A stockbroker recorded the number of clients she saw each day over 9-day period. Construct a box and whisker plot the data, find the quartile. 12, 23 12,27,18,20,23,27,40.
Answers
A box plot that represents the data set is shown in the image below.
The first quartile is equal to 15 and the third quartile is equal to 27.
How to determine the five-number summary for the data?In order to determine the statistical measures or the five-number summary for the number of clients, we would arrange the data set in an ascending order:
12,12,18,20,23,23,27,27,40
For the first quartile (Q₁), we have:
Q₁ = [(n + 1)/4]th term
Q₁ = (9 + 1)/4
Q₁ = 2.5th term
Q₁ = 2nd term + 0.5(3rd term - 2nd term)
Q₁ = 12 + 0.5(18 - 12)
Q₁ = 12 + 0.5(6)
Q₁ = 12 + 3
Q₁ = 15.
For the third quartile (Q₃), we have:
Q₃ = [3(n + 1)/4]th term
Q₃ = 3 × 2.5
Q₃ = 7.5th term
Q₃ = 7th term + 0.5(8th term - 7th term)
Q₃ = 27 + 0.5(27 - 27)
Q₃ = 27 + 0.5(0)
Q₃ = 27
In conclusion, a box plot for the given data set is shown in the image attached below.
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Related Questions
Dafydd bought a bike for £300 on 1st February 2010. Every year the value of the bike depreciates by 18% of its' value at the start of the year. Find the value of the bike on 1st February 2014.
Answers
Answer: £165.41
Step-by-step explanation:
Price of bike when purchased in 2010 = £300
Depreciation rate yearly = 18%
Value of bike in 2011
Purchased price - depreciation value
= £300 - £300 * 0.18
= £300 - £54
= £246
Value of bike in 2012
= 2011 Price - depreciation value
= £246 - £246 * 0.18
= £246 - £44.28
= £201.72
Value of Bike in 2013
= price of 2012 - depreciation value
= £201.72 - £201.72 * 0.18
= £201.72 - £36.31
= £165.41
Price in 2014 would be £165.41
How do you solve this?
Answers
Step-by-step explanation:
g(x) is also called y. the functional result value for an input value x is shown in the y direction above or below that x value on the x axis.
so, when it says g(x) = c, the solution is to find the values of x for which b the function g delivers c as result.
now, we look at the graphic.
for example, g(x) = 0 (c = 0) has actually 3 solutions, as the function crosses the x-axis (and that means y or g(x) = 0) 3 times. so, there are 3 different values of x that create g(x) = 0.
but we are looking for a c that has only one solution (one value of x to create that result).
c = 1 ?
let's imagine a horizontal line through y = 1.
we see, it cuts the function also 3 times. 3 solutions.
c = -1 ?
a similar horizontal line through y = -1 cuts the function also 3 times. 3 solutions
but c = 3 !
a horizontal line through y = 3 stays above all the waves of the function and then cuts the function only one time at the very right. 1 solution !
and that is therefore our answer.
To better understand the website builder market, Clutch surveyed individuals who created a website using a do-it-yourself (DIY) website builder. Respondents, categorized by the type of website they built—business or personal, were asked to indicate the primary purpose for building their website. The following table summarizes the findings:
Answers
As the importance of having a powerful online presence continues to grow, many people are chosen to build their own websites using do-it-yourself (DIY) tools.
These tools, also known as website builders, are relatively easy to use and inexpensive. Examples include Wix, Square Space, Weebly, and more.
Web builder users lean to create two various types of websites, either personal sites a creative display, blog or portfolio or business sites for online ecommerce, sales, or an online business presence.
Understanding what users of web builders design with the DIY tools is an important step in pick out what makes these tools stand out.
While the mass of users is familiar with the techniques needed to build a site, the actual types of websites being built vary. Nearly half of respondents (48%) specify that their website was built for personal purposes, while 42% said that their website is for business.
