If Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.
Given that Sam had Rs.350000,investment in house Rs.175000 at a rent of Rs.2000 per month and Rs.175000 in bank at rate of 12%, getting pension of Rs.3000 per month.
We are required to find the monthly income in 1996.
We have assumed that Sam was retired on 1st January, 1996 so the amount of rent, investment in bank and pension did not increase because they had to be increase in a year and we have to calculate the monthly income in which he was retired.
Monthly income=Rent of 1 month+Simple interest of 1 month+Pension per month
=2000+175000*1/100+3000
=2000+1750+3000
=Rs.6750
Hence if Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.
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People on a specific diet were examined for vitamin B deficiencies. One person is selected at random.
• Let M be the event that the person is deficient in vitamin B,subscript,2,baseline,.
• Let N be the event that the person is deficient in vitamin B,subscript,6,baseline,.
Option A shows the Venn diagram representing the union of these two events.
What is a Venn Diagram?A Venn Diagram divides a data-set into separate regions, which are correspond to each activity in the context of the problem.
The intersection region is the region that corresponds to the people sharing both features, with are M and B.
The union region is the region showing at least one of the two features, M and B, hence it is the region in which all the circles are painted.
Hence option a is the correct option in the context of this problem.
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1.2 Mr John is to deposit R 5,000 in his bank account. Deposits are calculated as follows: Cash deposit : At ATM: R4,80 +1,20% of the above value. At the Branch R8,00 + 1,50% of the above value. John claims that the difference of depositing R5 000 at ATM and at the Branch is R18, 20 Verify the stament (5) [23
The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20
What is simple interest?The simple interest formula is J = C ∙ i ∙ t, where J is interest, C is principal, i is interest rate, and t is time. To calculate the simple interest, just substitute the values in the formula and perform the calculation.
Calculate the deposit:
[tex]D=R4.80 + 1.20% of R5,000\\=R4.80 + (1.20/100) * R5,000\\= R4.80 + R60\\= R64.80[/tex]
Now, the deposit amount for the branch:
[tex]DB=R8.00 + 1.50% of R5,000\\= R8.00 + (1.50/100) * R5,000\\= R8.00 + R75\\= R83.00[/tex]
The difference will be:
[tex]Difference = R64.80 - R83.00\\Difference = -R18.20[/tex]
The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20. Therefore, John's statement is incorrect.
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A sequence can be generated by using an= 3an-1, where a1 = 10 and n is a whole number greater than 1.
What are the first 3 terms in the sequence?
A. 3, 13, 23
B. 10, 30, 90
C. 10, 13, 16
D. 3, 30, 300
Answer:
B
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] and a₁ = 10, then
a₁ = 10
a₂ = 3a₁ = 3 × 10 = 30
a₃ = 3a₂ = 3 × 30 = 90
the first 3 terms are 10 , 30 , 90
A 12 cm by 12 cm square piece of paper has 5 holes punched out of it. 4 of the holes are circles of radius 3 cm and 1 of the holes is a circle of radius 1 cm. The paper and punched holes can be visually interpreted as below. Determine the area of paper remaining after the holes have been punched out.
5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².
Firstly, we will calculate the area of the square of paper in which the holes are punched.
Side of square = 12 cm
Area of square = side²
= (12) ²
= 144 cm²
Now, we will calculate the area of the bigger punch holes
Radius of big punch hole = 3 cm
Area of 1 big punch = π (radius) ²
= 22/7 × (3)²
22 / 7 × 9
= 198 / 7 cm²
Area of 4 punches = 4 × 198/7
= 792/7 cm²
Now, we will calculate the area of smaller punch whose radius is 1cm
Area = 22/7 × 1²
= 22/7 cm²
Now, we will calculate the total area covered by circles
Total area covered by circles = area of small punch + area of 4 big punch
= 22/7 + 792/7
= 814 /7 cm²
Remaining area = area of square - area of circles
= 144 - 814/7
= (1008 - 814) / 7
= 194 / 7
= 27.714 cm²
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2. Find the amount of tax owed: commercial property valued at $340,000.00; assessed at 25%; taxed at $14.00 per hundred
dollars worth of property.
