If glass contains 320 cm³ of milk, the mass of the milk is 330 g, the density of the milk is approximately 1031 kg/m³.
Density is defined as the mass per unit volume of a substance. To find the density of milk in kg/m³, we need to convert the given volume and mass to the appropriate units.
First, we need to convert the volume from cm³ to m³. Since 1 m = 100 cm, 1 m³ = (100 cm)³ = 1,000,000 cm³. Therefore, we can convert 320 cm³ to m³ by dividing by 1,000,000:
320 cm³ ÷ 1,000,000 = 0.00032 m³
Next, we need to convert the mass from grams to kilograms. Since 1 kg = 1000 g, we can convert 330 g to kg by dividing by 1000:
330 g ÷ 1000 = 0.33 kg
Now that we have both the mass and volume in appropriate units, we can calculate the density by dividing the mass by the volume:
Density = mass ÷ volume = 0.33 kg ÷ 0.00032 m³ ≈ 1031 kg/m³
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Given the following probabilities, determine whether the events A and B are
independent or dependent.
P(A) = 2/3
P(B) = 1/4
P(A and B)= 2/7
If P(A)= [tex]\frac{2}{3}[/tex], P(B) = [tex]\frac{1}{4}[/tex] and P(A and B)= [tex]\frac{2}{7}[/tex], then the events A and B are dependent.
By comparing the probability of events A and B intersection (P(A and B)) to the product of their individual probabilities (P(A) * P(B)), we can find out whether the events are independent or dependent.
Condition of independent events,
If P(A) * P(B) = P(A and B)
Condition of dependent events,
If P(A) * P(B) ≠ P(A and B)
Given,
P(A) = [tex]\frac{2}{3}[/tex]
P(B) = [tex]\frac{1}{4}[/tex]
P(A and B) = [tex]\frac{2}{7}[/tex]
Calculating P(A) * P(B) and compare it to P(A and B):
P(A) * P(B) = [tex]\frac{2}{3}[/tex] * [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{12}[/tex] = [tex]\frac{1}{6}[/tex]
Since P(A and B) ≠ P(A) * P(B), therefore events A and B are dependent.
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Suppose currently Samsung's common stock is selling for $216. The company announced that it will give $1.14 dividend next year and it plans to grow the dividend by 5% every year. Given the information what is the market's required rate of return for the stock? (Round your answer to two decimal points)
The market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points
What is meant by the rate of stock?
The rate of stock refers to the price at which a particular stock is being bought or sold in the stock market, which can vary based on supply and demand.
What is decimal?
A decimal is a number system that uses the base 10 and includes a decimal point to separate the integer part from the fractional part. It is commonly used in mathematics and everyday life for expressing fractions, percentages, and monetary values.
According to the given information
We can use the constant-growth dividend discount model to calculate the market's required rate of return for the stock. The model is:
Current stock price = Dividend next year / (Required rate of return - Dividend growth rate)
We know the current stock price is $216, the dividend next year is $1.14, and the dividend growth rate is 5%. We need to solve for the required rate of return.
216 = 1.14 / (r - 0.05)
Multiplying both sides by (r - 0.05), we get:
216(r - 0.05) = 1.14
Expanding the left side, we get:
216r - 10.8 = 1.14
Adding 10.8 to both sides, we get:
216r = 11.94
Dividing both sides by 216, we get:
r = 0.0553 or 5.53%
Therefore, the market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points
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The market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points
What is meant by the rate of stock?
The rate of stock refers to the price at which a particular stock is being bought or sold in the stock market, which can vary based on supply and demand.
What is decimal?
A decimal is a number system that uses the base 10 and includes a decimal point to separate the integer part from the fractional part. It is commonly used in mathematics and everyday life for expressing fractions, percentages, and monetary values.
According to the given information
We can use the constant-growth dividend discount model to calculate the market's required rate of return for the stock. The model is:
Current stock price = Dividend next year / (Required rate of return - Dividend growth rate)
We know the current stock price is $216, the dividend next year is $1.14, and the dividend growth rate is 5%. We need to solve for the required rate of return.
