Explain why the greatest common factor of two numbers is sometimes 1.

Ratios and rates are used in Mathematics to solve various problems. They are used in unit conversions through conversion factors, in dimensional analysis, in calculation of relative rates of reaction, and in data measurements for statistical analysis.

Using ratios and rates in Mathematics can be extremely useful to solve a wide range of problems. Ratios are a way to compare two or more quantities, and rates are ratios that compare two different units.

For example, conversion factors, generated from ratios of equivalent quantities with different measurement units, can be very helpful in unit conversions. If we know that 2.54 cm is equivalent to 1 inch, we can set up a ratio of 2.54 cm/1 in. and use it as a conversion factor.

Dimensional Analysis is another technique where ratios play a vital role. It involves using rates or conversion factors to convert units. With practice, we can develop good estimation skills with dimensional analysis, guiding us whether our solution seems reasonable or not.

In addition, ratios can be used in Relative Rates of Reaction in Chemistry, where the rate of a reaction may be expressed as the change in concentration of any reactant or product. Depending on the stoichiometry of the reaction, we can relate reactants and products rates to each other.

Moreover, ratios are employed in data measurements, providing detailed information in fields like Statistics. For example, to analyse the data such as exam scores, we can order the results, calculate the differences, and express the results in ratio form.

https://brainly.com/question/32122042

#SPJ3

Answer:

Barney can make 3 costumes

Step-by-step explanation:

T = 16 1/5 = 81/5 yards

O = 5 2/2 = 27/5 yards/costume.

We have the total fabric (T) and the unitari costume requirement (O). Now, if we want to know the amount of costumes that Barney can make, we can divide total fabric (T) by the unitari costume requirement (O), the result will be the amount of costumes (A).

[tex]A = \frac{T}{O}=\frac{\frac{81}{5}}{\frac{27}{5}} =\frac{81*5}{5*27} =\frac{81}{27}\\A = \frac{81}{27} =\frac{9}{3} = 3 costumes[/tex]

Finally, we can conclude that Barney can make 3 costumes. 

Answer:

The answer for the area of the parking lot is 27,000m²

Step-by-step explanation:

Given that the shape of the parking lot is a rectangle we can model the area using the formula for area of a rectangle Which is

A= length *width

Step two :

Given length 20cm

Width 6cm

Furthermore the scale is

1cm:15m

That is 1cm represents 15m on paper

Therefore the length in meters

=20*15=300m

Width in meter

=6*15=90m

Area =300*90

Area =27,000m²

Answer:

12 hours 15 min

Step-by-step explanation:

Melissa has 14 reports to file.

She file 70% of report. She takes average of 1 hour and 15 minutes for each report.

First we find number of reported by Melissa.

Number of reported = 70% of 14

                                        = 9.8

1 hour 15 min [tex]=\dfrac{5}{4}[/tex] hours

For 1 report of file [tex]=\dfrac{5}{4}[/tex] hours

For 9.8 reports of file [tex]=9.8\times \dfrac{5}{4}\approx 12.25[/tex] hours

She will take 12.25 hours to report 70% of them.

12.25 hours = 12 hours 15 min

Hence, Melissa will take 12 hours 15 min to file 70% of report.

we know that

An equilateral triangle is a regular polygon, because all sides are equal

In a regular polygon the area is equal to

[tex]A=\frac{1}{2}*apothem*perimeter[/tex]

in this problem we have

[tex]apothem=2.16\ cm\\ perimeter=22.45\ cm[/tex]

substitute in the formula

[tex]A=\frac{1}{2}*2.16*22.45[/tex]

[tex]A=24.2\ cm^{2}[/tex]

therefore

the answer is

the area of the triangle is [tex]24.2\ cm^{2}[/tex]

The area of an equilateral triangle rounded to the nearest tenth is 24.2 [tex]cm^2[/tex].

Given the following data:

An equilateral triangle can be defined as a type of triangle or regular polygon that has equal length of sides.