Answer:
55.0ml is answer = 22.05
Step-by-step explanation:
What is the value of x in the given triangle, in inches?
The numerical value of side length x in the right triangle is 8.
What is the numerical value of x?The figures in the image are two similar right triagles.
Since the two right triangles are similar, we equate the ratio of the sides of the two triangles.
x/6 = (x + 4)/9
Cross multiply and solve for x:
6( x + 4 ) = x × 9
Apply distributive property:
6 × x + 6 × 4 = x × 9
Simplifying, we get:
6x + 24 = 9x
Subtract 6x from both sides:
6x - 6x + 24 = 9x - 6x
24 = 9x - 6x
24 = 3x
3x = 24
Divide both sides by 3:
x = 24/3
x = 8
Therefore, the value of 8.
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The length of timber cuts are normally distributed with a mean of 95 inches and a standard
deviation of 0.52 inches. In a random sample of 30 boards, what is the probability that the
mean of the sample will be between 94.7 inches and 95.3 inches?
O 0.998
O 0.436
O 0.002
O 0.950
The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.
How to find the probability that the mean of the sample will be between 94.7 inches and 95.3 inchesUsing the Central Limit Theorem.
The Central Limit Theorem states that for a large enough sample size, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution. In this case, we have a sample size of 30, which is considered large enough for the Central Limit Theorem to apply.
Calculate the standard error of the mean (SEM):
SEM = σ / √n
SEM = 0.52 / √30
SEM ≈ 0.095
Calculate the z-scores for the lower and upper limits:
z1 = (94.7 - μ) / SEM
z2 = (95.3 - μ) / SEM
z1 = (94.7 - 95) / 0.095 ≈ -0.526
z2 = (95.3 - 95) / 0.095 ≈ 0.316
Find the area under the normal distribution curve between the z-scores using a standard normal distribution table or a calculator. The area represents the probability.
Using a standard normal distribution table or a calculator, the area between -0.526 and 0.316 is approximately 0.436.
Therefore, the probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.
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How much less would Maria have to spend to have $70 per month available for saving?
A. $45.95
B. $75.95
C. $25.95
D. $24.05
Maria have to spend $ 45.95 less than what she spends now in order to save $ 70 per month.
Hence the correct option is (A).
From the given Maria's Income Statement we can see that,
Her total income from Fast food Restaurant = Gross Pay + Allowance = $ 580 + $ 50 = $ 630.
Total deductions by taxation = Federal Income Tax + State Income Tax + Social Security Tax = $ 58 + $ 16 + $ 24.36 = $ 98.36
So here net income = $ (630 - 98.36) = $ 531.64.
Here total expenses = Auto + Clothing + Food + Entertainment + Other = $ 290.02 + $ 92.29 + $90.28 + $ 32 + $ 3 = $ 507.59
So Her Savings = Net Income - Total Expenses = $ 531.64 - $ 507.59 = $ 24.05.
Now in order to save $ 70 per month Maria has to spend = $ 70 - $ 24.05 = $45.95 less than she spend now.
Hence the correct option will be (A).
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determine whether the function represents exponential growth or exponential decay
y=3(1.88)
Answer:
Exponential Growth
Step-by-step explanation:
The base of 1.88 is greater than 1, so there will be exponential growth
Tuition for one year at a state university is about $12,500. Greg would like to attend this university and will save money each month for the next 4 years. His parents will give him $4,600 for his first year of tuition. Which plan shows the minimum amount of money Greg must save to have enough money to pay for his first year of tuition?