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is 1/8(48m + 24) and 6m + 3 equivalent
Answers
1/8•8(6m+3)
Cancel out the gcf
Solution
6m+3
A cube has an edge length of 9 centimeters. If the side length is increased by a factor of 3, how much larger is the perimeter of a face of the new cube? 72 cm 72 cm2 108 cm 108 cm2
Answers
Answer:
72cm
Step-by-step explanation:
Original length of the cube = 9cm
Perimeter of the original cube = 4L
Perimeter of the original cube = 4(9)
Perimeter of the original cube = 36cm
If the cube is increased by a factor of 3, new length will be 3(9) = 27cm
Perimeter of the new cube = 4*27
Perimeter of the new cube = 108cm
Difference =108 - 36
Difference = 72cm
Hence the new cube is 72cm larger than the original
Answer:
72cm
Step-by-step explanation:
let the random variable z follow a standard normal distribution. find the value k, such that p( z > k) = 0.39.
Answers
If a random variable "z" follows a standard normal distribution and the probability of "z" being greater than "k" is 0.39, then the value of "k" such that satisfies the equation [p(z > k) = 0.39] will be 0.28
As per the question statement, a random variable "z" follows a standard normal distribution.
We are required to determine the value of "k" such that the equation [p(z > k) = 0.39] is satisfied.
To solve this question, first we will have to calculate the probability of "z" being greater than "k" and then from the Z-table, we will determine the z-score corresponding the above calculated probability value. This z-score will be our desired answer, i.e.,
Given, P(Z > k) = 0.39
Or, P(Z < k) = (1 - 0.39)
Or, P(Z < k) = 0.61
Now, from the Z table, we get the z-score corresponding to probability value of 0.61 is 0.28
Hence, (k = 0.28)
Normal Distribution: In Statistics and Probability Theory, a normal distribution is the bell-shaped frequency distribution curve of a continuous random variable, based on a set of values of the variable, which lie in a symmetrical fashion majorly situated around their mean and the rest taper off symmetrically toward either extreme.To learn more about Normal Distributions and Probability, click on the link below.
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explain why the language over consisting of strings not in the form of anb3n is not a regular language.
Answers
To see why this is the case, let us first define the language formally. The language anb3n consists of all strings of the form anb3n, where n is a non-negative integer. This means that the string starts with some number of a's, followed by exactly three b's, and ends with three times as many a's as there are b's. For example, some strings in this language are:
- aaabbb
- aaaabbbbbb
- aaaaaabbbbbbb
On the other hand, strings that are not in this language include:
- abbb
- aaabb
- aaaabbbbb
Now, suppose for contradiction that there exists a DFA that recognizes all and only the strings not in the form of anb3n. Since any DFA has a finite number of states, it follows that there must be some finite number k such that any string longer than k must contain a loop in the DFA. That is, if we read k or more symbols from any such string, we must encounter some state that we have already visited before.
Consider now the string w = ak+3bk+1. This string is longer than k and hence must contain a loop in the DFA. Let q be the state we reach after reading the first k symbols of w. Since w contains exactly k+3 b's, it follows that after reading these b's we must end up in a different state than q (otherwise w would be in the language). Let r be this new state.
Now consider the string wx, where x consists of k-2 a's followed by two b's. This string is also longer than k and hence must contain a loop in the DFA. Let s be the state we reach after reading the first k symbols of wx. Since x ends with two b's, it follows that after reading these b's we must end up in a different state than s (otherwise wx would be in the language). Let t be this new state.
Now consider the string wy, where y consists of k-1 a's followed by three b's. This string is also longer than k and hence must contain a loop in the DFA. Let u be the state we reach after reading the first k symbols of wy. Since y ends with three b's, it follows that after reading these b's we must end up in a different state than u (otherwise wy would be in the language). But since w and wy differ only in their last three symbols, it follows that after reading these symbols we must end up in the same state for both strings. In particular, we must end up in r for w and in u for wy.
However, this is a contradiction because r and u are different states, and hence there can be no DFA that recognizes all and only the strings not in the form of anb3n.
The language consisting of strings that are not in the form of anb3n is not a regular language because it cannot be described by a regular expression or a finite state machine.
In the language anb3n, every string has a certain pattern, where the letter "a" is followed by a number of "b"s, which are then followed by three times the number of "b"s as the number of "a"s. This pattern can be easily described by a regular expression or a finite state machine.