216 = 1.14 / (r - 0.05)
Multiplying both sides by (r - 0.05), we get:
216(r - 0.05) = 1.14
Expanding the left side, we get:
216r - 10.8 = 1.14
Adding 10.8 to both sides, we get:
216r = 11.94
Dividing both sides by 216, we get:
r = 0.0553 or 5.53%
Therefore, the market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points
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(2a^2)^3 fill in the blank
You have to apply the outside exponent to each piece inside the parentheses.
[tex]\begin{aligned}\left(2a^2\right)^3 &=(2)^3\cdot\left(a^2\right)^3\\[0.5em]&=8 a^6\end{aligned}[/tex]
You have to apply the outside exponent to each piece inside the parentheses.
[tex]\begin{aligned}\left(2a^2\right)^3 &=(2)^3\cdot\left(a^2\right)^3\\[0.5em]&=8 a^6\end{aligned}[/tex]
A _____________ shape is one that does not have an identifiable name. While still flat, 2-D enclosed areas, these shapes are more "freeform" and might resemble things that we see in nature.
Question 5 options:
Geometric
Organic
Symmetrical
Asymmetrical
A Organic shape is one that does not have an identifiable name. While still flat, 2-D enclosed areas, these shapes are more "freeform" and might resemble things that we see in nature.
What is Organic shape?Geometric shapes are well-defined, regular shapes described by mathematical formulas, including circles, squares, triangles, and rectangles. Symmetrical shapes exhibit mirror-like symmetry, like butterflies or snowflakes.
Organic shapes appear in natural objects like leaves or rocks; they are flowing and curvilinear in form, with varying size, proportions, and contours. Organic shapes are free from strict rules and symmetry, often used in art.
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Find the missing coefficient
Answer:
To fill in the blank, let's first expand the left-hand side of the equation:
(2d-5)(2d-4)
= 2d * 2d + 2d * (-4) -5 * 2d -5 * (-4) (using the distributive property)
= 4d^2 - 8d - 10d + 20
= 4d^2 - 18d + 20
Now, we can compare this with the right-hand side of the equation, which is 4d^2 + blank d + 20.
Comparing the coefficients of the like terms, we can see that the blank should be filled with -18, since the coefficient of d on the left-hand side is -18 (from -8d - 10d) and the coefficient of d on the right-hand side is blank.
So, the filled-in equation becomes:
(2d-5)(2d-4) = 4d^2 - 18d + 20
Brainlyest!?
Answer:
Step-by-step explanation:
(2d - 5) x (2d - 4)
= 4d^2 - 8d - 10d + 20
= 4d^2 - 18d + 20
Therefore Answer is -18.
What is the narrowest definition of the number -2
Step-by-step explanation:
The narrowest definition of the number -2 is that it is an integer that is less than zero and has an absolute value of 2. In other words, it is the additive inverse of the number 2, and can be written as "-2 = -1 * 2".
Please answer this question as quick as possible I’ll give brainliest if it’s correct, thank you
Answer:
(a) 3581 N
(b) 6.1 kJ
(c) 4.5 kJ
(d) 74.6%
Step-by-step explanation:
(a) To lift the piano straight up, we need to counteract the force of gravity acting on it. The force required can be calculated using the formula F = mg, where F is the force, m is the mass of the piano, and g is the acceleration due to gravity. So, F = (230 kg) x (9.81 m/s^2) = 3581 N.
(b) The work done in lifting the piano is given by the formula W = Fd, where W is the work done, F is the force required to lift the piano, and d is the height to which the piano is lifted. So, W = (3581 N) x (1.7 m) = 6.1 kJ.
(c) Using a ramp reduces the force required to lift the piano. The force required can be calculated using the formula F = mg sinθ, where θ is the angle of inclination of the ramp. We are given that the force required is 300 N and the length of the ramp is 15 m. So, sinθ = F/mg = 300/(230 x 9.81) = 0.1416. Therefore, θ = sin^-1(0.1416) = 8.13 degrees. The work done using the ramp can be calculated using the formula W = Fd, where d is the height to which the piano is lifted. Using trigonometry, we can find that the height to which the piano is lifted is 1.53 m. So, W = (300 N) x (15 m) x sin 8.13 degrees = 4.5 kJ.