A. save $658.33 per month for the next 4 years
B. save $383.33 per month for the next 4 year
C. save $260.42 per month for the next 4 years
D. save $164.58 per month for the next 4 years
Answer: $383.33 per month for the next 4 years
Step-by-step explanation:
The correct answer is save $383.33 per month for the next 4 years. Tuition for one year at a state university is about $12,500, and Greg would like to attend this university. His parents will give him $4,600 for his first year of tuition, so he must save the remaining $7,900. To have enough money to pay for his first year of tuition, Greg must save $383.33 per month for the next 4 years. This is the minimum amount of money he must save, as the other plans require him to save more money than necessary.
Sorry if this is wrong btw fr fr.
Answer:164.58 (D)
Step-by-step explanation:
12,500-4600= 7900
12 months x 4 years makes 48 months, so 7900/48 = 164.58 per month
A ramp has a vertical rise of 4 feet & the angle of elevation of the ramp is 12°. How long is the ramp?
Answer:
19.24 ft
Step-by-step explanation:
x = length of ramp
sin12 = 4/x
x = 4/sin12 = 19.24 ft
B cubed equals 8. Solve for b
Answer:
b=2
Step-by-step explanation:
You are given:
[tex]b^{3} =8[/tex]
What does [tex]b^3[/tex] mean?
It is simply, b·b·b
Therefore:
b·b·b=8
What number could be multiplied by itself three times and equal 8?
...
2
Yay! That's great!
HELPPP
Instructional Item I
A research group is trying to determine how many alligators are in a particular area. They
tagged 30 alligators and released them. Later, they counted 12 alligators who were tagged out
of the 150 they saw. What can the research group estimate is the total population of alligators
in that area?
Instructional Item 2
The local grocery store is going to donate milk and cookies to an upcoming middle school
event. They surveyed 150 students in the school to determine which type of milk they prefer
and recorded the results below.
Cow's Milk Soy Milk
82
25
Almond Milk
43
If there are 950 students in the school, how much soy milk should the store plan to donate?
The total population of alligators will be 375.
The amount of soy milk that the grocery store should plan to donate is: 158.
How to calculate the total population of alligators in the areaTo calculate the total population of alligators in the area, we will assign the following variables:
30 Tagged alligators = m
12 Counted alligators = k
150 alligators seen = n
The total population size (N bar) of alligators is calculated with the formula:
N bar = mn/k
= 30 * 150/12
= 4500/12
375
For the amount of soy milk, we can say that if 25 out of 150 students preferred soy milk, then the number that would prefer soy milk out of 950 will be: 950 * 25/150 = 158.
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help me pleaseeeeeeeeeeeeeeee
Find the surface area and volume of the for fire. Round to the nearest tenth
The surface area and the volume of the cone is 150.8 in², 116. 1in³. option A
How to determine the valuesThe formula for calculating the surface area of a cone is expressed as;
SA = πr² + πrl
Such that the parameters are;
r is the radius l is the lengthSubstitute the values, we have;
Surface area= 3.14 × 16 = 3.14 × 4 × 8
Multiply the values
Surface area = 50.24 + 100.48
Add the values
Surface area = 150.8 in²
Volume of the cone is;
Volume = 3.14 × 4² × 6.9/3
Volume = 3.14 × 16 × 6.9/3
Volume =116. 1in³
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Pierre produces wedges of aged cheddar cheese and sells them for $12 each. The table below shows the labor productivity
forPierre's cheese-making business. Fill in the missing values. Assume this is a perfectly competitive market.
Instructions: Round your answers to one decimal place.
Pierre's Cheese Business and Revenues
Labor
0
2
4
6
8
10
12
14
Total Product (wedges
of cheese)
(workers)
0
———
48
66
82
———
———
114
Marginal Product
(wedges of cheese)
/
12
——-
9
——-
7
5
4
Price
(dollars)
$12
12
12
12
12
12
12
12
Total Revenue
(dollars)
$0
288
———
792
984
———
1,272
———
Marginal Revenue
Product (dollars)
/
———
144
108
———
84
———
48
Answer: To fill in the missing values, we can use the formulas for marginal product and marginal revenue product:
Marginal Product = Change in Total Product / Change in Labor
Marginal Revenue Product = Price x Marginal Product
Using the given information, we can fill in the missing values as follows:
Labor Total Product Marginal Product Price Total Revenue Marginal Revenue Product
0 0 - $12 $0 -
2 48 24 $12 $288 $288
4 66 9 $12 $792 $108
6 82 7 $12 $984 $84
8 96 5 $12 $1,152 $60
10 114 9 $12 $1,368 $108
12 132 9 $12 $1,584 $108
14 150 9 $12 $1,800 $108
So the missing values are:
Total Product for labor = 0 and 14: 0 and 150, respectively.
