Answer:
C
Step-by-step explanation:
3³ = 27
(3x²)³ = 27x⁶
(y³)³ = y⁹
(z³)³ = z⁹
ans = (27x⁶y⁹)/z⁹, which is answer C
Please answer this question in two minutes
Answer:
t = 8; u = 14.
Step-by-step explanation:
If the two triangles are to be congruent, their side lengths and angles must be equal.
In this case, segment RQ corresponds with segment HI, and segment QS corresponds to segment IJ.
Since they are equal, we know that...
3u = u + 28
and
16t - 32 = 12t
Solve for both!
3u = u + 28
2u = 28
u = 14
16t - 32 = 12t
4t = 32
t = 8
So, t = 8 and u = 14.
Hope this helps!
Answer他媽的你你一個愚蠢的屁股妓女,你需要做你贏了他媽的作業傻瓜屁股
Step-by-step explanation:
1 Weather Forecast
The temperature forecast for a city predicts the high for the day to be a normal random variable
with expectation (mean) u=87.2 , and standard deviation a= 6.4 . What is the probability
that the high will exceed 100?
2. Quality Control
A manufacturing plant for AA batteries is set to produce batteries with a normally distributed
voltage, with mean V. Quality control requires the actual voltage to be between 1.45V
and 1.52V with at least 99% probability. What should the standard deviation of the production
be, so that this condition is satisfied (that is, if V is the random variable describing the voltage of
the batteries, what should be so that p[1.450.99 )?
Descriptive Statistics
1. Working with a "real" sample
The attached file Exchange-Traded_Funds.csv lists a sample of percent dividend yield for a
selection of ETFs. For the purpose of an exercise in descriptive statistics, consider it a simple
random sample of size 50 (even if we don’t really know how this sample was chosen)
Compute the following for the sample:
•Sample Mean
•Sample Variance
•Sample Standard Deviation
•Median
•1st and 3rd quartiles
•Have your spreadsheet draw a histogram
2 Regression
The data in the file lit-life.csv lists life expectancy and literacy rate for 107 countries. Determine
the correlation and the regression line equation, and include a data scatterplot, as well as a
residuals scatterplot. What do you think of the result? You might want to switch the two data
columns, using the literacy rate as explanatory variable, and the life expectancy as the response
variable, but, that’s not mandatory.
1. The probability that the high temperature will exceed 100 is 0.0228 or 2.28%.
2. To satisfy quality control requirements, the standard deviation (σ) of the battery production needs to be determined such that the probability of the voltage being between 1.45V and 1.52V is at least 99%.
1. To find the probability that the high temperature will exceed 100, we can standardize the variable using the z-score formula: z = (x - u) / a, where x is the value of interest, u is the mean, and a is the standard deviation. Then, we can calculate the probability using the standard normal distribution table or software. For this case, we need to find P(X > 100), where X is the high temperature. By standardizing, we get z = (100 - 87.2) / 6.4 ≈ 2.0. Consulting the standard normal distribution table, we find that the probability is approximately 0.0228 or 2.28%.
2. To determine the required standard deviation for the battery production, we need to find the z-scores corresponding to the lower and upper voltage limits (1.45V and 1.52V) using the formula z = (x - V) / σ, where V is the mean voltage and σ is the standard deviation. We want the probability of the voltage falling within this range to be at least 99%, so we need to find the z-scores that give the cumulative probability of 0.99 and (1 - 0.99)/2 = 0.005 on each tail. Once we have the z-scores, we can rearrange the formula to solve for σ. This calculation requires the use of the standard normal distribution table or software.
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Five hundred people per hour ride a bus route between Minneapolis and St Paul. The fare is $0. 50. If the bus operators increase the fare by $0. 10, they will lose 50 passengers. What should they charge to get the maximum profit?
The fare should be increased by $0.50 to get maximum profit with a fare of $1.00.
If the bus operators increase the fare by $0.10, they will lose 50 passengers. The original fare is $0.50 and five hundred people per hour ride a bus route between Minneapolis and St Paul.
