The adjusted trial balance for China Tea Company at December 31, 2021, is presented below:

Accounts Debit Credit
Cash $ 11,000
Accounts receivable 150,000
Prepaid rent 5,000
Supplies 25,000
Equipment 300,000
Accumulated depreciation $ 135,000
Accounts payable 20,000
Salaries payable 4,000
Interest payable 1,000
Notes payable (due in two years) 30,000
Common stock 200,000
Retained earnings 50,000
Dividends 20,000
Service revenue 400,000
Salaries expense 180,000
Advertising expense 70,000
Rent expense 15,000
Depreciation expense 30,000
Interest expense 2,000
Utilities expense 32,000
Totals $ 840,000 $ 840,000

Prepare an income statement for China Tea Company for the year ended December 31, 2021:

Prepare a classified balance sheet for China Tea Company as of December 31, 2021.(Amounts to be deducted should be indicated with a minus sign.)

Prepare the closing entries for China Tea Company for the year ended December 31, 2021. (If no entry is required for a transaction/event, select "No journal entry required" in the first account field.)

The formula for the exponential function that passes through the two given points is: f(x) = 4^x

Step-by-step explanation:

An exponential function has the form f(x) = a^x, where a is a constant base.

We can use the two points given to find the value of a.

Using the first point (0, 4), we get:

f(0) = a^0 = 1a = 4

So, a = 4.

Now, we can write the exponential function as:

f(x) = 4^x

To check if this function passes through the second point (3, 256), we substitute x = 3:

f(3) = 4^3 = 64 * 4 = 256

So, the function passes through both points (0, 4) and (3, 256).

Therefore, the formula for the exponential function that passes through the two given points is:

f(x) = 4^x

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Answer:

b=29 a=5.5 n=-13 r=12

Step-by-step explanation:

a: 5+8(4)=5+24=29

b: 3-5(-0.5)=3+2.5=5.5

c: 2(-2)^2-5=2(-4)-5=-8-5=-13

d= -3(-1-3)=-3(-4)=12

substitute the variable with the number and pedmas

variable is the letters in the equation: y=5+8x

The statement "A triangle can be formed with side lengths 3 in, 5 in, and 9 in" is false.

The a + b ≥ c symbol represents the Euclidean geometry theorem that the sum of any two triangle sides is larger than or equal to the third side. The basic tenet of the theorem is that a straight line connects any two locations.

To check if a triangle can be formed with side lengths 3 in, 5 in, and 9 in, we need to apply the triangle inequality theorem, which states that:

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check if this condition is satisfied for the given side lengths:

3 in + 5 in = 8 in, which is greater than 9 in. True

3 in + 9 in = 12 in, which is not greater than 5 in. false

5 in + 9 in = 14 in, which is greater than 3 in.True

Since the second condition is not satisfied, we cannot form a triangle with side lengths 3 in, 5 in, and 9 in. Therefore, the statement "A triangle can be formed with side lengths 3 in, 5 in, and 9 in" is false.

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Answer:

pretty sure its the first one

Step-by-step explanation:

Answer:

Both answers are 47 degrees

Step-by-step explanation:

1. This is an isosceles triangle so the angle x is going to be the same as the opposite angle given which is 47. So x = 47 degrees

2. For this one, we are given the angle outside the same base angles so we take the 86 given from 180. 180-86=94. This 94 needs to be split between the two remaining angles so we divide it by 2. 94/2 = 47 degrees.

Answer:

Step-by-step explanation:

Formula for depreciation =

\(A=P(1-\frac{r}{100})^n\)

Here A= Amount left after n periods

P= Principal amount

r= rate of depreciation

n= time period

Using the formula

\(21500(1-\frac{11}{100})^5= 21500*(\frac{89}{100})^5= 12005.72$\) $

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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Answer:

1/3

Step-by-step explanation:

Does the spinner only have these 3 sections?

If so, the probability of spinning an odd number is 1/3. There are a total of 3 possibilities (denominator), and only 1 is odd (numerator).

The P(odd) is the probability of spinning an odd number that would be equal to 1/3.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

You spin the spinner once.

6, 7, 8

There are a total of 3 possibilities (denominator), and only 1 is odd (numerator).

So, the probability of spinning an odd number = 1/3.

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Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;

The condition for being a subspace of Rⁿ

Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.

Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.

Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ

From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.

Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

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On solving this trigonometry, we find that (a) sec(sin⁻¹ \(\frac{12}{13}\)) = \(\frac{13}{5}\) and (b) tan(sin⁻¹ \(\frac{12}{13}\)) = \(\frac{12}{5}\)

(a) To find the exact value of sec(sin⁻¹ \(\frac{12}{13}\)), we can use the fact that sec(x) = \(\frac{1}{cos}\)(x). Let's draw a right triangle with opposite side 12 and hypotenuse 13. Using the Pythagorean theorem, we can find the adjacent side:

a² + b² = c²

a² + 12² = 13²

a² = 169 - 144

a = √25

a = 5

So our triangle has sides of length 5, 12, and 13. Now we can find cos(sin⁻¹  \(\frac{12}{13}\)) by looking at the adjacent/hypotenuse ratio in this triangle:

cos(sin⁻¹ \(\frac{12}{13}\)) =  \(\frac{5}{13}\)

Therefore, sec(sin⁻¹(12/13)) = 1/cos(sin⁻¹ \(\frac{12}{13}\))

                                            = 1/\(\frac{5}{13}\)

                                            = \(\frac{13}{5}\).

