The value of (f . g) (3) is 594 and (f + g) (3) is 42 when function is f(x) = 4x² - 3 and g(x) = 2x + 3.
i) (f . g) (3)
(f . g) (x) = f(x) . g(x)
(f . g) (3) = f(3) . g(3)
= 4(3)² - 3 * 2(3) + 3
= 36 - 3 * 6 + 3
= 33 * 18
(f . g) (3) = 594
The value of (f . g) (3) is 594 when function is f(x) = 4x² - 3 and g(x) = 2x + 3
ii) ( f + g )( 3 )
( f + g )( x ) = f ( x ) + g ( x )
( f + g )( 3 ) = f (3 ) + g ( 3 )
= 4(3)² - 3 + 2(3) + 3
= 4(9) + 6
= 36 + 6
( f + g )( 3 ) = 42
The value of (f + g) (3) is 42 when function is f(x) = 4x² - 3 and g(x) = 2x + 3.
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A student polls his school to see if students in the school district are for or against the new legislation regarding school uniforms. She surveys 600 students and finds that 480 are against the new legislation.
Required:
a. Compute a 90% confidence interval for the true percent of students who are against the new legislation and interpret the confidence interval.
b. In a sample of 300 students, 68% said they own an iPod and a smart phone. Compute a 97% confidence interval for the true percent of students who own an iPod and a smartphone.
Solution :
68 % of the students owns iPod and a smart phone. So
p' = 0.68
q' = 1'
= 1 - 0.68
= 0.32
Since CL = 0.97, we know that \($\alpha = 1 - 0.97 = 0.03 $\)
The area to the left of \($z_{0.015}$\) is 0.015 and the area to the right of \($z_{0.015}$\) is \($1 - 0.015 = 0.985 $\)
Thus using \($TI \ 83, 83+ \ or \ 84+$\) calculator function \($\text{InvNorm} (0.985, 0.1), z_{0.015} = 2.17$\)
\($\text{EBP} = z_{\alpha / 2} \times \left( \sqrt{\frac{p'q'}{n}}\right) $\)
\($\text{EBP} = 1.645 \times \sqrt{\frac{0.68 \times 0.32}{300}} $\)
= 0.0269
Therefore, we are ninety seven percent confident that a true proportion of all the students who has iPod as well as a smart phone is between the 0.6531 and 0.7069
a). (0.7731, 0.8269); We estimated that with 90% confidence, the true percentage of all the students in district who are against a new legislation is between 77.31% and 82.69%.
b). Now,
Press the 'STAT' and then arrow over to perform TEST.
Now arrow down to the A:1 - PropZint and then place Enter.
Arrow a down x and then enter the 300 x 0.68
Similarly arrow a down to given n and then enter the 300
Now arrow down to the C-level and the enter the 0.97
Arrow a down for calculating and press the enter button.
The confidence interval is (0.6531, 0.7069)
a). (0.7731, 0.8269); We estimated that with 90% confidence, the true percentage of all the students in district who are against a new legislation is between 77.31% and 82.69%.
f(x)= a(x+p)² +q and g(x)= 0 3 3.1 x + p 1. The turning point of f is (1;4) and the asymptotes of g intersect at the turning point of f. Both graphs cut the y-axic at 3. 3.2 3.3 3.4 a 10 g +94 (1:4) Determine the equation of f Determine the equation of g Determine the coordinates of the x-intercept of g For which values of x will f(x) ≥ g(x)? [9]
Step-by-step explanation:
Let's solve the given questions step by step:
1. Determine the equation of f:
From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:
f(x) = a(x + p)^2 + q
Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:
4 = a(1 + p)^2 + q
This gives us one equation involving a, p, and q.
2. Determine the equation of g:
The equation of g is given as g(x) = 0.3x + p1.
3. Determine the coordinates of the x-intercept of g:
The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.
Setting g(x) = 0, we can solve for x:
0 = 0.3x + p1
-0.3x = p1
x = -p1/0.3
Therefore, the x-intercept of g is (-p1/0.3, 0).
