The IQR (Interquartile Range) for the given data 10, 15, 17, 21, 25, 12, 16, 11, 13, 22 is option c) 6.25.
To compute the IQR, we need to find the difference between the first quartile (Q1) and the third quartile (Q3).
First, we arrange the data in ascending order: 10, 11, 12, 13, 15, 16, 17, 21, 22, 25.
Next, we find the median, which is the middle value of the dataset. In this case, the median is the average of the two middle values: (15 + 16)/2 = 15.5.
To find Q1, we consider the lower half of the data. The median of this lower half is the first quartile: (11 + 12)/2 = 11.5.
To find Q3, we consider the upper half of the data. The median of this upper half is the third quartile: (21 + 22)/2 = 21.5.
Finally, we calculate the IQR by subtracting Q1 from Q3: 21.5 - 11.5 = 10.
Converting the IQR to a decimal value: 10/1.6 ≈ 6.25.
Therefore, the IQR for the given data is approximately 6.25, corresponding to option c).
The IQR is a measure of statistical dispersion that provides valuable information about the spread of the dataset. It is robust against outliers and provides a clearer picture of the middle 50% of the data.
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A clothing retailer buys winter coats from one of its suppliers for $67.50. The regular selling price of the coats includes operational expenses of 46% of the selling price and a profit of 30% of the selling price. Due to an unexpected warm winter, the sales have been slow. The retailer decides to mark down this line of coats by 20% to increase sales. What is the operating profit or loss on the coats sold during the promotional sale?
The operating profit or loss on the coats sold during the promotional sale can be calculated using the equation: (0.80 * (SP - (0.46 * SP + 0.30 * SP))) - $67.50.
The operating profit or loss on the coats sold during the promotional sale can be calculated by considering the cost price, operational expenses, and profit margin. Here's how you can calculate it step by step:
1. Cost Price: The retailer buys the winter coats from the supplier for $67.50.
2. Selling Price: The regular selling price includes operational expenses and profit. Let's assume the selling price is represented by SP.
3. Operational Expenses: The operational expenses account for 46% of the selling price. So, the operational expenses can be calculated as 0.46 * SP.
4. Profit: The profit margin is 30% of the selling price. Hence, the profit can be calculated as 0.30 * SP.
5. Net Selling Price: The net selling price is the selling price minus the operational expenses and profit. It can be represented as SP - (0.46 * SP + 0.30 * SP).
6. Marked Down Price: The retailer decides to mark down the coats by 20%. Therefore, the marked down price is 80% of the net selling price. It can be calculated as 0.80 * (SP - (0.46 * SP + 0.30 * SP)).
7. Operating Profit or Loss: The operating profit or loss can be obtained by subtracting the cost price from the marked down price. Hence, the operating profit or loss is (0.80 * (SP - (0.46 * SP + 0.30 * SP))) - $67.50.
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Little help guys? Find the distance from the point (3, 6, 8) to the origin.
Write your answer as a whole number or as a decimal rounded to the nearest hundredth.
========================================================
Work Shown
The two points are [tex](x_1,y_1,z_1) = (0,0,0)[/tex] and [tex](x_2,y_2,z_2) = (3,6,8)[/tex]
Use the 3D version of the distance formula to get the following:
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}\\\\d = \sqrt{(0-3)^2+(0-6)^2+(0-8)^2}\\\\d = \sqrt{(-3)^2+(-6)^2+(-8)^2}\\\\d = \sqrt{9+36+64}\\\\d = \sqrt{109}\\\\d \approx 10.4403065\\\\d \approx 10.44\\\\[/tex]
You'll need your calculator for the second to last step.
