How can you solve problems involving equivalent expressions?

Absolute values in mathematics and Kelvin temperatures both provide 'absolute' measurements, with absolute value indicating distance from zero and the Kelvin scale starting at absolute zero, the theoretical absence of kinetic energy.

Both absolute values in mathematics and temperatures on the Kelvin scale represent 'absolute' measurements in their respective fields. In mathematics, the absolute value indicates the distance of a number from zero on the number line, irrespective of direction. Similarly, the Kelvin scale is used in physics and deals with the absolute temperature, where 0 K (absolute zero) represents a theoretical state where particles possess minimal vibrational motion, implying no kinetic energy.

The Kelvin scale is important in scientific work because it starts at this absolute zero point. Therefore, it allows for the measurement of true thermal energy. The Kelvin scale is similar to the Celsius scale in that the size of its degree is the same, but the Kelvin scale does not start at the freezing point of water. Instead, it starts at absolute zero, making it a true absolute scale that measures the fundamental property of temperature.

Final answer:

The price of organic sugar at the Belleville store increased from $4 to $5 per pound, which is a 25% increase in price.

Explanation:

The percent of increase in the price of organic sugar from $4 to $5 per pound can be calculated through a few steps. To determine the percentage increase, you subtract the old value from the new value, then divide the result by the old value. Finally, you multiply by 100 to convert it into a percentage.

Here is the step-by-step calculation:

Determine the increase in price: $5 - $4 = $1.

Divide the increase by the original price: $1 ÷ $4 = 0.25.

Multiply by 100 to get the percentage: 0.25 × 100 = 25%.

Therefore, the price of organic sugar increased by 25%.

The price of organic sugar at a healthy foods store in Belleville was recently increased from $4 per pound to $5 per pound. The percent of increase in the price of this item is 25%.

To find the percent of increase in the price of the organic sugar, we can use the formula:

Percent increase = ((new price - old price) / old price) * 100

First, let's calculate the percent increase:

Percent increase = (($5 - $4) / $4) * 100 = (1 / 4) * 100 = 25%

Therefore, the percent of increase in the price of organic sugar is 25%.

The slope of the points (-8, 18) and (-14, -3) will be 7/2.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points are,

⇒ (-8, 18) and (-14, -3)

Now,

Since, We know that,

The slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) will be;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, The slope of the line passing through the points (-8, 18) and

(-14, -3) will be;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

⇒ m = (- 3 - 18) / (- 14 - (-8))

⇒ m = - 21 / (- 14 + 8)

⇒ m = - 21 / - 6

⇒ m = 7/2

Thus, The slope of the points (-8, 18) and (-14, -3) will be 7/2.

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The student is asking to calculate the slope between two points, (-8, 18) and (-14, -3). By using the slope formula (rise over run), we computed the slope to be 3.5.

The student is asking for the calculation of the slope between two points, which is a concept in algebra and coordinate geometry. To find the slope, you can use the formula:

Applying this to the given points (-8, 18) and (-14, -3), we find:

Therefore, the slope is 3.5.

Final answer:

Juan has a total of x + 8 pieces of fruit, where x represents the number of apples and the 8 represents the fixed number of oranges.

Explanation:

The question involves a simple algebraic expression to determine the total number of pieces of fruit Juan has. Given that Juan has x apples and 8 oranges, the total number of pieces of fruit he has can be represented as the sum of these two quantities.

In algebraic terms, the total number of pieces of fruit Juan has is x + 8, where 'x' represents the unknown number of apples. There is no need for more complex operations or considerations; the answer simply requires the addition of the two amounts.

Answer:

1 x 10^-1m or A on edge

Step-by-step explanation:

just took the test

Answer:more variables are needed to solve

Step-by-step explanation:

Answer:

Step-by-step explanation:

The table is attached.

You can observe in the table that there's no a value for 29 minutes.

That means we need to find the linear expression and then calculate the answer.

First, we need to find the ratio of change using two pairs of the given table and the following formula, (20,220) and (40,440) are the points

[tex]m=\frac{440-220}{40-20}=\frac{220}{20} =11[/tex]

The ratio of change states that Jane burns 11 calories per minute. So, after 29 minutes, she will burn

[tex]11cal(29min)=319 cal/min[/tex]

Answer:

Between 29% and 49% (just took quiz on Edge)

The rest of the question is: To the nearest percent, with a confidence level of 95% (z*- score 1.96), what is the confidence interval for the proportion of cable subscribers who would be willing to pay extra for the new nature channel?

Using the properties of exponents, the expression is simplified as (4/3)x⁵y².