4. For which values of x will f(x) ≥ g(x)?
To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.
f(x) = a(x + p)^2 + q
g(x) = 0.3x + p1
We need to find the values of x for which f(x) ≥ g(x):
a(x + p)^2 + q ≥ 0.3x + p1
Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.
To summarize:
We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).
Brianna made 9 1/4 bags of popcorn for a movie night with some friends. Together they ate 4 bags of it. How much popcorn was left?
There were 5 1/4 bags of popcorn left after eating 4 bags.
To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.
Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:
9 1/4 = (4 * 9 + 1) / 4 = 37/4
Now, let's subtract the 4 bags eaten from the total:
37/4 - 4
To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:
37/4 - 4/1
Now, let's find a common denominator and subtract the fractions:
37/4 - 16/4 = (37 - 16) / 4 = 21/4
The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:
21/4 = 5 1/4
Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.
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What is the scale factor for the dilation of triangle ABC
to produce triangle A'B'C'?
A. 0.25
B. 0.5
C. 2
D. 3
What is the scale factor for the dilation of triangle ABC
to produce triangle A"B"C?
A. 0.25
B. 0.5
C. 2
D. 3
Answer:
1) B 0.5
2) C 2
Step-by-step explanation:
point A (-2, 2) (0.5) = (-1, 1) A'
point B (-2, -1) (0.5) = (-1, -0.5) B'
point C (3, -1) (0.5) = (1.5, -0.5) B'
point A (-2, 2) (2) = (-4, 4) A'
point B (-2, -1) (2) = (-4, -2) B'
point C (3, -1) (2) = (6, -2) B'
3
9
Alicia has 23 coins. The coins consist of pennies and quarters and total $3.11.
Write a system of equations that represents this situation.
CAN SOMEONE HELP? The answer has to be decimal.✨
The angle of elevation θ is equal to 1.13186 in radian rounded to five decimal place.
What is an angle of elevationThe angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
We shall evaluate for the angle of elevation θ in degree, and then convert the result to radian as follows:
θ = tan⁻¹(4255/2000)
θ = 64.82482°
we multiply by π/180 to convert to radian;
θ' = 64.82482° × π/180
θ' = 1.13186 rounded to five decimal place.
Therefore, the angle of elevation θ is equal to 1.13186 in radian rounded to five decimal place.
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total area of 3 figures
Given dimensions:
x=31 feet, y= 24 feet and z= 95 feet
We can split the shape above into 3 components: A, B, and C
To find the total area, we will find the sum of the areas of each component
For A
The shape of A is that of a semi-circle.
The area of a semi-circle is given to be
\(\text{Area}=\text{ }\frac{1}{2}\text{ x }\pi r^2\)The radius will be the diameter divided by 2
y= diameter
r= radius = y/2
r=24/2 =12 feet
pi=3.14
\(\begin{gathered} \text{Area}=\frac{1}{2}\text{ x 3.14 x 12 x 12} \\ \text{Area}=226.08\text{ ft}^2 \end{gathered}\)For B
The shape is a rectangle
The area of a rectangle is given by
A = l x b
where l = 31 and b = 24
Area = 31 x 24
Area = 744 square feet
For C
The shape is a triangle
The area of the triangle is given by
\(A=\frac{1}{2}\text{ x base x height}\)base = 64 feet, height = 24 feet
\(\text{Area}=\frac{1}{2}\text{ x }64\text{ x 24 =768 ft}^2\)The total area is
22
Determine a series of transformations that would map Figure J onto Figure K. J
Figure.
Figure
Figure J is rotated 90° clockwise and then translated by 3 units toward the right.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The translation does not change the shape and size of the geometry. But changes the location.
Figure J is rotated 90° clockwise and then translated by 3 units toward the right.
