a worker cuts a section from cake b to make it the same length as cake a . she sets aside the unneeded portion of cake. How long is the portion of cake she set aside?

After making all the necessary adjustments, the reconciled bank balance for ABC Company's ledger at the end of July is Br. 4,164.42.

To reconcile the bank statement balance with the company's ledger balance for ABC Company, we need to go through the provided information step by step and make the necessary adjustments. Let's calculate the adjusted bank balance:

Starting with the bank statement balance: Br. 4,964.47

Add the deposit made after banking hours: + Br. 410.90

New bank balance: Br. 5,375.37

Now let's make adjustments for the outstanding checks and other transactions:

Deduct the erroneously charged check: - Br. 973

New bank balance: Br. 4,402.37

Deduct the outstanding checks:

Check No. 801: Br. 100.00

Check No. 888: Br. 10.25

Check No. 890: Br. 294.50

Check No. 891: Br. 205.00

Total deduction: Br. 609.75

New bank balance: Br. 3,792.62

Correct the incorrectly charged check: + Br. 90

New bank balance: Br. 3,882.62

Add the proceeds from the collection of the interest-bearing note: + Br. 500.00

New bank balance: Br. 4,382.62

Add the interest earned on the average account balance: + Br. 24.75

New bank balance: Br. 4,407.37

Deduct the incorrectly recorded check: - Br. 90

New bank balance: Br. 4,317.37

Deduct the fee charged for handling the collection of the note: - Br. 5.00

New bank balance: Br. 4,312.37

Deduct the check returned due to insufficient funds: - Br. 50.25

New bank balance: Br. 4,262.12

Deduct the service charge for the month of July: - Br. 12.70

New bank balance: Br. 4,249.42

Deduct the erroneously recorded check: - Br. 85.00

New bank balance: Br. 4,164.42

Now, we compare the adjusted bank balance (Br. 4,164.42) with the ledger balance provided (Br. 4,173.83).

Adjusted bank balance: Br. 4,164.42

Ledger balance: Br. 4,173.83

The difference between the adjusted bank balance and the ledger balance is Br. 9.41. This difference is likely due to some unrecorded transactions or errors in recording. To reconcile the balances fully, further investigation is required to identify the specific cause of the discrepancy and make the necessary adjustments in the company's ledger.

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The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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Answer:

7 1/2-(3+7 1/3)= -17/6=-2 5/6 ≅ -2.8333333

Step-by-step explanation:

Step-by-step explanation:

To find the unit rate in kilometers per minute, we need to divide the distance traveled (52/2 kilometers) by the time taken (23/4 minutes).

52/2 kilometers = 26 kilometers

23/4 minutes = 5.75 minutes

So, the unit rate in kilometers per minute is:

26 kilometers / 5.75 minutes = 4.52 kilometers per minute (rounded to two decimal places)

The unit rate of the car that travels 5 2/5 km in 2 3/4 mins is 1.96 km/min.

Distance travelled by a car = 5 2/5 km = 5.4 km

Time travelled = 2 3/4 mins = 2.75 mins

The unit rate in km/min = 5.4/2.75

The unit rate in km/min = 1.96 km/min.

Happy to help, have a great day! :)

The total income for the month, considering the beginning balance of R15,000, sales of R25,000, and rent income of R5,000, amounts to R45,000.

To calculate the total income for the month, we need to consider the beginning balance, sales, and rent income.

Beginning balance: R15,000

Sales: R25,000

Rent income: R5,000

To find the total income, we sum up the beginning balance, sales, and rent income:

Total income = Beginning balance + Sales + Rent income

Total income = R15,000 + R25,000 + R5,000

Total income = R45,000

Therefore, the total income for the month is R45,000.

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No, his answer is not correct because each of the smaller divisions represents 1/6, not 3.

Mark's answer is not correct.

When dividing a number line into equal sections, the value of each section represents a fraction of the whole.

In this case, Mark divided the number line from 0 to 1 into 3 equal sections and then divided each of those sections into 2 equal parts.

Initially, the whole number line from 0 to 1 represents the number 1. When Mark divided it into 3 equal sections, each section represents 1/3 (one-third) of the whole.

