which is a better buy on apples? 5lbs for $5.25 or 10lbs for $10.25

Answer:B

Step-by-step explanation:

The equation that represents 4 1/4 as a sum of whole numbers and unit fractions is simply 4 + 1/4. This approach demonstrates the decomposition of a mixed number into its integral and fractional components.

To represent 4 1/4 as a sum of whole numbers and unit fractions, we can break it down into its components. This fraction essentially means 4 plus 1/4. The whole number part is straightforward, and the fraction part can be represented as a unit fraction. Thus, 4 1/4 can be expressed as the sum 4 + 1/4.

In mathematics, when decomposing mixed numbers into a sum of whole numbers and fractions, it’s essential to clearly distinguish between the integral and fractional parts. For example, similar numbers like 5 1/3 would decompose into 5 + 1/3. This helps illustrate how mixed numbers can be broken into more straightforward components, making them easier to work with in various mathematical operations and providing a bridge to understanding fractional expressions and addition.

Answer:

  4 1/4 = 1 + 3 + 1/6 + 1/12

Step-by-step explanation:

You want an equation that represents 4 1/4 as the sum of whole numbers and unit fractions.

The whole number portion of 4 1/4 is 4. The number 4 can be represented as a sum of whole numbers (plural) several ways:

  4 = 0 + 4
  4 = 1 + 3
  4 = 2 + 2

  4 = 0 + 1 + 3
  4 = 1 + 1 + 2

  4 = 1 + 1 + 1 + 1

Of course, any quantity of the whole number 0 can be added to any of these sums. We have shown a couple of instances of that.

In our answer here, we choose the representation to be 4 = 1 +3.

A unit fraction is a fraction with a numerator of 1. In the mixed number 4 1/4, the fraction portion, 1/4, is already a unit fraction. The problem statement here asks for a representation involving "unit fractions" (plural). We can divide 1/4 into any number of equal unit fractions:

  1/4 = 1/8 + 1/8 . . . . 2 equal unit fractions

  1/4 = 1/12 + 1/12 + 1/12 . . . . 3 equal unit fractions

This latter representation suggests a way to use unequal unit fractions to represent 1/4:

  1/4 = (1/12 + 1/12) +1/12 = 2/12 +1/12 = 1/6 +1/12

Using these two unit fractions, our equation can be written ...

  4 1/4 = 1 + 3 + 1/6 + 1/12

Final answer:

The triangles ABD and CDB are congruent by the Side-Angle-Side (SAS) postulate, leading to the conclusion that quadrilateral ABCD is a parallelogram.

Explanation:

The triangles ABD and CDB can be proved congruent by the Side-Angle-Side (SAS) postulate. Since side AB is parallel to side DC, the alternate interior angles angle ABD and angle BDC are congruent. With both triangles sharing side DB and having equal sides AB and DC, the two triangles satisfy the conditions of the SAS postulate.

By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) principle, angles DBC and ADB are congruent as well as sides AD and BC. Since angle DBC and angle ADB form a pair of alternate interior angles, this implies that AD is congruent and parallel to BC. This leads to the conclusion that quadrilateral ABCD is a parallelogram, characterized by its opposite sides being equal and parallel.

Final answer:

Calculate the sum of areas of squares with given side lengths to find the total area.

Explanation:

Area of a Square:

Calculate the area of each square:

14 km x 14 km = (14)² = 196 km²

12 km x 12 km = (12)² = 144 km²

8 km x 8 km = (8)² = 64 km²

5 km x 5 km =  (5)² = 25 km²

4 km x 4 km = (4)² = 16 km²

9 km x 9 km =  (9)² = 81 km²

Sum of Areas:

Add the areas of all squares together:

196 km² + 144 km² + 64 km² + 25 km² + 16 km² + 81 km² = 526 km²

Therefore, the total area is 526 km².

Answer:

[tex].06 = \frac{6}{100} = \frac{3}{50} [/tex]

The hourly charges to clean floors and to clean the rest of the house are $15 and $18, respectively. We determine this by setting up a system of equations from the provided scenarios and solving for x and y.

To solve for the hourly charges to clean floors (x) and to clean the rest of the house (y), we need to set up two equations based on the information provided:

Let's solve this system of equations step by step.

Step 1: From the second equation, we can express x in terms of y:
 x = 87 - 4y

Step 2: Substitute this expression for x in the first equation:
 2(87 - 4y) + 3y = 84

Which simplifies to:
 174 - 8y + 3y = 84

Combining like terms gives us:
 -5y = -90

Step 3: Solve for y:
 y = 18

Step 4: Now, plug the value of y back into the expression for x:
 x = 87 - 4(18)
 x = 15

Therefore, the hourly charges to clean floors and to clean the rest of the house are $15 and $18 respectively, which corresponds to option B. (15, 18).