(d) The efficiency of the ramp is the ratio of the work output to the work input, expressed as a percentage. The work output is the same as the work done using the ramp, which is 4.5 kJ. The work input is the same as the work done when lifting the piano straight up, which is 6.1 kJ. So, the efficiency of the ramp is (4.5/6.1) x 100% = 74.6%.
Identify which of the following is a geometric sequence. A. 3, 12, 48, . . . B. 3, 1, , . . . C. 0, 1, 3, 9, . . . D. 3, 6, 12, 21, . . .
The geometric sequence in the list of options is A. 3, 12, 48, . . .
Identify the geometric sequence.A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number.
A. 3, 12, 48, . . . is a geometric sequence because each term is obtained by multiplying the previous term by 4.
B. 3, 1, . . . is not a geometric sequence because there is no fixed ratio between terms.
C. 0, 1, 3, 9, . . . is not a geometric sequence because the ratio between terms is not constant.
D. 3, 6, 12, 21, . . . is not a geometric sequence because the ratio between terms is not constant.
Therefore, the only geometric sequence is A. 3, 12, 48, . . .
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Answer:
3, 12, 48, . . .
Step-by-step explanation:
got it right
Angles in a Triangle
Answer:
x = 115°
Step-by-step explanation:
The interior angle adjacent to the 115° angle measures:
180° - 115° = 65°
x is an exterior angle, so x = 65° + 50°
x = 115°
Answer:
115
Step-by-step explanation:
X has to be supplementary to that adjacent angle, so first the angle next to the 115 has to be defined. 180-115 (as the must be supplementary) is 65. 65+ 50= 115, which should be x. The 2 opposite angles will equal the opposite outside angle. Hope this helps!
from orlando to syracuse is 1053 miles. flying into headwinds on the way down. The trip takes 2.75 hrs. on the way back . the wind is still blowing at the same speed. the trip takes 1.75 hrs. so, what is the speed in the still air and how fast is the wind blowing
Step-by-step explanation:
distance / rate = time s = plane speed w = wind speed
Flying with wind 1053 / ( s+ w) = 1.75
solve for s = 601.714 -w
Flying against wind 1053 / (s-w) = 2.75 sub in for s (above)
1053 / ( 601.714 - w -w ) = 2.75
solve for w = 109.27 mi/hr
sub this 'w' into one of the equations to solve for 's'
1053 / ( s + 109.273) = 1.75 shows s = 492.44 mi/hr
A group consists of six men and seven women. Three people are selected to attend a conference. a. In how many ways can three people be selected from this group of thirteen? b. In how many ways can three women be selected from the seven women? c. Find the probability that the selected group will consist of all women.
a)There are 286 ways to select any three people from the group of 13.
b)There are 35 ways to select three women from the group of seven women.
c) The probability that the selected group consists of all women is 0.122 or approximately 12.2%
What is probability?
Probability is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 (impossible) and 1 (certain), or as a percentage between 0% and 100%. It is used to quantify uncertainty and make predictions in various fields such as mathematics, statistics, physics, engineering, economics, and social sciences
a. The total number of ways to select three people from a group of 13 is given by the combination formula,
C(13, 3) = 13! / (3! × (13 - 3)!) = 286
Therefore, there are 286 ways to select any three people from the group of 13.
b. The number of ways to select three women from a group of seven women is given by the combination formula,
C(7, 3) = 7! / (3! × (7 - 3)!) = 35
Therefore, there are 35 ways to select three women from the group of seven women.
c. To find the probability that the selected group consists of all women, we need to find the number of ways to select three women from the group of seven women and divide it by the total number of ways to select three people from the group of 13:
P(all women) = C(7, 3) / C(13, 3) = 35 / 286 = 0.122
Therefore, the probability that the selected group consists of all women is 0.122 or approximately 12.2%.
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Sasha has $850 into two accounts. Sasha will deposit $450 at 6% simple. She will deposit the rest at 2% compounded annually. Sasha will not make any withdrawals. How much more money will be in her account at 6% simple than at 2% compounded annually after 2 years.
Sasha will deposit $450 at 6% simple interest. The formula for calculating the balance of an account with simple interest is given by A = P(1 + rt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), and t is the time in years.
