The low Q₁ is 13 and the median Q₃ is 16.5, the high is 18 and the interquartile range is 3.5
The interquartile range is a measure of dispersion that tells us how spread out the middle 50% of a dataset is. To calculate the IQR, we first need to find the quartiles of the dataset. Quartiles divide a dataset into four equal parts, with the first quartile (Q₁) representing the 25th percentile, the second quartile (Q₂) representing the 50th percentile (also known as the median), and the third quartile (Q₃) representing the 75th percentile.
To find the quartiles of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18}, we first need to order the data in ascending order:
10, 13, 13, 14, 15, 15, 16, 17, 18
The low is the smallest value in the dataset, which is 10.
To find Q₁, we need to find the value that is 25% of the way through the dataset. Since we have 9 values in our dataset, 25% of 9 is 2.25. This means that Q₁ lies between the 2nd and 3rd values in the dataset, which are both 13. To find the exact value of Q₁, we can take the average of these two values:
Q₁ = (13 + 13) / 2 = 13
The median is the middle value in the dataset, which is 15.
To find Q₃, we need to find the value that is 75% of the way through the dataset. 75% of 9 is 6.75, which means that Q₃ lies between the 6th and 7th values in the dataset, which are 16 and 17, respectively. To find the exact value of Q₃, we can take the average of these two values:
Q3 = (16 + 17) / 2 = 16.5
The high is the largest value in the dataset, which is 18.
Now that we have found the quartiles, we can calculate the IQR by subtracting Q1 from Q₃:
IQR = Q₃ - Q₁ = 16.5 - 13 = 3.5
Therefore, the interquartile range of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18} is 3.5. This tells us that the middle 50% of the dataset is relatively tightly clustered around the median, with values ranging from 13 to 16.5.
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At a college, the ratio of faculty/staff to students is 3 to 13. If there are 4000
people at the college, how many students are there?
Answer:
Let's call the number of students at the college "x". Then, the number of faculty/staff is 3 times that number, or 3x. The total number of people at the college is the sum of the students and faculty/staff, which is x + 3x = 4x.
According to the problem, the ratio of faculty/staff to students is 3 to 13, so we can write an equation:
3x / x = 3 / 13
To find the number of students, we can solve for x:
4x = 4000
x = 1000
So, there are 1000 students at the college.
Laurence earned scores of 87, 80, 75, and 85 on four biology tests. What score must he earn on his next test to have an 85 average?.
To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.
We can use the formula for the average (or mean) of a series of variables to determine Laurence's next biology test score in order to achieve an average of 85:
Average = (sum of values) / (number of values)
The total of Laurence's marks on the first four biology exams can be calculated using the following formula:
Sum of scores = 87 + 80 + 75 + 85
= 327
We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.
Therefore, We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.
By deducting Laurence's first four scores from the desired total of all five scores, and dividing the result by one (the number of scores left), we can get the score that Laurence has to achieve in his next biology exam:
Next score = (sum of all five scores) - (sum of first four scores)
= (85 x 5) - 327
= 25
Therefore, To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.
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Slope int form or general form PLS HELP
Answer:
y = 4x + 32
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 = 4x ← is in slope- intercept form
with slope m = 4 and y- intercept = 0
• Parallel lines have equal slopes , then
y = 4x + c ← is the partial equation
to find c substitute (- 8, 2 ) into the partial equation
2 = 4(- 8) + c = - 32 + c ( add 32 to both sides )
34 = c
y = 4x + 32 ← in slope- intercept form
$10000 is deposited in an account earning 8% interest compounded continuously. Use the continuous interest formula below to determine how long it takes for the amount in the account to double. Round answer to 2 decimal places.
A=Pe^rt
____Years?
By using the continuous interest formula, we get 8.54 years that the amount will take to double itself.
What is continuous interest formula?The continuous interest formula is used to calculate the future value of a compound interest investment. It is written as follows:
Future Value = Principal × [tex](1 + r)^{n}[/tex]
where Principal is the original investment, r denotes the yearly interest rate, and n denotes the number of compounding periods.
The continuous interest formula is used to compute the future worth of an investment given its current value, yearly interest rate, number of times the interest is compounded each year, and number of years held.
In the given question,
A = A_0[tex]e^{rt}[/tex]
2A_0 = A_0[tex]e^{rt}[/tex]
2 = [tex]e^{rt}[/tex]
ln(2) = rt
t = [tex]\frac{2}{r}[/tex]
t = [tex]\frac{2}{0.08}[/tex]
t = 8.54 years
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You can work a total of no more than 32 hours each week at your two jobs. Tutoring pays $7 per hour and babysitting pays $8 per hour. You need to earn at least $256 each week to pay your bills.