What two ratios are equivalent to 11:1
Answer:
2:22, 3:33, 4:44, 5:55
Step-by-step explanation:
11:1 * 2= 2:22
I hope this helps! :D
Help me out pleaseeeee
Answer:
I believe the best answer is 0.45
Answer:
Option 3: 0.45
Step-by-step explanation:
if z is directly proprotional to x and z = 12 when x = 3, find the value of x when z = 18
Answer:
4.5Step-by-step explanation:
z is directly proportional to x
z = kx, where k is coefficientIf z = 12 when x = 3
Then we have
12 = 3k k = 4So the coefficient is 4
When z = 18, we have
18 = 4xx = 18/4 x = 4.5The table shows the amounts A (in billions of dollars) budgeted for national defense for the years 1998 to 2004. (Source: U.S. Office of Management and Budget)
(a) Use a graphing utility to create a scatter plot of the data. Let t represent the year, with t = 8 corresponding to 1998.
(b) Use the regression feature of a graphing utility to find a quadratic model for the data.
(c) Use a graphing utility to graph the quadratic model with the scatter plot from part (a). Is the quadratic model a good fit for the data?
(d) Use the model to estimate the amounts budgeted for the years 2005 and 2010.
(e) Do you believe the model is useful for predicting the national defense budgets for years beyond 2004?
(a) A scatter plot of the data is shown below.
(b) A quadratic model for the data is y = 5.58x² - 85.53x + 601.96.
(c) Yes, the quadratic model is a good fit for the data.
(d) An estimate of the amounts budgeted for the years 2005 and 2010 are $575 billion and $1123 billion respectively.
(e) Yes, I believe the model is useful for predicting the national defense budgets for years beyond 2004.
How to construct and plot the data in a scatter plot?In this exercise, we would plot the years on the x-axis of a scatter plot while the defense budget would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.
Part b.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a quadratic model of the line of best fit (trend line) on the scatter plot;
y = 5.58x² - 85.53x + 601.96
Part c.
Based on the equation of the line of best fit and the trend line above, we can reasonably infer and logically deduce that the quadratic model a good fit for the data.
Part d.
Based on the equation of the line of best fit above, the amounts budgeted for the year 2005 is given by:
Years, x = 1998 to 2005 = 15 years.
y = 5.58(15)² - 85.53(15) + 601.96
y = 574.51 ≈ $575 billion
Years, x = 1998 to 2010 = 20 years.
y = 5.58(20)² - 85.53(20) + 601.96
y = 1123.36 ≈ $1123 billion
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
does everybody use edgenuity
yes , i use edgenutiy. I have to at my school.
Step by step explanation for:
-(3a + 2) - 3(5a + 7)
Answer:
-18a-23
Step-by-step explanation:
-(3a+2)-3(5a+7) -- (multiply out the brackets)
-3a-2-15a-21 -- (collect like terms) (-3a-15a=-18a) and (-2-21=-23)
-18a-23
Answer:
- 18a - 23
Step-by-step explanation:
When there is a “-” in front of an expression in parentheses, change the sign of each term of the expression
- ( 3a + 2 ) - 3 ( 5a + 7 )
- 3a - 2 -3 ( 5a + 7 )
Multiply each term in the parentheses by - 3
- 3 ( 5a + 7 )
- 3 × 5a - 3 × 7
Calculate the product
- 3 × 5a - 3 × 7
- 15a - 3 × 7
Multiply the numbers
- 3 × 5a - 3 × 7
- 15a - 21
Collect like terms by calculating the sum or difference of their coefficients
- 3a - 15a
( - 3 - 15 )a
Calculate the difference
( - 3 - 15 )a
- 18a
Factor out the negative sign from the expression
- 2 - 21
- ( 2 + 21 )
Add the numbers
- ( 2 + 21 )
- 23
Answer
- 18a - 23
solve value for m
4(m-1) - 3(m-5) =12
Answer:
m =1
Step-by-step explanation:
4(m-1) - 3(m-5) =12
4m -4 -3m + 15 = 12
4m - 3m = 12-15 +4
m = 1
Answer:
4m-4 - 3m+15 =12
4m-3m +15-4 = 12
m +11 = 12
m = 12-11
m = 1
4.5kg of bananas and 3.5kg of apples cost £6.75. ^kg of apples cost £5.40. Calculate the cost of 1kg of bananas.
Answer: Let's assume the cost of 1 kilogram of bananas is represented by 'x'.
According to the given information, 4.5 kg of bananas and 3.5 kg of apples together cost £6.75. We also know that the cost of 1 kg of apples is £5.40.
