Step-by-step explanation:
3cos2x +sinx=1
3(1-2sin²x)+sinx=1
3-6sin²x+sinx=1
sinx(-6sinx+1)=1
either
sinx=1
sinx=sin(90)
:.x=90
or
-6sinx+1=1
-6sinx=1-1
sinx=0/-6
sinx=sin0,sin180
:.x=0,180and90
For a charity drive, each classroom is given a coin box made of cardboard like the one shown. The student council wants to construct a version of the coin box that has a scale factor of 3 times the classroom coin box. Is 100 square feet of cardboard enough to build the new coin box? Select the response with the correct answer and an argument that can be used to defend the solution
The classroom coin box required less than 11.11 Square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient
The 100 square feet of cardboard is enough to build the new coin box with a scale factor of 3 times the classroom coin box, we need to consider the relationship between the areas of the two boxes.
The area of the original classroom coin box is unknown, as it is not given in the problem. However, since we know that the new coin box has a scale factor of 3 times the original, we can infer that its area will be 3^2 = 9 times greater than the original.
Let's assume that the area of the classroom coin box is A square feet. In that case, the area of the new coin box would be 9A square feet.
Now, we are given that 100 square feet of cardboard is available. To determine if it's sufficient, we need to compare this value to the area of the new coin box, which is 9A.
If 100 square feet is greater than or equal to 9A, then it would be enough to build the new coin box. Conversely, if 100 square feet is less than 9A, it would not be enough.
Since we do not have a specific value for A, we cannot determine the exact answer. However, we can provide the argument to defend our solution.the classroom coin box required less than 11.11 square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient.
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Note the question be like :
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn from the bag without replacement, what is the probability that both marbles are red?
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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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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Please help quick! will mark brainliest!
Answer:
7, 14
Step-by-step explanation:
Look at the first column of numbers: 2.8 m in 2 min.
We can get a unit rate from those numbers:
2.8 m / 2 min = 1.4 m/min
He walks at a rate of 1.4 m/min
Now multiply the unit rate by each number of minutes to find the number of meter.
Let's do the second column as a check: time = 3 min
1.4 m/min × 3 min = 4.2 m
4.2 m is the number on the table, so our unti rate is correct.
5 min:
1/4 m/min × 5 min = 7 m
10 min:
1.4 m/min × 10 min = 14 m
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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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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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
1. Drag the cards so that each number sentence is true. (You will have one card left over.)
2. Describe your thinking.
The figures paired are given as follows:
| -3| = 3
|-2| > 1
0 < |-1|
The left over is 2. This is based on the principle of absolute values.
What is absolute values?The absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5.
A number's absolute value can be conceived of as its distance from zero along the real number line.
As a result, the absolute value of -3 is 3, which suggests that |-3| = 3.
-2 in absolute terms equals 2. That is |-2| greater than 1.
the inverse value of -1 equals 1. This equals 0 |-1|.
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help me pleaseeeeeeeeeeeeeeee
please answer i would appreciate it thank you
a) The triangles are congruent by the AAA criterion.
b) The triangles are congruent by the SAS criterion.
a) In the first triangle the interior angles are 40 degrees and 30 degrees.
The other interior angle would be 180 - (40 + 30) = 110 degrees.
As per the diagram, the triangles have equal proportionate-sized side lengths.
Therefore, the triangles are congruent by the AAA criterion.
b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.
Therefore, the triangles are congruent by the SAS criterion.
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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 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
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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The diagram represents the trajectory of an airplane at take off. The angle that represents the
trajectory of a jet is 15% greater than the trajectory of the airplane.
The diagram represents the trajectory of an airplane at take off the angle representing the airplane's trajectory is approximately 147.83 degrees.
To solve this problem, let's denote the angle of the airplane's trajectory as x degrees. According to the given information, the angle representing the trajectory of the jet is 15% greater than the airplane's trajectory.
The angle representing the trajectory of the jet can be calculated as:
x + 0.15x = 1.15x
Therefore, the angle representing the trajectory of the jet is 1.15x degrees.
Given that the airplane's trajectory is at 170 degrees, we can set up the following equation:
1.15x = 170
To solve for x, divide both sides of the equation by 1.15:
x = 170 / 1.15 ≈ 147.83
Thus, the angle representing the airplane's trajectory is approximately 147.83 degrees, and the angle representing the jet's trajectory is approximately 1.15 * 147.83 ≈ 170 degrees.
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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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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
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
In circle S, a sector is shaded. ZTSU measures 40°.
C
T
40°
(47)
S
What fraction of the interior of the circle is shaded?
Simplify your answer.
4 cm
Which expression represents the area of the shaded sector in square centimeters
(4x)
(16)
(167)
Given that in circle S, a sector is shaded and ZTSU measures 40°. We are to find out what fraction of the interior of the circle is shaded and simplify the answer.The correct answer is 16π/9 cm².
To find out the fraction of the interior of the circle that is shaded, we need to determine the measure of the central angle that intercepts the entire circle.The total measure of a circle is 360 degrees.
To find the fraction of a circle shaded, divide the number of degrees in the sector by
360.4x = (40/360) × πr² = (1/9) × πr².
We simplify the answer: 4x = πr²/9 Fraction of the interior of the circle that is shaded = 40/360 = 1/9.Expression for the area of the shaded sector in square centimeters is:
A = (40/360) × πr² = πr²/9 = π(4²)/9 = 16π/9 cm²
Therefore, the correct answer is 16π/9 cm².
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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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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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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: :)
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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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!
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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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 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
Find the greatest common factor of 15n³ and 9n.
11
9
X
3
physical sciences 2023
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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