However, when considering strings that are not in this form, there are several possible patterns and combinations of letters, making it difficult to define a regular expression or a finite state machine that describes them. For example, the language could include strings that have more "a"s than "b"s, strings that have "b"s in between the "a"s and "b"s, or strings that have a different number of "b"s than three times the number of "a"s.
Since a regular language can only be described by a regular expression or a finite state machine, the language consisting of strings not in the form of anb3n cannot be a regular language. Instead, it is considered a context-free language, which can be described by a context-free grammar or a pushdown automaton.
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Find the critical value za/2 that corresponds to the given confidence level. 81% Round to two decimal places.
Answers
The critical value zα/2 for an 81% confidence level is approximately 1.44
The critical value zα/2 is used in the calculation of confidence intervals for a normal distribution. It represents the number of standard deviations that the sample mean is away from the population mean.
A confidence level represents the level of certainty that a researcher has in the accuracy of their statistical results
To find the critical value zα/2 for an 81% confidence level, we need to find the z-score that corresponds to an area of (1-0.81)/2 = 0.095 to the right of the mean in the standard normal distribution.
Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to an area of 0.095 to the right of the mean is approximately 1.44.
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Ms. Carey grades 4 tests during her lunch. She grades 1/3 of the remainder after school. If she syill5has 16 test to grade after school, how many test are there?
Answers
Answer: 24 tests
Step-by-step explanation:
Ms. Carey graded 1/3 of the tests and still had 16 tests to go.
This means that the 16 tests represent the remaining proportion of the total number of tests:
= 1 - 1/3
= 2/3
2/3 of the total is equal to 16 tests. Assuming the total is x, the expression would be:
2/3x = 16
x = 16 ÷ 2/3
x = 16 * 3/2
x = 24 tests
KM and NP are parallel lines. which angles are supplementary angles?
Answers
Supplementary angles = The angles add up to 180 degrees / form a straight line.
Angle KLO and angle KLJ form a straight line -> they are supplementary angles.
Part I: Effective cost per hour
1 shift (8 hours) per day
5 holidays
7 days of vacation
Fringe: 37% of base wage
Base hourly wage: $12.30 per hour
30-minute lunch (paid) plus two 15-minute breaks (paid) per day
1. What is the effective cost per hour per employee? (20 points)
Part II: Reduction in labor cost
Assume 306,050 hours of work needed every year
Productivity increases from 70% to 85%
Round number of workers to whole numbers (below .5, round down; .5 and above, round up)
2. What is the total dollar change in labor expense from this 15% increase in productivity? (10 points) 3. What is the percent change in labor expense from this 15% increase in productivity? (10 points)
Answers
The total dollar change in labor expense from this 15% increase in productivity is [calculated value]. The percent change in labor expense is [calculated value].
Part I: Effective cost per hour per employee
To calculate the effective cost per hour per employee, we need to consider various factors such as base wage, fringe benefits, paid time off, and the number of working hours per year.
Base hourly wage: $12.30 per hour
Number of working hours per day: 8 (1 shift)
Number of holidays: 5
Number of vacation days: 7
First, let's calculate the total fringe benefits per hour:
Fringe benefits = 37% of base wage = 0.37 * $12.30 = $4.551
Next, let's calculate the paid time off per hour:
Paid time off = (Number of holidays + Number of vacation days) * 8 hours = (5 + 7) * 8 = 96 hours
Now, let's calculate the effective cost per hour per employee:
Effective cost per hour = Base hourly wage + Fringe benefits + (Paid time off * Base hourly wage)
Effective cost per hour = $12.30 + $4.551 + (96 * $12.30)
Part II: Reduction in labor cost
To calculate the reduction in labor cost due to a 15% increase in productivity, we need to consider the total number of working hours needed and the change in productivity.
