Solve the following math problems: 1. One day in Chamonix the temperature at noon was 6°C. At midnight the temperature was 11°C lower. What was the temperature at midnight? 2. Fac... Solve the following math problems: 1. One day in Chamonix the temperature at noon was 6°C. At midnight the temperature was 11°C lower. What was the temperature at midnight? 2. Factorise w+w³. 3. Liz takes 65 seconds to run 400 m. Calculate her average speed. 4. Complete the list of factors of 36. The list starts with 1, 2,... 5. Increase $22 by 15%. 6. (a) Write 209 802 correct to the nearest thousand. (b) Write 4123 correct to 3 significant figures. Read more

Steps to Solve

1. Calculate the temperature at midnight

The temperature at noon was $6^\circ C$, and at midnight it was $11^\circ C$ lower. To find the temperature at midnight, we subtract 11 from 6:

$6 - 11 = -5$

2. Factorize the expression

To factorize the expression $w + w^3$, we look for common factors in both terms. Both terms have $w$ as a factor. Factoring $w$ out, we get:

$w + w^3 = w(1 + w^2)$

3. Calculate Liz's average speed

Liz runs 400 meters in 65 seconds. To find her average speed, we divide the distance by the time: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

$\text{Speed} = \frac{400 \text{ m}}{65 \text{ s}} \approx 6.1538 \text{ m/s}$ Round to 2 significant figures: $6.2 \text{ m/s}$

4. Complete the list of factors of 36

The factors of 36 are the numbers that divide evenly into 36. We are given 1 and 2. The full list is:

1, 2, 3, 4, 6, 9, 12, 18, 36

So we must fill 3, 4, 6, 9, 12, 18

5. Increase $22 by 15%

To increase $22 by 15%, we first calculate 15% of $22:

$0.15 \times 22 = 3.3$

Then we add this amount to the original $22:

$22 + 3.3 = 25.3$

6. Rounding numbers

(a) Round 209,802 to the nearest thousand: The thousands digit is 9, and the next digit is 8, which is 5 or greater, so we round up. 209,802 rounded to the nearest thousand is 210,000.

(b) Write 4123 correct to 3 significant figures: The first three significant figures are 4, 1, and 2. The next digit is 3, which is less than 5, so we don't round up. Replacing the 3 with a 0, we get 4120.