Using this information, we can set up the following equation:
4.5x + 3.5(£5.40) = £6.75
Now let's solve for 'x':
4.5x + 3.5(£5.40) = £6.75
4.5x + £18.90 = £6.75
4.5x = £6.75 - £18.90
4.5x = -£12.15
x = (-£12.15) / 4.5
x ≈ -£2.70
The cost of 1 kilogram of bananas, based on this calculation, is approximately -£2.70. However, it's important to note that a negative cost doesn't make sense in this context. It's possible there may be an error in the given information or the setup of the equation.
A - Bln (p) = Suppose a product has a log_linear demand given by:ln(Q) dQ -BQ a. Express Q as a function of p and show that: dp р dQ b. Express "p" as a function of Q and find: dp dp dQ c. Show mathe
a. To find the relationship between Q and p, we can express Q as a function of p using the equation Q = e^(-BQ).
b. Expressing p as a function of Q, we have p = e^(-BQ).
c. To differentiate e^(-BQ) with respect to Q, we use the chain rule. The derivative is dp/dQ = -B * e^(-BQ).
The log-linear demand for a product can be expressed as ln(Q) = -BQ, where Q represents the quantity demanded and B is a constant coefficient. In order to find the relationship between price (p) and quantity (Q) and calculate the derivative dp/dQ, let's follow the steps below:
a. Express Q as a function of p:
To find the relationship between Q and p, we need to exponentiate both sides of the equation ln(Q) = -BQ. This gives us:
Q = e^(-BQ).
Now, we can solve for Q in terms of p by substituting p for Q:
p = e^(-Bp).
To calculate dp/dQ, we differentiate the expression with respect to Q:
dp/dQ = d/dQ(e^(-BQ)).
b. Express p as a function of Q and find dp/dQ:
To express p as a function of Q, we start with the equation p = e^(-Bp) and solve for p:
p = e^(-BQ).
To find dp/dQ, we differentiate the expression with respect to Q:
dp/dQ = d/dQ(e^(-BQ)).
c. Show mathematical steps for differentiation:
To differentiate e^(-BQ) with respect to Q, we can use the chain rule. Let's denote f(Q) = e^(-BQ), then:
df/dQ = (df/dQ)(dQ/dQ) = (d/dQ(e^(-BQ))) * 1 = -B * e^(-BQ).
Therefore, dp/dQ = -B * e^(-BQ).
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7 times the sum of a number an 24?
f(x) = -2x2 + 7
Find f(-5)
Answer:
f(-5) = -43
Step-by-step explanation:
Step 1: Define
f(x) = -2x² + 7
f(-5) is x = -5
Step 2: Substitute and Evaluate
f(-5) = -2(-5)² + 7
f(-5) = -2(25) + 7
f(-5) = -50 + 7
f(-5) = -43
verify the equivalence of your combined expression (4b) and the given expression (8b-4b) by evaluating both at the given value of b =5
Can anybody explain how to do this
Answer:
Step-by-step explanation:
First get y alone
So add 4x to each side
Then divide by 3 on each side
The perimeter of the rectangle below is 114 units. Find the length of side RS.
Write your answer without variables.
S
4x
R
RS =
15x + 3
Q
Step-by-step explanation:
Perimeter = 114 units
2 (4x + 5x + 3) = 114
18x + 6 = 114
X = 6
Length of RS = 4x = 24
In the figure below, G is between E and H. and F is the midpoint of EG. If FG=6 and EH= 17, find GH.
Answer:
5
Step-by-step explanation:
EH = EG + GH;
17 = EF + FG + GH; EF = FG = 6;
17 = 6 + 6 + GH;
GH = 5
The measure of the segment GH will be equal to 5.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that in the figure below, G is between E and H. and F is the midpoint of EG. If FG=6 and EH= 17.