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4
-3+x=17
5
11= -9 - x
6
14- X = 4
7
x - 30 = -44
8
16 = 27+ x
9
-75 = x - 50
10
15+ x = -15
11
-9 + x = -34
12
-27=-5-x
13
6+ x = 20
14
-8=x+7
15
13=3- X
ton nations
4. -17/3
5. -20
6. 10
7. -14
8. -11
9. -25
10. -30
11. -25
12. 22
13. 14
14. -15
15. -10
Solve each system by elimination
4x - 7y=13
6x -8y = 2
Answer:
Step-by-step explanation:
To solve the system by elimination, we can multiply the first equation by 8 and the second equation by 7 to get:
32x - 56y = 104
42x - 56y = 14
Now we can subtract the second equation from the first:
(32x - 56y) - (42x - 56y) = 104 - 14
Simplifying and solving for x:
-10x = 90
x = -9
Now we can substitute x = -9 into either of the original equations to solve for y. Let's use the first equation:
4x - 7y = 13
4(-9) - 7y = 13
-36 - 7y = 13
-7y = 49
y = -7
Therefore, the solution to the system is x = -9 and y = -7.
What are the coordinates of point A?
(8, –6)
(–6, 8)
(–5, 7)
(7, –5)
Answer:
d my friend
Step-by-step explanation:
17 9) When Abdul goes shopping for a couch at a furniture store, a salesperson offers a financing plan with zero interest for one year. To take advantage of the offer, Abdul has to give a down payment of $50. The rest of the purchase price will be evenly split into 12 monthly payments. *
Answer:
A. $25
Explanation:
From the question, We are given the following;
Cost of the couch = $350
Down payment = $50
Balance after the down payment = $350 - $50 = $300
This means that Abdul is to spread the balanve within 12 months.
$350 = 12 months
His monthly payment = Balance/Total number of month
His monthly payment = $300/12
His monthly payment = $25
Hence Abdul's each monthly's payment will be $25. Option A is correct
Please help solve question 12 and through 14
( will give brianlst :))
Answer:
12. The slope is 2
The y-intercept is 5
13. The slope is 1
The y-intercept is 5
14. The slope is 0.99
The y-intercept is 10
Step-by-step explanation:
12. If you use the rise over run method you go up by 2 and over 1. If you put rise over run you get 2/1 and that is equal to 2. So, slope is 2. The y-intercept is where x=0. If you look you can see that when x is 0, y is equal to 5. Therefore, the y-intercept is 5.
13. The slope is 1 because if you use the slope formula you can use two points like (1,6) and (2,7) in it to find that the slope is 1. You can also see that both the x and y variables go up by 1 each time, so the slope has to be 1. Once again the y-intercept is where x equals 0, even though it isn't shown on the graph we can infer it. At 0 days, the length of the kudzu would be 5 (because 5 is one step less than 6, remember the slope is 1).
14. The slope would have to be 0.99 because each consecutive download is 99 cents. There is a base membership fee of $10 so that has to be the y-intercept.
I hope this helps!!
If you have any questions let me know!
- Kay :)
Estimate the area of the circle.Round to the nearest whole number
Answer:
3 square units
Step-by-step explanation:
radius r = 1 unit
area = πr² = π ≅ 3 square units
(7, 4.7) across the y-axis
Answer:
picture description: ( 7y, 4.7x )
hope it helps!
What is the domain of f(x)? {x | 1 < x < 5} {x | 1 < x < 5} {y | −4 < y < 1} {y | −4 < y < 1}
The domain of function f(x) is given as follows:
{x | 1 ≤ x < 5}.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.The values of x of the function given at the end of the answer are as follows:
Starts at x = 1(closed interval).Ends at x = 5 (open interval).Hence the domain is given as follows:
{x | 1 ≤ x < 5}.
Missing InformationThe function is given by the image presented at the end of the answer.
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Answer:
A - {x | 1 < x < 5}
Step-by-step explanation:
took the Quiz
The figure below is a net for a right rectangular prism.
11 m
13 m
11 m
7 m
11 m
11 m
What is the surface area of the right rectangular prism, in square meters?
The surface area of the right rectangular prism is given as follows:
358 m².
How to obtain the surface area?The surface area of a prism is obtained with the sum of the areas of each part of the prism.
The parts that compose the prism are given as follows:
Two rectangles of dimensions 7 ft and 12 ft.Two rectangles of dimensions 5 ft and 12 ft.Two rectangles of dimensions 5 ft and 7 ft.The area of a rectangle is given by the multiplication of each of the dimensions of the rectangle.
Hence the surface area of the prism is calculated as follows:
S = 2 x (7 x 12 + 5 x 12 + 5 x 7) = 358 m².
(multiplication by two due to the two rectangles with each of the dimensions).
Missing InformationThe prism is given by the image shown at the end of the answer.
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On Saturday, Mrs. Colton buys 2
soda cans for $1.50. On Sunday.
she spends $2.52 on a 4-pack.
Which is a better deal?
Desmond is 5 inches taller than Niki.
If we let
represent Niki's height in inches, write an algebraic expression for Desmond's height.
The algebraic expression for Desmond's height is x + 5.
write an algebraic expression for Desmond's height.If we let "x" represent Niki's height in inches, then Desmond's height can be represented by "x + 5", since Desmond is 5 inches taller than Niki.
So the algebraic expression for Desmond's height is x + 5.
What are algebraic expression?Algebraic expressions is consist of variables, numbers, and mathematical operations (such as addition, subtraction, multiplication, and division).
They can contain one or more variables and can be evaluated for different values of the variables.
For example, the expression 3x + 5y - 2z is an algebraic expression that contains three variables (x, y, and z) and three coefficients (3, 5, and -2) that are multiplied by those variables. Algebraic expressions are commonly used in algebra to represent mathematical relationships and solve problems.
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Megan goes on walking holiday for five days.
The table shows how far she walked on the first four days.
Monday-14km,Tuesday-23km,Wednesday-13km,Thursday-13km
Megan says,'My average for the first four days is more than 15km.'
Explain why Megan is correct.
Friday is her last day.
She wants to increase her average to 17 km.
How many kilometres must she walk on Friday?
Answer:
a) Megan's total so far is 3 km more than necessary for an average of 15 km
b) 22 km
Step-by-step explanation:
a) The total of differences from 15 is ...
-1 + 8 + (-2) +(-2) = 3
Since this is more than 0, Megan's average is more than 15.
__
b) The total of differences from 17 is ...
-3 +6 -4 -4 = -5
To increase her average to 17 km, Megan must walk 17+5 = 22 km on Friday.
_____
Comment on the approach
In general, I find it easier mentally to deal with small numbers than with larger ones. So adding small differences can be easier than computing larger sums.
a) By computing the difference from the supposed average, we have effectively found the difference of the sum of values from the total necessary to give the required average. That is, Megan's average would be 15 if her total distance were 4·15 = 60. Her total distance is (4·15 +3) = 63, so her average is more than 15.
b) By finding out how much the total is below that necessary for the desired average, we determine the amount above that average the final number needs to be.
(14 -17) +(23 -17) +(13 -17) +(13 -17) +(Friday -17) = 0 . . . . the Friday value to make an average of 17
14 +23 +13 +13 +Friday = 5·17 . . . . . . . add 5·17
(14 +23 +13 +13 +Friday)/5 = 17 . . . . . . shows the Friday amount gives the required average
Friday = 17 -((14 -17) +(23 -17) +(13 -17) +(13 -17)) . . . . first equation rearranged to show how we computed Friday
Friday = 17 -(-5) = 17 +5 = 22
Carla asked students at a lunch table what their main course they liked. Out of these students, 28n liked pizza, 15 liked chicken nuggets, and 8 liked both. what is the probability that a randomly selected student will like pizza but not chicken nuggets?
The probability that a randomly selected student will like pizza but not chicken nuggets is (28n - 8)/(28n + 7), where 28n is the students who like pizza and 8 is students who like both pizza and chicken nuggets.
To find the probability that a randomly selected student will like pizza but not chicken nuggets.
Let P = the number of students who like pizza but not chicken nuggets
Then, P = the number of students who like pizza - the number of students who like both pizza and chicken nuggets
P = 28n - 8
So, the probability that a randomly selected student will like pizza but not chicken nuggets is:
P(Pizza but not nuggets) = P/(Total number of students)
We can find the total number of students who like either pizza or chicken nuggets by adding the number of students who like pizza and the number of students who like chicken nuggets, and then subtracting the number of students who like both:
Total number of students = 28n + 15 - 8 = 28n + 7
So, the probability that a randomly selected student will like pizza but not chicken nuggets is:
P(Pizza but not nuggets) = P/(Total number of students) = (28n - 8)/(28n + 7)
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Identify the range of the function shown in the graph
Answer:
[-1, 1]
Step-by-step explanation:
The range will be all y-values that the function reaches. Here, we see that the function is periodic which goes through a pattern of waves. It will go forever in both directions of the x-axis. However, in the y-dimension, it ranges from -1 to 1. It will have brackets as it touches 1 and -1 instead of approaching.
Solve the inequality įx - 2 Ž. Which number line represents the graph of the solution?
7 8 9 10 11 12 13 14 15
th
-5-4-3-2-1 0 1 2 3 4 5
-1
3
4
niwa
1
4
0
H
8
-
7
9
0
-1
1
9
-
No
2 5 4 1 2
3 9939
Answer:
2 ND option
solve and write
Insert a digit to make numbers that are divisible by 24 96__4
(-2ab^-5)(4a^-2b)^-2
Answer:
-a^5/(8b^7)
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^-b = 1/a^b
__
\((-2ab^{-5})(4a^{-2}b)^{-2}=(-2ab^{-5})(4^{-2}a^{-2(-2)}b^{-2})\\\\=\dfrac{-2}{16}a^{1+4}b^{-5-2}=\boxed{-\dfrac{a^5}{8b^7}}\)
Solve for y.
Thanks!!
Ngày 24/01/2014, Báo Người Lao động đưa thông tin: “Số liệu thống kê cho thấy nếu năm 2010, lượng
kiều hối đổ về Việt Nam đạt mức 8,26 tỉ USD thì đến năm 2011 đã tăng 9 tỉ USD. Năm 2012, con số
này cán mốc 10 tỉ USD, đưa Việt Nam lọt vào danh sách 10 nước nhận kiều hối cao nhất thế giới. Đến
năm 2013, Việt Nam tiếp tục đón dòng kiều hối lên đến 11 tỉ USD, cao hơn so với mức dự báo 10,6 tỉ
USD của Ngân hàng Thế giới (WB) và tiếp tục đứng trong danh sách 10 quốc gia nhận kiều hối nhiều
nhất thế giới.”
a. Trong điều kiện các yếu tố khác không đổi thì việc lượng kiều hối tăng mạnh sẽ ảnh hưởng
như thế nào đến tỷ giá hối đoái tại thị trường Việt Nam (giải thích ngắn gọn) và minh họa bằng
đồ thị mô hình cung, cầu ngoại tệ
b. Giả sử Việt Nam áp dụng chế độ tỷ giá cố định thì Ngân hàng Trung ương cần làm gì để ổn
định tỷ giá trong trường hợp nêu ở câu (a)?
Answer:
i wish i could understand what you sre saying so i could help
Answer:
Step-by-step explanation:gày 24/01/2014, Báo Người Lao động đưa thông tin: “Số liệu thống kê cho thấy nếu năm 2010, lượng
kiều hối đổ về Việt Nam đạt mức 8,26 tỉ USD thì đến năm 2011 đã tăng 9 tỉ USD. Năm 2012, con số
này cán mức 10 tỉ USD, đưa Việt Nam lọt vào danh sách 10 nước nhận kiều hối cao nhất thế giới. Đến
năm 2013, Việt Nam tiếp tục đón dòng kiều hối lên đến 11 tỉ USD, cao hơn so với mức dự báo 10,6 tỉ
USD của Ngân hàng Thế giới (WB) và tiếp tục đứng trong danh sách 10 quốc gia nhận kiều hối nhiều
nhất thế giới.”
a. Trong điều kiện các yếu tố khác không đổi thì việc lượng kiều hối tăng mạnh sẽ ảnh hưởng
như thế nào đến tỷ giá hối đoái tại thị trường Việt Nam (giải thích ngắn gọn) và minh họa bằng
đồ thị mô hình cung, cầu ngoại tệ.
b. Giả sử Việt Nam áp dụng chế độ tỷ giá cố định thì Ngân hàng Trung ương cần làm gì để ổn
định tỷ giá trong trường hợp nêu ở câu
A boat’s velocity, measured in meters per second, is described by vector b⇀=⟨3,4⟩. In two or more complete sentences explain how to find the speed of the boat and the direction it is traveling in standard position. In your final answer, include all of your calculations.
for this i got 5 m/s and 413 but i need to know more about it. i have to factor in WHERE the vector is before calculating the direction- and i dont quite understand how to do that so help would be MUCH appreciated <3
Answer: Velocity is a vector, so it has a magnitude and direction.
Speed is its magnitude, which is obtained from
|〈-3, 4〉 m/s| = √((-3 m/s)² + (4 m/s)²) = √(25 m²/s²) = 5 m/s
Its direction is an angle θ made with the positive horizontal axis, satisfying
tan(θ) = (4 m/s) / (-3 m/s) = -4/3 → θ = arctan(-4/3) + 180°n
where n is any integer. Now you have to consider that the x coordinate is negative and the y coordinate is positive, so 〈-3, 4〉 points into the second quadrant, and we get an angle there for n = 1 of about
θ ≈ 126.87°
Alternatively, you can use the vector 〈1, 0〉 in place of the axis, then compute the angle by relating it to the dot product, so θ is such that
〈-3, 4〉 • 〈1, 0〉 = |〈-3, 4〉| |〈1, 0〉| cos(θ)
(-3)•1 + 4•0 = √((-3)² + 4²) • √(1² + 0²) cos(θ)
-3/5 = cos(θ) → θ = arccos(-3/5) + 360°n
where again, n is any integer, and we get the same solution θ ≈ 126.87° in the second quadrant when n = 0.
Step-by-step explanation:
if 3/2p = 15 what is p
Answer:
p= 1/10
Step-by-step explanation:
i looked it up
1493600÷8 i need full steps
When 1,493,600 is divided by 8 the quotient is 186,700.
To divide 1,493,600 by 8, you can follow these steps:
We have to write down the dividend (1,493,600) and the divisor (8).
Now start with the largest place value in the dividend (the leftmost digit) and perform the division.
Divide 1 by 8. Since 1 is smaller than 8, you move to the next digit.
Bring down the next digit (4) and combine it with the previous quotient (0). This gives you 04.
Divide 4 by 8. Since 4 is smaller than 8, you move to the next digit.
Bring down the next digit (9) and combine it with the previous quotient (0). This gives you 09.
Divide 9 by 8. The quotient is 1, and the remainder is 1.
Bring down the next digit (3) and combine it with the remainder (1). This gives you 13.
Divide 13 by 8. The quotient is 1, and the remainder is 5.
Bring down the next digit (6) and combine it with the remainder (5). This gives you 56.
Divide 56 by 8. The quotient is 7, and there is no remainder.
Bring down the next digit (0) and combine it with the quotient (7). This gives you 70.
Divide 70 by 8. The quotient is 8, and there is no remainder.
There are no more digits to bring down, and the division is complete.
The quotient is the result of the division. In this case, 1,493,600 divided by 8 is equal to 186,700.
Therefore, the result of 1,493,600 ÷ 8 is 186,700.
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