Marginal Product for labor = 0, 8, and 14: -, 5, and 9, respectively.
Total Revenue for labor = 4, 6, and 8: $792, $984, and $1,152, respectively.
Marginal Revenue Product for labor = 0, 4, and 6: -, $84, and $60, respectively.
Step-by-step explanation: :)
A total of $48,000 is invested in two municipal bonds that pay 4.25% and 5.75% simple interest. The investor wants an annual interest income of $2400 from the investments. What amount should be invested in the 4.25% bond
Use the Law of Sines to solve (if possible) the triangle: A = 25° 4', a = 9.5, b = 22? Round answer to two decimal places.
The measure of the angle B of the triangle is 78.15 degrees
How to determine the possible solutions from the triangleFrom the question, we have the following parameters that can be used in our computation:
A = 25 degrees
a = 9.5 units
b = 22 units
Using the law of sines, the angle B is calculated as
sin(A)/a = sin(B)/b
So, we have
sin(25)/9.5= sin(b)/22
This gives
sin(b) = 22 * sin(25)/9.5
Evaluate
sin(b) = 0.9787
Take the arc sin of both sides
b = 78.15
Hence, the measure of the angle is 78.15 degrees
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1. An isosceles triangle has a base with a length of 14 inches and base angles that measure 68° each. Which
expression below correctly calculates the area of this isosceles triangle?
(1) 7²-tan (68°)
(2) 14²-sin (68°)
(3) 7²-cos (68°)
(4) 14-7-sin (68°)
None of the given expressions (1), (2), (3), or (4) correctly calculates the area of the isosceles triangle. The correct expression is (1/2) * 14 * (7 * tan(44°)).
To calculate the area of an isosceles triangle, we need the base length and the height of the triangle. In this case, the base length is given as 14 inches, but the height is not provided.
However, we can use trigonometry to find the height of the triangle by using one of the base angles. Since the triangle is isosceles and the base angles are each 68°, we know that the remaining angle (at the top of the triangle) is 180° - 68° - 68° = 44°.
We can then use the trigonometric function tangent (tan) to find the height. The formula is: tan(angle) = opposite/adjacent.
tan(44°) = height/7, where 7 represents half of the base length.
Rearranging the equation, we have: height = 7 * tan(44°).
Now, we can calculate the area of the triangle using the formula: area = (1/2) * base * height.
Substituting the given values, we get:area = (1/2) * 14 * (7 * tan(44°)).
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What is the missing step in solving the inequality 4(x-3) + 4 ≤ 10+ 6x?
1. The distributive property: 4x-12 + 4 ≤ 10+ 6x
2. Combine like terms: 4x -8 ≤ 10+ 6x
3. The addition property of inequality: 4x ≤ 18 + 6x
4. The subtraction property of inequality: -2x ≤ 18
5. The division property of inequality:
O x≤-9
O x≥-9
0 x≤ - 1/2
0 x>-1
The value of inequality : x≤-9
Given,
Inequality 4(x-3) + 4 ≤ 10+ 6x
Firstly,
The distributive property: 4x-12 + 4 ≤ 10+ 6x
Then,
Combine like terms: 4x -8 ≤ 10+ 6x
Then,
The addition property of inequality: 4x ≤ 18 + 6x
Then,
The subtraction property of inequality: -2x ≤ 18
Then,
The division property of inequality:
Divide both sides of inequality by 2,
So,
x≤-9
Hence after last step the value of x is less than or equal to -9 .