The measure of the line segment GH will be calculated as,
EH = EG + GH;
17 = EF + FG + GH; EF = FG = 6;
17 = 6 + 6 + GH;
GH = 5
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Eileen’s cookies charges $0.40 per cookie with a delivery fee of $8. Insomnia cookies charges $1.50 per cookie with a $2.50 delivery fee. How many cookies must you buy for the costs to be equal?
help plssss
Answer: 5 cookies
Step-by-step explanation: 8 + .4c = 2.5 + 1.5c
8 + 0.4c = 2.5 + 1.5c
8 · 10 + 0.4c · 10 = 2.5 · 10 + 1.5c · 10
80 + 4c = 25 + 15c
4c = 15c - 55
4c - 15c = 15c - 55 - 15c
-11c = -55
c = 5
What is an equation for the line parallel to y = -x + 7 that passes through (7,-2)?
Answer:
y = -x + 5Step-by-step explanation:
Parallel line has same slope with the given, so the line is
y = -x + bUsing the given point, finding the value of b
-2 = -7 + bb = 7 - 2b = 5The equation is
y = -x + 5a total of 750 students attended a conference at avenel high school the attendance of the number of girls was twice that of the number of boys how many boys attended the conference?
please helpp!!!!
Answer:
250 boys attended the conference.
Step-by-step explanation:
First, divide 750 by 3 (one-third of the conference is boys) and you will get 250 (number of boys). If you wanted to find the number of girls too, you would simply double 250 to get 500 girls.
A)
A meteorologist in Denver recorded Y = the number of days of rain during a 30-day period.
Does Y have a binomial distribution? If so, are the values of both n and p given?
B) A market research firm has hired operators who conduct telephone surveys. A computer
is used to randomly dial a telephone number, and the operator asks the answering person
whether she has time to answer some questions. Let Y = the number of calls made until the
first person replies that she is willing to answer the questions. Is this a binomial experiment?
Explain.
A) In this situation, the number of trials, p, and the probability of success cannot be established.
B) No, it is not a binomial experiment.
A) A meteorologist in Denver recorded Y = the number of days of rain during a 30-day period.
Y does not have a binomial distribution.
For a distribution to be binomial, the following four conditions must be met:
There must be a fixed number of trials; the trials must be independent of one another;
the probability of success (p) must be constant for each trial;
and the probability of success (p) must be identical for each trial.
B) A market research firm has hired operators who conduct telephone surveys.
A computer is used to randomly dial a telephone number, and the operator asks the answering person whether she has time to answer some questions.
Let Y = the number of calls made until the first person replies that she is willing to answer the questions.
No, it is not a binomial experiment. In this scenario, the number of trials is unknown since the researchers do not know how many times they must call before obtaining a response.
The number of trials in a binomial experiment is constant and predetermined. Furthermore, each trial's probability of success is unknown since the respondent's willingness to participate cannot be estimated with certainty.
Finally, the trials are not independent since the results of each trial influence the next, and the probability of success changes with each attempt, making it unsuitable for a binomial distribution.
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What is π is it a rational or irrational
Answer: Irrational
Step-by-step explanation: 3.14 is π. (You can write it as a fraction of two integers: 314100 so it is irraitonal. π (3.14) cannot be written as a fraction of two integers.
Need help with this it due now right now assignment Geometry so hard pls been waiting for so long
Step-by-step explanation:
Application of Formulas in Geometry By textbook tactics
99,096 views•May 25, 2012
This Video should help you solve your equation
Hope it Helps :)
Is it true that the sum of products is always 1.?
Answer:
yes
Step-by-step explanation:
Answer:
trueeeeeeee
Step-by-step explanation:
hope this helps
A sample of college students was asked how much they spent
monthly on . Approximate the standard deviation for the cost.
Monthly cost ($) Number of students 5,14,24,20,9 10.00-19.99
20.00-29.
A sample of college students was asked how much they spent monthly on cost. Approximate the standard deviation for the cost.To calculate the standard deviation for the given data, we first need to calculate the mean and deviations of each data point from the mean.
The given data can be arranged in a table as below. Monthly cost ($) Number of students Deviation from Mean Deviation squared ($) 5 1 -11.2 125.44 14 1 -2.2 4.84 20 1 3.8 14.44 24 1 7.8 60.84 9 1 -7.2 51.84 Total 5 256.4From the above table, the mean of the given data can be calculated as below.