In this case, the initial principal balance P is $450, the annual interest rate r is 6% or 0.06 as a decimal, and the time t is 2 years. Plugging these values into the formula gives us:
A = 450(1 + 0.06 * 2)
Evaluating this expression gives us a final amount of approximately $477 in the account after two years.
Sasha will deposit the rest of her money ($850 - $450 = $400) at 2% compounded annually. The formula for calculating the balance of an account with annual compounding is given by A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per unit time (per year in this case), and t is the time in years.
In this case, the initial principal balance P is $400, the annual interest rate r is 2% or 0.02 as a decimal, n is 1 since it’s compounded annually, and the time t is 2 years. Plugging these values into the formula gives us:
A = 400(1 + 0.02/1)^(1 * 2)
Evaluating this expression gives us a final amount of approximately $416.16 in the account after two years.
Therefore, there will be approximately $60.84 more money in Sasha’s account at 6% simple interest than at 2% compounded annually after two years.
Lindsey estimated the amount of liquid in a container to be 5 oz. The actual amount
of liquid was 4 oz.
What is the percent error?
10%
15%
20%
25%
The percent error is 25%
The first step is to calculate the error
= 5 - 4
= 1
The percent error can be calculated as follows
= 1/4 × 100
= 0.25 × 100
= 25%
Hence the percent error is 25%
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Find the area I will give brainliest
The area of the triangle is 22 miles square
Finding the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle
Where we have
Base = 11 miles
Height = 4 miles
using the above as a guide, we have the following:
Area = 1/2 * Base * Heigt
substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 11 * 4
Evaluate
Area = 22 miles square
hence, the area is 22 miles square
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Students are painting a mural. So far the mural is painted one fourth blue two 8 red and three 12 green
A homeowner installed and kitchen cabinets and countertops for $4,500.00. He paid 15% down and financed the balance with 24-month fixed installment loan with an APR of 7.0%. Determine the total final charge and monthly payment for the loan.
Answer:
4,500.00 rupees
Step-by-step explanation:
A student surveyed some friends about their favorite type of ice cream. The results are shown in the bar graph below.
Part A: Choose one ice cream flavor. Determine the percentage of friends who named the flavor you chose. Show all necessary work. (3 points)
Part B: Based on the student's findings, are you able to determine that the most popular ice cream flavor for the general population is the Pistachio and Vanilla? Explain your reasoning. (2 points)
Part(A),
The percentage of friends who named Chocolate Chip is 18%.
Part(B),
We cannot determine that the most popular ice cream flavour for the general population is Pistachio and Vanilla based solely on the student's findings.
A bar chart is a graphical representation of data that uses bars of varying heights or lengths to represent the values of a set of data. The bars can be horizontal or vertical, and they are usually spaced equally apart to represent the categories or groups being compared.
Part A:
Let's say we choose the Chocolate Chip flavour. From the bar graph, we can see that 18% of the surveyed friends named Chocolate Chip as their favourite flavour. Therefore, the percentage of friends who named Chocolate Chip is 18%.
Part B:
We cannot determine that the most popular ice cream flavour for the general population is Pistachio and Vanilla based solely on the student's findings. The survey only represents a small sample size of the student's friends, and may not accurately reflect the preferences of the entire population. It is possible that the most popular flavour for the general population is different from what was found in the survey.
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What does f equal in f/3 + 22 = 17
Answer:
f = -15
Step-by-step explanation:
Use algebra to solve!
f/3 + 22 = 17
f/3 = 17 - 22 (bring 22 to the other side, this changes the sign from plus to minus)
f/3 = -5 {because 17-22 = (-5)}
f = (-5) (3) {to eliminate 3 from the denominator of f, you do the opposite of division which is multiplication, so -5 times 3}
therefore, f = -5
You can also check this answer by putting it back into the original equation, -15/3 is -5 and then -5 + 22 = 17.
Xzavier stops by Sweet Treats after school to get a birthday surprise for his mom. He has $11. The table shows the prices of his mom's favorite treats.
Sweet Treats
Candy Price per Pound
Chocolate-covered Cashews $13.88
Chocolate-Peanut Butter Cups $11.46
Chocolate-Caramel Bites $9.62
Gourmet Gummy Bears $8.24
After looking at the prices, Xzavier decides to get two different one-half pound bags of candy for his mom. Do not consider tax. If Xzavier spends the greatest amount possible for two different one-half pound bags of candy, which two candies did he buy?