Let X = the number of hours tutoring. Let Y = the number of hours babysitting
Answer: The correct system of linear inequalities that represents this situation is:
X + Y ≤ 32 (to represent the maximum number of hours you can work)
7X + 8Y ≥ 256 (to represent the minimum amount of money you need to earn)
X ≥ 0, Y ≥ 0 (to represent that you can only work a non-negative number of hours at each job)
Where X represents the number of hours you spend tutoring and Y represents the number of hours you spend babysitting. The first inequality represents the maximum number of hours you can work, and the second inequality represents the minimum amount of money you need to earn. The last two inequalities represent that you can only work a non-negative number of hours at each job.
Step-by-step explanation:
Graph the line with slope 2 passing through the point (-3, -4).
The solution is, the equation is y=2/3x.
What is meant by graph?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
A diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.
here, we have,
so the line is in slope intercept form
y=mx+b, m=slope and b=y intercept
we know the slope so just solve for b
y=2/3x+b
subsitute
3 for x and 2 for y
2=2/3(3)+b
2=2+b
subtract 2 from both sdies
0=b
so the equaiton is
y=2/3x+0 or just simply
y=2/3x
here is the graph
just input values for x and get y values exg
x=3 y=2
x=6 y=4
x=0 y=0
x=-3 y=-2
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x + 17 = -50 + x + 34 + 33
What is the correct answer answer asap for brainlist
Based on the information provided, the passage that explains the citation is "The outcome...is situational irony..." (option A).
What does explaining a citation mean?When you cite information from other sources or authors, there are three elements that should be included:
Introduction: Introduce your citation, for example by saying "Twain claimed that..."Citation: Here you add the words of the author or you paraphrase them.Explanation: This step requires connecting the citation to your text by explaining its meaning.Learn more about citation in https://brainly.com/question/30066031
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Consider event A and event B. What is the probability that event B occurs, given that event A has already occurred?
P(BNA)
P(A)-P(B)
OA
O B.
O C.
O D.
P(BNA)
P(A)
P(BOA)
P(B)
P(BUA)
P(5)
P(B A)=P(B)
Step-by-step explanation:Given situation that two events occurred event A and event B event A has already occurredtherefore, there is no relationship between them event A and event B since, the probability of B does not depend on any activity of A therefore, P(B A)=P(B)
The probability that event B occurs, given that event A has already occurred is P(A) = P(A ∩ B) / P(B | A).
What is an Event?An event is the outcome of a chance experiment or a collection of similar outcomes.
As the sample space is a collection of all potential outcomes of a random experiment, it might be defined as every subset of that space.
When the event B is dependent on event A,
P(A ∩ B) ≠ P(A) x P(B)
When the event A comes before event B. So, the probability of B given A:
P(B | A) = P(A ∩ B) / P(A)
P(A) = P(A ∩ B) / P(B | A)
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It is known that g(x) is the inverse function of f (x). This means that the domain of
f (x) is equal to the [Select]
✓of g (x).
The domain of f(x) is equal to the range of inverse function g(x).
What are inverse functions?
A function from a set X to a set Y in mathematics assigns each element of X the exact same number of elements from Y. A function's inverse function reverses the action of a function or f. If and only if the function is bijective, the inverse of f is true.
Given two functions f(x) and g(x).
It is also said that g(x) is the inverse of f(x).
One of the properties of inverse functions is that only one-to-one functions are inverse. If g is equal to f's inverse, then f is equal to g's inverse.
Both f and g are one-to-one functions if they are the inverses of one another.
f and g are inverses of each other if (fog)(x) = x, x ∈ the domain of g.
The range of g equals the domain of f, and the domain of f equals the range of g.
Therefore the domain of f(x) is equal to the range of inverse function g(x).
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Solve the quadratic equation by the square root method and write the solutions in radical form. Simplify the solutions.
(3x+20)2=125
Answer:
Step-by-step explanation:
To solve the equation (3x + 20)^2 = 125 using the square root method, we start by taking the square root of both sides:
√[(3x + 20)^2] = √125
3x + 20 = ± 5
Next, we subtract 20 from both sides:
3x = -20 ± 5
Finally, we divide both sides by 3:
x = -8 or x = 3/3
So, the two solutions to the equation (3x + 20)^2 = 125 are x = -8 and x = 1. These solutions are in radical form and are already simplified.