Mathematically, the area of an equilateral triangle is given by this formula:

[tex]Area = \frac{1}{2} \times apothem \times perimeter[/tex]

Substituting the given parameters into the formula, we have;

[tex]Area = \frac{1}{2} \times 2.16 \times 22.45\\\\Area = \frac{1}{2} \times 48.492[/tex]

Area = 24.246 ≈ 24.2 [tex]cm^2[/tex].

Read more on equilateral triangle here: https://brainly.com/question/11844452

The number of people ride the Ferris wheel in 2 hours is 270.

Augmentation is an activity that addresses the fundamental thought of rehashed expansion of a similar number. The numbers that are multiplied are referred to as the factors, and the result that is produced when two or more numbers are multiplied together is referred to as the product of those numbers. Repeated addition of the same number can be made easier by using multiplication.

Given  Ferris wheel can accommodate 54 people in 24 minutes

number of people can ride in 1 minute = 54/24

number of minute in 2 hours is 2 x 60 = 120 minutes

no. of people can ride in 2 hours or 120 minutes is

54/24 x 120 = 270

Hence the 270 people could ride the Ferris wheel in 2 hours.

Learn more about multiplication;

https://brainly.com/question/24327297

#SPJ2

The least number of spiders is 6 and ants is 8.

In mathematics, multiples are the results of multiplying an integer by a given number.

Manifold is the fundamental definition of multiplicity. A multiple in mathematics refers to the outcome of multiplying two numbers together.

For example, multiples of 5 are: 10, 15, 20, 25, 30…etc. Multiples of 7 are: 14, 21, 28, 35, 42, 49…etc.

Given:

A spider has 8 legs.

An ant has 6 legs.

So, multiples of 8= 8, 16, 24, 32, 40, 48

and, multiples of 6= 6, 12, 18, 24, 30, 36, 42, 48

So, least number of spiders because= 8 x 6= 48

and, least number of ants = 6 x 8 = 48

Learn more about multiple here:

https://brainly.com/question/5992872

#SPJ2

To fill a 99-ounce tank with a 1:10 oil to gasoline ratio, you need 9 ounces of oil and 90 ounces of gasoline.

A lawn mower uses a mixture of gas and oil, with a ratio of 10 ounces of gasoline to every 1 ounce of oil. To find out how many ounces of oil and gasoline are required to fill a 99-ounce tank, we set up a proportion.

Let's denote the amount of oil needed as x ounces. Since the ratio is 1:10, then the amount of gasoline needed will be 10x ounces. The sum of oil and gasoline should equal the tank's capacity:

Combining like terms gives us:

Dividing both sides by 11 yields:

Therefore, there would be 9 ounces of oil and 90 ounces of gasoline (since 10 * 9 = 90) required to fill the 99-ounce tank completely.

Final answer:

A 99-ounce tank requires 9 ounces of oil and 90 ounces of gasoline to be filled completely, keeping the ratio of 1 ounce of oil to 10 ounces of gasoline.

Explanation:

The question is about determining the correct ratio of oil to gasoline needed to fill a lawn mower's tank, which holds a mixture of the two. Specifically, for every ounce of oil, the mixture requires 10 ounces of gasoline. To find out how many ounces of oil and gasoline are needed for a 99-ounce tank, we can set up a simple proportion. Let's denote the amount of oil as 'o' in ounces, and since for each ounce of oil we need 10 ounces of gasoline, we thus need '10o' ounces of gasoline.

Therefore, to fill a 99-ounce tank, we would need 9 ounces of oil and 90 ounces of gasoline.

The total number of candies are 3¹² if there are  (3⁶)² . 3⁰ candies in a store; the answer is 3¹² candies option (D) 3¹² is correct.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The number expression is:

= (3⁶)² . 3⁰

As we know, from the properties of the integer exponent:

After using the properties of the integer exponent:

(3⁶)² = 3¹²

3⁰ = 1

(3⁶)² . 3⁰ = 3¹²

Thus, the total number of candies are 3¹² if there are  (3⁶)² . 3⁰ candies in a store; the answer is 3¹² candies option (D) 3¹² is correct.

Learn more about the integer exponent here:

brainly.com/question/4533599

#SPJ2