Using the vertex form the quadratic model for Jordan's monthly revenue is y = 20 / 9(x - 13.5)² + 844.44.
We can use the vertex form of a quadratic equation to create a model for Jordan's monthly revenue:
y = a(x - h)² + k
where y is the monthly revenue, x is the price that Jordan sets for all pieces, and (h, k) is the vertex of the parabola. We can find the vertex by using the formula:
h = -b / 2a
where b and a are coefficients in the standard form of the quadratic equation (y = ax² + bx + c).
To get started, we can substitute two points from the given data to form a system of equations:
864 = a(12 - h)² + k
884 = a(13 - h)² + k
When we deduct the first equation from the second, we obtain:
20 = a(13 - h)² - a(12 - h)²
Simplifying, we get:
20 = a(25 - 24h + h²) - a(16 - 24h + h²)
20 = 9a(h² - 1)
Solving for a, we get:
a = 20 / 9(h² - 1)
Next, we can use the third point to solve for h:
896 = a(14 - h)² + k
Substituting the expression we found for a, we get:
896 = 20 / 9(h² - 1)(14 - h)² + k
Simplifying, we get:
h = 13.5
Now we can solve for k by substituting in the values we found for h and a:
864 = a(12 - h)² + k
k = 844.44
Finally, we can write the quadratic model for Jordan's monthly revenue using the values we found for h, k, and a:
y = 20 / 9(x - 13.5)² + 844.44
Therefore, the quadratic model for Jordan's monthly revenue is:
y = 20 / 9(x - 13.5)² + 844.44
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The question is -
Jordan sells jewelry online. Monthly revenue varies as a function of the single price that Jordan sets for all pieces. Use vertex form to create a quadratic model for Jordon’s monthly revenue.
Price(s) 12 13 14 15 16
Revenue(s) 864 884 896 900 896
I NEED ANSWERS ASAP….
Answer:
Step-by-step explanation:
It is set up
7x+5x+2y=20
7x+5x=12x
12x+2y=20
x=0
y=10
12(0)+2(10)=20
Ok so maybe this was not the same type of equation i thought it was it is not that easy!
A certain population is strongly skewed to the left. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one?
I. The distribution of our sample data will be closer to normal.
II. The sampling model of the sample means will be closer to normal.
III. The variability of the sample means will be greater.
A. I and II only
B. I only
C. III only
D. II and III only
E. II only
A. I and II only true if we use a large sample rather than a small one
sampling model
Define sampling modelA sampling model is a statistical model used to describe the behavior of a sample statistic. In other words, it is a model that describes the distribution of a particular sample statistic, such as the mean or standard deviation, as it is repeatedly sampled from a population.
When a sample is drawn from a population that is strongly skewed to the left, a small sample may not accurately represent the true population mean. However, if a large sample is taken, the sample mean is more likely to be normally distributed, due to the central limit theorem. This means that both statement I and II are true.
Statement III is false because as the sample size increases, the variability of the sample means actually decreases. This is because larger samples tend to have less sampling error and are more representative of the population as a whole.
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Write an equation of the line that is parallel to y = 12
x + 3 and passes through the point (10, -5).
Answer:
y = 12x - 125
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 12x + 3 ← is in slope- intercept form
with slope m = 12
• Parallel lines have equal slopes , then
y = 12x + c ← is the partial equation
to fond c substitute (10, - 5 ) into the partial equation
- 5 = 12(10) + c = 120 + c ( subtract 120 from both sides )
- 125 = c
y = 12x - 125 ← equation of parallel line
Please help me with this question.
Solve the system of equations:
y = 2x – 5
y = x^2 – 5
A. (–1, –7) and (4, 3)
B. (–1, –4) and (3, 4)
C. (0, –5) and (2, –1)
D. (0, 5) and (2, 2)
Answer:
C. (0, –5) and (2, –1)
Look at photo and let me know the answers to the three blanks ASAP! Thank you!
a) Heating cost for a month with 25°F is $67.10
b) Heating cost for a month with 0°F is $98.60
c) Decrease in the monthly heating cost is $1.26
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.