A city bowling league is holding a tournament in which the top 8 bowlers with the highest three-game totals are awarded cash prizes. First place will win $1250, second place $1132, third place $1014, and so on.
(a) Write a sequence a, that represents the cash prize awarded in terms of the place n in which the bowler finished
(b) Find the total amount of prize money awarded at the tournament.
The sequence will be aₙ=$1250-118ⁿ⁻¹ where n= place at which a bowler finished.
What exactly is a sequence?
A sequence is a collection of numbers that follows pattern. Olivia, for example, has been offered a position with a beginning monthly pay of $1000 and a yearly raise of $500. To figure out her monthly pay for the first three years? The prices will be $1000, $1500, and $2000. Note that Olivia's income over a number of years creates a sequence as they follow a pattern where the numbers increase by $500 each time.
Now,
given award money for 1, 2, 3 places is given as $1250, $1132 and $1014
that means for the sequence, first term is 1250 and difference between the next terms will be 118 (less)
So, the sequence will be aₙ=$1250-118ⁿ⁻¹
where
n=place at which a bowler is placed.
Hence,
The sequence will be aₙ=$1250-118ⁿ⁻¹.
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Can anybody help me with question 20 please?
Answer:
N?A
Step-by-step explanation:
NEED HELP FAST for 25pts
The coordinates of point C in the given right triangle ABC is (2, 2√3-2)
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Given that, triangle ABC is a 30°-60°-90° triangle, where two vertices are A(-4, -2) and B(4, -2).
Now, AB=4-(-4)=8
AC=AB×sin60°= 8×√3/4√3
In right triangle ACD
AD=AC×cos30°
= 4√3×√3/2
= 6
Xc=6-4=2
Yc=AC×sin30°-2
= 4×3×1/2-2
= 2√3-2
The coordinates of point C(2, 2√3-2)
Therefore, coordinates of C(2, 2√3-2).
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find angle AED
please help
The angle AED of arc AD of the circle is calculated to be equal to 8100/πr
How to evaluate for the angle AED of arc length AD of the circleWe shall use the formula:
arc length = (arc angle/360) × 2 × π × radius
where arc angle is measured in degrees and radius is the distance from the center of the circle to the point on the circle where the arc begins.
If AD = 45 and r the radius, we evaluate the arc angle m ∠AED as follows:
(arc angle/360°) × 2 × π × r
by cross multiplication;
arc angle AED = (360 × 45)/2πr
2 can divide 360° to give;
arc angle AED = (180 × 45)/πr
arc angle AED = 8100/πr
Therefore, the angle AED of arc AD of the circle is calculated to be equal to 8100/πr
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25. KAYAKING It takes 3 hours to paddle a kayak
12 miles downstream and 4 hours for the
return trip upstream. Find the rate of the
kayak in still water.
Let k = the rate of the kayak in still water and
c = the rate of the current. (Lesson 6-4)
R t d rt=d
Upstream. k+c 3 12 3(k + c) = 12
Downstream k-c 4 12 4(k - c) = 12
Answer:
Step-by-step explanation:
For part a:
Mean: Use the AVERAGE function to find the mean of the "Number" column.
Median: Use the MEDIAN function to find the median of the "Number" column.
Mode: There is no built-in function to find the mode in Excel, but you can use a combination of the IF, COUNTIF, and MAX functions to find the most frequently occurring value.
Maximum: Use the MAX function to find the maximum value in the "Number" column.
Minimum: Use the MIN function to find the minimum value in the "Number" column.
For part b:
Mean: Use the AVERAGE function to find the mean of the "Percent" column.
Median: Use the MEDIAN function to find the median of the "Percent" column.
Mode: There is no built-in function to find the mode in Excel, but you can use a combination of the IF, COUNTIF, and MAX functions to find the most frequently occurring value.
Maximum: Use the MAX function to find the maximum value in the "Percent" column.
Minimum: Use the MIN function to find the minimum value in the "Percent" column.
For part c:
The statistics on children whose parents do not have secure employment provide important insights into the state of the economy. In this case, the mean and median of the number of children in each state seem to be around 450,000. The mode cannot be determined since there are no repeated values in the "Number" column. The maximum number of children is 678,000 in Ohio, while the minimum number is 141,000 in Iowa.