A. chocolate-covered cashews and chocolate-caramel bites
B. chocolate-peanut butter cups and chocolate-caramel bites
C. gourmet gummy bears and chocolate-caramel bites
D. chocolate-peanut butter cups and gourmet gummy bears
Option B is the correct answer: chocolate-peanut butter cups and chocolate-caramel bites.
How will Xzavier decide which two candids he buy?Xzavier should choose the two candies with the highest price per pound to maximize his spending.
The prices per pound are as follows:
$13.88 for chocolate-covered cashews
$11.46 for chocolate-covered peanut butter cups
$9.62 for Chocolate-Caramel Bites
$8.24 for Gourmet Gummy Bears
Chocolate-covered Cashews and Chocolate-Peanut Butter Cups are the two chocolates with the highest per-pound pricing.
As a result, Xzavier purchased a half-pound of Chocolate-covered Cashews and a half-pound of Chocolate-Peanut Butter Cups.
Option B is the correct answer: chocolate-peanut butter cups and chocolate-caramel bites.
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Jake measured a hotel and made a scale drawing. The scale of the drawing was 8 inches : 7 feet. If the actual length of a room in the hotel is 21 feet, how long is the room in the drawing?
Jake measured a hotel and made a scale drawing, the length of the room in the drawing is 24 inches.
If the scale of the drawing is 8 inches : 7 feet, this means that for every 8 inches in the drawing, there are 7 feet in real life.
To find out length of the room is in the drawing, we need to set up a proportion:
8 inches / 7 feet = x inches / 21 feet
where x is the length of the room in the drawing.
We can cross-multiply and solve for x:
8 inches × 21 feet = 7 feet × x inches
168 inches = 7 feet × x inches
Dividing both sides by 7, we get:
24 inches = x
Therefore, the length of the room in the drawing is 24 inches.
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In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Paul has scored 82 , 88 , and 87 on the first three. What range of scores on the fourth test will give Paul a C for the semester (an average between 70 and 79 , inclusive)? Assume that all test scores have a non-negative value.
Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).
The sum of the scores on the first three, hundred point tests
= 82 + 88 + 87 = 257.
The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.
The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.
Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.
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w transaction list
ournal entry worksheet
<
1
2
3
Transactions
Note: Enter debits before credits.
4
Record the entry to receive October's rental bill of $1,200; set it aside.
Pont Even
5
6
General Journal
Debit
C
The journal entry for the given information is below:
How to solveJournal entries:
S.no. Accounts title andd explanations Debit $ Credit $
a. Accounts receivable 2500
Service revennue 2500
b. Cash account 2000
Service revenue 2000
c. Cash account 500
Unearned service revenue 500
d. Accounts receivabale 1500
Cash account 1500
e. Rent Payable 500
Cash account 500
f. Rent expenses 750
Rent payable 750
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The triangular front has a base of how many feet and a height of how many feet? The length of the tent is __ft?
The Dimensions of the tent are: Base of triangular face (b): 4.46 ft, Height of triangular face (0.5b): 2.23 ft, Length of tent (b + 1): 5.46 ft.
What is a triangular prism?With two triangular bases and three rectangular sides, a triangular prism is a three-dimensional geometric form. The rectangular faces link the matching edges of the bases, which are connected by the parallel triangular bases. This produces a form with a triangular cross-section along the prism's length. The distance between the vertices of the triangle bases is referred to as the length, whereas the height of the prism is the perpendicular distance between the bases.
Given:
Volume of tent = [tex]63 ft^3[/tex]
Let's assume the base of the triangular face of the tent is "b" feet. The height of the triangular face is half of the base, so it would be "0.5b" feet.
The length of the tent is given to be 1 foot more than the base, so the length would be "b + 1" feet.
Mathematically, the volume of a triangular prism can be given by:
[tex]Volume = (1/2) * base * height * length[/tex]
Substituting the given values and rearranging the formula to solve for "b":
[tex]63 = (1/2) * b * (0.5b) * (b + 1)\\126 = b^2 * (0.5b) * (b + 1)\\0.5b^3 + 0.5b^2 - 126 = 0[/tex]
Solving this cubic equation, we get "b ≈ 4.46" (rounded to two decimal places).