Therefore, the revenue earned per hour with the original fare is:Revenue = 500 × 0.50 = $250per hour
If the fare is increased by $0.10, the new fare will be $0.50 + $0.10 = $0.60As per the problem, If the bus operators increase the fare by $0.10, they will lose 50 passengers.
Therefore, the total number of people who will ride the bus at the increased fare would be:Total passengers = 500 – 50 = 450
Therefore, the revenue earned per hour with the increased fare would be:Revenue = 450 × 0.60 = $270 per hour.Now, to maximize profit, we need to find the fare that generates maximum revenue.
Let's suppose that fare to be x dollars.If the fare is increased by x dollars, then the number of passengers that will ride the bus would be:Total passengers = 500 – 50(x/0.10) = 500 – 5x
Therefore, the revenue earned per hour with the increased fare of x dollars would be:Revenue = (500 – 5x) x = $500x – 5x²
Since revenue is maximized when the derivative of revenue is zero, we differentiate the revenue function and equate it to zero:Revenue = $500x – 5x²
dRevenue/dx = 500 – 10x = 0
⇒ 10x = 500
⇒ x = 50
Thus, the fare should be increased by $0.50 to get maximum profit with a fare of $1.00. Therefore, the correct answer is $1.00.
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The work shows the long division of 647 ÷ 3.
Find the values of a and b in the long division problem.
a =
b =
So, 647 3 = 215 +
I'm assuming ratio of a to b is the remainder of the long division.
3
Michael split
pounds of candy among 8 people.
What is the unit rate in pounds per person?
Write your answer in simplest form.
Answer:
1/8
Step-by-step explanation:
The question is incomplete, here is the complete question
Michael split 3/4
pounds of candy among 8 people.
What is the unit rate in pounds per person?
Write your answer in simplest form
SOLUTION:
Micheal splits 3/4 candy among 8 people
Therefore the unit rate per pounds per person can be calculated as follows
= 3/4 ÷ 8
= 3/4 × 1/8
= 3/24
= 1/8
Hence the unit per pound per person is 1/8
Type the missing number in this sequence:
-5,
20,
-80,
-1,280,
5,120
Answer:
320
Step-by-step explanation:
multiples of -4
Answer:
320
Step-by-step explanation:
it looks as if it is multiplied by -4 every time.
-5 x -4 = 20
20 x -4 = -80
-80 x -4 = 320
If it costs $500 per ton to ship a vehicle, which vehicles can be shipped for less than $1,250?
According to linear inequality w ≤ 2.5, any vehicle weighing 2.5 tons or less can be shipped for less than $1,250.
What are linear inequalities, exactly?
Linear inequalities are mathematical statements that compare two linear expressions using the inequality symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Linear inequalities involve variables that represent unknown quantities, and the inequality indicates that one expression is less than or greater than another.
For example, a linear inequality might look like this:
2x + 3y ≤ 6
Now,
To determine which vehicles can be shipped for less than $1,250, we need to know the weight of the vehicles being shipped.
Let's assume that the weight of each vehicle is measured in tons. Then, we can set up an inequality to represent the cost of shipping a vehicle:
500w ≤ 1250
where w = weight of the vehicle.
To solve for w, we can divide both sides of the inequality by 500:
w ≤ 1250/500
w ≤ 2.5
This means that any vehicle weighing 2.5 tons or less can be shipped for less than $1,250. Vehicles weighing more than 2.5 tons would cost more than $1,250 to ship.
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In the method of proof, the rules are not used jointly but are applied one at a time and once per line. Group of answer choices True False
The given statement "In the method of proof, the rules are not used jointly but are applied one at a time and once per line" is True.
In a proof, each step must be justified by a logical rule or principle. These rules are not applied all at once, but rather one at a time and in a specific order. This allows for a clear and organized progression of the proof, and ensures that each step is based on a sound and valid reasoning.
For example, in a proof by contradiction, we assume the opposite of what we want to prove and then show that this assumption leads to a contradiction. In each step of the proof, we apply a logical rule or principle, such as the law of non-contradiction or the transitive property of equality.
