Question

1. In Cecilia’s CD collection, 1/5 of her Jazz CDs represents 1/10 of all her CDs. What is the ratio of her Jazz CDs to her non-Jazz CDs?
2. How would you change 5^6(50) to a number times 25?

Answer 1

Answer:

1)

Ratio is 1:1.

2)

The required number is:

$5^4\times 50$

Step-by-step explanation:

1)

Let us consider that Cecilia's has a total of 'x' CDs

and let 'y' represent the number of Jazz CDs.

Now we are given information that:

1/5 of her Jazz CDs represents 1/10 of all her CDs.

i.e. $\dfrac{1}{5}y=\dfrac{1}{10}x\\\\y=\dfrac{5}{10}x\\\\y=\dfrac{1}{2}x$

i.e. the Jazz CDs are half of the total CDs.

Hence, the number of Non-Jazz CDs(z)

= $x-\dfrac{x}{2}\\\\=\dfrac{x}{2}$

Hence, the ratio of Jazz to Non-Jazz CDs

$=\dfrac{y}{z}\\\\=\dfrac{\dfrac{x}{2}}{\dfrac{x}{2}}\\\\=\dfrac{1}{1}$

Hence, the required Ratio is 1:1.

2)

How would you change $5^6\times (50)$ to a number times 25?

We will find the number by dividing the quantity   $5^6\times (50)$ by 25 to find the required number.

i.e. $\dfrac{5^6\times 50}{25}=\dfrac{5^6\times 50}{5^2}=5^{6-2}\times 50=5^4\times 50$

Hence the required number is:

$5^4\times 50$

Answer 2

1. The ratio of Jazz and non-Jazz CDs is 1:1.

2. The given expression can be written as 25 times 31250 .

1. Given information:

In Cecilia’s CD collection, 1/5 of her Jazz CDs represents 1/10 of all her CDs.

Let jazz CDs be J in number and T be the total number of CDs.

The given condition can be written as,

$\dfrac{J}{5}=\dfrac{T}{10}\\T=2J$

So, the ratio of Jazz CDs to non Jazz CDs will be,

$\dfrac{J}{T-J}=\dfrac{J}{2J-J}\\=1:1$

Therefore, the ratio of Jazz and non-Jazz CDs is 1:1.

2. The given expression is $5^6(50)$. It is required to write the given number as a number times 25.

So, it can be written as,

$5^6(50)=5^2\times 5^4(50)\\=25\times 625(50)\\=25\times 31250$

Therefore, the given expression can be written as 25 times 31250 .

For more details, refer to the link:

https://brainly.com/question/23598305