Number of working hours needed every year: 306,050
Productivity increase from 70% to 85%: 85% - 70% = 15%
First, let's calculate the initial number of workers needed:
Initial number of workers = Number of working hours needed / (Productivity rate / 100)
Initial number of workers = 306,050 / (70 / 100)
Next, let's calculate the new number of workers needed after the productivity increase:
New number of workers = Number of working hours needed / (New productivity rate / 100)
New number of workers = 306,050 / (85 / 100)
Finally, let's calculate the total dollar change in labor expense:
Total dollar change in labor expense = (Initial number of workers - New number of workers) * Effective cost per hour * Number of working hours per year
To calculate the percent change in labor expense, we can use the following formula:
Percent change in labor expense = (Total dollar change in labor expense / Initial labor expense) * 100
Please provide the values for Effective cost per hour and Initial labor expense to calculate the final answers in Part I and Part II.
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What is the y-intercept of the line with the equation below?
Y = 10x - 7
Answers
Answer:
-7
Step-by-step explanation:
the y intercept is the value that is not a foefficient of x or y
answer is: -7
Alex is correct
Find the Surface area of the trapezoid
please help
show work
Answers
Answer:
259.5
Step-by-step explanation:
8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5
the safe load, l, of a wooden beam of width w, height h, and length l, supported at both ends, varies directly as the product of the width and the square of the height, and inversely as the length. a wooden beam 4 inches wide, 7 inches high, and 240 inches long can hold a load of 2540 pounds. what load would a beam 5 inches wide, 8 inches high, and 216 inches long, of the same material, support? round your answer to the nearest integer if necessary.
Answers
The safe load, l, of a wooden beam of width w, height h, and length l, then the nearest integer is, L = 4607.7 pounds.
Based on the given conditions,
The safe load = L
A wooden beam of width = w
Height = h
Length = l
The safe load L, of the beam varies directly as the product of the width and the square of the height.
L∝ (w × h²)
And varies inversely as the length of the wooden beam.
L∝ (w × h²)/l
L = \(\frac{k*w*h^{2} }{l}\) (Equation-1)
Where k = proportionality constant
If w = 4 inches, h = 7 inches, l = 240 inches and L = 2540 pounds
Then,
We can substitute values in equation-1,
L = \(\frac{k*w*h^{2} }{l}\)
2540 = (k*4*\(7^{2}\))/240
2540 = (k*4*49)/240
2540 = (k*196)/240
2540*240 = k*196
609600 = k*196
609600/196 = k
3110.20 = k
If w = 5 inches, h = 8 inches and l = 216 inches
L = \(\frac{k*w*h^{2} }{l}\)
L = ( 3110.20 * 5 * \(8^{2}\) )/216
L = ( 3110.20 * 5 *64 )/216
L = 995264/216
L = 4607.7 pounds
Therefore,
The safe load, l, of a wooden beam of width w, height h, and length l, then the nearest integer is, L = 4607.7 pounds.
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what divided by 5/6 equals 3/5
Answers
Answer:
let the decided no. be x
Now
\( \frac{5}{6} \times \frac{1}{x} = \frac{3}{5} \)
\(5 \times 5 = 3 \times 6x\)
\(x = \frac{25}{18} or1 \frac{7}{18} \)
is a required answer.
when
no. divided by 5/6 equals 5/3
now
\( \frac{5}{6} \times \frac{1}{x} = \frac{5}{3} \)
\(5 \times 3 = 5 \times 6x\)
\(x = \frac{15}{30} \)
\(x = \frac{1}{2} \)is a required answer.
The following cone has a slant height of 17
cm and a radius of 8
cm.
What is the volume of the cone?
Responses
480π
320π
544π
Answers
The formula for the volume of a cone is:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is pi.
In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:
h² = s² - r²
h² = 17² - 8²
h² = 225
h = 15
Now that we have the height, we can plug in the values for r and h into the formula for the volume:
V = (1/3)π(8²)(15)
V = (1/3)π(64)(15)
V = (1/3)(960π)
V = 320π
Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.
A restaurant offers pizzas with 2 types of crust, 7 different toppings, and in 5 different sizes. how many different pizzas could be ordered?
Answers
There are 70 different types of pizzas could be ordered
A permutation is an act of arranging the objects or numbers in order.
Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter
Given,
Number of options on crust=2
Number of options on topping= 7
Number of options on size= 5
Therefore for each type of crust there are 7 different topping, for each toppings there are 5 different sizes
The total number ways of ordering pizza=2×7×5=70
Hence, there are 70 different types of pizzas could be ordered
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Explain why subtracting a positive number is the same as adding its inverse.
Answers
This is best explained by an example:
8 - 3 = 5
This is the same as: 8 + (-3) = 5.
A positive and a negative equates to a negative and so forth. :)
I need some help better understanding Area Volume/Differential Equations, as ive been stuck on this single string of questions in my workbook for some time now, any and all help would be appreciated.
"Let R be the region in quadrant 1 bounded by y=3sin(2x) and y=e^x "
1) Find the area of R
2) Let S be the solid generated by rotating R around the x-axis. Find the volume of S.
3) Let Q be the solid generated by rotating R around the horizontal line y=5. Find the volume of Q
4) Let P be the solid whose base is R and whose cross sections perpendicular to the x-axis are semicircles. Find the volume of P.
Answers
Answer:
Refers to the attachment given below!
Step-by-step explanation:
Jack bought a coin for $200, which he sold later for $175. Find the percent of change. Did Jack make a good investment?
Answers
Donell compared the hours students spent each day on social networks to the hours they spent on homework. His data is shown below. Which statements are true? Check all that apply.
2 dots plots. A dot plot titled Number of hours spent on social networks goes from 0 to 4.5. 0 has 3 dots, 0.5 has 5 dots, 1 has 2 dots, 2.5 has 4 dots, 3 has 3 dots, 3.5 has 1 dot. A dot plot titled Number of hours spent on homework goes from 0 to 4.5. 0 has 1 dot, 0.5 has 1 dot, 1 has 4 dots, 1.5 has 8 dots, 2 has 3 dots, and 4.5 has 1 dot.
The mean number of hours spent on each activity are equal.
There is a greater variability in the hours spent on social networks.
The average student spends more time on homework than on social networks.
The range for the number of hours spent on homework is greater.
Students are more consistent in the time spent on homework than the time spent on social networks.
Answers
Answer:
A,D,E
Step-by-step explanation:
Lol i took the test on edge and got it correct.
:P
Answer:
the answers are a d and e
Step-by-step explanation:
Use the following function rule to find f(-2).
f(x) = |x-10|
f(-2) =
Answers
-2-10 is -12
Does this graph show a function? Explain how you know.
Answers
Answer:
A is the correct one
cause according to function rule the vertical line should cut only on a one point to be function
as here we can see that vertical line cuts here at two point
HELP! IS THIS RIGHT?
Answers
Answer:
Yes a 1:3 ratio
Step-by-step explanation:
Yes triangle A is 3 times bigger than triangle B. So it takes 3 B triangles to make one A triangle.
Find the area.
a. 238.5 dm²
b. 257.5 dm²
c. 157.5 dm²
d. 315 dm²
Answers
The correct option is- c. 157.5 dm². The area of shown Trapezium in the figure is found to be 157.5 dm².
Explain about the trapezium?An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezium or trapezium.
A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium may additionally be parallel. The parallel sides may be vertical, horizontal, or angled.The altitude is the measurement of the angle perpendicular to the parallel sides.Area of Trapezium = 1/2 × (a + b) × height
In which
a = 8.5 dmb = 26.5 dmheight h = 9 dmArea of Trapezium = 1/2 × (8.5 + 26.5) × 9
Area of Trapezium = 157.5
Thus, the area of shown Trapezium in the figure is found to be 157.5 dm².
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The nth term of a sequence is 4n-5
The nth term of a different sequence is 3n+2
Write down two numbers that are in both sequences,
and between 10 and 30.
Answers
The two numbers that are in both sequences and between 10 and 30 are 14 and 26.
What is a sequence?An ordered set of numbers that adhere to a pattern or rule is referred to as a sequence in mathematics. Sequences can be defined in a variety of ways, such as a formula or a recursive definition, and they can be finite or infinite. Several branches of mathematics, including calculus, algebra, and number theory, employ sequences to explore and answer problems related to the behaviour of functions. For instance, sequences may be used to create fractals and other geometric patterns, predict the rise of populations or the spread of illnesses, and examine the distribution of prime numbers.
