Answer:1.2. Between which two consecutive integers does √138 lie?
We can approximate the square root of 138 by finding the perfect squares on either side of it. We know that 11^2 = 121 and 12^2 = 144, so 138 must be between those two numbers. Therefore, √138 is between 11 and 12.
1.3. Rewrite 0,26 as a proper fraction (in the form of 5), show all steps.
To write 0,26 as a fraction, we can use the fact that the decimal point separates the ones place from the tenths place. Therefore, 0,26 = 26/100. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2. Therefore, 0,26 = 26/100 = 13/50.
2.2. Divide 240g in the ratio 5: 3: 4.
The total ratio is 5 + 3 + 4 = 12. To divide 240g in the ratio 5:3:4, we need to divide it into 5 + 3 + 4 = 12 equal parts, and then multiply each part by 5, 3, and 4, respectively. Each part is equal to 240/12 = 20g. Therefore, we have:
5 parts of 20g = 100g
3 parts of 20g = 60g
4 parts of 20g = 80g
Therefore, 240g divided in the ratio 5:3:4 is 100g, 60g, and 80g, respectively.
2.4. Thoriso can either walk to school at 5 km/h or ride her bicycle at 15 km/h. If she rides her bicycle, it takes her 10 minutes to get to school.
2.4.1. How long will it take her if she walks to school?
Let's assume the distance to school is d km. If Thoriso rides her bicycle at 15 km/h, she covers the distance in 10 minutes, which is 10/60 = 1/6 hours. Therefore, we have:
d = 15 × 1/6 = 2.5 km
If Thoriso walks to school at 5 km/h, the time it takes her to cover the distance d is given by:
time = distance ÷ speed = d ÷ 5
Substituting d = 2.5 km, we get:
time = 2.5 ÷ 5 = 0.5 hours = 30 minutes
Therefore, it will take Thoriso 30 minutes to walk to school.
2.4.2. Is this direct or indirect proportion? Give a reason for your answer.
This is a direct proportion, because the time it takes Thoriso to cover a certain distance is directly proportional to her speed. This means that if her speed doubles, the time it takes her to cover the distance will be halved, and if her speed is tripled, the time will be divided by three.
2.5. Brian wants to exchange South-African rand for British pound. If R1 is worth 0,075199 pound, how many pounds will he get for R2 100 if he must pay an agent commission of 1,5%?
To find out how many pounds Brian will get for R2,100, we first need to find out how many pounds he will get for R1, and then multiply by R2,100. We know that R1 is worth 0,075199 pound.
Explanation: