Answer:

Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
In this problem

Rewrite

Answer:
The members of the cabinet can be appointed in 121,080,960 different ways.
Step-by-step explanation:
The rank is important(matters), which means that the order in which the candidates are chosen is important. That is, if we exchange the position of two candidates, it is a new outcome. So we use the permutations formula to solve this quesiton.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:

If there are 14 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?
Permutations of 8 from a set of 14. So

The members of the cabinet can be appointed in 121,080,960 different ways.
Answer:
LCM = 1274
Step-by-step explanation:
98 = 2 × 7²
182 = 2 × 7 × 13
LCM(98 ; 182) = 2 × 72 × 13 = 1274
Answer:
a : c = 7 : 10
Step-by-step explanation:
The two ratios (a : b and b : c) both have b in common, so to work out what a : c is, we can use b to 'bridge' the two ratios together.
However, in a : b, b is 4. But in b : c, b is 2. We need to make sure b is the same in both ratios before we can combine the ratios together. The easiest way to do this is to multiply b : c by 2 to get b : c = 4 : 10. Now b is 4 in both ratios.
So now, we can combine the two ratios together to get a : b : c = 7 : 4 : 10. Since we only want a : c though, we can just drop the b and get a : c = 7 : 10. No simplifying is necessary since the ratio is already in its simplest form.
Hope that helps! :)
The <span>Pythagorean Theorem tells us that

where c is the </span><span>hypotenuse and a and b are the other two sides. To solve for one of the shorter sides we need to rearrange:

We can then substitute known values, and solve:
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