Case 1. ABY is the accounting expert for a firm that has many small clients that need monthly accounting services. ABY has been asked by the partner in charge to analyze the asset section of firms’ statements of financial positions which follow below:


2017
2018

Cash

$2,500
$3,900

Accounts receivable, net

35,000
40,000

Inventory

85,000
122,000

Other current assets

3,400
4,110

Total current assets

125,900
170,010

Property, plant & equipment, net

180,000
230,000

Other assets

15,000
26,000

Total assets

$320,900
$426,010

Required:
Prepare a Horizontal analysis of the assets section of the project statement of financial position for 2017 & 2018.and interpret any significant change in assets values. Round all percentage answers to one decimal place.

The amount paid with discount for the laptop is $ 660.

Discount is the amount of money removed from the price of an object being sold.

Amount paid is the total cost of an item.

Since laptop computer that you want to purchase was originally priced at $750. You will receive a 20% student discount, and the sales tax rate is 8%.

First, we need to know how much discount is given.

Since there is a 20 % discount, the amount of discount removed is 20% × $750 = 0.2 × % 750 = $ 150

Also, there is a sales tax rate of 8%. So, the amount of sales tax added is 8% × $750 = 0.08 × $ 750 = $ 60

So, the total amount paid is T =  price - discount + tax

= $ 750 - $ 150 + $ 60

=  $ 660

So, the amount paid is $ 660.

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Answer:

First add, then subtract
10

Step-by-step explanation:

First subtract, then determine the result:

27 + 33 = 60

60 - 50 = 10

Macy has 10 stickers left.

The operations needed to solve the problem are:

First add, then subtract.

The evaluation of the two more bids Bruno received, and the equations, table and graph obtained from the bids are as follows;

x = The number of books

y = The total charge based on the pricing

The equations are;

Bid 7: y = 15·x + 3

Bid 8: y = 10·x + 40

Please find the completed table in the following explanation part

Part B;

Please find attached the graph of the two equations, created with MS Excel

An equation is a mathematical statement indicating that the quantity, magnitude or values of two expressions are the same.

The amount Bid 7 charges per book = $15

Amount paid upfront for Bid 7 = $5

Amount Bid 8 charges upfront = $40

Amount Bid 8 charges per book = $10

The variables are;

The equations are;

The table of values can be presented as follows;

                   Bid 7               [tex]{}[/tex]        Bid 8

x             [tex]{}[/tex] y = 15·x + 5              y = 10·x + 40

0               [tex]{}[/tex]       5               [tex]{}[/tex]          40

3               [tex]{}[/tex]       50               [tex]{}[/tex]        70

5               [tex]{}[/tex]       80               [tex]{}[/tex]        90

7               [tex]{}[/tex]       110               [tex]{}[/tex]        110

10               [tex]{}[/tex]     155               [tex]{}[/tex]       140

Part B;

Please find attached the required graph of the two equations, showing the legend and the scale for the x and y axis created with MS Excel.

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The average is 9.99, the very first percentile is 8.01, as well as the upper quartile is 13.33 as a result.

From smallest to highest number, 25% is the first quartile. Second quartile: 25.1% to 50% (till median) 51% to 75%, third quartile (above the median) 25% of the biggest values are in the fourth quartile.

The data must first be arranged in ascending order before we can calculate the median or quartiles of the provided data:

5.24, 6.02, 6.67, 7.30, 7.59, 7.99, 8.03, 8.35, 8.81, 9.45, 9.61, 10.37, 10.39, 11.86, 12.22, 12.71, 13.07, 13.59, 13.89, 15.42

There are a total of 20 data points, and the median is calculated as that of the average of a 10th and 11th pieces of data:

(9.61 + 10.37) / 2 = 9.99; median

The very first quartile (Q1) must be determined in order to determine.

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Answer:

The solution is 1/8

Step-by-step explanation:

[tex] \sf \displaystyle \lim_{x \to 16}  \sf \frac{ \sqrt{x} - 4 }{x - 16} \\ \\ \sf {a}^{2} - {b}^{2} = (a - b) (a + b)\\ \\ \sf \displaystyle \lim_{x \to 16}  \sf \frac{ \sqrt{x} - 4 }{( \sqrt{x} - 4) \times ( \sqrt{x} + 4)} \\ \\ \sf \displaystyle \lim_{x \to 16}  \sf \frac{ \cancel{\sqrt{x} - 4} }{(\cancel{ \sqrt{x} - 4) }\times ( \sqrt{x} + 4)} \\ \\ \sf \displaystyle \lim_{x \to 16}  \sf \frac{1}{ \sqrt{x} + 4} \\ \\ \sf \frac{1}{ \sqrt{16} + 4} \\ \\ \sf \frac{1}{ 4 + 4} \\ \\ \sf \frac{1}{8} [/tex]

The investment with annual compounding yields a higher future value of $1,520.10 compared to $1,489.36 for the given investment method.

