Sultan Inc. was organized on January 1, 2020. It reported the following for its first two years of operations:
Net earnings for 2020 $ 31,000
Dividends for 2020 14,200
Total shareholders’ equity at end of 2020 130,000
Net earnings for 2021 42,000
Dividends for 2021 18,700
Total shareholders’ equity at end of 2021 250,000
Required:
Compute the ending balance of retained earnings for Sultan Inc. as at December 31, 2021.
The ending balance of retained earnings for Sultan Inc. as at December 31, 2021 is $40,100
What is the retained earnings at the end of 2020?
The retained earnings at the end of 2020 is the net earnings for 2020 minus the dividends paid in 2020 , in other words, the 2020 ending balance of retained earnings are computed as shown below:
retained earnings for 2020=$31,000-$14,200
retained earnings for 2020=$16,800
However, we need to determine additional retained earnings in 2021 which is also ascertained as net earnings minus dividends paid
additional retained earnings in 2021=$42,000-$18,700
additional retained earnings in 2021=$23,300
the ending balance of retained earnings for Sultan Inc. as at December 31, 2021=2021 balance of retained earnings+ additional retained earnings in 2021
the ending balance of retained earnings for Sultan Inc. as at December 31, 2021=$16,800+$23,300
the ending balance of retained earnings for Sultan Inc. as at December 31, 2021=$40,100
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Solve 2 - ax = -8 for x. Assume a ≠ 0
The expression is simplified to x = 10/ a
What is subject of formula?Subject of formula is defined as a variable which is expressed in terms of other variables involved in a given formula or expression.
Given the expression;
2 - ax = -8
Let's make 'x' the subject of formula
collect like terms
-ax = -8 - 2
Subtract like terms
-ax = - 10
Divide both sides by -a
-ax/ -a = - 10/-a
Find the ratio
x = 10/ a
Thus, the expression is simplified to x = 10/ a
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Use the figure below to list the slopes m₁, m₂, m3, and m4 in order of decreasing size.
the order, from largest to lowest, is:
Purple line, Green line, Blue line, Red line.
How to list the slopes in decreasing order?
A linear equation written in the slope-intercept form is:
y = a*x + b
Such that a is the slope, and it tells us how fast the function changes.
Positive slopes mean that the lines go upwards (purple or green in this case)
Negative slopes mean that the lines go downwards (blue or red in this case)
As larger is the slope, more steep is the function (for the cases with positive slope, is the opposite for negative slopes).
Then the order, from largest to lowest, is:
Purple line, Green line, Blue line, Red line. (y can't see the subindices of the slopes in the lines, so I only can identify the colors).
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Please Help!! I keep getting this question wrong and have two attempts left
A Global Positioning System satellite orbits d = 13,500 miles above Earth's surface (see figure). Find the angle of depression (in degrees) from the satellite to the horizon. Assume the radius of Earth is 4,000 miles. (Round your answer to two decimal places.)
Using relations in a right triangle, it is found that the angle of depression from the satellite to the horizon is of 89.35º.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.First, we consider that:
The opposite side to the internal angle at the satellite is of 4000 mi.The hypotenuse is of 4000 mi + d mi = 17500 mi.Hence the sine of the angle is given as follows:
sin(θ) = 4000/175000
θ = arcsin(4000/175000)
θ = 1.31º.
Twice the angle of depression x and θ are supplementary, hence:
2x + 1.31 = 180
2x = 178.69.
x = 178.69/2
x = 89.35º.
The angle of depression from the satellite to the horizon is of 89.35º.
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Select interior, exterior, or on the circle (x - 5) 2 + (y + 3) 2 = 25 for the following point.
(3, 2)
Answer:
exterior
Step-by-step explanation:
You want to know if (3, 2) is an interior or exterior point of the circle defined by (x -5)² +(y +3)² = 25.
Distance from centerWe can find the square of the distance of the point from the center of the circle using the equation for the circle.