The standard deviation for the given data is approximately 8.01.Most statistical analyses of survey data requires the analyst to explore and understand patterns and trends in the data. One of the most important measures of dispersion is the standard deviation. In the above question, a sample of college students was asked how much they spent monthly on cost and the question asks us to approximate the standard deviation for the cost. By calculating the mean, deviation and deviation squared for each data point and using the formula for calculating standard deviation, we can approximate the standard deviation for the given data to be 8.01.
In statistics, standard deviation is one of the most essential concepts that helps in determining how much data deviates from the mean. In other words, it shows the extent of variation or deviation of values from the mean. The standard deviation is the square root of the variance. It is measured in the same units as the data values and is used to represent the average degree to which each data value varies from the mean.
A sample of college students was asked how much they spent monthly on cost. The given data can be arranged in a table to calculate the mean, deviation, and deviation squared for each data point. The mean can be calculated as the sum of all the observations divided by the total number of observations. Deviation is the difference between each observation and the mean. Deviation squared is obtained by squaring the deviation for each observation. The standard deviation can be calculated using the formula, standard deviation is the square root of the average of the squared deviations. In the above question, the standard deviation for the given data is approximately 8.01.
The standard deviation is an important concept in statistics that measures how much the data deviates from the mean. In this question, the given data shows how much college students spend monthly on cost. The standard deviation can be calculated using the formula, and it is an important tool in analyzing data as it gives an idea of how widely the data is spread out. From the calculations above, we can approximate that the standard deviation for the given data is approximately 8.01.
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Rewrite the function in the form g(x)=(a)/(x-h) +k.
g(x)=(7x+4)/(x-3)
Which of the following represents the graph of the function?
Describe the graph of g as a transformation of the graph of f(x)=a/x.
The graph of g is a translation ? units and ? units ?
The function f(x) = 2x + 5 can be rewritten in the form g(x) = (a)/(x - h) + k as:g(x) = 2/(x - (k - 5)/2) + kThe graph of g is a translation 2 units upwards and (k - 5)/2 units in the x-direction.
The given function is f(x) = 2x + 5. It is required to rewrite the function in the form g(x) = (a)/(x - h) + k, where the graph of g is a translation a units in the x-direction and b units in the y-direction.
Let's begin by rewriting the given function in the required form.g(x) = (a)/(x - h) + kLet's assume a point (h, k) lies on the graph of the function g(x).Then, g(h) = (a)/(h - h) + k= a + k
This implies that the point (h, k) lies on the graph of g(x) and is at a distance of 'a' units from the x-axis as g(h) gives the value of the y-coordinate of the point.
Thus, 'a' is the required translation in the y-direction.Next, to find the value of 'h', substitute x = h in the equation g(x).
Then,g(h) = (a)/(h - h) + k= a + kSince the point (h, k) lies on the graph of g(x), it also lies on the graph of f(x).
Thus,f(h) = 2h + 5Since the graph of g(x) is a translation 'a' units upwards from the graph of f(x), it can be concluded that f(h) = g(h) - a.Substituting the values of f(h) and g(h), we get2h + 5 = a + k - a= kHence, h = (k - 5)/2
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Given that √6.4 = 2.53, find the value of √640 + √64
Answer:
255.53
Step-by-step explanation:
..................
Factor by grouping.
r^2-15tw+5wr-3tr
A football team scored 38 points in a game. They scored 3 points for each field goal and 7 points for each touchdown with an extra point. How many touchdowns and field goals did they score?
i will mark brainliest!! :)
Answer:
5 TD 1 FG
Step-by-step explanation:
Answer:
5 Touchdowns 3 Field goals
But this could also another way with 5 Touchdowns and 1 Field goal because 7x5+3 = 38
Step-by-step explanation:
7+7+7+7+7+3 = 38
Or
7x5+3 = 38
This could go so many ways
Find equations if the following lines: Line that is parallel to the graph of y = 3x – 2 and contains the point (-2,-5)
