Solve the following math problems: 1. The probability that Kim wins a game is 0.72. In one year Kim will play 225 games. Work out an estimate of the number of games Kim will win.... Solve the following math problems: 1. The probability that Kim wins a game is 0.72. In one year Kim will play 225 games. Work out an estimate of the number of games Kim will win. 2. (a) Write 4.82 x 10^-3 as an ordinary number. (b) Write 52 million in standard form. 3. Solve (1-p)/3 = 4 4. Factorise completely: 2a + 4b - ax - 2bx
Understand the Problem
The image presents a series of math problems. Question 7 asks for an estimated number of games Kim will win based on given probability and total games played. Question 8 involves converting a number from scientific notation to ordinary form (a) and writing a large number in standard form (b). Question 9 requires solving a linear equation for p. Question 10 involves factorising an algebraic expression completely.
Answer
7. $162$ 8. (a) $0.00482$ (b) $5.2 \times 10^7$ 9. $p = -11$ 10. $(a + 2b)(2 - x)$
Answer for screen readers
- $162$
- (a) $0.00482$ (b) $5.2 \times 10^7$
- $p = -11$
- $(a + 2b)(2 - x)$
Steps to Solve
- Estimate the number of games Kim will win
Multiply the probability of winning a game by the total number of games played.
$0.72 \times 225 = 162$
- Write $4.82 \times 10^{-3}$ as an ordinary number
Since the exponent is -3, move the decimal point 3 places to the left i.e. $4.82 \times 10^{-3} = 0.00482$
- Write 52 million in standard form
52 million is 52,000,000. To write this in standard form, we write it as $5.2 \times 10^n$ where $n$ is the number of places we moved the decimal point. $52,000,000 = 5.2 \times 10^7$
- Solve the equation for $p$
Multiply both sides of the equation $\frac{1-p}{3} = 4$ by 3:
$1 - p = 12$
Subtract 1 from both sides:
$-p = 11$
Multiply both sides by -1:
$p = -11$
- Factorise the expression completely
We have $2a + 4b - ax - 2bx$. We can factor by grouping:
$(2a + 4b) - (ax + 2bx)$
Factor out the common factors from each group:
$2(a + 2b) - x(a + 2b)$
Now factor out the common binomial factor $(a + 2b)$:
$(a + 2b)(2 - x)$
- $162$
- (a) $0.00482$ (b) $5.2 \times 10^7$
- $p = -11$
- $(a + 2b)(2 - x)$
More Information
Standard form, also called scientific notation, is a way of writing very large or very small numbers compactly. It is written as $a \times 10^n$, where $1 \le |a| < 10$ and $n$ is an integer.
Factorisation is the process of writing an expression as a product of its factors.
Tips
- When writing numbers in standard form, students sometimes incorrectly place the decimal point or calculate the exponent.
- When factorising, students may not factorise completely or may make errors when grouping terms. Remember to look for common factors after grouping.
- With question 9 students may make an error while rearranging the equation.
AI-generated content may contain errors. Please verify critical information