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A fish tank holds 75 gallons of water and has a density of 0.12 fish per gallon. How many. How many fish are in the fish tank
Answer: 9 fish
Step-by-step explanation:
To find the answer all you have to do is multiply the amount of fish per gallon (0.12) to the total amount to gallons (75).
75 x 0.12 = 9
A 75-gallon aquarium will hold about 8 fish.
Stocking guidelines are 1 inch of adult fish per gallon of tank water. When applying this rule of thumb, we have to keep in mind that a 75 gallons water tank only holds about 70 gallons of water.
Then the number of fish in the tank would be:
Number of fish = density of fish * volume of water in the tank
Number of fish = 0.12 * 70
Number of fish = 8.4
So there are about 8 fish in the tank.
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Find the greatest common factor of 15n³ and 9n.
11
9
X
3
physical sciences 2023
What is the meaning of "the notational convention"?
In mathematics, notation is used to simplify and make our understanding of equations and problem statements easier.
Mathematical notation makes use of various symbols in order to represent operations, unspecified numbers, relations, and any other mathematical objects or entities, and proceeds to assemble them into understandable expressions and formulas.
A notational convention is a set of representatives consisting of symbols that are used to express mathematical equations, in this case, the notational convention adopted is that all the free variables of a formula are among u1, u2, u3 . . . un. as shown in the image provided.
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A ladder is leaning against a building, forming a 70° angle with the ground: The base of the ladder is 8.2 ft from the base of the
building.
What is the length of the ladder?
Round your answer to the nearest tenth of a foot.
22.5 ft
24.0 ft
28.0 ft
28.7 ft
The length of the ladder that is leaning on the building would be = 24ft. That is option B.
How to determine the length of the ladder?To determine the length of the ladder, the sine rule needs to be obeyed. That is
= a/sinA = b/sinB
Where;
a = 8.2 ft
A = 180-( 70+90
= 180- 160
= 20°
b = X
B = 90°
That is;
8.2/sin20° = b/sin90°
Make b the subject of formula;
b = 8.2×1/0.342020
= 23.9
= 24 ft
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Los estudiantes de la escuela organizan reuniones del equipo verde para planear maneras de proteger el medioambiente. Esta semana hay 144 miembros en la reunión, que es ek 90% del total del grupo
¿Cuál es el número total de miembros en el equipo verde?
If this week there are 144 members at the meeting, which is 90% of the total group, the total number of members on the green team is 160.
If 144 members represent 90% of the total group, we can set up the equation:
144 = 0.9x
where x is the total number of members on the green team.
To solve for x, we can divide both sides of the equation by 0.9:
144 ÷ 0.9 = x
This simplifies to:
160 = x
To check our answer, we can verify that 144 is indeed 90% of 160:
144 ÷ 160 = 0.9
which confirms that our answer is correct.
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Find the area of the green shaded sector of the circle. Show all of your work. Write your answer in terms of pi.
The area of the sector with an angle of 285 degrees and a radius of 6 units is 28.5π square units.
To find the area of a sector, we can use the formula:
Area of Sector = (Central Angle / 360 degrees) × π × (Radius²)
Given that the central angle is 285 degrees and the radius is 6, we can substitute these values into the formula:
Area of Sector = (285 degrees / 360 degrees) × π × (6²)
Area of Sector = (19/24) × π × 36
Area of Sector = (19/24) × 36π
Area of Sector = (19 × 36π) / 24
Area of Sector = 684π / 24
Area of Sector = 28.5π
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Solve and graph. |2x(x-1)+12|<=18
The solution of the inequality is -1 ≤ x ≤ 3.
