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1 year ago

How is 25:5 and 10:2 equivalent ratios to 5:1 and 15:3

Mathematics

1 answer:

3241004551 [841]1 year ago

8 0

All the ratios 25:5, 10:2, 5:1, and 15:3 are equivalent to each other.

Ratio:

Ratio is referred as the an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

Here we have the ratio 25:5 and 10:2 equivalent ratios to 5:1 and 15:3.

Basically, the equivalent ratios are calculated as by either dividing or multiply with some other real numbers in order to simplify it.

First, we have to take the ratio 25: 5,

When we simplify it by dividing the term by 5, then we get, 5:1.

So, the term 25: 5 is equivalent to 5:1.

Similarly, when we take 10:2 and then we simply divide it by 2, then we get 5:1.

So, both ratio are equivalent one with 5:1. But not associated with the other ratio 15:3.

But when we simplify 15:3 by dividing it using 3, then we get 5:1.

Therefore, all the ratios 25:5, 10:2, 5:1, and 15:3 are equivalent to each other.

To know more about Ratio here.

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Which strategy best explains how to solve this problem?

Rufina [12.5K]

This is a geometric sequence because each term is twice the value of the previous term. So this is what would be called the common ratio, which in this case is 2. Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a(n)=nth value, a=initial value, r=common ratio, n=term number

In this case we have r=2 and a=1 so

a(n)=2^(n-1) so on the sixth week he will run:

a(6)=2^5=32

He will run 32 blocks by the end of the sixth week.

Now if you wanted to know the total amount he runs in the six weeks, you need the sum of the terms and the sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r) where the variables have the same values so

s(n)=(1-2^n)/(1-2)

s(n)=2^n-1 so

s(6)=2^6-1

s(6)=64-1

s(6)=63 blocks

So he would run a total of 63 blocks in the six weeks.

4 0

3 years ago

Read 2 more answers

The groundhog population of Punxsutawny, Pennsylvania is closely monitored each year. Two years ago the population decreased by

kap26 [50]

Answer:

There was a increase of 1.7% over these three years

Step-by-step explanation:

Multipliers:

For a decrease of a%, we multiply by: $\frac{100-a}{100}$

For a increase of a%, we multiply by: $\frac{100+a}{100}$

What was the percentage increase/decrease of groundhogs over these three years?

Decrease of 12%(multiplication by 0.88).

Increase of 6%(multiplication by 1.06).

Increase of 9%(multiplication by 1.09).

After these three years:

0.88*1.06*1.09 = 1.017

1.017 - 1 = 0.017

0.017*100% = 1.7%

There was a increase of 1.7% over these three years

3 0

3 years ago

It is known that 1.4< square root of 2 <1.5. Find all possible values of the expression 2-square root of 2. How do I find

horsena [70]

Answer:

0.5<2-√2<0.6

Step-by-step explanation:

The original inequality states that 1.4<√2<1.5

For the second inequality, you can think of 2-√2 as 2+(-√2).

Because of the "properties of inequalities", we know that when a positive inequality is being turned into a negative, the numbers need to swap and become negative. So, the original inequality becomes -1.5<-√2<-1.4. (Notice how the √2 becomes negative, too). This makes sense because -1.5 is less than -1.4.

Using our new inequality, we can solve the problem. Instead of 2+(-√2), we are going to switch "-√2" with both possibilities of -1.5 and -1.6. For -1.5, we would get 2+(-1.5), or 0.5. For -1.4, we would get 2+(-1.4), or 0.6.

Now, we insert the new numbers into the equation _<2-√2<_. The 0.5 would take the original equation's "1.4" place, and 0.6 would take 1.5's. In the end, you'd get 0.5<2-√2<0.6. All possible values of 2-√2 would be between 0.5 and 0.6.

Hope this helped!

4 0

3 years ago

What is the reciprocal of 17 1/2

Aneli [31]

Answer:

2/35

Step-by-step explanation:

If you convert 17 1/2 to a improper fraction, it becomes 35/2. Then to find the reciprocal, flip the numerator and denominator. So, 2/35

Hope this helps!

4 0

2 years ago

A store buys stereo from the manufacturer for $443. After applying a markup of 45% to the item, the store then tries to sell it

attashe74 [19]

Multiply $443.00 by .45 = $199.35

8 0

3 years ago