(x -5)² +(y +3)² = r²
(3 -5)² +(2 +3)² = 4 +25 = 29 > 25 . . . . use (x, y) = (3, 2) in the equation
The point is farther away from the center than points that are on the circle. The point (3, 2) is an exterior point.
the digit 8 in which number represents 0.08
Answer:
c
Step-by-step explanation:
2 spaces after the decimal
If PR = 24 and RS = 11, what is PS?
PS = 42
PS = 13
PS = 27
PS = 35
The length of the line segment PS will be 35 units when PR is 24 units and RS is 11 units.
We are given the length of two line segments as:
PR = 24 units
RS = 11 units
Now, we need to find the length of PS.
We will use the operation of addition here as PS will be equal to the sum of PR and RS. Addition refers to the basic operation of mathematics that is used to simplify and evaluate an expression or an equation.
So, we get that:
PS = PR + RS
Substituting the values, we get that:
PS = 24 units + 11 units
PS = 35 units
Therefore, we get that, the length of the line segment PS will be 35 units when PR is 24 units and RS is 11 units.
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The number line below is correctly represented by which of the following intervals?
The intervals that represent the number line is c) {[tex]x|-8\leq x < 3[/tex]}
Which intervals are included in the number line?
It is a means of expressing subsets of the real number line. The numbers between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all other integers between 0 and 5 is the set of values x satisfying [tex]0\leq x\leq 5[/tex].
Numbers from [tex]x=-8[/tex] (inclusive because the circle is closed) to [tex]x=3[/tex](exclusive because the circle is closed) make up the painted range.
Hence,{ [tex]x|-8\leq x < 3[/tex]}
Therefore, the intervals that represent the number line is
c){[tex]x|-8\leq x < 3[/tex]}
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please i need help with this
1. Finding the first five numbers in each sequence is as follows:
Sequence 1: 0 2 4 6 8 10Sequence 2: 0 4 8 12 16 20.2. The ordered pairs with the corresponding terms of the sequences are (0, 0), (2, 4), (4, 8), (6, 12), (8, 10), and (10, 20).
3. For the graph, I cannot draw one for you, but Sequence 1 will be on the Y-axis, starting with zero, and Sequence 2 on the X-axis.
The line intercepts will subsequently meet at (2, 4), (4, 8), (6, 12), (8, 10), and (10, 20).
What is a sequence?A sequence is an ordered pattern of numbers or objects.
The length of a sequence describes the number of elements.
Data and Calculations:Pattern rule for Sequence 1: Start with zero and add 2
Pattern rule for Sequence 2: Start with zero and add 4
Sequence 1: 0 2 (0 + 2) 4 (2 + 2) 6 (4 + 2) 8 (6 + 2) 10 (8 + 2)
Sequence 2: 0 4 (0 + 4) 8 (4 + 4) 12 (8 + 4) 16 (12 + 4) 20 (16 + 4)
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The simplified expression of
5
x
−
8
−
2.25
x
+
3
5x−8−2.25x+3 is
Answer:
44.5x - 13
Step-by-step explanation:
Combine like term.
How is the product of a complex number and a real number represented on the complex plane?
Consider the product of 2−4i and 3.
The product of a complex number and a real number represented on the complex plane is 6 - 12i
Complex numberComplex number is a number expressed in the form a + ib
where
a is the real part
b is the imaginary part
Given the complex and real number as shown;
3(2−4i)
Using the distributive law;
3(2) - 3(4i)
6 - 12i
Hence the product of a complex number and a real number represented on the complex plane is 6 - 12i
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Which of the following is most likely the next step in the series?
)DO
O A.
• B.
•
Following the pattern, the most likely next step in the series is given by the pentagon in option B.
What is the most step for the series?We have to look at the number of points in each figure, hence:
The first figure, with the line segment, has two points.The second figure, with the triangle, has three points.The fourth figure, with the rectangle has four points.Hence, the number of points increases by one for each figure, meaning that in the next step, the figure should have 5 points, representing a pentagon.