So far, this is correct.

However, when Mark further divided each of the 1/3 sections into 2 equal parts, each part represents 1/2 (one-half) of the 1/3 section.

So, each of these smaller divisions represents 1/2 [tex]\times[/tex] 1/3 = 1/6 (one-sixth) of the whole.

Therefore, the correct representation of each of the smaller divisions is 1/6, not 3.

Mark made an error by mistakenly assuming that each smaller division represents the number 3.

In summary, Mark's answer of 3 is incorrect because each of the smaller divisions represents 1/6, not 3.

The correct representation for dividing the number line as described is 1/6.

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The ratio of total cholesterol to HDL cholesterol can be found by dividing the total cholesterol by the HDL cholesterol. So, the patient's ratio of total cholesterol to HDL cholesterol is:185 mg/dl ÷ 40 mg/dl = 4.625 mg/dl (dividing both numerator and denominator by 5)⇒ 37/8 (after simplification).

Thus, the patient's ratio of total cholesterol to HDL cholesterol is 37/8

The y-intercept of the linear function means that her initial distance from the finish line is of 10 kilometers.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 10, hence the intercept b is given as follows:

b = 10.

The y-values represent the distance in the context of this problem, hence the initial distance is of 10 km.

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A) The interval where the graph is increasing is: (0,0) to (40, 4)

The  interval where the graph remains constant is from: (120, 3) to (140, 3).

The  interval where the graph is decreasing in depth is from: (140, 3) to (180, 0).

B) The domain is from 0 to 180 minutes.

The range of the graph is from 0 to 4 feet.

C) Yes, the graph represents a function

D) The graph depicts the filling of the pool from 0 to 4 feet, followed by a period of constant depth, and finally, the draining of the pool back to 0 feet.

Part A:

- Increasing interval:

The interval where the graph is increasing is from the starting point coordinate (0,0) to the coordinate (40, 4)

- Constant interval:

The  interval where the graph remains constant at a depth of 4 feet which is from (40, 4) to (80, 4) and then from where the depth is 3 feet which is from the coordinates (120, 3) to (140, 3).

- Decreasing interval:

The  interval where the graph is decreasing  in depth is from the coordinates (140, 3) to (180, 0).

Part B:

- Domain: The domain of the relation is the set of time values represented on the x-axis. The domain here is from 0 to 180 minutes.

- Range: The range of the relation is the set of depth values represented on the y-axis. The range of the graph is from 0 to 4 feet.

Part C:

Yes, the graph represents a function. This is because, each input (x-value) is associated with a unique output (y-value).

Part D:

The graph represents the depth of water in a kids' swimming pool over a certain amount of time between 0 and 180 minutes.

At the beginning, the pool is empty, and then the depth slowly increases with time. From 0 to 40 minutes, the depth increases at a constant rate until it reaches 4 feet. Thereafter, it remains constant at that depth for the next 40 minutes, indicating the pool is full. Afterward, there is a gradual decrease in depth over time. From 140 to 180 minutes, the water is drained from the pool, and the depth eventually reaches 0 feet.

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The percentage of the world population that is in the U.S. is approximately 4.3%.

To find the percentage of the world population that is in the U.S., we need to divide the population of the U.S. by the world population and then multiply the result by 100.

Let's calculate the percentage:

Percentage = (U.S. population / World population) * 100

Given that the U.S. population is approximately 310 million and the world population is approximately 7.2 billion, we can substitute these values into the equation:

Percentage = (310 million / 7.2 billion) * 100

To perform the calculation, we need to convert the populations to the same units. Let's convert 310 million to billion:

310 million = 310 / 1000 billion

          = 0.31 billion

Now, let's substitute the converted values:

Percentage = (0.31 billion / 7.2 billion) * 100

Simplifying the equation:

Percentage = 0.04305555556 * 100

          = 4.305555556

Rounding the result to the nearest tenth of a percent, the percentage of the world population that is in the U.S. is approximately 4.3%.

Therefore, approximately 4.3% of the world population is in the U.S.

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The answer is 50 then when added together the 3 unknown sides is 150

Answer:

The population of the bacteria at the end of Week 12 is approximately 1,148

Step-by-step explanation:

A graph of the polar equation r = 2sin3(θ) is shown below.