By applying the rules one at a time and once per line, we can carefully follow the logical reasoning and ensure that the proof is valid. If we were to apply multiple rules at once or skip steps, the proof could become muddled and the validity of the argument could be called into question. Therefore, it is important to use the rules of logic in a methodical and systematic way when constructing a proof.
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Donna borrowed $10, 500 at a simple interest rate of 4% for 3 years to buy her new car. How much interest would Donna pay and how much is the car altogether?
Donna borrowed $10,500 at a simple interest rate of 4% for 3 years to buy her new car. How much interest would Donna pay and how much is the car altogether ?
Answer:-Given:-\( \bullet \) Principal (P) = $10,500
\( \bullet \) Rate of interest (r) = 4%
\( \bullet \) Time (t) = 3 years
To Find:-Interest of Donna and amount of car altogether.
Solution:-We know,
\( { \boxed{\rm \red {I \: = \frac{Prt}{100}}}} \)
\( \therefore \) I = \( \frac{10,500 \: × \: 4 \: × \: 3}{100} \)
I = \( \frac{126,000}{100} \)
I = $1260
Now,
Amount of the car = $ (10,500 + 1260)
= $ 11,760
$1260 interest would Donna pay and $11,760 is the car altogether. [Answer]Step-by-step explanation:
We know that Interest = Principal×Rate×Time/100
So,
10,500×4×3/100
= 10,500×3/25 (by cancelling 100 by 4)
=31500/25
= 1260
Therefore,
$1260 Answer
hope it helps.....
HELP ME PLEASE I don’t want to fail also I’m give Brainlist and 10 points
Answer:
theres no question or answers
Step-by-step explanation:
Answer:
Where is the question? I don't see it did you forget to attach it?
Step-by-step explanation:
write an equation in slope-intercept form of the line that passes through (1,8) and perpendicular to 3x 7y
The equation in slope-intercept form of the line that passes through (1,8) and is perpendicular to 3x + 7y = 0 is :
y = (7/3)x - (19/3).
To write the equation in slope-intercept form, we need to find the slope of the line that passes through (1,8) and is perpendicular to 3x + 7y = 0.
First, we need to rearrange the equation 3x + 7y = 0 into slope-intercept form:
7y = -3x
y = (-3/7)x
The slope of this line is -3/7.
Since the line we are trying to find is perpendicular to this line, its slope will be the negative reciprocal of -3/7:
m = 7/3
Now we can use the point-slope formula to write the equation of the line that passes through (1,8) with slope 7/3:
y - 8 = (7/3)(x - 1)
Finally, we can rearrange this equation into slope-intercept form:
y = (7/3)x - (19/3)
So, the equation in slope-intercept form of the line that passes through (1,8) and is perpendicular to 3x + 7y = 0 is y = (7/3)x - (19/3).
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3. Rhombus KLMN with vertices K(-3, 2), L(1, 4),
and N(-5, -2): (x,y) → (x, y-5)
M(-1,0)
The coordinates of KLMN after reflection along the y-axis is K'(3,2); L'(-1,4); M'(1,0); and N'(5,-2).
What is reflection?A reflection in mathematics is a mapping from a Euclidean space to itself that is an isometry with a set of fixed points known as the hyperplane, also known as the axis or plane of reflection. The mirror image of a figure in the axis or plane of reflection is the image produced by a reflection.So, the coordinates of KLMN when reflected across the y-axis:
When reflected along the y-axis, the image of (x, y) is (-x,y).
Vertex K(-3,2image )'s after reflection along the y-axis is K' (3,2)After reflection along the y-axis, the image of vertex L(1,4) is L' (-1,4)Vertex M(-1,0image )'s after reflection along the y-axis is M' (1,0)Vertex N(-5,2image )'s after reflection along the y-axis is N' (5,-2)Therefore, the coordinates of KLMN after reflection along the y-axis is K'(3,2); L'(-1,4); M'(1,0); and N'(5,-2).
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The correct question is given below:
Given a rhombus KLMN with vertices K(-3,2), L(1,4), M(-1,0), and N(-5,-2). What would the coordinates of its image be when reflected across the y-axis?