Among the options given for the answer, only one, option B, has 5 points, with the pentagon, as:
Option A has one point.Option C has four points.Option D has three points.Hence, the most likely next step in the series is given by the pentagon in option B.
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5/6 divided by 3/5 =
A. 18/25
B. -25/18
C. 25/18
D. -18/25
Answer: 25/18 ==> C
Step-by-step explanation:
5/6 divided by 3/5=
5/6 / 3/5 =
5/6 * 5/3 = ==> dividing by a number is the same as multiplying by its reciprocal
5*5/(6*3)=25/18 ==> C
the cordinate point of X on PQ such that PX to XQ is 2:1 is (geometry pcture below help)
The value is XY : QR = 1 : 3
What is similarity?Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.
Given: Δ PQR, Point X and Y are on sides PQ and PR,
XY || QR
In Δ PQR
∠PXY = ∠PQR ( Corresponding angles )
∠PYX = ∠PRQ ( Corresponding angles )
Now, In ΔPQR and ΔAXY
∠P = ∠P ( common )
∠PXY = ∠PQR ( given )
∠PYX = ∠PRQ ( given )
ΔPQR ~ ΔAXY by AAA similarity Criteria.
We get,
PX/ XQ = PY/PR = XY/QR
PX/ XQ = PY/PR = 1/2
PQ = 1 + 2 = 3
PX/ PQ=1/3
hence, the ratio is XY : QR = 1 : 3
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Match the following. Given D = {x | x is a whole number} E = {x | x is a perfect square < 100} F = {x | x is an even number between 10 and 20} 1. D ∩ (E ∪ F) {1, 4, 9, 16, 25, 36, 49, 64, 81, 12, 14, 18} 2. D ∩ E {1, 4, 9, 16, 25, 36, 49, 64, 81} 3. D ∪ (E ∩ F) {12, 14, 16, 18} 4. D ∩ (E ∩ F) {all whole numbers} 5. D ∩ F {16}
The values of the set functions after the matching are:
D∩F = FD∩E = EDU(E∩F) = DD∩(E∩F) = {16}D∩(EUF) = {1,,4,9,12.14,16,18,35,36,47,64,81}What do we mean by different types of sets' functions?The intersection of two sets is represented by ∩.This refers to shared values between the sets under consideration.U represents the union of two sets.This includes all values from all sets considered.So, we have D = {x | x is a whole number}.
Then: D = {0,1,2,3,4,5,6,7,8,.........}Similiarly, E = {x | x is a perfect square < 100}.
So: E = {1,,4,9,16,35,36,47,64,81}Similarly, F = {x | x is an even number between 10 and 20}.
Then: F = {12,14,16,18}Now, D∩E = The common values from sets D and E.
Here we have: = E (all perfect square < 100 )D∩F = F
Where: This means all even numbers between 10 and 20}Now, D∩(E∩F) = {16}.
Then: E∩F = {16}Hence, The only value common to both set D and E∩F is 16.DU(E∩F) = D ( This means all whole numbers)
Then we can say: E∩F = {16}D∩(EUF) = {1,,4,9,12.14,16,18,35,36,47,64,81}
We obtain: EUF = {1,,4,9,12.14,16,18,35,36,47,64,81}Therefore, the values after the matching are:
D∩F = FD∩E = EDU(E∩F) = DD∩(E∩F) = {16}D∩(EUF) = {1,,4,9,12.14,16,18,35,36,47,64,81}Know more about sets functions here:
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Mr. Richmond wants to purchase notebooks for his students. Each notebook costs $1.60. Mr. Richmond has
$60. What is the most amount of notebooks Mr. Richmond can purchase?
Answer: 37 Notebooks
Step-by-step explanation:
Set up and inequality equation where x is the unknown amount of notebooks Mr. Richmond can purchase.