The polar equation r = 2sinθ is symmetric with respect to the polar axis.

In Mathematics and Geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar equations:

a = rcos(θ)    ....equation 1.

b = rsin(θ)     ....equation 2.

Where:

Based on the information provided above, we can logically deduce the following polar equation r = 2sin3(θ), which would be plotted on a coordinate axis by using an online graphing tool.

By critically observing the graph of this polar equation r = 2sin3(θ), we can logically conclude that it is symmetric with respect to the polar axis;

-r = -2sin3(π - θ)

-r = -2sin(3π - 3θ)

-r = 2sin(-3θ)

-r = -2sin(3θ)

r = 2sin3(θ)

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Answer: pretty sure it's C but im not sure

Step-by-step explanation:

exam review on ed 2023

B alone can finish the work in 15 days.

Let's assume that B takes x days to finish the work alone.

If A takes 5 days less than B to finish the work, then A takes (x - 5) days to finish the work alone.

We are given that A and B working together can finish the work in 6 days.

Using the concept of work rates, we can set up the following equation:

1/(x - 5) + 1/x = 1/6

To solve this equation, we can find a common denominator:

(x + x - 5)/(x(x - 5)) = 1/6

Simplifying the equation:

[tex](2x - 5)/(x^2 - 5x) = 1/6[/tex]

Cross-multiplying:

[tex]6(2x - 5) = x^2 - 5x[/tex]

[tex]12x - 30 = x^2 - 5x[/tex]

Rearranging the equation:

[tex]x^2 - 17x + 30 = 0[/tex]

Factoring the quadratic equation:

(x - 2)(x - 15) = 0

Setting each factor equal to zero:

x - 2 = 0   or   x - 15 = 0

Solving for x:

x = 2   or   x = 15

We discard the solution x = 2 since it suggests that B can complete the work in two days, which contradicts the fact that A takes five days fewer than B.

Therefore, B alone can finish the work in 15 days.

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A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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The area of triangle YCX is given as follows:

G. 2 units squared.

The area of square WXYZ is 16, hence the side length is given as follows:

s² = 16

s = 4.

Considering the midpoints, we have that the sides of the right triangle are given as follows:

YC = CX = 4/2 = 2

Hence the area of the triangle is given as follows:

0.5 x 2 x 2 = 2 units squared.

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Answer:

Step-by-step explanation:

1 oz = $1152

1 oz = 28 grams

0.1 oz = 2.8 grams

21/2.8 = 7.5

0.1 x 7.5 oz = (2.8 x 7.5)grams

0.75 oz = 21 grams

75% of 1152 is 864

So,

0.75 oz = $864

For the ordinal number, this statement means;

1. "α < β if an only if α ∈ β": This is saying that an ordinal number α is less than an ordinal number β if and only if α is a member of β and α is a subset of β.

2.  "α = {β : β < α}" can be interpreted as: "α is the set of all ordinals β such that β is less than α".

1. "α < β if an only if α ∈ β": This is saying that an ordinal number α is less than an ordinal number β if and only if α is a member of β.

In other words, α is less than β if and only if α is contained within β and every element of α is less than or equal to every element of β.

This is a fundamental property of ordinal numbers and is based on the von Neumann definition of ordinals where each ordinal is the well-ordered set of all smaller ordinals.

For an example of how this definition can be used. Let α = 1 and β = 2. Then, α is a member of β because 1 is a natural number and 2 is a natural number.

Additionally, α is a subset of β because every element of α, which is just 1, is less than or equal to every element of β, which is just 2. Therefore, α < β according to the definition.

2.  "α = (β : β < α)" is a definition of ordinal numbers in set theory. It says that an ordinal number α is the set of all ordinal numbers that are less than α. In other words, α is the set of all ordinal numbers that are smaller than α.

For example, when we use the von Neumann definition, the ordinal number 3 would be represented as the set {0, 1, 2} because 0, 1, and 2 are the ordinal numbers less than 3.

