in standard form.

A car travels $150\text{ km}$ in $2.5\text{ hours}$. What is its average speed in $\text{km/h}$?

Decrease $120$ in the ratio $3:4$.

On a map, a distance of $5\text{ cm}$ represents an actual distance of $2\text{ km}$. What is the scale of the map?

If $10$ workers can produce $500$ items in $5$ hours, how many items does each worker produce per hour on average?

If $y$ is inversely proportional to $x^2$, what happens to the value of $y$ if the value of $x$ is doubled?

A model airplane is built to a scale of $1:72$. If the actual wingspan of the airplane is $36\text{ meters}$, calculate the wingspan of the model in centimeters.

A currency exchange office charges a $2\%$ commission. If the exchange rate is $\$1 = 0.85$ Euro, how many Euros will a customer receive for $\$1000$ after the commission is deducted?

If $z$ varies jointly as $x$ and $y$, and $z=12$ when $x=2$ and $y=3$. Find $z$ when $x=5$ and $y=7$.

A metal cube is melted and recast into small spheres. If the radius of each sphere is $1/10$ of the side of the cube, how many spheres can be made (approximately, using $\pi \approx 3$ for simplicity)?

The ratio of the ages of a father and son is $7:2$. Five years ago, the ratio was $6:1$. What is the father's current age?

An investment of $\$10,000$ grows at $3\%$ compound interest per year. What is the total amount after $2$ years?

Calculate the simple interest on $\$1200$ at $2.5\%$ per year for $4$ years.

If $40\%$ of a number is $28$, what is the original number?

Find the total amount after $3$ years for an investment of $\$200$ at $5\%$ compound interest per year.

A piece of jewelry is sold by a retailer for $\$1122$, representing a $10\%$ profit on the price the retailer paid to the manufacturer. The manufacturer had already made a $20\%$ profit on the original production cost when selling it to the retailer. Calculate the original production cost of the jewelry.

Calculate the total value of $\$5000$ after $2$ years if interest is $4\%$ per annum, compounded quarterly.

A principal of $\$1800$ earns $\$216$ in simple interest at a rate of $4\%$ per year. How many years was the money invested for?

A debt of 5000 dollars is to be repaid in two years with compound interest at 10% per annum. If the debt is settled by paying 2000 dollars at the end of the first year and the remainder at the end of the second year, how much is the final payment?

A sum of money tripling in 10 years at compound interest (compounded annually) will become 9 times itself in how many years?

A machine's value depreciates by 20% every year. At the end of 3 years, its value is 32000 dollars. What was its value at the end of the first year?

What is $n(\emptyset)$?

If $V = \{a, e, i, o, u\}$, which of the following is a subset of $V$?

Which of the following describes a finite set?

If $A = \{10, 20, 30, 40\}$ and $B = \{30, 40, 50, 60\}$, what elements are in $A \cup B$?

If $n(A) = k$, how many subsets of $A$ contain exactly one element?

Let $A$ be the set of odd numbers between 1 and 10, and $B$ be the set of prime numbers between 1 and 10. Find $A \Delta B$.

In a group of 50 people, 30 speak Spanish, 25 speak French, and 10 speak both. How many speak neither?

If $n(A) = 100$, $n(B) = 150$, and $n(A \cap B) = 50$, find $n(A \Delta B)$.

In a group of 30 people, 18 play the piano, 15 play the guitar, and 5 play neither. How many play only the guitar?

If $A$ and $B$ are two sets such that $n(A) = 7$, $n(B) = 8$, and $n(A \cup B) = 10$, find $n(P(A \cap B))$.