1.60x less than or equal to $60.
Inverse Operations 60/1.60 = 37.5
But, round down, since you can't buy half a notebook so;
Mr. Richmond can purchase 37 notebooks.
What is 36 divided by 3/4 in simplest form?
Answer:
48
Step-by-step explanation:
3/4 becomes 0.75 in decimal form
36/0.75=48
The solution of 36 divided by 3/4 in simplest form is,
⇒ 48
We have to given that,
To simplify 36 divided by 3/4 in simplest form.
It can be written as,
⇒ 36 ÷ (3/4)
⇒ 36 × 4/3
⇒ 12 × 4
⇒ 48
Therefore, The solution of 36 divided by 3/4 in simplest form is,
⇒ 48
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Pablo had 638 grams of cashew nuts and 594 grams of peanuts. He mixed the nuts and packed them into 7 packets. Each packet of nuts had a mass of 120 grams. How many grams of nuts did Pablo have left?
The nuts left with Pablo after using 840 g of nuts to make 7 packets is 392 g.
We are given that:
Pablo has
Cashew nuts = 638 g
Peanuts = 594 g
He now has mixed the nuts.
Total amount of nuts will be calculated by using addition.
Total amount of nuts = T = 638 g + 594 g
T = 1232 g
He has made a total of 7 packets and in each packet, he has put 120 g of nuts.
Total nuts used = 7 × 120 g = 840 g
Nuts left with Pablo = 1232 g - 840 g
Nuts left = 392 g
Therefore, we get that the nuts left with Pablo after using 840 g of nuts to make 7 packets is 392 g.
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1) Write 35/
37
in lowest term
Answer:
it is already lowest terms
Step-by-step explanation:
Distinguish what a ray, line segment and line are in your own words. Then, compare
and contrast the three geometric figures.
Answer: A ray starts from a point and goes to infinity. A line has no end points. A line segment has two endpoints. A line segment connects both endpoints.
Step-by-step explanation:
did this explain it
what is the total capacity in gallows of a rectangular tank 5 meters in height knowing that it will hold 200 liters per foot?
729.1 is the total capacity in gallows of a rectangular tank .
What is rectangle?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.1 Foot height can store = 200 ltrs
Height of tank = 5 m = 500/30.48 = 16.4 ft
Total Capacity = 200 * 16.4 =3280.8 ltr
There were several gallons in use. One gallons is roughly = 4.5 ltr
Hence the capacity in gallon = 3280.8/4.5 = 729.1
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Steve went on holiday.
He recorded the number of photos he took each day.
Steve saves his photos on a memory card.
The memory card has 1000 megabytes of memory space.
Each photo uses 2.4 megabytes of memory space.
Steve has saved 320 photos on the memory card.
Work out how many more photos Steve can save on the memory card.
You start at (5, -4). You move up 6 units and down 1 unit. Where do you end?
Answer:
(5, 1)
Step-by-step explanation:
-4+6-1=1.
12x – 6 + 4 – 5x = 26
Write 5.92 x 10^5 in standard notation
Which point on the number line best represents
A Point A
B Point B
C Point C
D Point D
A
45°
B C
-3
?
2+
Answer:
A 45 the only reason why I choose number one because you said which point on the line on the bed response point a point b point c point d a 54 or whatever but yeah becausehelp me find the measures
c=26
d=31
You can church my answer by substituting them in and finding the inner two missing angles. per triangle all three angles should add up to 180.
Using the equation from #5, (d=20g) how many miles can a car drive if it has 13 gallons of gas?
Answer:
If d meaning mile it will be 20x13
-1/2 + 2/3 DO THIS THANKS GUYSSSSS
Answer: 0/5
Step-by-step explanation:
Answer:
1/6 I used a calculator
Step-by-step explanation:
-1/2 + 2/3 =1/6
23=2 rearrange the equation to solve for f
Answer:
23 doesn't equal 2
Step-by-step explanation: