Answer:
B
Step-by-step explanation:
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal (starting amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = time (in years)
We can plug in the given values:
P = $1,500
r = 0.0825 (8.25% expressed as a decimal)
n = 1 (compounded annually)
t = 2
A = $1,500(1 + 0.0825/1)^(1*2)
A = $1,500(1.0825)^2
A = $1,757.71
Therefore, the total balance after 2 years will be $1,757.71. Answer choice B is correct.
7 cards were drawn from a standard deck of cards without replacement what is the probability of getting 4 hearts and 3 spades
Total No. of cards in a deck = 52
Total no. of suits = 4
Total number of cards in one suit = [tex]\frac{52}{4} \\[/tex] = 13
Ways of selecting combinations of 4 from 13 hearts (combination) = [tex]\frac{13!}{9! 4!}[/tex]
= 715
Ways of selecting combinations of 3 from 13 spades (combination) = [tex]\frac{13!}{10! 3!}[/tex]
= 286
Combining the two independent choices, there are 715×286=204490
ways to select a seven-card hand with 4 hearts and 3 spades.
Ways of selecting 7 cards from 52 cards = [tex]\frac{52!}{7! 45!}[/tex] = 133784560
Probability of getting 4 hearts and 3 spades on drwaing 7 cards from the deck = [tex]\frac{204490}{133784560}[/tex] = 0.0015285 (approx.)
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The weights of three children are in the properation 6:5:4 If the weight of the smallest chill is 25 Kg. find the weights of the other 2 Children.
The weight of the other children are 37.5 kg and 31.25 kg
How to calculate the weight of the other children?
The weight of the three children are 6:5:4
6x, 5x and 4x
The weight of the smallest child is 4x
4x= 25
x= 6.25
The weight of the other two children can be calculated as follows
6(6.25)
= 37.5
5(6.25)
= 31.25
Hence the weight of the other two children are 37.5 kg and 31.25 kg
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Total Surplus The sum of consumer surplus and producer surplus is called the total surplus; it is one measure economists use as an indicator of the economic health of a society. Total surplus is maximized when the market for a good is in equilibrium. A camera company estimates that the demand function for its new digital camera is and the supply function is estimated to be here is measured in thousands. Compute the maximum total surplus.
The total surplus at the equilibrium point is: $200,000
This is the maximum total surplus that can be achieved in the market for the digital camera.
To compute the maximum total surplus, we need to find the equilibrium quantity and price in the market for the digital camera, and then calculate the consumer and producer surplus at that point.
First, we need to set the demand and supply functions equal to each other to find the equilibrium quantity:
50 - 2P = 2P - 10
4P = 60
P = 15
Substituting this equilibrium price into either the demand or supply function, we can find the equilibrium quantity:
Q = 50 - 2(15) = 20
So the equilibrium price is $15, and the equilibrium quantity is 20,000 digital cameras.
Next, we can calculate the consumer and producer surplus at the equilibrium point. Consumer surplus is the difference between the maximum price a consumer is willing to pay for a good and the market price, summed over all consumers in the market. Producer surplus is the difference between the market price and the minimum price a producer is willing to accept for a good, summed over all producers in the market.
The demand function gives us the maximum price consumers are willing to pay for each quantity of digital cameras:
P = 25 - 0.5Q
So at the equilibrium quantity of 20,000 digital cameras, the maximum price consumers are willing to pay is:
P = 25 - 0.5(20) = 15
This is exactly the same as the market price, so there is no consumer surplus at the equilibrium point.
The supply function gives us the minimum price producers are willing to accept for each quantity of digital cameras:
P = 0.5Q - 5
So at the equilibrium quantity of 20,000 digital cameras, the minimum price producers are willing to accept is:
P = 0.5(20) - 5 = 5
The market price is $15, so the producer surplus is:
(15 - 5) * 20 = $200,000
Therefore, the total surplus at the equilibrium point is:
$200,000
This is the maximum total surplus that can be achieved in the market for the digital camera.
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i just need the equation
Answer:
The decimal 6.25 would be 6 25/100 as a mixed number. In lowest terms, it would be 6 1/4.
An international company has 12,700 employees in one country if this represents 18.7% of the company's employees how many employees does it have in total?
Round yiur answer to the nearest whole number
Answer:
67,914
Step-by-step explanation:
Let x = total employees.
18.7% of x = 12,700
0.187x = 12,700
x = [tex]\frac{12700}{0.187}[/tex] = 67914.438 → 67,914
Would anyone understand this?
Stuart has enough money to buy 4 kg of onions.
How do we calculate?we must first find the cost of 4 kg of onions.
We know that 2.5 kg of onions and 2 kg of carrots cost £2.36.
The cost of 15 2.5 kg of onions is 15 × 2.5 = 37.5 kg of onions.
The cost of 1 kg of onions is 2.36 ÷ 37.5 = 0.06293 = £0.063.
3 kg of carrots cost £1.74. and we need to find how much 1kg of carrots cost.
Therefore, the cost of 1 kg of carrots is 1.74 ÷ 3 = 0.58 = £0.58.
Now we can use the above information to find the cost of 4 kg of onions:
The cost of 1 kg of onions is £0.063.
Hence, the cost of 4 kg of onions is 4 × 0.063 = £0.252.
We then can say since Stuart has £2, and we have found that the cost of 4 kg of onions is £0.252. Stuart has enough money to buy 4 kg of onions.
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A player hits the bullseye with a dart 8% of the time. Based on this relative frequency, how many times can the bullseye be expected to be hit when the player throws the dart 40 times. WRONG ANSWER = BLOCKED
The probability of hitting the bullseye if the dart is thrown 40 times is approx. 3 times.
What is relative frequency?The quantity of occurrences of an event is referred to as its frequency. The concept of relative frequency is experimental rather than theoretical. It is experimental, therefore if we repeat the trials, we can get different relative frequencies. To determine the frequency, we must first:
Number of occurrences for the entire population
Frequency count for a particular demographic segment
If we know the two frequencies mentioned above, we can use the following formula to get the relative frequency probability. A subgroup's formula is as follows:
Subgroup Count / Overall Count: Relative Frequency
Given that, a player hits the bullseye with a dart 8% of the time.
The probability of hitting the dart is = 8/100.
Now, the probability of hitting the bullseye if the dart is thrown 40 times is:
p = 40 (8/100) = 3.2 times = 3 times.
Hence, the probability of hitting the bullseye if the dart is thrown 40 times is approx. 3 times.
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The question is in the picture.
The angles in the quadrilateral are as follows;
x = 77°
y = 103 degrees
z = 52 degrees
How to find angles in a quadrilateral?The diagram above is a quadrilateral. The angles x, y and z can be found as follows:
x + 103 = 180(sum of angles on a straight line)
x = 180 - 103
x = 77 degrees
Therefore,
y = 103 degree(vertically opposite angles)
Vertically opposite angles are congruent.
The sum of angles in a triangle is 180 degrees.
Therefore,
103 + 25 + z = 180
z = 180 - 128
z = 52 degrees.
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You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case.
While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 80.4%.
(Report answer accurate to three decimal places with appropriate rounding.)
Answer: To find the critical value for a 80.4% confidence interval for a normal approximation of a binomial distribution, we need to find the z-score that corresponds to the 80.4% confidence level. We can do this using a standard normal table or using a z-score calculator.
Using a z-score calculator, we can find that the z-score corresponding to 80.4% confidence level is approximately 0.931. This means that 80.4% of the data falls within 0.931 standard deviations of the mean.
So, the critical value that corresponds to a confidence level of 80.4% is approximately 0.931.
Step-by-step explanation:
Which value of a would make a-5>-1 true?
A,2
b.-2
c. 3
d. 6
Answer:
d. 6
Step-by-step explanation:
Given, a-5> -1
Both sides add 5, and we get
a > 4
So a is 6.
Quadrilateral QRST is shown, with side lengths in inches (in.) and angle measurements in degrees.
2 in.
R
135°
3 in.
√18 in.
45°
S
5 in.
Lynn draws quadrilateral WXYZ, which is similar to quadrilateral QRST, with WX = 5 in
Enter values in the blank boxes to make the statement true.
The length of WZ is
2
degrees.
inches and the measure of angle Y is
Answer:
Y will be 65°
Step-by-step explanation:
Since angle S is 65°, angle Y will also be 65°
What are similar shape ?
Similar shapes are shapes that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Since quadrilateral QRST is similar to quadrilateral WXYZ, then angle Q = angle W , angle R = angle X and angle S = angle Y and angle T = angle Z.
Since angle S is 65° from the diagram shown, angle will be measured as 65°.