Which property is used to write the equivalent expressions below? (2x7) x3=2x (7x3)
Answer:
Associative Property of Multiplication
Step-by-step explanation:
The Associative Property of Multiplication states that the answer to an equation will stay the same even if the grouping of the numbers changes.
Answer:
9
Step-by-step explanation:9x5
Suzie, Georgia and Bernadette do a project together. Suzie does 5/18 of the project, Georgia does 2/9 of the project and Bernadette does 1/2 of the project
How much of the project should still be completed? And who do you think should do the last section of the project?
Answer:
the project has been completed.
Step-by-step explanation:
5/18 +4/18 + 9/18 = 18/18 or 1
so therefore no one has to complete the project, as it has already been completed
why is paying back along with a nominal interest rate of 13.62% if the interest is compounded quarterly, how much greater is white effective interest rate than his nominal interest rate
The required white effective interest rate is 0.71% more than his nominal interest rate.
What is compound interest?Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Here,
White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent
So
Difference in interest = 14.33%-13.62%
=0.71%
Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.
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Does the ordered pair (0,3) satisfy the following system of equations?-4x+4y=20-3x+4y=15
We are given the following system of equations:
\(\begin{gathered} -4x+4y=20,(1) \\ -3x+4y=15,(2) \end{gathered}\)we are asked to determine if the point (0, 3) is a solution of the equation. To do that, we will replace the points x = 0 and y = 3 in each of the equations to see if they are both satisfied:
Replacing in equation (1):
\(\begin{gathered} -4(0)+4(3)=20 \\ 0+12=20 \\ 12\ne20 \end{gathered}\)Since equation (1) is not satisfied by the point this means that this is not a solution.
Geoffrey actively participates in a rental real estate activity. During the year, his total rental real estate income was $25,000 His only other income for the year was $180,000 in wages, and he has no adjustments to income. He has one qualifying dependent, and he will use the head of household filing status. How much of Geoffrey's income is subject to the net investment income tax?
$5,000
$25,000
$205,000
$25,000 of Geoffrey's income is subject to the net investment income tax.
The net investment income tax applies to certain types of income, including rental real estate income, and is calculated based on an individual's modified adjusted gross income (MAGI) and filing status. In the case of Geoffrey, his rental real estate income of $25,000 is subject to the net investment income tax.
To calculate the net investment income tax, we need to determine Geoffrey's MAGI. His total income for the year consists of $25,000 in rental real estate income and $180,000 in wages, totaling $205,000. Since he has no adjustments to income, his MAGI is equal to his total income of $205,000.
Therefore, the amount of Geoffrey's income subject to the net investment income tax is $25,000.
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easy please helppp match the following defintion with the correct term: the vertical distance between two points on a line
1. run
2. rate of run
3. slope
4. rise
Answer:
4. rise
match the following definition with the correct term:
the vertical distance between two points on a line
1. run
2. rate of run
3. slope
4. rise
Determine the global extreme values of the (x,y)=11x−5yf(x,y)=11x−5y if y≥x−9,y≥x−9, y≥−x−9,y≥−x−9, y≤6.y≤6.
(Use symbolic notation and fractions where needed.)
The function $f(x, y) = 11x - 5y$ has a global maximum of $105$ at $(0, 6)$ and a global minimum of $-54$ at $(0, -9)$, the first step is to find the critical points of the function.
The critical points of a function are the points where the gradient of the function is equal to the zero vector. The gradient of the function $f(x, y)$ is: ∇f(x, y) = (11, -5)
```
The gradient of the function is equal to the zero vector at $(0, 6)$ and $(0, -9)$. Therefore, these are the critical points of the function.
The next step is to evaluate the function at the critical points and at the boundary of the region. The boundary of the region is given by the inequalities $y \ge x - 9$, $y \ge -x - 9$, and $y \le 6$.
The function $f(x, y)$ takes on the value $105$ at $(0, 6)$, the value $-54$ at $(0, -9)$, and the value $-5x + 54$ on the boundary of the region.
Therefore, the global maximum of the function is $105$ and it occurs at $(0, 6)$. The global minimum of the function is $-54$ and it occurs at $(0, -9)$.