The process through which an investment earns returns on both the principal and the accrued interest over time is known as compounding. To put it another way, it is the reinvestment of interest income into an investment that enables the investment to increase exponentially over time.

Compounding works on the basic premise that interest earned on an investment is added to the principal amount. The interest is then calculated using the new, higher principal amount during the subsequent interest period, yielding even more interest. When the money generated is reinvested and grows over time, this cycle keeps repeating, increasing the investment's value more swiftly.

The investment given has a principal of $1,000, an annual interest rate of 3%, and interest periods of 4 per year. The investment is held for 15 years. To compare this investment to one with the same principal and annual interest rate compounded annually, we need to calculate the future value of the investment using both methods and compare the results.

Using the given investment method, we can calculate the future value as follows:

FV = P(1 + r/n)^(nt)

FV = 1000(1 + 0.03/4)^(4*15)

FV = $1,489.36

Using annual compounding, we can calculate the future value as:

FV = P(1 + r)^t

FV = 1000(1 + 0.03)^15

FV = $1,520.10

So, the investment with annual compounding yields a higher future value of $1,520.10 compared to $1,489.36 for the given investment method. This difference occurs because compounding more frequently leads to more frequent accumulation of interest, resulting in a higher final amount.

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Answer:

So we have two possible values for the width: W = 16 or W = 7.5.

If W = 16, then L = 130/16 ≈ 8.125. This gives us a perimeter of 2(8.125) + 2(16) = 48.25, which is too much fencing.

If W = 7.5, then L = 130/7.5 ≈ 17.333. This gives us a perimeter of 2(17.333) + 2(7.5) ≈ 46.666, which is close enough to 46. Therefore, the dimensions of the field are approximately L = 17.333 m and W = 7.5 m.

Step-by-step explanation:

Let the length of the rectangular plot be L, and let the width be W. Then we have:

The perimeter of the plot is 2L + 2W, and this must equal the length of fencing that Morgan has, which is 46 m. So we have the equation:

2L + 2W = 46

The area of the plot is LW, and we know that this equals 130 square meters. So we have the equation:

LW = 130

We can solve for one variable in terms of the other from the second equation, so let's solve for L:

L = 130/W

Now we can substitute this expression for L into the first equation:

2(130/W) + 2W = 46

Simplifying this equation, we get:

260/W + 2W = 46

260 + 2W^2 = 46W

2W^2 - 46W + 260 = 0

Dividing by 2, we get:

W^2 - 23W + 130 = 0

This is a quadratic equation that we can solve using the quadratic formula:

W = [23 ± √(23^2 - 4(1)(130))] / (2(1))

W = [23 ± 9] / 2

So we have two possible values for the width: W = 16 or W = 7.5.

If W = 16, then L = 130/16 ≈ 8.125. This gives us a perimeter of 2(8.125) + 2(16) = 48.25, which is too much fencing.

If W = 7.5, then L = 130/7.5 ≈ 17.333. This gives us a perimeter of 2(17.333) + 2(7.5) ≈ 46.666, which is close enough to 46. Therefore, the dimensions of the field are approximately L = 17.333 m and W = 7.5 m.

Answer:

Length = 13

Width = 10

Step-by-step explanation:

Let L = length and W = width of the plot

The area is given by LW and is given as 130 square meters

LW = 130   (1)

The perimeter = 2(L + W) and given as 46 meters(length of fencing)
2(L + W) = 46
L+W = 23        (2)

In equation 1, isolate L by dividing both sides by W
LW/W = 130/W
L = 130/W

Substitute this value for L in equation (2)
L + W = 23
130/W + W = 23

Multiply throughout by W:
130/W x W + W x W = 23x W
130 + W² = 23W

Subtract 130W from both sides:
130 + W² - 23W= 0

Rewrite as

W² - 23W + 130 = 0

This is a quadratic equation which can be solved by factoring

Factoring W² - 23W + 130 = 0
(W - 13)(W-10) = 0

This means W = 13 or W = 10
If W = 13, L = 130/W = 120/13 = 10
If W = 10, L = 130/W= 130/10 = 13

So the possible values for L, W are
L = 13, W = 10

or

L = 10, W =13

Choosing the larger value for L gives us:
L = 13, W = 10

This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

This is a binomial distribution problem, where the probability of success (a household tuned to Pretty Betty) is p = 0.26 and the number of trials is n = 14.