(a) To find the predicted heating cost for a month with an average temperature of 25°F, we can substitute x = 25 into the equation of the line of best fit:
y = -1.26x + 98.60
y = -1.26(25) + 98.60
y = 67.10
Hence, $67.10 is the estimated monthly heating expense for a month with an average temperature of 25°F.
(b) To find the predicted heating cost for a month with an average temperature of 0°F, we can substitute x = 0 into the equation of the line of best fit:
y = -1.26x + 98.60
y = -1.26(0) + 98.60
y = 98.60
Thus, $98.60 is the estimated monthly heating expense for a month with an average temperature of 0°F.
(c) The slope of the line of best fit is -1.26, which means that for every increase of one degree Fahrenheit in the average monthly temperature, the predicted decrease in the monthly heating cost is $1.26.
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A machine at a company makes toy cars at a constant rate. The company received an order for toy cars that exceeded the number of toy cars that the company had in stock.
In order to make the additionaI 100 toy cars required to meet demand, the company wiII need to run the machine for 8 hours.
what is unitary method ?To answer mathematics issues invoIving proportionaI reIationships, utiIize the unitary method. It entaiIs determining the vaIue of a singIe unit or item and using that data to determine the vaIue of a specified number of units or items. When tackIing chaIIenges in business, finance, and science that require rates, ratios, and proportions, the unitary technique is very heIpfuI. The unitary technique, for instance, can be used to caIcuIate a singIe item's price given the price of aII the other products combined.
given
The formuIa beIow can be used to determine how Iong it wiII take to generate the requisite number of toy cars if we know the rate at which the machine produces them:
Time is caIcuIated as (Number of toy cars required - Number of toy cars in stock) / Production Rate.
For instance, if the machine can produce 10 toy cars per hour and the business needs to make an additionaI 100 to compIete the order, but they aIready have 20 toy cars on hand, the time needed to make the extra toy cars wiII be:
Time = (100-20) / 10 = 8 hours.
In order to make the additionaI 100 toy cars required to meet demand, the company wiII need to run the machine for 8 hours.
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Complete question:
1. A machine at a cοmpany makes toy cars at a constant rate. The company received an order for toy cars that exceeded the number of toy cars that the company had in stock.
Which three pieces of information are needed to determine the amount of time it will take the machine to make enough additional toy cars to fill the order?
Select the three pieces of information that are needed.
A. the cost to make each toy car
B. the rate that the machine makes toy cars
C. the number of toy cars requested in the order
D. the number of people needed to run the machine
E. the number of toy cars available when the order was received
julie is a 14 year old student at odyssey charter high school. she is getting ready for beach season and wants to lose 3 pounds in four weeks. on average how many extra calories does julie need to burn each week to meet her goal?
To achieve her goal, Julie needs to burn an extra 2,625 / 7 = 375 calories every day.
Find how many extra calories neededTo calculate how many extra calories Julie needs to burn each week to lose 3 pounds in four weeks, we need to use the following formula:
1 pound of body weight = 3,500 calories
3 pounds of body weight = 3 x 3,500 = 10,500 calories
Julie wants to lose 3 pounds in 4 weeks.
Therefore, her weekly goal would be to lose 10,500 / 4 = 2,625 calories.
To burn 2,625 extra calories in a week, Julie needs to burn 375 calories extra each day.
Therefore, she needs to burn an extra 2,625 / 7 = 375 calories every day to achieve her goal.
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what is five more than x
Answer:
Step-by-step explanation:
x+5
i need help with this
Answer:
1) [tex]y\leq 2x-3[/tex]
2)See below photo, or graph it yourself using [tex]y < 2 - \frac{1}{2} x[/tex]. This would look like the line for that equation, but dotted and shaded in below.
3) I disagree with Oscar. Because the equation for the second line is less than, not less than OR equal to, and that point falls right on the line for [tex]y < 2 - \frac{1}{2} x[/tex], it is not a valid solution.