2 A customer applied for a loan for $15,000 to buy a motorcycle. The customer qualified for different loan options. Which loan option would allow the customer to pay the least amount of interest? (A A 3-year loan with an 7% annual simple interest rate B A 4-year loan with a 5% annual simple interest rate CA 5-year loan with a 4.5% annual simple interest rate A 6-year loan with a 3.7% annual simple interest rate
From the calculations, the best loan option is
A. 3-year loan with a 7% annual simple interest rate
How to find a better loan optionTo determine which loan option would allow the customer to pay the least amount of interest, we need to compare the amount of interest charged by each loan option.
For the 3-year loan with a 7% annual simple interest rate,
the interest charged would be $15,000 x 7% x 3 = $2,550.
For the 4-year loan with a 5% annual simple interest rate,
the interest charged would be $15,000 x 5% x 4 = $3,000.
For the 5-year loan with a 4.5% annual simple interest rate,
the interest charged would be $15,000 x 4.5% x 5 = $3,375.
For the 6-year loan with a 3.7% annual simple interest rate,
the interest charged would be $15,000 x 3.7% x 6 = $3,870.
From the calculations, it is clear that the 3-year loan with a 7% annual simple interest rate would result in the least amount of interest charged, with $2,550.
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Kristen has 5 dozen pencils.She wants to put them in equal groups so that the number of groups is at least 3, but less than 11. What are all the possible equal sized groups she can make with the pencils? *There are 12 item in a dozen*
The possible number of equal sized group is given by set N = 5 groups
What is union and intersection of sets?The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B
The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
The intersection of two sets is a new set that contains all of the elements that are in both sets
Given data ,
Let the total number of pencils be represented as n = 5 dozen = 60 pencils
The number of equal groups should be at least 3 and less than 11
So , the groups are represented by sets A , B , C , D , E
where the value of set A is
Set A = { 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 }
The set A contains 6 pencils of 10 groups
Set B = { 10 , 10 , 10 , 10 , 10 , 10 }
The set B contains 10 pencils of 6 groups
Set C = { 12 , 12 , 12 , 12 , 12 }
The set C contains 12 pencils of 5 groups
Set D = { 15 , 15 , 15 , 15 }
The set D contains 15 pencils of 4 groups
Set E = { 20 , 20 , 20 }
The set E contains 20 pencils of 3 groups
Therefore , the total number of sets N = 5 sets
Hence , the sets are solved
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Amir invests £785 for n years into a savings account.
Amir was paid 1.5% per annum compound interest.
At the end of the n years Amir had £1105.58 in the savings account.
Work out the value of n.
on=
Submit Answer
years
The number of years for the speculation to reach from £785 to £1,105.58 will be 23 years.
What is compound interest?Let 'A' is the amount, 'P' is the initial amount, 'r' is the rate of interest, and 'n' is the number of years.
Then the compound interest is written as,
A = P(1 + r)ⁿ
Then the equation is given as,
£1,105.58 = £785 × (1 + 0.015)ⁿ
1.40838 = (1.015)ⁿ
n log 1.015 = log 1.40838
n = 23 years
The number of years for the speculation to reach from £785 to £1,105.58 will be 23 years.
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Find the height of a triangle that has a base of 5/4 and an area of 10 sq cm?
Answer:
Height = 16
Step-by-step explanation:
Area = (Base * Height) / 2
Height = (2 * Area) / Base
Height = (2 * 10) / (5/4)
Height = (2 * 10) / (5/4) * (4/4)
Height = (2 * 10 * 4) / 5
Height = (80 / 5)
Height = 16
Can somebody answer this question please.
The line plot which can be used to represent the teachers record of how many miles each student ran during gym class is attached.
What is a line plot?A Line plot can be defined as a graphical representation of data as points or check marks above a number line, showing the frequency of each value along a line. It is used to analyze data
Given Data:
3/4, 1/4, 1/2, 3/4, 1/2, 1/2, 1/4, 3/4, 1/4, 1/2, 1/4, 3/4
From the given Data, the frequency of
1/4 = 5
1/2 = 4
3/4 = 3
Therefore, the line plot is attached as a diagram.
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PLEZ HELP WILL MARK Brainliest WITH ALL OF THEM DUE TONIGHT!!!!
Answer:
the answer you are looking for here is 3/7
Answer:
3/7
Step-by-step explanation:
6/7 ×1/2 = 6×1 × 7×2 = 6/14 ÷ 2 = 3/7
Mrs. Smith asked her students to write a situation that could describe the relationship between all of the values of x and y in the table.
X 0 1 2 3
Y 8 9 10 11
Which situation best describes the relationship between all the values of x and y in the table?
