Compare and contrast expressions equations and inequalities

Answer:

Alaina will require 1.5 cups of flour to make [tex]\frac{2}{3}[/tex] batches of cookies.  

Step-by-step explanation:

We are given the following information in the question:

Amount of flour required per batch of cookies =

[tex]2\displaystyle\frac{1}{4}\text{ cups}[/tex]

Number of batches of cookies Alaina wants to make = [tex]\displaystyle\frac{2}{3}[/tex]

Formula:

[tex]\text{Flour required} = \text{Flour required to make 1 batch of cookies}\times \text{Number of batches}\\\\=2 \displaystyle\frac{1}{4}\times \frac{2}{3}\\\\= \frac{9}{4}\times \frac{2}{3} = \frac{3}{2} = 1.5\text{ cups of flour}[/tex]

Hence, Alaina will require 1.5 cups of flour to make [tex]\frac{2}{3}[/tex] batches of cookies.

Answer:

C

Step-by-step explanation:

The person weighs 560 more on Mars than on the moon.

On comparing the weight of the individual on Earth, Mars and Moon, we concluded -

W[Earth] > W[Mars] > W[Moon]

Weight is the force exerted by the earth on an object at the surface of the earth. Mathematically -

W = m x g

where -

[m] is the mass of object

[g] is acceleration due to gravity

Given is a person who weighs 240 pounds on Earth.

The weight of the individual in kg m/s² (Newtons) on earth would be -

W[Earth] = 240 x 0.45359237 x 9.8 = 1066.84 N

The weight of the same individual on mars would be -

W[Mars] = 240 x 0.45359237 x 3.11 = 333.56 N

The weight of the same individual on moon would be -

W[Moon] = 240 x 0.45359237 x 1.625 = 176.90 N

Therefore, we can conclude that W[Earth] > W[Mars] > W[Moon].

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Final Answer:

2(x−15)

Step 1: Translate the problem into a system of equations

We are given that the triangle is isosceles, meaning two sides have the same length. Let's call this length x. The third side is 30 meters shorter than twice the length of each congruent side, so it has a length of 2x−30. The perimeter of the triangle is the sum of all three side lengths, which is equal to 570 meters.

Therefore, we can set up the following equation:

x+x+(2x−30)=570

Step 2: Solve the system of equations

Combining like terms, we get:

4x−30=570

Adding 30 to both sides, we get:

4x=600

Dividing both sides by 4, we get:

x=150

Step 3: Find the side lengths

Now that we know the value of x, we can find the lengths of all three sides:

The first and second sides have a length of x, which is 150 meters each.

The third side has a length of 2x−30, which is 2(150) - 30 = 270 meters.

Answer:

The lengths of the sides of the triangle are:

First side: 150 meters

Second side: 150 meters

Third side: 270 meters

Final Answer:

2(x−15)


The probbale question can be: The triangle shown at the right is isosceles. That is, it has two sides of an equal length. The third side is 30 m shorter than twice the length of each congruent side. The perimeter is 570 m. Find the length of each side.

R 10 m; 6 m; 9 m

X

X

2x - 30'

Leo and Robyn receive $15,862 and $23,793 respectively.

A ratio is an ordered pair of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two ratios are specified to be equal.

Given data;

Total funding= $39655.

Funding in the ratio = 2:3

If x is the part by which one person receive;

The equation is found as;

2x+3x=$39655.

5x=$39655.

x=7931

Leo gets;

2x=2×$7931= $15,862

Robyn gets;

3x=3×$7931== $23,793

Hence,Leo and Robyn receive $15,862 and $23,793 respectively.

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To arrange the numbers 1/6, 0.29, 23%, 3/5, and 0.027 from smallest to largest, convert them to decimals and then compare. The order from smallest to largest is: 0.027, 1/6 (0.166...), 23% (0.23), 0.29, and 3/5 (0.6).

Explanation:

To arrange the numbers 1/6, 0.29, 23%, 3/5, and 0.027 from smallest to largest, we first need to convert them all to the same format. We can convert percentages to decimals by dividing by 100 and fractions to decimals by division. Here are the conversions:

Now that they are all in decimal form, we can easily compare them:

A 6-pound bag of sugar can make 14 whole batches of muffins and the cost for sugar per each batch is approximately $0.32.

The subject of this question is in the field of Mathematics, specifically dealing with ratios and proportions. To determine the number of whole batches of muffins a bag of sugar can make, you will first need to find the number of cups in the bag. Given that 1 cup is equivalent to 48 teaspoons and the 6-pound bag of sugar contains 681 teaspoons, divide 681 by 48 to get roughly 14.1875. Since we cannot make a fraction of a batch, round down to 14, which is the number of whole batches we can make.

To find the cost per batch, divide the total cost ($4.49) by the number of batches (14) to get a per-batch cost of roughly $0.32.

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