So the exact value of sec(sin⁻¹ \(\frac{12}{13}\)) is \(\frac{13}{5}\).

(b) To find the exact value of tan(sin⁻¹ \(\frac{12}{13}\)), we can use the fact that tan(x) = sin(x)/cos(x). Let's use the same right triangle as before.

Then sin(sin⁻¹ \(\frac{12}{13}\))=  \(\frac{12}{13}\) and cos  \(\frac{12}{13}\)) = \(\frac{5}{13}\)  , so

tan(sin⁻¹ \(\frac{12}{13}\)) = sin(sin⁻¹ \(\frac{12}{13}\))/cos(sin⁻¹\(\frac{12}{13}\))

                        = \(\frac{12}{13}\) / \(\frac{5}{3}\)

                        = \(\frac{12}{5}\)

So the exact value of tan(sin⁻¹ \(\frac{12}{13}\)) is \(\frac{12}{5}\).

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Answer:

No its not but each time a car come you need to move to your side of the lane

To create the figure with the new scale of 1 unit = 3 yd. The steps are mentioned below.

Scale refers to the proportional relationship between the measurements of an object or a system and the corresponding measurements on a representation or a model of that object or system. It is commonly used in many fields, including mathematics, engineering, architecture, art, and geography.

In mathematics, scale can be expressed as a ratio or a fraction, which indicates how much the measurements on the representation or model have been reduced or enlarged relative to the actual measurements of the object or system. For example, a scale of 1:100 means that every measurement on the representation or model is 100 times smaller than the corresponding measurement on the actual object or system.

In art and architecture, scale is used to create a sense of proportion and perspective in a work. For example, an artist might use a smaller scale for a background object to make it appear farther away, while using a larger scale for a foreground object to make it appear closer.

To create the figure with the new scale of 1 unit = 3 yd. Here are the steps:

Determine the dimensions of the rectangle in yards using the original scale of 1 unit = 6 yd.

Divide the dimensions by 2 to get the new dimensions using the new scale of 1 unit = 3 yd.

Draw a rectangle on a new grid using the new dimensions.

If you want to place the rectangle in a specific location on the grid, you can use the coordinates on the grid to position it.

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Answer:

6 bghyjy UC Houston post Getty photo Getty hide and the new Yorker

Answer: y=4x+5

Step-by-step explanation:

Let x be the amount invested in the 5-yr CD and y be the amount invested in the 18-month CD.

We have the following equations:

0.044x + 0.03(x - 2000) = 1102.50 (total interest equation)

x + (x - 2000) = Total amount invested

Solving this system of equations will give the values of x and y

To determine how much was invested in each CD, we can set up a system of equations. Let x represent the amount invested in the 5-yr CD and y represent the amount invested in the 18-month CD.

The interest earned from the 5-yr CD can be calculated using the formula I = Prt, where I is the interest, P is the principal (amount invested), r is the interest rate, and t is the time in years. In this case, the interest equation for the 5-yr CD is 0.044x.

The interest earned from the 18-month CD can be calculated in the same way, using the formula I = Prt. However, since the time is given in months, we need to convert it to years by dividing by 12. The interest equation for the 18-month CD is 0.03(x - 2000).

The total interest earned from both CDs is $1102.50, so we have the equation 0.044x + 0.03(x - 2000) = 1102.50.

Additionally, the total amount invested is the sum of the amounts invested in each CD, which is x + (x - 2000).

By solving this system of equations, we can determine the values of x and y, representing the amounts invested in each CD. The solution to the system will provide the specific amounts invested in the 5-yr CD and the 18-month CD.

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Answer:

Step-by-step explanation:

5x-14=8x+4

-5x. +14    -5x. +14

3x=18

x=6

7x-4=3+8x

-7x. -3   -7x -3

x=-7

Answer:

Number of fish in 2006 = 845 fishes (Approx.)

Step-by-step explanation:

Given;

Number of fish in 2000 = 1,150 fishes

Decreasing rate = 5% per year

Find:

Number of fish in 2006

Computation:

Exponential decay function:

F = P[1-r]ⁿ

Number of year = 2006 - 2000

Number of year =  6 year

Number of fish in 2006 = 1,150[1-5%]⁶

Number of fish in 2006 = 1,150[1-0.05]⁶

Number of fish in 2006 = 1,150[0.95]⁶

Number of fish in 2006 = 1,150[0.735]

Number of fish in 2006 = 845.25

Number of fish in 2006 = 845 fishes (Approx.)

Answer:

1,227

Step-by-step explanation:

3,000 divided by 3 is 1,000

600 divided by 3 is 200

80 divided by 3 is 26 r2

1 + r2 =3

and 3 divided by 3 is 1

1,000 + 200 + 26 + 1 = 1,227

Answer:

50 pounds.