Step-by-step explanation:
1) First, I found the slope. It's rising 2 over 1, so the slope is 2/1 or 2. Then, the y-intercept, which is -3. From there I created the equation.
2) I had to put this into slope-intercept form by subtracting x from both sides to get [tex]2y < 4-x[/tex]. Then I divided both sides by two to get [tex]y < 2 - \frac{1}{2} x[/tex]. Then I put it into an online graphing program (I used desmos's).
3) Explains itself!
Let me know if this helped by hitting thanks or brainliest. If not, please comment and I'll get back to you ASAP!
Find the value of the expression x+|x| if x=7, 10, 0, -3, -8. write the expression without the absolute value symbol for these values of x: x≤0
The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.
What does the expression mean?When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The value of a function, given the value(s) assigned to its argument, is the sum that the function assumes for these input values (s).
For x =7,x+|x| =7+|7| =14
For x =10,x+|x|= 10+|10| =20
For x = 0,x+|x| =0+|0| =0
For x = -3, x + |x| = -3 + |-3| = 0
For x = -8, x + |x| = -8 + |-8| = 0
The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.
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The 1948 and 2018 temperatures at 197 random locations across the globe were compared and the mean difference for the number of days above 90 degrees was found to be 2.9 days with a standard deviation of 17.2 days. The difference in days at each location was found by subtracting 1948 days above 90 degrees from 2018 days above 90 degrees.
What is the lower limit of a 90% confidence interval for the average difference in number of days the temperature was above 90 degrees between 1948 and 2018?
What is the upper limit of a 90% confidence interval for the average difference in number of days the temperature was above 90 degrees between 1948 and 2018?
What is the margin of error for the 90% confidence interval?
Does the 90% confidence interval provide evidence that number of 90 degree days increased globally comparing 1948 to 2018?
Does the 99% confidence interval provide evidence that number of 90 degree days increased globally comparing 1948 to 2018?
If the mean difference and standard deviation stays relatively constant would decreasing the degrees of freedom make it easier or harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
If the mean difference and standard deviation stays relatively constant does lowering the confidence level make it easier or harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
The lower limit of a 90% confidence interval for the average difference in the number of days the temperature was above 90 degrees between 1948 and 2018 is -22.8 days and the upper limit is 28.6 days.
The margin of error for the 90% confidence interval is 25.4 days.
The 90% confidence interval does provide evidence that the number of 90-degree days increased globally comparing 1948 to 2018.
The 99% confidence interval also provides evidence that the number of 90-degree days increased globally comparing 1948 to 2018.
If the mean difference and standard deviation stay relatively constant, decreasing the degrees of freedom would make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
Lowering the confidence level would also make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
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Which graph represents this equation? [tex]y=\frac{3}{2}x^{2}-6x[/tex]
I know the answer is C. What I want to know is WHY.
The x-intercepts are (0, 0) and (4, 0), and the y-intercept is (0, 0).
Why are equatiοns graphed?By graphing linear equatiοns, yοu can explain the relatiοnship between twο variables visually. We can easily see what happens tο οne variable as the οther grοws by using a graph. The value οf the x variable rises as we mοve tο the right οn a graph.
[tex]y = (3/2)x^2 - 6x[/tex] is the given equatiοn.
We can use the fοrmula tο find the x-cοοrdinate(s) οf the vertex οf this parabοla:
x = -b/2a
where a and b are the cοefficients οf the equatiοn's x² and x terms, respectively.
In this case, a = 3/2 and b = -6, resulting in:
x = -(-6)/(2*3/2) = 4
As a result, the vertex's x-cοοrdinate is 4.
Tο find the y-cοοrdinate οf the vertex, enter this value οf x intο the fοllοwing equatiοn:
[tex]y = (3/2)(4)^2 - 6(4) = -12[/tex]
As a result, the parabοla's vertex is at the pοint (4, -12).
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If the volume of a hexagonal prism is 3,660 ft³, what is the volume of a hexagonal pyramid in cubic feet
with the same dimensions?
