pranav's school is selling tickets to a play. On the first day of tickets sales the school sold 8 adult tickets and 4 child tickets for a total of $80. The school took in $64 on the second day by selling 6 adult tickets and 4 child tickets. What is the price each of one adult ticket and one child ticket?

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.

Answer: The length of row of bricks is 68 inches.

Step-by-step explanation:

Since we have given that

Number of bricks = 8

Length of bricks = [tex]8\dfrac{1}{2}=\dfrac{17}{2}[/tex]

So, Length of the row of bricks is given by

Number of bricks × length of brick

[tex]8\times \dfrac{17}{2}\\\\=4\times 17\\\\=68\ inches[/tex]

Hence, the length of row of bricks is 68 inches.

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.

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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].

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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.

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Answer: 0.4

Step-by-step explanation:

Given : The number of times Jackson tossed the coin = 10

The number of times he got heads = 4

Now , the experimental probability that he will get head on next flip is :_

[tex]\text{P(Head)}=\dfrac{\text{P(Number of times he got head)}}{\text{Number of times he tossed the coin}}\\\\=\dfrac{4}{10}=0.4[/tex]

Thus , the experimental probability that Jackson will flip heads on his next flip is 0.4.

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

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