Step-by-step explanation:

25000 / 500 = 50 pounds.

Answer:

50

Step-by-step explanation:

25,000 / 500 = 50

P Q R S, a square with the vertices P (5, 4), Q (2, 8), R (6, 1), and S (-1, -3), is equal to 2, -4. Consequently, S"s coordinates will be ( 1 , 3 ).

The vertex positions of the square P Q R S are P(-5, 4), Q(2, 8), R(6, 1), and S(-1, -3). The rule to rotate a point by 180 degrees about the origin is (x, y) → (-x, -y) This rule dictates that the image's new coordinates are P(-5, 4) ⇒ P' ( 5 , -4 ) , Q(2, 8) ⇒ Q' ( -2 , -8 ) , R(6, 1) ⇒ R' ( -6 , -1 ) , S(-1, -3) ⇒ S' (1 , 3 )

Consequently, S"s coordinates will be ( 1 , 3 ).

pre-images, singular pre-images (mathematics) The set of all domain elements that are mapped into a certain subset of the co-domain for a given function;ƒ : X → Y and a subset B ⊆ Y, the set ƒ−1(B) = {x ∈ X : ƒ(x) ∈ B}.

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Answer:

-3/7

Step-by-step explanation:

find two lattice points

the ones I found are (-3, 3) and (4, 0)

use the slope formula

(0-3)/(4-(-3)) = -3/7

The simplified form of the given complex fraction is 3 / (2m^2 - 4mn + 2n^2).

To simplify the given complex fraction, let's start by simplifying the numerator and denominator separately.

Numerator:

The numerator is (9/(m-n) divided by 3. To divide by 3, we can multiply the numerator by the reciprocal of 3, which is 1/3.

(9/(m-n) (1/3)

Simplifying further, we can multiply the numerators and the denominators:

(9 1) / (3  (m-n)

= 9 / (3m - 3n)

Denominator:

The denominator is (2m - 2n).

Putting the simplified numerator and denominator together, the complex fraction becomes:

[9 / (3m - 3n)] / (2m - 2n)

Now, to divide by a fraction, we multiply by its reciprocal. Therefore, we can multiply the numerator by the reciprocal of the denominator:

[9 / (3m - 3n)]  (1 / (2m - 2n)

Simplifying further, we multiply the numerators and the denominators:

9 / [(3m - 3n)  (2m - 2n)]

= 9 / (6m^2 - 6mn - 6mn + 6n^2)

= 9 / (6m^2 - 12mn + 6n^2)

= 3 / (2m^2 - 4mn + 2n^2)

Therefore, the simplified form of the given complex fraction is 3 / (2m^2 - 4mn + 2n^2)

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Answer:

292 and 2092

Step-by-step explanation:

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

Total : 240 + 600 + 90 = 730

So, cost of painting = 730/25 x 10 = 29.2 x 10 = 292

Total: 292 + 1800 = 2092

The total cost of paint would be 2092 dollars.

The area of the cuboid is the sum of product of the length, breadth of the given prism.

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

The Total area: 240 + 600 + 90 = 730

So, The cost of painting = 730/25 x 10

= 29.2 x 10

= 292

Total: 292 + 1800 = 2092

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Answer:

4 x 10^5

Step-by-step explanation:

To divide (4.8x10^3) by (1.2x10^-2), we need to divide 4.8 by 1.2, and then multiply the result by 10^3 / 10^-2.

4.8 divided by 1.2 is 4.

10^3 / 10^-2 can be simplified as 10^3 * 10^2 = 10^(3+2) = 10^5.

So, the expression can be written as:

(4.8x10^3) / (1.2x10^-2) = (4 / 1.2) x 10^5

= 4 x 10^5

The standard form of this expression is 4 x 10^5.

Answer:

25.4 degrees

Step-by-step explanation:

Use the inverse sine function to calculate

In the expression y - 2x + 7, there are several operations in use.

Let's break it down and examine each aspect:

Operations:

Subtraction (-): The expression involves subtraction as seen in y - 2x.

Addition (+): The expression also involves addition as seen in -2x + 7.

Terms:

A term is a combination of constants, variables, and coefficients separated by addition or subtraction signs. In this expression, there are three terms:

y: This is a term containing the variable y.

-2x: This is a term containing the product of the coefficient -2 and the variable x.

7: This is a term consisting of the constant 7.

We can identify the operations and count the terms by examining the expression based on the symbols and structure. In this case, the subtraction and addition signs indicate the operations being used. The expression is organized into three distinct terms, each separated by addition or subtraction signs. By recognizing these patterns and symbols, we can determine the operations and the number of terms in the expression.

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Answer:

-19 degrees

Step-by-step explanation:

13+6=19

you would need to add the negative since it said dropped in temperature and the temperature was already negative.

Answer:

6

Step-by-step explanation:

x/18 = 1/3

3x = 18

x = 6

Answer:

Step-by-step explanation:

Drag and drop the options mentioned before each box and that will give you perfect solution:

first box: third option

2nd box: 7th option

3rd box: 4th option

4th box: 1st option

5th box: 6th option