The probability that none of the households are tuned to Pretty Betty is:

P(none) = (1 - p)ⁿ = (1 - 0.26)¹⁴≈ 0.031

The probability that at least one household is tuned to Pretty Betty is:

P(at least one) = 1 - P(none) = 1 - 0.031 ≈ 0.969

The probability that at most one household is tuned to Pretty Betty is:

P(at most one) = [tex]P(0) + P(1) = (1 - p)^n + np(1 - p)^{(n-1)[/tex] ≈ 0.500

However, if more than one household is tuned to Pretty Betty, it may indicate that the share value is inaccurate.

Therefore, This means that if at most one household is tuned to Pretty Betty, it is not unusual and does not necessarily indicate that the 26% share value is wrong.

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Answer:

Area = 380 square inch

Volume = 697 cubic inch

Step-by-step explanation:

Diameter = 11

=> radius = 11/2 = 5.5

A = 4πr^2 =4·π·(5.5^2) ≈ 380 square inch

V=4/3πr^3=4/3·π·(5.5^3) ≈ 697 cubic inch

The minimum number of trips needed to haul 20,000 cubic feet of dirt is B) 17.

What is capacity?

The ability to hold or contain something. The maximum amount or number that can be contained in a room's seating capacity.

The capacity of the dump bin is:

21 feet (length) x 8 feet (width) x 6 feet (height) = 1,008 cubic feet

The dump bin can hold dirt equivalent to 1.2 times its capacity, which is:

1.2 x 1,008 cubic feet = 1,209.6 cubic feet

To haul 20,000 cubic feet of dirt, you need:

20,000 cubic feet / 1,209.6 cubic feet per load = 16.52 loads

Since you can't have a fraction of a load, you need to round up to the nearest whole number, which is 17 loads.

Therefore, the minimum number of trips needed to haul 20,000 cubic feet of dirt is B) 17.

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Answer:

Examples below

Step-by-step explanation:

How many milliseconds are in 3.25 days?  

How many grams are in 12.6 ounces ?

How many meters are in 2 3/4 miles ?

Answer:

n = 14

Step-by-step explanation:

Theorem:

In a triangle, the measure of an exterior angle equals the sum of the measures of the two remote interior angles.

12n - 8 = 8n - 4 + 52

4n = 56

n = 14

Therefore, the length of diagonal A'C' is also 2 units after the polygon translates 3 units further to the left and 4 units down.

A polygon is any form having three sides. Although a circle is curved and devoid of sides and angles, it is not categorised as a polygon even if it is a plane figure.

If the polygon translates 3 units to the left and 1 unit down, the coordinates of the new vertices would be:

A' (0, 3)

B' (2, 2)

C' (0, 1)

D' (-2, 2)

To find the length of diagonal AC, we can use the distance formula:

AC = √[(3-3)^2 + (2-4)^2] ≈ 2 units

If the polygon translates 3 units further to the left and 4 units down, the coordinates of the new vertices would be:

A'' (-3, -1)

B'' (-1, -2)

C'' (-3, -3)

D'' (-5, -2)

To find the length of diagonal A'C', we can use the distance formula:

A'C' = √[(0-0)^2 + (1-3)^2] ≈ 2 units

Therefore, the length of diagonal A'C' is also 2 units after the polygon translates 3 units further to the left and 4 units down.

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Answer:

0.1369

Step-by-step explanation:

(37/100)^2=0.1369

Answer:

A≈50.27in²

Step-by-step explanation:

A=πr2=π·42≈50.26548in²

To determine the height of the rock at a specific time, we need to substitute the time value into the equation y = 20t - 1.87t². For example, to find the height of the rock after 3 seconds, we substitute t = 3 into the equation:

y = 20(3) - 1.87(3)²

y = 60 - 16.83

y = 43.17

Therefore, the height of the rock after 3 seconds is 43.17 meters.