The given sequence is 4n - 5, and the nth term is 3n + 2.
For numbers between 10 and 30 in the sequence we have:
4n - 5 ≥ 10
4n ≥ 15
n ≥ 3.75
And,
4n - 5 ≤ 30
4n ≤ 35
n ≤ 8.75
Now, we calculate the sequence for n from 4 to 8:
When n = 4, 3n + 2 = 14
When n = 5, 3n + 2 = 17
When n = 6, 3n + 2 = 20
When n = 7, 3n + 2 = 23
When n = 8, 3n + 2 = 26
Hence, the two numbers that are in both sequences and between 10 and 30 are 14 and 26.
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The following time series shows the number of emergency calls for an ambulance over the past four months. The number of calls is as follows. May = 66, June = 72, July = 60, August = 73. That is the forecast for ambulance calls for September using a two period moving average forecast? 66.5 79.5 67.8 71.5
Answers
The two-period moving average forecast of ambulance calls for September is 67.8. Moving average method is a statistical method of forecasting.
In this method, the forecast for a future period is equal to the average of the most recent data values available.A moving average forecast is used when the trend in the historical data is fairly stable and there are no major unusual fluctuations in the data. In a two-period moving average, the forecast for the next period is the average of the two most recent periods. In this question,
we have to forecast the number of emergency calls for an ambulance for September using a two-period moving average forecast. The given data is as follows:May = 66June = 72July = 60August = 73To find the two-period moving average forecast for September, we take the average of the August and July values since they are the most recent two data values given in the question.Thus,Two-period moving average = (60 + 73) / 2= 133 / 2= 67.8Therefore, the two-period moving average forecast for ambulance calls for September is 67.8.
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results from a study using the following sampling method(s) can be generalized to at least the population from which the sample was drawn... a. simple random sampling b. stratified random sampling c. availability/convenience sampling d. snowball sampling e. both a and b f. both c and d
Answers
Simple random sampling is a sampling method that can be generalized to at least the population from which the sample was drawn.
Using simple random sampling, each component of the population has an equal probability and likelihood of being chosen. This sampling strategy is also frequently referred to as a method of chance since the selection of items in this case completely rests on chance or luck.
Simple random sampling is a simple sampling technique that is readily integrated into more sophisticated sampling techniques. Every sample has the same chance of being picked, which is the key characteristic of this sampling technique.
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Let x be a discrete random variable. if pr(x<6) = 1/7, and pr(x>6) = 1/4, then what is pr(x=6)?
Answers
Answer:
\(pr(x=6)=\frac{17}{28}\)
Step-by-step explanation:
Well the probabilities should all up to 1. This means pr(x<6) + pr(x=6) + pr(x>6) = 1.
So plugging in the known values we get: \(\frac{1}{7} + pr(x=6) + \frac{1}{4}=1\)
To make things easier, let's multiply the 1/7 by 4/4 and 1/4 by 7/7
\(\frac{4}{28}+pr(x=6)+\frac{7}{28}=1\)
Now combine like terms: \(pr(x=6)+\frac{11}{28}=1\)
Subtract 11/28 from both sides
\(pr(x=6)=\frac{17}{28}\)
DESPERATE WILL GIVE BRAILIST AND THNX
Marcus currently has $42 and plans to save an additional $5 each week to buy a pair of shoes. He made a table showing the total amount of money he will have saved for different weeks.
Number of weeks 0 2 5 8
Total amount of money ($) 42 52 67 82
Which equation represents the relationship between the number of weeks, x, and the total amount of money, y, Marcus will have saved?
A. 5x + y = 42
B. 5x−y=−42
C. x−5y=−42
D. x + 5y = 42
Answers
Answer:
y=5x+42
subtract 5x from both sides
-5x+y=42
Step-by-step explanation:
subtract 5x from both sides
-5x+y=42
multiply by -1
5x-y=-42
In standard form, Ax+By=C, the variable A cannot be a negative. However, this is not an option so go with c.