Comparing the states, Indiana has a slightly higher mean and median percent of children whose parents do not have secure employment at 27%, compared to the other surrounding states which range from 20% to 31%. However, there is no clear state with the best or worst data as the range of the percent values is not too wide.
In terms of comparison, the number of children may provide a more comprehensive understanding of the extent of the problem, as it gives a clearer picture of the actual number of children affected. However, the percentage provides a more relative comparison between the states, allowing for easier comparison and a clearer understanding of the proportion of children affected in each state.
Winnie made headbands to sell at the school craft fair. She sells each
headband for $6.25 and her goal is to earn at least $50.00. Write and solve
an inequality to represent this situation, where h represents the number
of headbands Winnie must sell in order to reach her goal.
Answer:
6.25 x h = 50.000
Step-by-step explanation:
Answer:
8 headbands.
Step-by-step explanation:
Winnie needs to sell AT LEAST 8 headbands. 50 divided by 6.25 is 8. Remember that the phrase "at least" is represented by a greater-than-or-equal-to symbol.
On a standard dice, what is the probability of not landing a 3
Answer:
5/6
Step-by-step explanation:
HELP!
The figure on the right is a scaled copy of the figure on the left, though it might have
also been rotated.
U
W
Η,
Which side in the figure on the right corresponds to segment UW?
What is the scale factor?
Answer:
HI
The scale fact from the smaller to the larger is 3. The scale factor from the larger to the smaller is 1/3
Step-by-step explanation:
Rewrite in simplest terms:-2(-10v+1)-6v
Answer:
14v-2
Step-by-step explanation:
1. distribute
2. combine like terms
see photo for more information
When we are given the value of the ______ variable, we can use the least-squares regression line to predict the value of the ______ variable.
When we are given the value of the explanatory variable, we can use the least-squares regression line to predict the value of the outcome variable.
The least square method is the process of finding the best-fitting curve or line of best fit for a set of data points by reducing the sum of the squares of the offsets (residual part) of the points from the curve. During the process of finding the relation between two variables, the trend of outcomes is estimated quantitatively. This process is termed as regression analysis. The method of curve fitting is an approach to regression analysis. This method of fitting equations that approximates the curves to give raw data is the least squares.
It is quite obvious that the fitting of curves for a particular data set is not always unique. Thus, it is required to find a curve having a minimal deviation from all the measured data points. This is known as the best-fitting curve and is found by using the least-squares method.
When we are given the value of the explanatory variable, we can use the least-squares regression line to predict the value of the outcome variable.
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A scientist wants to know how far monarch butterflies travel when they migrate. The scientist decides to tag a sample of 50 butterflies from one location in California. Are conclusions drawn from this sample likely to be true for all monarch butterflies? Explain.
Conclusions drawn from a sample of 50 monarch butterflies tagged from one location in California may not be entirely true for all monarch butterflies.
What is the sample?A sample is a subset of data drawn from a larger population by a researcher using a predetermined selection process. These components are referred to as sample points, sampling units, or observations.
The sample size is relatively small compared to the entire population of monarch butterflies. Additionally, the sample is only taken from one location, so the results may not be representative of the entire migration pattern.
The monarch butterfly is known to have a wide geographic range, migrating across North America, and covering a distance of thousands of miles during their annual migration. Thus, to make conclusions that apply to the entire population of monarch butterflies, a more comprehensive and representative sample size from various locations along their migration route would be needed.
In scientific research, it is essential to have a large and representative sample size to minimize the margin of error and to obtain accurate results. Therefore, a larger sample size and a more diverse geographical representation would provide a better understanding of the migration patterns of monarch butterflies.
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Kate had some stickers.
She kept 2/5 of them for herself and gave 5/6 of the remaining stickers to 6 of her
friends equally.
(a) What fraction of her stickers did Kate give to her 6 friends?
(b) What fraction of Kate's stickers did each of her 6 friends receive?
a) The fraction of the stickers that Kate gave to her 6 friends was 1/2.
b) The fraction of Kate's stickers that each friend received from the 1/2 of stickers was 1/12.
What is the fraction?The fraction is the portion or part of a whole.
Fractions can be proper, improper, and complex fractions, depending on the relative value of the numerator and the denominator.
The total number of stickers that Kate possesses = 1/1
The fraction Kate kept for herself = 2/5
The remaining portion of Kate's stickers = 3/5 (1 - 2/5)
The fraction Kate gave to her 6 friends to share equally = 5/6 of 3/5 = 1/2
The fraction of Kate's stickers that each friend received = 1/2 ÷ 6 = 1/12
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The area of Rhode Island is about 1000
square miles. The area of Alaska is about
5.7 x 105 square miles.