Answer:

The area of sector GPH is equal to [tex]50\pi\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=15\ units[/tex]

substitute

[tex]A=\pi(15)^{2}=225 \pi\ units^{2}[/tex]

[tex]360\°[/tex] subtends the complete circle of area [tex]225 \pi\ units^{2}[/tex]

so

By proportion

Find the area of sector GPH

[tex]\frac{225 \pi}{360}\frac{\ units^{2} }{degrees} =\frac{x}{80}\frac{\ units^{2} }{degrees}\\ \\x=80*225\pi /360\\ \\x=50\pi\ units^{2}[/tex]

i think your answer is

x(number of club members) is equal(=) or larger(>) to 25

im not sure its right though

To compare the amount of sand in the top cone of an hourglass when the height is one inch, calculate the volume using the formula volume = length × width × height. Compare the original volume to the new volume with a height of one inch to determine the difference in the amount of sand.

The question asks to compare the amount of sand in the top cone of an hourglass to the amount when the height of the sand in the top cone is only one inch. In an idealized model of the hourglass, the volume of the stack of sand in the top cone can be calculated using the formula volume = length × width × height. From the given information, the volume of the stack is 9 in³. To find the amount of sand when the height is one inch, we can calculate the new volume using the same formula with the new height.

By comparing the original volume of 9 in³ to the new volume with a height of one inch, you can determine the difference in the amount of sand in the top cone of the hourglass.

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The amount of sand in the top cone when the height of the sand is h is h times the amount of sand there will be when the height of the sand is only one inch.

The volume of a cone is given by the formula:

V = (1/3)πr²h

where r is the radius of the base of the cone and h is the height of the cone.

If the height of the sand in the top cone is currently h, then the volume of the sand in the top cone is:

V₁ = (1/3)πr²h

When the height of the sand in the top cone is only one inch, the volume of the sand in the top cone will be:

V₂ = (1/3)πr²(1 inch)

To compare the two volumes, we can divide V₁ by V₂

V₁ / V₂ = (1/3)πr²h / (1/3)πr²(1 inch)

V₁ / V₂ = h / 1 inch

Therefore, the amount of sand in the top cone when the height of the sand is h is h times the amount of sand there will be when the height of the sand is only one inch.

For such more question on height

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Answer: it is 7.7

Step-by-step explanation:

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Answer:

C

Step-by-step explanation:

I got it right and here is proof

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Answer:

The value of A is 3 square units.

Step-by-step explanation:

Given: [tex]s=\frac{1}[2}[/tex] unit  and A is given by [tex]A=12s^2[/tex]

We have to find the value of A.

Consider the given formula [tex]A=12s^2[/tex]

Put [tex]s=\frac{1}[2}[/tex]

We get,

[tex]A=12(\frac{1}{2})^2[/tex]

Simplify, we have,

[tex]A=12\cdot\frac{1}{4}[/tex]

Further simplify, we have,

[tex]A=3[/tex]

Thus, The value of A is 3 square units.

Answer:

The answers are solved below.

Step-by-step explanation:

we have to solve the given expressions

Part A: The expression (-7)(-7)(-7)

[tex] (-7)(-7)(-7)=(-1)^37^3[/tex]

Option 3 is correct

Part B: [tex]2(5 - 3)^2 + 6^2[/tex]

First step to solve the above expression is to simplify (5-3) by BODMAS rule then to square the simplification.

Option 3 is correct.

Part C: To choose the expression  "five to the third power"

"five to the third power" is

[tex]5^3=5.5.5=125[/tex]

All 3 represents the expression  "five to the third power"

Option 1,3,4 are correct.

Part D: The expression -8 · -8 · -8 · -8

The above expression can be written as

[tex](-8)^4[/tex]

Option 2 is correct

Part E: [tex]\text{The value of } -6^2[/tex]

[tex]-6^2=-(6\times 6)=-36[/tex]

Option 1 is correct

Part F: [tex]\text{The value of } |5| - 4(3^2 - 2)[/tex]

[tex]|5| - 4(3^2 - 2)=5-4(9-2)=5-4(7)=5-28=-23[/tex]

Option 4 is correct.

Part G: Evaluate [tex]\frac{8}{ -2}\times 4^2 + 9[/tex]

[tex]\frac{8}{ -2}\times 4^2 + 9=-4\times 16+9=-64+9=-55{ [/tex]

Option 2 is correct.

Part H:  Simplify [tex]-5^2 + 8|-1| + (-3)[/tex]

[tex]-5^2 + 8|-1| + (-3)=-25+8-3=-17-3=-20[/tex]

Option 3 is correct.