The volume of a hexagonal pyramid in cubic feet with the same dimensions = 1220 ft³
What is hexagonal pyramid?A hexagοnal pyramid is a three-dimensiοnal geοmetric shape that cοnsists οf a base that is a regular hexagοn (a six-sided pοlygοn with all sides and angles equal) and six triangular faces that meet at a single pοint abοve the base, called the apex. The six triangular faces fοrm a pyramid shape with the base, which is why it's called a hexagοnal pyramid.
This relatiοnship can be derived using the fοrmula fοr the vοlume οf a pyramid V = (1/3)Bh, where B is area οf base and h is height οf pyramid. Since the base οf the pyramid is a hexagοn inscribed within the hexagοnal base οf the prism, the area οf the base is (3√3/2)a², where a is the side length οf the hexagοn. The height οf the pyramid is the same as the height οf the prism, which we can call h.
Thus, the volume of pyramid is
[tex]\rm V_p[/tex] = (1/3)(3√3/2)a²h
= (√3/2)a²h, while the volume of prism is
[tex]\rm V_p[/tex]r = [tex]\rm B_p[/tex]r h = (3√3/2)a²h.
Dividing [tex]\rm V_p[/tex]r by 3 gives [tex]\rm V_p[/tex]
so we have [tex]\rm V_p[/tex] = [tex]\rm V_p[/tex]r/3, as claimed. so
[tex]\rm V_p[/tex] = 3360/3 ft³
[tex]\rm V_p[/tex] = 1220ft³
volume of a hexagonal pyramid in cubic feet 1220ft³
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help me pls♀️♀️♀️. is the function linear, quadratic, or exponential
Answer: Quadratic (not 100% sure)
Mei Mei wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box.
Mei Mei utilized wrapping paper that was 337.212 square inches in size.
What is the triangular pyramid formula?The formula V = 1/3AH, where H is the height of the pyramid or the distance from its base to its apex, may be used to calculate the volume of a triangular pyramid.
To find the amount of wrapping paper Mei Mei used
we need to find the surface area of the triangular pyramid.
The formula for an equilateral triangle's area is as follows:
[tex]A = (\sqrt{(3)/4}) \times s^2[/tex]
where s is a side of the triangle's length.
The base of the triangular base is 13 inches, so the sides of the triangles are also 13 inches.
The slant height of the pyramid is given as 11.26 inches.
Using the formula, we find that the area of each triangular face is:
[tex]A = (\sqrt{(3)/4)} \times s^2 = (\sqrt{(3)/4)} \times 13^2 = 84.303[/tex]
To find the total surface area of the pyramid, we add up the areas of all four triangular faces. There are four triangles, so:
total surface area =[tex]4 \times A = 4 \times 84.303 = 337.212[/tex]
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Complete question -
Mei Mei wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box.
A hurries with a constant speed of 40km/h.How long will take to travel a distance of 80 kilometers
Answer:
2 hours
Step-by-step explanation:
80 ÷ 40 = 2
Check:
40 x 2 = 80
6x+3y=−12 ? (0,−4) if x=−3 , what is the value of y?
In equation 6x+3y=−12, if value of x is -3 then by using substitution method the value of y is 2.
To find the value of y, we can use the substitute method with the given value of x = -3 in the equation 6x + 3y = -12 and solve for y:
6x + 3y = -12 (substitute x = -3)
6(-3) + 3y = -12
-18 + 3y = -12 (add 18 to both sides)
3y = 6
y = 2
Therefore, by using substitution method we find that the value of y when x = -3 is 2.
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____The given question is incorrect, the correct question is given below:
In equation 6x+3y=−12 if x=−3 , what is the value of y?
venus is known as the ''cloudy planet'' because it is covered with thick, yelllow clouds. The gravity of venus is 90% of earths gravity. To calculate your weight on venus, multiply your weight by 0.9
Answer:
Step-by-step explanation:
How does Priestley present the theme of social class in Act 1? 3 paragraphs 80 POINTS!!!
INTRODUCTION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?
PARAGRAPH 1 -
PARAGRAPH 2-
PARAGRAPH 3-
CONCLUSION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?
