Ramon needs 12 oranges to make 3 glasses of juice. What is the unit rate? Explain what it means in this situation.

We can choose a starting number to be 1. Following the rules from card one, the sequence would be as follows;

1, 2.6, 2.93, 9.43, 9.68

How to write the terms in a sequence

To write the terms in the sequence above, we started with the number 1. This is followed up by applying the rules listed on the card. So, we first add 1.6 to 1, then add 0.33, 6.5, and add 0.25. The resulting values that are borne from this addition would be 1, 2.6, 2.93, 9.43, 9.68.

Description of the pattern is a method that describes the rule or pattern governing the sequence without providing a specific formula or recursion. We could describe a sequence as increasing by 2  or alternating between 1 and 2.

To demonstrate proportionality between two objects, utilize a table to observe constant ratios, plot points on a graph to confirm a linear relationship passing through the origin, and formulate an equation representing the proportional relationship.

To demonstrate proportionality between two objects, you can use a table, graph, and equation.

Firstly, create a table with corresponding values of the two objects. If they are proportional, their ratios should remain constant.

Secondly, plot the points on a graph with one object on the x-axis and the other on the y-axis.

If the points form a straight line passing through the origin, it indicates proportionality.

Lastly, formulate an equation representing the relationship between the two objects.

For example, if the objects are x and y, and they are proportional, then y = kx, where k is the constant of proportionality.

By analyzing the table, graph, and equation, you can conclusively establish proportionality between the two objects.

The requried ratio of the mark let to the amount of money Fred had left is 3:4.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
mark an Fred had some money in the ratio 6:1. Mark gave half of his money to Fred.
Total proportion of money = 6 + 1 = 7,
Now,
assume that Mark has 6 coins and Fred has 1 coin,
Mark giving half of his coin to Fred means mark give 3 coins to fred,
Now,
Mark has 3 coins and Fred has 4 coins,
the ratio is given as
= 3 / 4

Thus, the requried ratio of the mark had left to the amount of money fred had left is 3:4.

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Keywords:

Tank, capacity, water, gallons, rule of three, variable, days

For this case we have a tank with a capacity of 18,000 gallons, we want to know how many days 12000 gallons of the tank are emptied, with the use of water following an average rate of 450 gallons per day. So we make a rule of three according to the use of water per day:

450 gallons -----------> 1 day

12000 gallons -------> x

Where the variable "x" represents the number of days when water takes to reach 6000 gallons.

[tex]x = \frac {12000 * 1} {450}\\x = 26.67[/tex]

Rounding the nearest whole we have:

[tex]x = 27[/tex]

Answer:

For the tank to go from 18,000 gallons of water to 6000 gallons of water, it should take approximately 27 days, using the water at an average rate of 450 gallons per day.

[tex]x = 27\ days[/tex]

To find the cost per pound of flour, we set up two equations based on the purchases and solved the system of linear equations, resulting in a cost of $0.30 per pound of flour.

The question involves solving a system of linear equations to determine the cost per pound of flour. By setting up two equations based on the given transactions, we can solve for the prices of sugar and flour. Let's designate the cost per pound of flour as f and the cost per pound of sugar as s.

The first purchase equation is: 12s + 15f = $9.30.
The second purchase equation is: 4s + 10f = $4.60.

To solve for f, we can multiply the second equation by 3, which gives us 12s + 30f = $13.80, then subtract the first purchase equation from this to eliminate s and solve for f. By subtracting we get: 15f - 30f = $13.80 - $9.30, which simplifies to -15f = $4.50.

Dividing both sides by -15 gives us the cost per pound of flour: f = $0.30.

Final answer:

To determine how many times 48 goes into 132, perform a division, resulting in 48 going into 132 exactly 2 times with a remainder of 36.

Explanation:

The student has asked how many times 48 goes into 132. To find out, we perform a division, with 132 being the dividend and 48 being the divisor.

We start the division process by seeing how many times 48 can fit into 132. Dividing 132 by 48, we get:

48 goes into 132 twice (2 times), which equals 96.

Subtract 96 from 132, which leaves us with a remainder of 36.

Since 36 is less than 48, we cannot divide any further without getting into fractions or decimals.

The result is that 48 goes into 132 a total of 2 full times with a remainder of 36.

The baker will need 27 cups of flour to go with the 18 cups of sugar when making the oversized sheet cake for the school dance.

The given ratio states that for every 2 cups of sugar, 3 cups of flour are needed in the recipe. We are given that the baker is using 18 cups of sugar and we need to find the corresponding amount of flour.

To determine the amount of flour needed, we can set up a proportion based on the ratio. Let's use "x" to represent the unknown amount of flour:

2 cups of sugar / 3 cups of flour = 18 cups of sugar / x cups of flour

Cross-multiplying the proportion, we get:

2 cups of sugar * x cups of flour = 18 cups of sugar * 3 cups of flour

Simplifying further:

2x = 54

Dividing both sides by 2, we find:

x = 27

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