The first step is to find the critical points of the function. The critical points of a function are the points where the gradient of the function is equal to the zero vector. The gradient of the function $f(x, y)$ is: ∇f(x, y) = (11, -5)
The gradient of the function is equal to the zero vector at $(0, 6)$ and $(0, -9)$. Therefore, these are the critical points of the function.
The next step is to evaluate the function at the critical points and at the boundary of the region. The boundary of the region is given by the inequalities $y \ge x - 9$, $y \ge -x - 9$, and $y \le 6$.
We can evaluate the function at each of the critical points and at each of the points on the boundary of the region. The results are shown in the following table:
Point | Value of $f(x, y)$
$(0, 6)$ | $105$$(0, -9)$ | $-54$$(x, x - 9)$ | $11x - 45$ for $x \ge 9$$(x, -x - 9)$ | $-5x + 54$ for $x \ge 9$$(x, 6)$ | $11x - 30$ for $-9 \le x \le 6$The largest value in the table is $105$, which occurs at $(0, 6)$. The smallest value in the table is $-54$, which occurs at $(0, -9)$. Therefore, the global maximum of the function is $105$ and it occurs at $(0, 6)$. The global minimum of the function is $-54$ and it occurs at $(0, -9)$.
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irst consider a public good of value to Ann and Bob with the property that the value of the good can be expressed in monetary terms. In this case, the Samuelson condition states that the efficient level of the good is determined by MV +MVP where p is the per A B unit price of the good, and, for example, MV is Ann's marginal value of the good. Now consider a public good of value to Ann and Bob, the value of which CANNOT be expressed in monetary terms. In this case A O a. The Samuleson condition continues to work as in the case where values CAN be expressed in monetary terms. O b. We need more information before we can know how to modify the Samuelson condition. O c. The Samuelson condition is of no use because we cannot compare Ann's utility to Bob's. O d. The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.
The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.
When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.
Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.
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What is the probablity of rolling a 3 on a 6 numbered dice?
Answer:
1/6
Step-by-step explanation:
theres only 1, 3 and 6 possibilities
Answer:
Possible Outcomes and Sums Just as one die has six outcomes and two dice have 6 2 = 36 outcomes, the probability experiment of rolling three dice has 6 3 = 216 outcomes. This idea generalizes further for more dice.
1. How do you identify the terms in an expression? 2. How do you determine the coefficient of a term if you don’t see a number in the term?
A term is an expression is a set of constants, variables, and exponents, while the coefficient of a term is the numerical value present in the term.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
A term in an expression is a set of constant or numerical values, variables, and exponents. Each term of an expression is differentiated from others by a mathematical operation. For example, in the expression 2x²+6x-5, 2x², 6x, and -5 all three are terms and it is differentiated from others by the '+' and '-' operators.
The coefficient of a term is the numerical value present in the term. Let's understand this with the similar example above.
In term 2x², 2 is the coefficient.
In term 6x, 6 is the coefficient.
Hence, a term is an expression is a set of constants, variables, and exponents, while the coefficient of a term is the numerical value present in the term.
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7 + (1 + 9) = (7 + 1) + 9 Is this identity commutative or associate??
Step-by-step explanation:
it is associative
because in commutative a+b=b+a
but in associates a+(b+c)=(a+b)+c
Datech 20.23
. You want to take a taxi to the next Cowboys game, so you call Cowboy Taxi. The initial meter drop
$2.25 and $1.80 for each additional mile. Given the linear equation, y = 1.80x +2.25 answer the fo
questions.
In the equation, what does 2.25 represent? Z
a) What is the rate of change? 0.15
b) How much does it cost to ride 20 miles? 9.66
c) If you have $20, how many miles can you ride in the taxi? 16 miles
X
-6
9
12
f(x)
5
-5
-7
2. Given the following information, answer the following questions.
a) Write a linear equation in function notation:
b) Find f(21)
c) If f(x) = 11, find the value for x.
a. The rate of change is 2.25. b. It would cost $38.25 to ride 20 miles in the taxi. c. You can ride about 9.86 miles in the taxi with $20.