A. Danee had eight dance classes per week.
B. Yolanda had eight books and bought one new book each week.
C. Lincoln started with zero stamps in his collection for the first 8 months and then started to collect one stamp per month.
D. Gavin caught one fish in the first minute of fishing and eight fish each minute after.
The solution is Option B.
The equation of line is y = x + 8 , where the slope is m = 1
Yolanda had eight books and bought one new book each week
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P (
Let the second point be Q (
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we getWhat is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 8 )
Let the second point be Q ( 1 , 9 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 9 - 8 ) / ( 1 - 0 )
Slope m = 1
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 8 = 1 ( x - 0 )
On simplifying the equation , we get
y - 8 = x
Adding 8 on both sides of the equation , we get
y = x + 8
Hence , the equation of line is y = x + 8
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Answer: B
Step-by-step explanation:
Select the correct answer.
Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection?
Use the table of randomly generated outcomes to answer the question. Each letter represents the first letter of the bead color.
Outcomes
PBBB GPBP PBPP GGGG BPBP GBPB GPBP GBPB
PBPP PPGP PBGG GPPB PPPG BPPP PPPG BPGP
GGGG PGPG PPPP PPPP BBBG PPGB BBBG PPGB
PBPB BPPG PBBG BPBB PGPP PBPP PPPP PBPP
PPBP PPBB PGBP BPPB PPPB PPPB PGGB BBBB
A.
0.05
B.
0.10
C.
0.45
D.
0.55
The estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is 0.45 which is denoted as option C.
What is Probability?
This is referred to as a number that indicates how likely the event is to occur.
Probability for drawing at least 5 beads before she picks a grey bead from her collection
= 1-Probability for drawing at least one grey bead in the first 5 draws.
No of grey beads drawn in first 5 trials = (5, 80/80+160+240)
= (5, 1/6)
Probability for drawing at least one grey bead in the first 5 draws.
=1 - Prob of no grey
Required probability = P(X=0 in first 5 draws) = (1/6)⁵ = 0.4018 and th nearest value is therefore 0.45.
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how do you write 9.3E6 in standard form?
what is a congruent triangles worksheet
A congruent triangles worksheet is a type of educational resource that provides practice problems and exercises for students to work on to help them understand and apply the concept of congruent triangles.
The worksheet typically includes a variety of problems, such as identifying pairs of congruent triangles, determining congruent sides and angles, and applying congruence postulates or theorems to solve problems. The problems may involve using the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), or hypotenuse-leg (HL) congruence criteria.
Congruent triangles are triangles that have the same size and shape. In other words, they are identical in every way except for their position and orientation in space. Understanding congruent triangles is important in geometry, as it can help students to solve problems involving triangles, as well as more complex geometric figures.
Worksheets are a useful tool for students to practice and reinforce their understanding of congruent triangles, and can be used in the classroom or as homework assignments.
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The rectangular floor of a classroom is 24 feet in length and 40 feet in width. A scale drawing of the floor has a length of 6 inches. What is the area, in square inches, of the floor in the scale drawing?
Answer:
60 square inches
Step-by-step explanation:
Measure of length in scale drawing = Measure of actual length
6 inches = 24 feet
∴ 1 inch = [tex]\frac{24}{6}[/tex] feet
∴Unit multiplier applied:
∴1 inch in scale drawing = 4 feet of actual measurement
Measure of width in scale drawing = Measure of actual width
x inches = 40 feet
∴ x inches = (40 feet) × ([tex]\frac{1 inch}{4 feet}[/tex])
Measure of width in scale drawing = 10 inches
Area of rectangular floor in the scale drawing = (Length) × (Width)
= (6 inches) × (10 inches)
= 60 square inches
What is the average cost of living for a retiree per year?
O around $50,000
O around $60,000
O around $70,000
O around $80,000
We can infer from the foregoing description that the typical annual cost of living for a retiree is (A) around $50,000.
Who is a retiree?One who has retired is known as a retiree.
Many seniors underestimate their retirement income by not accounting for inflation.
Wages, a gauge of the income that retirees must replace, will be the basis for benefits.
One who has retired is known as a retiree.
According to the U.S. Bureau of Labor Statistics most recent Consumer Expenditure Survey, the typical retiree household—one that is headed by a person 65 or older—spends $50,220 annually.
Comparatively, the average yearly household expenditure is $63,036.
So, from the above description, we can state that the average cost of living for a retiree per year is (A) around $50,000.
Therefore, we can infer from the foregoing description that the typical annual cost of living for a retiree is (A) around $50,000.