Using the table and definition of inverse functions we will get:

f ⁻¹ (6) = 10.

Remember how inverse functions work, we know that for two inverse functions f(x) and f ⁻¹ (x)?

if f(x) =y

Then:

f ⁻¹ (y) = x

So now we want to find  f ⁻¹ (6), then if:

f ⁻¹ (6) = k

f(k) = 6

Looking at the table we can see that f(10) = 6, then f ⁻¹ (6) = 10.

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Simplifying this expression, we get: E[X] = n * (1 + (1-pm)/(n-1)) * H_{n-1} where H_{n-1} is the (n-1)th harmonic number.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

In the first scenario where we have imperfect throwers, the probability that a ball lands in a particular bin is (1-pm)/n, where pm is the probability that the ball misses all the bins. The probability that a ball does not land in a particular bin after k throws is (1- (1-pm)/n)^k.

Let X_i be a random variable representing the number of throws required to fill the ith bin for the first time. We know that X_i follows a geometric distribution with probability of success p_i = (1-pm)/n.

The expected value of X_i is given by:

E[X_i] = 1/p_i = n/(n - (1-pm))

Now, let X be the random variable representing the number of throws required to fill all n bins for the first time. We want to find the expected value of X, denoted as E[X].

Since each bin is being filled independently, the number of throws required to fill all n bins is given by the maximum of the X_i. Therefore, we have:

X = max(X_1, X_2, ..., X_n)

Using the formula for the expected value of the maximum of n independent and identically distributed random variables, we can write:

E[X] = n * E[X_i] - (n-1) * E[X_i, X_j]

where E[X_i, X_j] is the expected value of the minimum of X_i and X_j.

Since the X_i are identically distributed, we have E[X_i, X_j] = E[X_i]^2.

Substituting the value of E[X_i] in the above equation, we get:

E[X] = n * (n / (n - (1-pm))) - (n-1) * (n / (n - (1-pm)))^2

This is the expected number of throws required to fill each bin at least once, accounting for the probability that the balls may miss all bins with probability pm.

Therefore, Simplifying this expression, we get: E[X] = n * (1 + (1-pm)/(n-1)) * H_{n-1} where H_{n-1} is the (n-1)th harmonic number.

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Answer:

R=47/pi

Step-by-step explanation:

If the of circumference of the circle is 94 cm, the diameter is 94/pi makin the radius 47/pi.

Bobby used deductive reasoning because he started with a stated fact and used logical steps to arrive at the desired conclusion.

Elaine used proof by contradiction because she made the assumption that the opposite of the desired conclusion and showed that it led to a contradiction, which gives further proof that the original assumption must be true.

Deductive reasoning is described as formal system in which  an abstract structure is used for inferring theorems from axioms according to a set of rules.

The set rules are used for carrying out the inference of theorems from axioms, which are then seen as the logical calculus of the formal system.

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Answer:

are you trying to find the derivative if so the answer will be 0

Step-by-step explanation:

Answer: 3/8

Step-by-step explanation: All you do is 1/2 times 3/4. Numerator times numerator. The Denominator times denominator.

Answer:

(1,-1)

Step-by-step explanation:

Answer:

Option B: [tex](1, -1)[/tex]

Step-by-step explanation:

The two equations are linear simultaneous equations, which can be solved by either the substitution, elimination or graphical method.

Substitution method:

Formulate an expression for x in terms of y by isolating x and making it the subject of the equation:

   [tex]x + 2y = -1[/tex]

                  ∴ [tex]x = -2y -1[/tex] —— (equation i)

                     [tex]2x - 3y = 5[/tex] ——- (equation ii)

Substitute (equation i) in (equation ii) to solve for y:

                                      [tex]2(-2y -1) - 3y = 5[/tex]

Expand the brackets or parenthesis using the Distributive Law:

                                       [tex]-4y -2 -3y = 5[/tex]

Bring all the like terms together. Isolate the y terms together on one side of the equation and move all the other terms to the other side:

[tex]-4y -3y = 5 + 2[/tex]

= [tex]-7y = 7[/tex]

= [tex]y = -\frac{7}{7}[/tex]

∴ y = [tex]-1[/tex]

Substitute this calculated value of y into any of the equations to solve for x:

      [tex]x = -2(-1) - 1[/tex]

         [tex]= 2 - 1[/tex]

   ∴ x = [tex]1[/tex]

Together these x and y values form an ordered pair. In addition, this ordered pair is a solution to both the equations and also considered the point of intersection of the two equations

∴ Option B: [tex](1, -1)[/tex]

(a) Ann used 4/10 blue beads i.e. 80.

