An animal shelter takes cats and dogs - Leaving Cert Mathematics - Question 7 - 2022

The stem-and-leaf plot indicates that the weights of the dogs have generally increased from Day X to Day Y. On Day X, the weights cluster around lower values (ranging from 4.5 kg to 7.4 kg), while on Day Y, the weights are slightly higher (from 4.8 kg to 8.1 kg). This suggests that the dogs may have gained weight over the period.

$r$ is likely to be $0.9$. This high positive value suggests a strong correlation between the weights on Day X and Day Y, indicating that as one weight increases, the other weight also tends to increase.

To complete the table:

• Total number of cats is 14.
• Total number of dogs is given as 11, so Total = 30 - 14 = 16 dogs.
• Total animals = 40, thus the combined total is 40, hence the four missing values are:

The probability of randomly selecting a cat from the total of 40 animals is given by:

$P(cat) = \frac{Number of Cats}{Total Animals} = \frac{14}{40} = \frac{7}{20}$

Thus, the probability that the first animal picked was a cat is ( \frac{7}{20} ).

To find this probability, we first need to determine the total distributions:

• Number of male dogs = 11
• Total animals = 40

The probability of picking three male dogs in succession without replacement is:

$P(3 \text{ male dogs}) = \frac{11}{40} \times \frac{10}{39} \times \frac{9}{38} = \frac{990}{59280} \approx 0.017$

The number of different possible arrangements of 9 female cats in 9 separate pens is calculated using the factorial formula:

$9! = 362880$

Therefore, there are 362880 different arrangements in which the 9 female cats could be placed into the pens.

Initially, there were 40 animals in total. By the end of the week, 10 animals had left the shelter. If the probability of picking a dog is (\frac{11}{15}), we calculate the number of remaining dogs:

$\text{Remaining animals} = 30, \text{Remaining dogs} = 11, \text{Remaining cats} = \text{Total} - \text{Dogs} = 30 - 11 = 19$

Hence, originally there were 22 cats, and 6 cats must have left the shelter during this week.