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Complete question:
What is the average cost of living for a retiree per year?
A. around $50,000
B. around $60,000
C. around $70,000
D. around $80,000
Select the subtraction problem represented by the fraction model.
The subtraction problem represented by the fraction model is given above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Given is a figure as shown in the image.
We can write the fractional problem as -
" A rectangle is divided into eight equal rectangles. Smith colored six of these rectangles. How much percentage fraction of the image is colored."
Therefore, the subtraction problem represented by the fraction model is given above.
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QUICKK!! Which sentence is correct? A. -4 > 3 B. -4< -6 C. -4 > -7 D. -5 > -4
Answer:
C
Step-by-step explanation:
-4 is greater than -7
Find the coordinates of the circumcenter of AABC with vertices A(9,-4), B(5,-2), and C(0, -1).
The coordinates of the circumcenter are
Coordinates of the circumcenter are (7.7, -6.6)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
we first need to find the midpoint of each side, and then find the intersection of the perpendicular bisectors of each side.
Midpoint of AB is (7, -3)
Midpoint of BC is (2.5, -1.5)
Midpoint of AC is (4.5, -2.5)
The slope of the line passing through A and B is:
m= (-4 - (-2))/(9 - 5) = -1/2
the slope of the perpendicular bisector is 2
By point slope form
y - (-3) = 2(x - 7)
y = 2x - 17
And the equation of the perpendicular bisector of AC is:
y - (-2.5) = -1/2(x - 4.5)
y = -1/2x + 5
Now 2x - 17 = -1/2x + 2.25
2.5x = 19.25
x = 7.7
Substituting x = 7.7 into the equation for the perpendicular bisector of AB, we get:
y = 2(7.7) - 17
y = -6.6
Hence, coordinates of the circumcenter are (7.7, -6.6)
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The radius of a cylinder is 3 inches, and the cylinder's height is 10 inches.
What is the exact volume of the cylinder?
Responses
1. 30π in³
2. 60π in³
3. 90π in³
4. 300π in³
Given:-
[tex] \rm{radius= \bold{ 3}}[/tex][tex] \rm{height = \bold{ 10}}[/tex][tex] \: [/tex]
To find:-
[tex] \rm{volume \: of \: the \: cylinder = \: ?}[/tex][tex] \: [/tex]
By using formula:-
[tex]\underline{ \boxed{ \rm{ \red{volume \: of \: the \: cylinder = πr²h}}}}[/tex][tex] \: [/tex]
Solution:-
[tex] \rm{v = πr²h}[/tex][tex] \: [/tex]
[tex] \rm{v = π×( 3 )² × 10}[/tex][tex] \: [/tex]
[tex] \underline{\boxed{ \color{purple}{\rm{v = 90π in³}}}}[/tex][tex] \: [/tex]
The volume of the cylinder is 90π in³
[tex] \: [/tex]
hope it helps!:)
how to read 2/10 net 30 ?
2/10 Net 30 represents credit given to the buyer for the sale of goods or services. 2/10 net 30 means that the customer gets a 2% discount if the outstanding balance is paid within 10 days. Otherwise, full payment is due within 30 days.
2/10 Net 30:
The terms and conditions of the transaction are set forth in the purchase order and the corresponding invoice. These terms include terms of credit between the seller (also known as the payee) and the buyer (also known as the payer). A typical net credit period of 30 means the balance must be paid within 30 days of the invoice date. 2/10 Net 30 (also known as 2 10 Net 30) means that if a buyer pays within the first 10 days, their balance will be reduced by 2%. So "2" is the discount amount (2%) and "10" is the due date (10 days).
For example, if your company purchased $500 worth of goods or services on June 1st, you have entered into a loan agreement with the seller. If your company pays the net amount between June 1st and June 10th, you get a 2% discount, bringing the total amount to $490.
This example 2/10 net 30 step by step.
Day Start counting days from the invoice date.
Quick Formula: 100% Discount % x Invoice Amount.
100% - 2% = 98% x $500 = $490.
Formula:
(immediate discount) x (invoice amount) = less payment
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A rectangular prism measures 1 2/3 inches by 2 1/3 inches by 3 inches. How many cubes with edge length 1/3 inch fit in the prism?
Use the expression (10p+10)+(8p−1)
Simplify using properties of operations and then factor the expression using the GCF.
factored and simplified
answer :
9(2p+1)
steps
(10p+10)+(8p−1)
18p+9
9(2p+1)
chatgpt