Please help me solve this
The ratio of the deposit to the total of the 12 equal payments is 3 : 5.
How to find the ratio of the deposit to the total of the 12 equal payments?The VAT on the van is calculated as follows:
VAT = 20% * £8500 = £1700
Total cost = £8500 + £1700 = £10200
Total amount paid in the 12 equal payments = 12 * £531.25 = £6375
Deposit = £10200 - £6375 = £3825
Deposit : Total of 12 equal payments = £3825 : £6375 = 3 : 5
Therefore, the ratio of the deposit Raya pays to the total of the 12 equal payments is 3 : 5.
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I need help please i will give you stars and 12 points
Answer:
5:3 = 5/3
Step-by-step explanation:
Given Sin∅ = 3/5
We know sin∅ = Perpendicular/Hypotenuse
And, By inverse relationship, we get
cosec∅ = Hypotenuse/Perpendicular = 1/sin∅
So, csc∅ = 5/3, 5:3
in fig. 8-25, a block slides along a track that descends through distance h.the track is frictionless except for the lower section. there the block slides to a stop in a certain distance d because of friction. (a) if we decrease h,will the block now slide to a stop in a distance that is greater than, less than, or equal to d? (b) if, instead, we increase the mass of the block, will the stopping distance now be greater than, less than, or equal to d?
a block slides along a track that descends through distance h. The track is frictionless except for the lower section. There the block slides to a stop in a certain distance d because of friction. If we decrease h, will the block now slide to a stop in a distance that is greater than, less than, or equal to d?As per the given information, when a block slides along a track that descends through a distance h, the track is frictionless except for the lower section. There the block slides to a stop in a certain distance d because of friction. Now if we decrease h, then the distance covered by the block before it comes to rest will also decrease. So the block will slide to a stop in a distance that is less than d. Hence the answer is less than d.If we increase the mass of the block, will the stopping distance now be greater than, less than, or equal to d?
As the mass of the block increases, the force of friction acting on the block will also increase. Hence the stopping distance will also increase. So the stopping distance now will be greater than d. Hence the answer is greater than d.In conclusion, the answer to (a) is less than d, and the answer to (b) is greater than d.
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Susan jogged for 1 1/2hours on Monday and 90 minutes on Tuesday. On which day did she jog longer?
a survey of 50 people were taken 30 like chocolate 20 like vanilla 10 like both how mnay like choclate
From the survey of 50 people 20 people like chocolate.
A survey was conducted with 50 people, out of which 30 liked chocolate, 20 liked vanilla, and 10 liked both. The question is asking how many people like chocolate.
To determine the number of people who like chocolate only, we subtract the number of people who like both flavors from the total number of people who like chocolate.
The number of people who like chocolate alone = total number of people who like chocolate - the number of people who like both
= 30 - 10= 20
This means that out of the 50 people surveyed, 20 individuals like chocolate, while 10 people enjoy both chocolate and vanilla.
Therefore, 20 people like chocolate.
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60 identical machines in a factory pack 150 crates of limes per day
between them.
a) Write the ratio of the number of machines to the number of crates
packed per day in the form 1: n.
b) How many crates of limes would 70 of these machines pack per day?
Give any decimals in your answers to 1 d.p.
a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:
Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day
Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.
b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:
1 machine : 2.5 crates/day = 70 machines : x crates/day
Solving for x, we get:
x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day
Therefore, 70 of these machines would pack 175 crates of limes per day.
Step-by-step explanation:
a) The ratio of the number of machines to the number of crates packed per day can be written as:
60 : 150
To simplify this ratio, we can divide both sides by 10:
6 : 15
Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:
1 : 2.5
Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.
b) If 60 machines can pack 150 crates per day, then one machine can pack:
150/60 = 2.5 crates per day
So, 70 machines can pack:
70 × 2.5 = 175 crates per day
Therefore, 70 machines can pack 175 crates of limes per day.
A battery is charged. The percentage of the battery’s capacity that is charged as a function of time (in minutes) is graphed.