Complete the statement based on the
information above:
Alaska's area is ___ times the area of rhode island
Answer:
57
Step-by-step explanation:
To find the ratio of the area of Alaska to the area of Rhode Island, we need to divide the area of Alaska by the area of Rhode Island.
The area of Rhode Island is 1000 square miles and the area of Alaska is 5.7 x 10^5 square miles.
So, the ratio is: 5.7 x 10^5 / 1000 = 57
Therefore, Alaska's area is 57 times the area of Rhode Island.
5.7 x 10^5 divided by 1000 = 57.
A deli is trying out new labels for their cylindrical-shaped wheels of cheese. The label covers the entire wheel except the circular top and bottom.
If the wheel has a radius of 30 centimeters and a height of 20 centimeters, how many square centimeters of the wheel does the label cover? (Approximate using pi equals 22 over 7)
792,000 over 7 square centimeters
66,000 over 7 square centimeters
26,400 over 7 square centimeters
2,640 over 7 square centimeters
The label covers approximately 4,800 square centimetres of the wheel of cheese.
What is the lateral surface area of a cylinder?
The lateral surface area of a cylinder can be found using the formula:
L = 2πrh
where L is the lateral surface area, r is the radius of the cylinder, and h is the height of the cylinder.
In this case, we need to find the lateral surface area of the wheel of cheese, so we can use the given radius of 30 centimetres and height of 20 centimeters to calculate:
L = 2 x (22/7) x 30 x 20
L = 4,800 square centimetres
This is the total surface area of the cylindrical-shaped wheel of cheese. However, the label does not cover the circular top and bottom, so we need to subtract their areas from the total surface area to find the area covered by the label.
The area of a circle can be found using the formula:
A = πr²
where A is the area of the circle, and r is the radius of the circle.
In this case, we have two circles (top and bottom), so the total area of the circles that are not covered by the label is:
2 x (22/7) x 30²
= 56,400/7 square centimeters
Subtracting this from the total surface area, we get:
4,800 - 56,400/7
= 33,600/7 square centimeters
= 4,800 square centimeters (rounded to the nearest whole number)
Therefore, the label covers approximately 4,800 square centimeters of the wheel of cheese.
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pls help me i’ll give you brainlist!
For the linear equation 3x + y = 9 we have:
x-intercept (3, 0)y-intercept (0, 9).How to find the x and y-intercepts?Here we want to find the two intercepts for the linear equation:
3x + y = 9
First, the x-intercept is the point that we get when we evaluate on y = 0.
3x + 0 = 9
3x = 9
x = 9/3
x = 3
Then we get: x-intercept (3, 0)
And for the y-intercept we need to evaluate in x = 0.
3*0 + y = 9
y = 9
Then the y-intercept is (0, 9).
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A tailor charges a basic fee of $20 plus $4 per letter to sew an athlete's name on the back of a jacket. Write a linear equation that will find the cost c to have a name containing x letters
The equation will be;
c = 20 + 4x
What are Linear Equations?Linear equations are equations of the first order. When a linear equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can also have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line.
A linear equation that will find the cost c to have a name containing x letters will be;
c = $20 + 4x
where c = cost
$20 = basic fee
x = number of letters
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HELP ME i need help please
A transformation rule, if applied to a polygon on a coordinate grid, which does not preserve congruence include the following: C. (x, y) → (3x, 3y).
What is dilation?In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric figure and the location of its points based on the scale factor, but not its shape.
Generally speaking, a dilation is not a rigid transformation because it can preserve angle measure, orientation, perpendicular lines, betweenness of points, parallel lines, and collinearity in any geometric figure.
In conclusion, we can reasonably infer and logically deduce that dilations does not preserve congruence.
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Help with these questions pls?
Answer:
76
Step-by-step explanation:
(16x3)+28
Its 16x3 because there's 3 half hours in 1.5hrs
(5^-4)^2 using only positive exponents
Hi there, here's your answer:
Given the question:
[tex](5^{-4})^{2}[/tex]
We know that a number [tex]x[/tex] raised to the power of a negative integer [tex]-y[/tex] is evaluates as [tex]\frac{1}{x^{y} }[/tex]
Hence, on evaluating this expression we get:
[tex](\frac{1}{5^{4} })^{2}[/tex] = [tex](\frac{1}{625} )^2 = \frac{1}{390625}[/tex]
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