To solve the inequality |2x(x-1)+12| ≤ 18, we can break it down into two separate inequalities:
2x(x-1) + 12 ≤ 18
-(2x(x-1) + 12) ≤ 18
Solving the first inequality:
2x(x-1) + 12 ≤ 18
2x² - 2x + 12 ≤ 18
2x² - 2x - 6 ≤ 0
Solving the second inequality:
-(2x(x-1) + 12) ≤ 18
-2x(x-1) - 12 ≤ 18
-2x² + 2x - 12 ≤ 18
2x² - 2x + 30 ≤ 0
Now, let's solve each inequality separately.
For the first inequality, 2x² - 2x - 6 ≤ 0:
We can factor this quadratic equation:
(2x + 2)(x - 3) ≤ 0
To determine the sign of the inequality, we need to consider the intervals where the expression is positive or negative. We set each factor equal to zero to find the critical values:
2x + 2 = 0 => x = -1
x - 3 = 0 => x = 3
Plotting these critical values on a number line and testing intervals, we find that the solution is -1 ≤ x ≤ 3.
For the second inequality, 2x² - 2x + 30 ≤ 0:
This quadratic equation does not have real solutions, so there are no solutions to this inequality.
Combining the solutions from both inequalities, we have -1 ≤ x ≤ 3.
To graph the solution, we plot the interval -1 ≤ x ≤ 3 on the number line. The shaded region on the number line represents the solution set.
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please answer i would appreciate it thank you(pls add the reasons)
The solution is: the value of the angles a, b and c are : a = 60, b = 90, c = 100.
Here,
We have that in line CHF, it has two given and one unknown angle.
The total angle of one straight line is 180.
Given that:
a = 180 - 50 -70 = 60
The angle intersecting the CHFD line can be computed by the the total angle inside the triangle.
Angle on EFH would give 180-40-60 = 80 and on EFD the angle would be 100 from 180-80.
Since angle C is congruent to the angle EFD.
c = 100
Take note that in a 4 sided polygon (GEFH), the total exterior angle is 360 degrees.
The different angle would be
angle GHF = 50 + a = 50+60 = 110
angle EFH = 80
angle FEG = 180- c = 180-100 = 80
ANGLE EGH = 360 - GHF -EFH -FEG = 360 - 110-80-80 = 90
since angle AG is congruent to EGH, we can calculate for the angle b which is congruent to its opposite. This would give us formula of
360 = (90+90) + (b) +(b)
360 = 180 +2b
b = 90
Hence, The solution is: the value of the angles a, b and c are : a = 60, b = 90, c = 100.
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A student scored 80% on a test. If the test had 50 questions worth one point each, how many questions did the student answer correctly?
Answer:
40
Step-by-step explanation:
All questions are worth the same, 1 point each.
80% of 50 = 0.8 × 50 = 40
Answer: 40
Answer:
40
Step-by-step explanation:
80/100*50 = 40
Use the table to add 199+61 vertically. The top row will be for regrouping (numbers that are "carried"). The bottom row will be for your answer. The addends have already been filled in for you.
The sum of the number 199 + 61 by vertical table will be 260.
Since, Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Use the table to add 199 + 61 vertically. Then we have
Hundreds Tens Ones
Regrouping 1 1
First addend 1 9 9
Second addend 0 6 1
Sum 2 6 0
Thus, The sum of the number 199 + 61 by the vertical table will be 260.
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The table to add 199+61 vertically is shown below.
To add 199 and 61 vertically, we'll set up the addition table as follows:
1 9 9
+ 6 1
_________
Let's start by adding the digits in the rightmost column, which is the ones place:
9 + 1 = 10
We write down 0 in the bottom row and carry over the 1 to the top row: 1 9 9
+ 6 1
_________
0
Now, let's add the digits in the next column (the tens place), including the carry-over:
1 + 9 + 1 = 11
We write down 1 in the bottom row and carry over the 1 to the top row:
1 9 9
+ 6 1
_________
1 1
Finally, let's add the digits in the leftmost column (the hundreds place), including the carry-over:
1 + 1 = 2
We write down 2 in the bottom row:
1 9 9
+ 6 1
_________
2 1
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