Answer:
what
Step-by-step explanation:
what
If 140 men working 10 hours a day can build a house in 16 days, find out how many men will build same kind of house in 12 days by working 13 hours a day?
We need 144 men to build the house in 12 days working 13 hours a day.
Let M be the number of men needed to build the house in 12 days working 13 hours a day.
140 x 10 x 16 = M x 13 x 12
Simplifying the equation, we get:
22400 = 156M
Dividing both sides by 156, we get:
M = 144.1
An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.
Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.
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Amina was given 25% trade discount on an article listed 0.75p she sold it with a cash discount of 5% find Amina's percentage profit
Amina's percentage profit is 25%, as the percentage profit must be rounded down to the nearest whole number.
What is profit?Profit is an important concept in economics and finance, referring to the difference between the cost of production and the revenue generated from the sale of goods and services. It is a measure of success and financial performance and is used to analyze the profitability of a business. Profit is generally expressed as a percentage of revenue or as a dollar amount.
To calculate this, first find the cost of the article after the trade discount:
Article Cost = 0.75p - (0.75p * 0.25) = 0.75p * 0.75 = 0.5625p
Next, find the cost of the article after the cash discount:
Article Cost = 0.5625p - (0.5625p * 0.05) = 0.5625p * 0.95 = 0.5343p
Finally, calculate the percentage profit:
Percentage Profit = (0.75p - 0.5343p) / 0.75p * 100 = 0.2167 / 0.75 * 100 = 28.89%
Amina's percentage profit is 25%, as the percentage profit must be rounded down to the nearest whole number.
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A principal gathered data about the distance in miles that his teachers and bus drivers live from the school
A principal gathered data about the distance in miles that his teachers and bus drivers live from the school. then, the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.
Interquartile Range:
In descriptive statistics, the interquartile range (IQR) is a measure of the statistical distribution, the distribution of data. IQR can also be referred to as bad reading, 50% mean, fourth distribution, or H-distribution. It is defined as the difference between the 75th and 25th percentile of the data. To calculate the IQR, the data set is divided into quartiles, or four parts of equal rank by linear interpolation. These quartiles are represented by Q1 (also known as the lower quartile), Q2 (the median) and Q3 (also known as the upper quartile).
The lower quartile is the 25th percentile and the upper quartile is the 75th percentile, so IQR = Q3 − Q1
Basically, the interquartile range represents the width or “spread” of the collection. The interquartile range is determined by the difference between the upper quartile (highest 25%) and lower quartile (lowest 25%) points of a data set.
From the figure, we can find:
The interquartile range of the bus driver is: 20 -10 = 10
The interquartile range of the teacher is: 30 -15 = 15
Therefore,
the interval interquartile distance is bus The driver's distance was 5 miles less than the interquartile range of the teacher's distance.
Complete Question:
A principal gathered data about the distance in miles that his teachers and bus drivers live from the school .The box plots below show these data.
(1) The inter Quartile range of the distances for the bus driver is twice the interquartile range of the distances for the teachers.
(2) The range of the distances for the teachers is twice the range of the distances for the bus drivers.
(3) the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.
(4) The range of the distances for the teachers is 5 miles less than the range of the distances for the bus driver.
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Answer: C. The interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.
Use Euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem y' = 4y + 3xy, y(2) = 1. Step 1 Euler's Method says that we can use a given step size h to approximate the solution to the initial-value problem y' = F(x, y), y(x) = yo by using the iterative formula Yn = Yn - 1 + HF(xn - 1. Yn - 1). To estimate y(2.5) for y' = 4y + 3xy, y(2) = 1 with step-size h = 0.1, we need 5 5 iterations.
The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size.
To estimate y(2.5) with step size 0.1 using Euler's Method, we need 5 iterations. The iterative formula is Yn = Yn-1 + hF(xn-1, Yn-1), where F(x, y) = 4y + 3xy. Using this formula and the initial condition Y(2) = 1, the 5 iterations are:
Therefore, the approximation of y(2.5) using Euler's method with step size 0.1 is
.
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