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In mathematics, a horizontal asymptote is a horizontal line that a function approaches as the input values (usually x) approach positive or negative infinity. It describes the behavior of a function as its input values become extremely large or small.

For a rational function, which is a function expressed as the ratio of two polynomials, the degree of the numerator and denominator determines the existence and location of horizontal asymptotes. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the x-axis (y = 0).

If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

For example, consider the function [tex]f(x) = (3x^2 + 2x + 1) / (2x^2 + 5)[/tex]. In this case, both the numerator and denominator have a degree of 2. Therefore, the horizontal asymptote is the ratio of the leading coefficients: y = 3/2.

Horizontal asymptotes help understand the long-term behavior of functions and are useful for graphing and analyzing mathematical models in various fields, including economics, physics, and engineering.

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Answer:

a. Three students preferred swimming over running and walking.

b. Fourteen students chose running or walking.

c. Alex and Jose preferred swimming and walking, but not running.

The derivatives limit of sin(πx)/(1-x) as x approaches 1 and x<1 is equal to -π/2.

To calculate the limit of sin(πx)/(1-x) as x approaches 1 and x<1, we have to use L'Hopital's Rule.

In L'Hopital's Rule, we differentiate the numerator and denominator separately until we get a value, or the limit turns out to be undefined, or infinite.In this case, we get:lim (x → 1) sin(πx)/(1-x)We can apply L'Hopital's Rule.

The rule states that the limit of a quotient of two functions is equal to the limit of the quotient of their derivatives, provided that both limits exist and the denominator does not equal zero.Therefore, we get:lim (x → 1) sin(πx)/(1-x)= lim (x → 1) πcos(πx)/(-1)= -π/2cos(π) = -π/2.

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Answer:

Area of the shaded region= 4 units

Step-by-step explanation:

width (x-axis)= 3-1 = 2

length (y-axis) = 2-0 = 2

Area of rectangle= Length × Width

= 2 × 2 = 4

The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.

The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.

Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).

The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).

To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.

In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.

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Answer:

Step-by-step explanation:

Answer:

112.5

67.5

Step-by-step explanation:

We know the ratio is:

5:3

So, we can write it as:

5x+3x=180, with 5x being one angle, and 3x being the other

combine like terms

8x=180

divide both sides by 8

x=22.5

5(22.5)=112.5

3(22.5)=67.5

So, one angle is 112.5 and the other is 67.5.

Hope this helps!

Check the picture below.

so the lateral area is really just the area of the green triangles.

[tex]\stackrel{ \textit{area of the four triangles} }{4\left[\cfrac{1}{2}(\underset{b}{10})(\underset{h}{13}) \right]}\implies \text{\LARGE 260}~in^2[/tex]

Answer:

A) Photo attached

B) 260

Step-by-step explanation:

A) Image Attached

B) LSA = 2bs where, b = base, s = slant height

LSA = 2*10*13

= 260

OR

LSA = sum of area of the 4 triangles

= 4 * area of the triangle

= 4 * (base * height/2)

= 4 * (10*13/2)

= 4*(5*13)

= 4*65

= 260

Answer:

x^2

Step-by-step explanation:

1^2=1

2^2=4

3^2=9

Step-by-step explanation:

Podemos escribir las relaciones como:

a = 7x

b = 5x

c = 8x

Sustituyendo las expresiones anteriores en la ecuación a+b+c=80, obtenemos:

7x + 5x + 8x = 80

20x = 80

x = 4

Sustituyendo el valor de x en las expresiones de a, b y c:

a = 7(4) = 28

b = 5(4) = 20

c = 8(4) = 32

Por lo tanto, c - b = 32 - 20 = 12

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  =  $272,090

      A) - Calculate the Percentage of the Value Remaining After the Decrease

       B) - Calculate the NEW VALUE of the house

A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE

      100%  -  9%  =  91%

        0.91

B) - Calculate the NEW VALUE of the house:

NEW VALUE  =  OLD VALUE  *  REMAINING PERCENTAGE

NEW VALUE  =  299,000  *  0.91

A) - The NEW VALUE in terms of the old value is 0.91  times the old value.

B) - The NEW VALUE of the HOUSE is:  299,000  *  0.91  = $272,090

I hope it helps!