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The following loan is discounted. Find (a) the discour P = $1510.00, r=42%, t = 4 years Part: 0 / 3 Part 1 of 3
The remains of an ancient ball court include a rectangular playing alley with a perimeter of about 24 m. The length of the alley is two times the width. Find the length and the width of the playing alley.
Select the statement that shows equivalent measurements.
14 grams = 0.14 decagrams
14 grams = 1.4 decigrams
14 grams = 140 centigrams
14 grams = 14,000 milligrams
Answer:
14 grams = 14,000 milligrams
Step-by-step explanation:
since multiply the grams by 1000 will convert it to milligrams
The interior angles formed by the sides of a hexagon have measures that sum to 720°.
What is the measure of angle F?
Enter your answer in the box.
Answer:
140
Step-by-step explanation:
First you want to add up the numbers inside of the hexagon and set them equal to 720. Your starting equation should be 3x+240=720. Then your going to subtract 240 from each side giving you 3x=480. Next divide each side by 3 giving you x=160. Plug 160 in for x and you should get 160-20= 140.
Answer:
140
Step-by-step explanation:
First you want to add up the numbers inside of the hexagon and set them equal to 720. Your starting equation should be 3x+240=720. Then your going to subtract 240 from each side giving you 3x=480. Next divide each side by 3 giving you x=160. Plug 160 in for x and you should get 160-20= 140.
Knowledge Check 01
The allowance method of accounting for bad debts has the following advantages over the direct write-off method including: (You may
select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and
double click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be
automatically graded as incorrect.)
*Records estimated bad debts expense in the pertod when the related sales are recorded.
Records estimated bad debts expense when the account receivable is determined to be uncollectible.
*Reports accounts receivable on the balance sheet at the estimated amount of cash to be collected
• Reports sales on the income statement at the estimated amount of cash to be collected.
The correct options are - A. In the period in which the corresponding sales are recorded, records the expected bad debt expenditure. and C. Reports accounts receivable at the estimated amount of cash to also be collected on the balance sheet.
Explain the benefits of allowance method:The measure that the company uses to set aside money for its bad debts or uncollectible accounts is known as the allowance method of accounting. This accounting technique reflects the accrual basis.
The key benefit of applying the allowance technique in business is that it enables the company to give interested parties accurate financial reporting. By the allowance approach, the precise account receivable with in balance sheet can be estimated. Also, the management will be able to make decisions about their creditors plus bad debt collection with the use of these trustworthy disclosures. The business can determine the precise number of account heads there in statement of business by conducting a proper examination of its holdings and receivables.Know more about the allowance method
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Correct question:
The allowance method of accounting for bad debts has the following advantages over the direct write-off method including: (You may select more than one answer. ):
A. Records estimated bad debts expense in the period when the related sales are recorded.
B. Records estimated bad debts expense when the account receivable is determined to be uncollectible.
C. Reports accounts receivable on the balance sheet at the estimated amount of cash to be collected
D. Reports sales on the income statement at the estimated amount of cash to be collected
in the diagram below, DE is parallel to AB. if the length of AB is the same as the length of DG, AC=17, and DE=6, find the length of DC.
The length of the side DC is 10.099 units.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same. It is denoted by the ‘~’ symbol.
Given that DE is parallel to AB. Therefore, the two triangles, ΔCDE and ΔABC are similar to each other.
For a similar triangle, the ratio of the corresponding sides are in the same ratio, therefore, it can be written as,
DC/AC = DE/AB = CE/BC
Take the first two terms,
DC/AC = DE/AB
DC × AB = DE × AC
As the length of AB is the same as the length of DC,
DC × DC = DE × AC
DC² = 6 units × 17 units
DC² = 102 units²
DC = 10.099 units
Hence, the length of the side DC is 10.099 units.
Learn more about Similar Triangles here:
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The complete question with the image of the triangle is mentioned below.
Question: In the diagram below, DE is parallel to AB. if the length of AB is the same as the length of DC, AC=17, and DE=6, find the length of DC.
I want to know what the scale factor is of this
Answer:
scale factor = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
the side corresponding to WX is EH
the scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{EH}{WX}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]