To simplify the given expression, we need to use properties of exponents

Taking the numerator;

[(2x³y)⁴] = (2⁴)(x³)⁴(y)⁴ = 16x¹²y⁴

Next, let's simplify the denominator:

3x²(4x⁵y²) = 3 * 4 * x² * x⁵ * y² = 12x⁷y²

This can be expressed as;

[(2x³y)⁴] / [3x²(4x⁵y²)] = (16x¹²y⁴) / (12x⁷y²)

Take the common factors and divide both of them;

(16x¹²y⁴) / (12x⁷y²) = (4/3)(x¹² / x⁷)(y⁴ / y²) = (4/3)x¹²⁻⁷y⁴⁻² = (4/3)x⁵y²

Therefore, the simplified expression is (4/3)x⁵y².

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Answer:

90 + 50 = 140 square cm

Measurement of the bookcase on the scale drawing using the scale 3cm:2 feet is width =19.5 cm and height = 36 cm

Scaling an object means multiplying every linear dimension of it by the same factor

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

Width of the bookcase = 13 feet

Height of the bookcase = 24 feet

Given scale is 3cm : 2 feet

Therefore for 1 feet = 1.5 cm

Then,

Width of the bookcase = 13×1.5= 19.5 cm

Height of the bookcase = 24×1.5= 36 cm

Hence, the measurements of the bookcase after scaling is width =19.5 cm and height = 36 cm

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To determine the unknown side length of a golden rectangle, set up a proportion and solve a quadratic equation.

The golden rectangle is a rectangle in which the ratio of the longer side to the shorter side is equal to the golden ratio, approximately 1.618. To determine the unknown side length, we can set up a proportion using the given side length and the golden ratio:

s / t = (s + t) / s

Substituting the given values, we have:

s / 9 = (s + 9) / s

Cross multiplying and simplifying, we get:

s^2 = 9(s + 9)

By solving this quadratic equation, we find that the unknown side length is approximately 4.94. Therefore, the correct answer is c. 4.94.

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Answer:

(1,14)

Step-by-step explanation:

Answer:

Vertex of the parabola is ( 1 , 14 ).

Step-by-step explanation:

Given Equation of parabola is [tex]y=-2^2+4x+12[/tex]

We have to find the vertex of the parabola.

We first convert the given equation of parabola in standard equation of parabola using completing the square method.

Standard equation of parabola,

[tex](x-h)^2=4a(y-k)[/tex]  

here, ( h , k ) is coordinates of the vertex of the parabola.

consider,

y = -2x² + 4x + 12

y = -2( x² - 2x - 6 )

y = -2 ( x² - 2x  + 1² - 1² - 6 )

y = -2 ( x -1 )² - 7 × ( -2 )

y - 14 = -2 ( x - 1 )²

[tex](x-1)^2=\frac{1}{2}(y-14)[/tex]

By comparing,

vertex = ( 1 , 14 )

Therefore, Vertex of the parabola is ( 1 , 14 ).

Answer:

1600

Step-by-step explanation:

There will be 1600 E. coli bacteria, in 1 hour.

In maths, to multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem.

Given that, Mitosis is a process of cell reproduction in which one cell divides into two identical cells. E. coli is a fast-growing bacterium that is often responsible for food poisoning in uncooked meat. It can reproduce itself in 15 minutes.

In the beginning, there are 100

After 15 minutes, there are 2*100=200

After 30 minutes, there will be 2*200 =400

After 45 minutes = 400*2 = 800

After 60 minutes = 800*2 = 1600

Hence, in 1 hour there will be 1600 E. coli bacteria.

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Statement 1 is true: the majority of seniors read between 0 and 5 books. Statement 2 is false: the average number of books read is around 6-7, not between 10 and 11. Statement 3 is true: more seniors read 11-15 books than 16-20 books.

To determine which statement is true, let's first analyze the data provided in the table. Since the table isn't available, I'll make some assumptions to guide us through the explanation. Let's say the table looks like this:

Number of Books Read                Number of Seniors

0-5                                                  20

6-10                                                 15

11-15                                                 10

16-20                                               5

Now, we'll examine each statement to see if it aligns with the data:

"The majority of seniors read between 0 and 5 books in the past year."

This statement is true if the number of seniors who read 0-5 books is greater than the total number of seniors who read in other ranges. In this case, 20 seniors read 0-5 books, which is the highest count among all ranges. So, this statement is true.

"The average number of books read by seniors is between 10 and 11."

To find the average, we multiply the midpoint of each range by the number of seniors in that range, sum them up, and then divide by the total number of seniors. Doing the calculation, the average comes out to around 6-7 books, not 10-11. So, this statement is false.

"More seniors read 11-15 books than 16-20 books."

To verify this, we check the counts for each range. If the count for 11-15 books is greater than the count for 16-20 books, the statement is true. In this case, if 10 seniors read 11-15 books and 5 seniors read 16-20 books, the statement is true.

Based on this analysis, statements 1 and 3 are true, while statement 2 is false.

complete question=

Which statement is true regarding the survey conducted by a researcher who randomly surveyed seniors at a high school and asked about the number of books they read in the past year, as depicted in the provided table?