Respuesta :
Answer:
Each value has been identified below.
Step-by-step explanation:
(1) We have to describe two ways the numbers in each proportion are related;
(a) 5 : 20 = 125 : 500
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
20 [tex]\times[/tex] 125 = 5 [tex]\times[/tex] 500
2500 = 2500
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 5 : 20 = 125 : 500
We will check that; [tex]\frac{5}{125}[/tex] is equal to [tex]\frac{20}{500}[/tex] or not.
[tex]\frac{5}{125} = \frac{20}{500}[/tex]
[tex]\frac{1}{25} = \frac{1}{25}[/tex]
This shows that the given proportion is related.
(b) 10 : 1 = 120 : 12
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
1 [tex]\times[/tex] 120 = 10 [tex]\times[/tex] 12
120 = 120
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 10 : 1 = 120 : 12
We will check that; [tex]\frac{10}{120}[/tex] is equal to [tex]\frac{1}{12}[/tex] or not.
[tex]\frac{10}{120} = \frac{1}{12}[/tex]
[tex]\frac{1}{12} = \frac{1}{12}[/tex]
This shows that the given proportion is related.
(c) 75 : 25 = 300 : 100
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
25 [tex]\times[/tex] 300 = 75 [tex]\times[/tex] 100
7500 = 7500
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 75 : 25 = 300 : 100
We will check that; [tex]\frac{75}{300}[/tex] is equal to [tex]\frac{25}{100}[/tex] or not.
[tex]\frac{75}{300} = \frac{25}{100}[/tex]
[tex]\frac{1}{4} = \frac{1}{4}[/tex]
This shows that the given proportion is related.
(d) 1 : 3 = 16 : 48
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
3 [tex]\times[/tex] 16 = 1 [tex]\times[/tex] 48
48 = 48
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 1 : 3 = 16 : 48
We will check that; [tex]\frac{1}{16}[/tex] is equal to [tex]\frac{3}{48}[/tex] or not.
[tex]\frac{1}{16} = \frac{3}{48}[/tex]
[tex]\frac{1}{16} = \frac{1}{16}[/tex]
This shows that the given proportion is related.
(2) Now we have to determine each value of n in the following given ratios;
(a) 2 : 5 = 8 : n
As we know that Product of means = Product of extremes
5 [tex]\times[/tex] 8 = 2 [tex]\times[/tex] n
40 = 2n
[tex]n=\frac{40}{2}[/tex] = 20
Hence, the value of n is 20.
(b) 2 : n = 6 : 9
As we know that Product of means = Product of extremes
n [tex]\times[/tex] 6 = 2 [tex]\times[/tex] 9
6n = 18
[tex]n=\frac{18}{6}[/tex] = 3
Hence, the value of n is 3.
(c) n : 5 = 12 : 20
As we know that Product of means = Product of extremes
5 [tex]\times[/tex] 12 = n [tex]\times[/tex] 20
60 = 20n
[tex]n=\frac{60}{20}[/tex] = 3
Hence, the value of n is 3.
(d) 8 : n = 4 : 15
As we know that Product of means = Product of extremes
n [tex]\times[/tex] 4 = 8 [tex]\times[/tex] 15
4n = 120
[tex]n=\frac{120}{4}[/tex] = 30
Hence, the value of n is 30.
(3) Now we have to determine each value of z in the following given ratios;
(a) 4 : 8 = 3 : z
As we know that Product of means = Product of extremes
8 [tex]\times[/tex] 3 = 4 [tex]\times[/tex] z
24 = 4z
[tex]z=\frac{24}{4}[/tex] = 6
Hence, the value of z is 6.
(b) 5 : z = 6 : 18
As we know that Product of means = Product of extremes
z [tex]\times[/tex] 6 = 5 [tex]\times[/tex] 18
6z = 90
[tex]z=\frac{90}{6}[/tex] = 15
Hence, the value of z is 15.
(c) z : 14 = 10 : 20
As we know that Product of means = Product of extremes
14 [tex]\times[/tex] 10 = z [tex]\times[/tex] 20
140 = 20z
[tex]z=\frac{140}{20}[/tex] = 7
Hence, the value of z is 7.
(d) 3 : 21 = z : 56
As we know that Product of means = Product of extremes
21 [tex]\times[/tex] z = 3 [tex]\times[/tex] 56
21z = 168
[tex]z=\frac{168}{21}[/tex] = 8
Hence, the value of z is 8.