What is function notation?Using symbols and variables, a mathematical function may be represented using function notation. It includes expressing the function as f(x), where x is the independent variable or input value and f is the function's name. The symbol f(x), which may also be interpreted as "f of x," stands for "the value of the function f at the value x". We may find the value of the function f, which is the dependent variable or output value, by supplying the value of x. When a function has a complex formula or contains many variables, function notation provides a clear and practical approach to represent mathematical connections.
Given that the equation of the line is y = 1.80x +2.25.
In the given equation, 2.25 indicates the first drop on the meter or the set fare for a taxi, which is charged regardless of how far you go.
b. For x = 20 mile we have:
y = 1.80(20) + 2.25 = 36 + 2.25 = 38.25
c. Solving for x for $20 we have:
20 = 1.80x + 2.25
1.80x = 20 - 2.25
1.80x = 17.75
x = 9.8611.
Hence, it would cost $38.25 to ride 20 miles in the taxi. c. You can ride about 9.86 miles in the taxi with $20.
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Katherine is conducting an experiment with bacteria where she cools the temperature of one bacteria to -51°C and the other bacteria to -76°C. What was the temperature difference in the two experiments?
Answer:
Difference in temperature = 25°C
Step-by-step explanation:
Given:
Temperature 1 = -51°C
Temperature 2 = -76°C
Find:
Difference in temperature
Computation:
Difference in temperature = Temperature 1 - Temperature 2
Difference in temperature = -51°C - [-76°C]
Difference in temperature = -51°C + 76°C
Difference in temperature = 25°C
To find a two-digit number such that if the places of its digits are interchanged, a number will be obtained that is four and a half times greater than the given
Let p represent "It is the morning."
Let q represent "I am tired."
What is the symbolic representation of:
"I am tired, if and only if, it is the morning."
Answer:
\( p \longleftrightarrow q \)
2. Given the regular polygon below, what is the measure of each measured angle? *
12
Om<1 = 72; m>2 =
108
m<1 = 36; m>2 = 72
Om<1 = 72; m>2 = 54
Om<1=36; m>2 = 144
The measure of the angles m∠1 and m∠2 for the polygon are 72° and 54° respectively.
How to calculate for the interior angles of a polygonTo calculate the sum of interior angles of a polygon, you can use the following formula:
Sum of interior angles = (n-2) x 180 degrees
Where "n" represents the number of sides (or vertices) of the polygon.
Given the 5 sided polygon;
(5 - 2) × 180 = 540
one interior angle = 540/5 = 108°
m∠2 = 108°/2
m∠2 = 54°
m∠1 = 180 - [2(54°)]
m∠1 = 180 - 108
m∠1 = 72°
Therefore, the measure of the angles m∠1 and m∠2 are 72° for the polygon and 54° respectively.
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9, 14, 7, 9, 3, 12, 5,4
Find the mean and median travel times for these students.
If necessary, round your answers to the nearest tenth
Mean: _ minutes
Median: __ minutes
Answer:
mean: 65
median: 9
Step-by-step explanation:
You take all the numbers you have and add them up. Make it simple by adding smaller numbers together. Then once you have the total which is 65 you divide it by the total of numbers you have and then round because after dividing you get 8.125 and the safest way to round is to 9.
For the past 10 periods, MAD was 25 units while total demand was 1,000 units. What was mean absolute percent error (MAPE)?
Multiple choice question.
10%
25%
50%
75%
The mean absolute percent error (MAPE) is 25%.
The mean absolute percent error (MAPE) is a measure of forecasting accuracy that quantifies the average deviation between predicted and actual values as a percentage of the actual values. In this case, the mean absolute deviation (MAD) is given as 25 units for the past 10 periods, and the total demand is 1,000 units.
To calculate the MAPE, we need to divide the MAD by the total demand and multiply by 100 to express it as a percentage. In this scenario, the MAPE is calculated as follows:
MAPE = (MAD / Total Demand) * 100
= (25 / 1,000) * 100
= 2.5%
Therefore, the MAPE is 2.5%, which means that, on average, the forecasts have a 2.5% deviation from the actual demand.
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