HCF of 522, 1624, 1276​

The watch is less expensive in Geneva, Switzerland by £20. Step-by-step explanation: To identify the city where the watch is cheaper, we need to convert the watch's price to the same currency. Since pounds are utilized in part b of the question, using this currency would simplify the calculations. In Geneva, the watch's price is 193.75 CHF from our conversion: £1 = 1.55 CHF, thus, £x = 193.75 CHF. By cross-multiplying, we solve for x: (193.75 * 1) / 1.55 = 193.75/1.55 = £125. This demonstrates that the watch is cheaper in Geneva and more expensive in Manchester. To find out by how much, we simply deduct the Geneva price from the Manchester price: 145 - 125 = £20 cheaper.

For one day:
= £9.20 × 7
= £64.40

For six days:
£64.40 × 6 = £386.40

After sharing with his mom:
£386.40/7 × 5
= £55.20 × 5
= £276

To purchase a car worth £1932:
£1932/£276 = 7

Thus, he needs 7 weeks to save enough for the car priced at £1932.

The test statistic (Z) is 2.5767, and the p-value of the test is 0.009975. The null hypothesis suggests that the smoking rate among students has not changed, while the alternative indicates otherwise. The z-statistic for the sampled proportion is computed, yielding z ≈ 2.5767. As we investigate whether the smoking percentage has shifted over the preceding five years, the two-tailed p-value is found to be 0.009975. This result is significant at a 99% confidence level, demonstrating substantial evidence that the percentage of smoking students has changed.

The fox’s speed needs to exceed that of the rabbit to successfully catch up. Thus, the required speed for the fox is expressed as 35/t + 40.

The distance separating the rabbit from the fox is 35 feet.

The speed of the rabbit is 40 feet per second.

Fox's speed = F

To calculate a precise speed for the fox, a specific time for the pursuit must be provided.

Let’s denote the time as t.

Recall that:

Speed = distance / time

Distance = speed × time

The distance the rabbit moves away from the fox after time t will be:

35 + (40 × t) = 35 + 40t

The distance traveled by the fox after time t is: fox speed × t = F × t.

To catch the rabbit, both the fox and rabbit must cover the same distance:

Rabbit's distance at time t equals Fox's distance at that time.

35 + 40t = Ft

To determine F, the fox's speed:

Dividing both sides by t yields:

(35 + 40t) / t = Ft/t

35/t + 40 = F

<pThus, the speed of the fox should be: 35/t + 40

To find out the exact speed of the fox, a specific time value must be provided.

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