(b) Ann had 160 beads in the end.

The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

According to mathematicians, any real number may be expressed using the four basic operations, also referred to as "arithmetic operations." The four mathematical operations that produce quotient, product, sum, and difference, respectively, are divide, multiply, add, and subtract.

(a) We are given that Ann had a total of 285 red and blue beads, and she used 45 red beads and 40% of the blue bead.

Let the red beads be x and blue beads be y

So, we get

x + y = 285

x = 285 - y

After using the beads, we get another equation as

⇒(x - 45) / (y - 0.4y) = 1/3

⇒(285 - y - 45) / (y - 0.4y) = 1/3

⇒(240 - y) / (0.6y) = 1/3

⇒720 - 3y = 0.6y

⇒720 = 3.6y

⇒y = 200

So, x = 85

Blue beads used = 40% of 200 = 80

(b) Since, Ann has used 80 blue beads and 45 red beads, so

Beads in the end = 285 - 45 - 80 = 160

Hence, Ann had 160 beads in the end.

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The perimeter of the triangle is 24 units.

what is perimeter ?

Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the length of all four sides, while the perimeter of a circle is the distance around the circle. Perimeter is typically measured in units such as centimeters, meters, feet, or miles.

Given by the question:

To find the perimeter of the triangle, we need to find the distance between each pair of vertices and then add them up.

Distance between (-4, -2) and (2, -2):

[tex]d = sqrt[(2-(-4))^2 + (-2-(-2))^2] = sqrt[6^2 + 0^2] = 6[/tex]

Distance between (2, -2) and (2, 6):

[tex]d = sqrt[(6-(-2))^2 + (2-2)^2] = sqrt[8^2] = 8[/tex]

Distance between (2, 6) and (-4, -2):

[tex]d = sqrt[(-4-2)^2 + (-2-6)^2] = sqrt[(-6)^2 + (-8)^2] = sqrt[36 + 64] = sqrt[100][/tex]= 10

Now we add up the distances:

Perimeter = 6 + 8 + 10 = 24

Therefore, the perimeter of the triangle is 24.

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Therefore , the solution of the given problem of fraction comes out to be the restaurant could make 48 cups of pudding from the 8 quarts they have.

An whole can be represented by any set of related sums or fractions. In standard English, a percentage is used to represent the quantity of a specific size. 8, 3/4. Also wholes are fractions. Numbers are expressed in mathematics using the ratio of it's own portion to the bottom. These fractions are all made up of basic numbers. Due to variances in actual percentage calculations, numerators, and numerators, a difficult fraction contains a fraction. A measurement that reflects a portion of the whole is a percentage.

Here,

There are different ways to approach this problem, but one possible method is to use unit conversions to find how many cups are in 8 quarts, and then divide by 1/6 of a quart per cup.

1 quart = 4 cups (by definition of quart)

Therefore, 8 quarts = 8 x 4 cups = 32 cups

1/6 of a quart = 1/6 x 4 cups = 2/3 cups

Therefore, the number of cups of pudding that could be made is:

32 cups / (2/3 cups) = 48 cups

Therefore, the restaurant could make 48 cups of pudding from the 8 quarts they have.

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The length of the hypotenuse of the triangle is 6√3 inches

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The given parameters are:

Angle, θ = 60°

Shortest side = 3√3

The attached diagram illustrates the right triangle, From the diagram, we have:

cos(θ) = Shortest/Hypotenuse

This gives

cos(60°) = 3√3/Hypotenuse

This gives

Hypotenuse = 3√3/cos(60°)

Evaluate cos(60°)

Hypotenuse = 3√3/0.5

Evaluate the quotient

Hypotenuse = 6√3

Hence, the length of the hypotenuse of the triangle is 6√3 inches

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The complete question is given below.

The shortest side of a right triangle measures 3V3 inches. One angle of the triangle measures 60°. What is the length in inches, of the hypotenuse of the triangle?

Answer:

Using the equation y = 2x, some ordered pairs are as follows (- 1, - 2), (0, 0), (1, 2), (2, 4), (3, 6).

Step-by-step explanation:

BY WAY UR GLY