An army contingent of 104 members is to march behind an army band of 96 members in a parade.

Mathematics

1 answer:

Trava [24]2 years ago

3 0

You can dispose a number $x$ of elements in a matrix-like formation with $n\times m$ shape if and only if $n$ and $m$ both divide $x$ , and also $nm=x$ .

So, we need to find the greatest common divisor between $104$ and $96$ , so that we can use that divisor as the number of columns, and then.

To do so, we need to find the prime factorization of the two numbers:

$104 = 2^3\times 13$

$96 = 2^5 \times 3$

So, the two numbers share only one prime in their factorization, namely $2$ , but we can't take "too many" of them: $104$ has "three two's" inside, while $96$ has "five two's" inside. So, we can take at most "three two's" to make sure that it is a common divisor. As for the other primes, we can't include $3$ nor $13$ , because it's not a shared prime.

So, the greater number of columns is $2^3=8$ , which yield the following formations:

$104 \to 8\times 13$

$96 \to 8\times 12$

You might be interested in

A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mea

uysha [10]

Answer:

The 90th percentile for the distribution of the total contributions is $6,342,525.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .