13. (4pts) Give a complete explanation (show work and give written explanation) of the problem 216) 5897 using the scaffolding approach.
Answers
5897 ÷ 216 equals 40 with a remainder of 33 when using the scaffolding approach.
To solve the division problem 5897 ÷ 216 using the scaffolding approach, we break down the division into smaller steps as follows:
We start by dividing the leftmost digit of the dividend (5) by the divisor (2). Since 5 is less than 21 (the largest multiple of 2 less than or equal to 5), the quotient for this step is 0. We bring down the next digit (8) to the right of the 0.
Now, we divide the number formed by the previous quotient and the next digit (08) by the divisor (216). Since 216 is greater than 80, the quotient for this step is also 0. We bring down the next digit (9) to the right of the 08.
We divide the number formed by the previous quotient and the next digit (089) by the divisor (216). This time, 216 is greater than 890, so the quotient for this step is 0. We bring down the next digit (7) to the right of the 089.
Finally, we divide the number formed by the previous quotient and the next digit (0897) by the divisor (216). Now, 216 is less than 897, so we find the largest multiple of 216 that fits into 897. The largest multiple is 4 (216 * 4 = 864). We subtract 864 from 897, resulting in a remainder of 33. Therefore, the quotient for this step is 4.
The final result is a quotient of 40 and a remainder of 33. Thus, 5897 ÷ 216 equals 40 with a remainder of 33 when using the scaffolding approach.
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Related Questions
Write the number for four million forty thousand .
Answers
Answer:
4.040,000
Step-by-step explanation:
The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 14 people reveals the mean yearly consumption to be 60 gallons with a standard deviation of 20 gallons. Assume that the population distribution is normal. (Use t Distribution Table.) a-1. What is the value of the population mean? Unknown 20 60 a-2. What is the best estimate of this value? Estimate population mean c. For a 95% confidence interval, what is the value of t? (Round your answer to 3 decimal places.) Value of t d. Develop the 95% confidence interval for the population mean. (Round your answers to 3 decimal places.) Confidence interval for the population mean is and . e. Would it be reasonable to conclude that the population mean is 52 gallons? Yes It is not possible to tell
Answers
Rounded to 3 decimal places, the 95% confidence interval for the population mean is approximately (48.450, 71.550).
What is confidence interval?
A confidence interval is a range of values that is used to estimate an unknown population parameter based on sample data. It provides a measure of the uncertainty or variability associated with the estimation. The confidence interval consists of two numbers, an upper bound and a lower bound, which define a range within which the true population parameter is likely to fall.
a-1. The value of the population mean is unknown. We are trying to estimate it using the sample data.
a-2. The best estimate of the population mean is the sample mean, which is 60 gallons.
c. For a 95% confidence interval, we need to find the value of t with (n-1) degrees of freedom. In this case, the sample size is 14, so the degrees of freedom is 14 - 1 = 13. Consulting the t-distribution table or using a statistical calculator, the value of t for a 95% confidence level with 13 degrees of freedom is approximately 2.160.
d. To develop the 95% confidence interval for the population mean, we can use the formula:
Confidence Interval = Sample Mean ± (t * Standard Error)
Standard Error = Standard Deviation / √Sample Size
Using the given values, we can calculate the standard error:
Standard Error = 20 / √14 ≈ 5.348
Substituting the values into the formula, we have:
Confidence Interval = 60 ± (2.160 * 5.348) ≈ 60 ± 11.550
Rounded to 3 decimal places, the 95% confidence interval for the population mean is approximately (48.450, 71.550).
e. It would not be reasonable to conclude that the population mean is 52 gallons because the value of 52 falls outside the 95% confidence interval. Since the confidence interval includes the range of plausible values for the population mean, any value outside the interval is less likely to be the true population mean.
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What will be the value stored in the variable x after the execution of the following code snippet?
int a = 10;
int b = 20;
int c = 2;
int x = b / a /*c*/;
a) 1
b) 2
c) 4
d) The code has a syntax error
Answers
The value stored in the variable x after the execution of the following code snippet will be b) 2.
The right-click context menu option or a combination of hotkeys can be used to add code snippets, which are compact chunks of reusable code, to a code file. Although try-finally and if-else blocks, for example, are frequently used code blocks found in code snippets, you can also use them to add whole classes or methods.
Learn more about using the templates tool to create reusable emails. Applications and web pages use snippets. Snippets are made to be reusable and to add functionality, like connecting various parts of a program.
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Please solve the equation shown in the image below
Answers
The value of angle <4 is 63 degrees
How to solve for angle <4?In a triangle, an exterior angle equals the sum of the opposite interior angles.
This means that:
<4 = 31 + 32
Evaluate the sum
<4 = 63
Hence, the value of <4 is 63 degrees
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You can triple and then subtract by 1 to get 29
Answers
Answer: 10*3=30. 30-1=29
Step-by-step explanation: The number you are looking for is 10
HURRY PLS ANSWER NOW!!
What is the area of the trapezoid?
33 in2
52.5 in2
82.5 in2
91 in2
Answers
Answer:
91 in2
Step-by-step explanation:
11+15 over 2 , times by 7 equals 91 ??
Riley is building an ant farm for his school's science fair. He has enough materials to build a farm that is 1000 square inches in total, 9 square inches of which will be taken up for food and water sources. Of the remaining available space, each ant needs at least 1 square inches to themselves. What is the maximum amount of ants Riley's ant farm can house?
Answers
Answer:
991 ants
step by step explanation:
amount of area excluding the area needed for food and resources= 1000-9=991 Square inches
area each ant needs= 1 square inch
number of ants= 991÷1= 991 ants
The requried number of Riley's ant houses is given as 991 houses.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
He has enough materials to build a farm that is 1000 square inches in total, 9 square inches of which will be taken up for food and water sources. Of the remaining available space, each and needs at least 1 square inch to itself.
Let the number of ants be x,
According to the quesiton,
1×x + 9 = 1000
x = 1000 - 9 /1
x = 991 / 1
x = 991 houses.
Thus, the requried number of ant houses is given as 991 houses.
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What is order of magnitude?
Answers
The magnitude of the number of the minutes in the school is 2.
What magnitude is 0 in?Although the order of magnitude of zero is not specified, it is occasionally stated to have a magnitude of. Zero is less than any other positive number, and so is its order of magnitude, according to this infinitely negative order of magnitude.
Can a magnitude order be negative?There can be no negative magnitude. The component of the vector that lacks direction is its length (positive or negative).
The order of magnitude is the approximate representation of the logarithmic of the order's value and is typically considered to be 10 taken as the base.
On a scale of 10 logarithmic, the difference in the order of magnitude can be quantified.
The value storage is where you may find the number into the various magnetic.
As a result, the number of minutes spent in school is 2.
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Complete question -
What is the Order of Magnitude of the number of minutes in a school day?
Soledad buys 5 ounces of frozen yogurt for $2.25. What is the unit price of the frozen yogurt in dollars per ounce?
Answers
Answer:
0.45
Step-by-step explanation:
You divided 2.25 by 5
hence, you divide 2.25 by 5.
Suppose you decide to put $12,500 in an account earning 9% interest compounded quarterly. How much interest would you earn after 1 year?
Answers
Step-by-step explanation:
you add 9% to a number by multiplying that number by 1.09.
because adding 9% gives us in the end 109% of the original amount.
anyway, the formula for quarterly compounded interest is
Cq = P [ (1+r)^(4*n) – 1 ]
P is the starting principal amount
r is the interest rate per quarter (= interest rate / 4)
n would be the number of years (= 1 in our case).
so, the interest after 1 year is
12500((1 + 0.09/4)⁴ - 1) = 12500(1.0225⁴ - 1) =
= 12500 × 0.093083319 = $1,163.541485 ≈ $1,163.54
Sarah is trying to run a certain number of miles by the end of the month. If Sarah is 80% of the way to achieving her goal and she has already run 40 miles, how many miles is she trying to run by the end of the month?
Answers
Answer: 50 miles
Step-by-step explanation:
Let the miles that she is trying to run by the end of the month be denoted by x.
Since she is 80% of the way to achieving her goal and she has already run 40 miles. This can be expressed as:
80% of x = 40
80/100 × x = 40
0.8x = 40
x = 40/0.8
x = 50
The miles that she is trying to run by the end of the month is 50 miles.
A student uses the equation tan theta= s^2/49 o represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline theta where sin theta =1/2
Answers
After finding the value of theta, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.
The equation tan(theta) = s^2/49 represents the speed, s, in feet per second, of a toy car driving around a circular track with an angle of incline, theta, where sin(theta) = 1/2.
To solve this problem, we need to use the given information about sin(theta) to find the value of theta. Since sin(theta) = 1/2, we can determine that theta is equal to 30 degrees.
Now that we know the value of theta, we can substitute it into the equation tan(theta) = s^2/49. Plugging in 30 degrees for theta, the equation becomes tan(30) = s^2/49.
The tangent of 30 degrees is equal to √3/3. So, we have √3/3 = s^2/49.
To solve for s, we can cross multiply and solve for s^2. Multiplying both sides of the equation by 49 gives us 49 * (√3/3) = s^2.
Simplifying, we get √3 * 7 = s^2, which becomes 7√3 = s^2.
To find the value of s, we take the square root of both sides. So, s = √(7√3).
Therefore, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.
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CarCoCo (CCC) and AceAuto(AA) are competing auto body shops that specialize in painting cars. Three types of labor are required to complete a paint job: Sanding/Filling, Masking, and Spraying. The number of hours required to complete each job at the two shops are given in the first table and the matrix L . Labor costs, in dollars per hour, are given in the second table and the matrix C . Hours to Complete Each Job Sanding/ Filling Masking Spraying CCC 9 5 3 AA 7 5 5 Labor Costs (in dollars per hour) Sanding/Filling 14 Masking 10 Spraying 24 The labor-hours and wage information is summarized in the following matrices: L = [ 9 5 3 7 5 5 ] C = ⎡ ⎢ ⎣ 14 10 24 ⎤ ⎥ ⎦ a . Compute the product L C . 245 239 Incorrect b . What is the ( 2 , 1 ) -entry of matrix L C ? ( L C ) 21 = 239 Incorrect c . What does the ( 2 , 1 ) -entry of matrix ( L C ) mean?
Answers
The (2, 1)-entry of the matrix LC means the value in the second row and first column. (2, 1) is interpreted as row 2 and column 1. Using the value of LC that we obtained in part a, we can determine that ;LC = [238 271].
Let's begin by multiplying the two matrices L and,
C;L × C = [ 9 5 3 7 5 5 ] × ⎡ ⎢ ⎣ 14 10 24 ⎤ ⎥ ⎦
= ⎡ ⎢ ⎣ 9 × 14 + 5 × 10 + 3 × 24 7 × 14 + 5 × 10 + 5 × 24 ⎤ ⎥ ⎦
= ⎡ ⎢ ⎣ 238 271 ⎤ ⎥ ⎦. Therefore, the product of the two matrices is; LC = [238 271].
The (2, 1)-entry of the matrix (LC) is obtained by multiplying the second row of matrix L by the first column of matrix C, which gives the total cost of labor at Ace Auto for the Masking process.
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how to you find out the angles in a regular polygon
Answers
Answer:
Answer is on the pic
Step-by-step explanation:
I hope it's helpful!
Tanner is 2 years younger than his
brother. Tanner's age t in years is 2
less than his brother's age b.
dependent variable:
independent variable:
equation:
Answers
The equation will be:
t = b - 2
And we can see that:
independent variable = brother's age.dependent variable = Tanner's age.How to identify the variables?Here we have two variables:
t = taner's age
b = age of Tanner's brother.
The independent variable is the one that does not depend on the other, in this case (for how it is worded) is the brother's age.
The dependent variable depends on the other, on this case, Tanner's age.
Now let's write the equation, we know that Taner's age is 2 years less than his brother, then:
t = b - 2
That is the equation.
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ifferentiate the following functions:
(a) f(x)=6x3+2x2−x+12 (4 Pts) (b) f(x)=4x (4 Pts) (c) f(x)=e−x(x−2) (4 Pts)
(d) f(x)4x3/(2x2−x) (4 Pts)
(e) f(x)=ln(x−3) (4 Pts)
Answers
Answer. I think is A
Step-by-step explanation:
Hannah needs to calculate the cotangent of an angle. She uses the ratio
opposite leg
for her calculation. Did Hannah correctly calculate the cotangent of the angle?
adjacent leg
A
B.
Yes, Hannah correctly calculated the cotangent of the angle.
adjacent leg
No, Hannah should have used the ratio
opposite leg
hypotenuse
No, Hannah should have used the ratio
opposite leg
O c.
D.
No, Hannah should have used the ratio
adjacent leg
hypotenuse
Answers
Answer:
B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)
Step-by-step explanation:
✍️The formula for calculating cotangent of an angle is given as:
\( cot = \frac{adjacent}{opposite} \).
The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.
Therefore, Hannah did not calculate the cotangent of the angle correctly.
She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.
2/9( 9/4x - 9)
Simplify
Answers
The simplified expression of the given Linear expression is \(\frac{x}{2} - 2\)
As per the question statement, we are supposed to find out the simplified expression of the given Linear expression \(\frac{2}{9} (\frac{9x}{4} -9)\)
Before solving this, we need to be clear about the algebraic expressions basics and integers operations and how we can deduce an algebraic expression into its simplest form.
\(\frac{2}{9} (\frac{9x}{4} -9)\\=\frac{2}{9}(\frac{9x-36}{4} )\\=\frac{9x-36}{2*9} \\=\frac{9x}{18} - \frac{36}{18} \\=\frac{x}{2} -2\)
Hence \(\frac{x}{2} - 2\) is the simplified expression of the given Linear expression.
Linear expression: A linear expression is any algebraic expression in which each term is either a constant or is a variable raised to the some power.
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When performing a statistical analysis, why do we usually work with a sample rather than an entire population?
Select one:
a. The p-values only work with samples, not populations.
b. A t-test doesn't produce results when a population is used.
c. We don't work with samples, we only work with entire populations.
d. We often lack the manpower and resources to gather an entire population for a statistical analysis
Answers
When performing a statistical analysis, we work with sample rather than the entire population because, we often lack manpower or resources to gather data. So option D is correct.
Statistical work is usually done with a sample. This is done because, if we try to include and collect data from the whole population, it will be very time consuming and need more manpower and resources. It will become a much tedious process.
So a sample which is representative of the whole population is needed. Selecting a sample size and determining the sample must follow certain criteria. They are population parameters we want to estimate, Cost of sampling, Variability of the population, how hard is it to collect data and how precise we want the final estimates to be. All these are taken into consideration and a sample that properly represent the population is determined without bias.
So, option D is the correct answer.
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What would be the coordinates of the image if this pre-image is reflected across the x-axis? (-2, 2), (1, -1), (3, 1), (2, 4) (2, -2), (-1, 1), (-3, -1), (-2, -4) (-2, -2), (-1, 1), (-3, -1), (-2, -4) (-2, 2), (1, 1), (3, 1), (2, 4)
Answers
Answer:
(-2,-2),(1,1),(3,-1),(2,-4),(2,2),(-1,-1),(-3,1),(-2,4),(-2,2),(-1,-1),(-3,1),(-2,4),(-2,-2),(1,-1),(3,-1),(2,-4)
Step-by-step explanation:
just multiply the y coordinate by -1
Answer:
just multiply the y coordinate by -1
Step-by-step explanation:
if a restaurateur wants to know how many dollars the restaurant makes per day, which process metric is needed?
Answers
To determine how many dollars a restaurant makes per day, the restaurateur would need to measure the "revenue" metric.
Revenue is the total amount of money a business earns from its sales or services provided over a specific period of time, in this case, daily. It includes all income generated by the restaurant from selling food and drinks to customers.
Measuring revenue is essential for any business as it helps the owner understand the financial health of their enterprise. By tracking revenue over time, the restaurateur can identify patterns and trends and make informed decisions to increase profits and improve the business's overall performance.
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I’ll really appreciate it if you help me out on this one , im currently failing this class please help
Answers
33x-33+99=33x-33-99
99=-99
Since 99 __equal -99 the equation has many solutions
The cylinder x^2 + y^2 = 81 intersects the plane x + z = 9 in an ellipse. Find the point on such an ellipse that is farthest from the origin.
Answers
The point on the ellipse x^2 + y^2 = 81, which is formed by the intersection of the cylinder and the plane x + z = 9, that is farthest from the origin can be found by maximizing the distance function from the origin to the ellipse. The point on the ellipse that is farthest from the origin is (-9, 0, 0).
To find the point on the ellipse that is farthest from the origin, we need to maximize the distance between the origin and any point on the ellipse. Since the equation of the ellipse is x^2 + y^2 = 81, we can rewrite it as x^2 + 0^2 + y^2 = 81. This shows that the ellipse lies in the xy-plane.
The plane x + z = 9 intersects the ellipse, which means that we can substitute x + z = 9 into the equation of the ellipse to find the points of intersection. Substituting x = 9 - z into the equation of the ellipse, we get (9 - z)^2 + y^2 = 81. Simplifying this equation, we obtain z^2 - 18z + y^2 = 0.
This is the equation of a circle in the zy-plane centered at (9, 0) with a radius of 9. Since we are interested in the farthest point from the origin, we need to find the point on this circle that is farthest from the origin, which is the point (-9, 0, 0).
Therefore, the point on the ellipse that is farthest from the origin is (-9, 0, 0).
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the prefix that multiplies a basic si unit by 0.01 is
Answers
SI unit is an international system of measurements that are used universally in technical and scientific research to avoid the confusion with the units. Having a standard unit system is important because it helps the entire world to understand the measurements in one set of unit systems.
SI system“The International System of Units is abbreviated as SI.The SI system has seven base units.The SI system allows the use of prefixes to indicate the multiples or submultiples of a unit.SI prefix for \(10^-^9\)The SI prefix for \(10^-^9\) is nano.The symbol for nano is n.Learn more about SI unit at:
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The given question is incomplete, complete question is:
What is the SI prefix for each of the following multiples and submultiples of a unit?
\(10^-^9\)
The slope of the line below is -8/7.
Answers
Answer:
A
Step-by-step explanation:
Find the area of the
trapezoid (explain ur answer)
Answers
Answer:
49
Step-by-step explanation:
8*7=56
7*6=42
56+42=98
98/2=49
Triangle XYZ has coordinates X(2, 4), Y(−3, 4), and Z(−3, 1). If the triangle is translated using the rule (x, y) → (x − 2, y + 1), what are the coordinates of Y'?
Y'(–5, 5)
Y'(0, 5)
Y'(–5, 2)
Y'(–1, 3)
Answers
Answer:
Y'(-5, 5)
Step-by-step explanation:
To find the coordinates of Y' after the translation, we apply the given rule to the coordinates of point Y(-3, 4).
Using the translation rule (x, y) → (x - 2, y + 1), we can substitute the coordinates of Y(-3, 4) into the rule:
x' = x - 2 = -3 - 2 = -5
y' = y + 1 = 4 + 1 = 5
Therefore, the coordinates of Y' are (-5, 5).
help please ASAP super hard
Answers
Answer:
B.
Step-by-step explanation:
LO3
Ollie is paid 65p for each pizza he delivers. He is
paid £49.45 for a weekend shift including £12.40 in
tips.
How many pizzas did he deliver during the shift?
You must show your working.
Answers
I’m American so I’m not sure how British money works, don’t be mad if im not right
Have an AWESOME day! :)
Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or neither (if the set is not a relation).
A = {(1, 2) (2, 2) (3, 2) (4, 2)}
Answers
Answer:
Function
Step-by-step explanation:
Since each x value corresponds to a single y value