The probability that Mr Smith will have coffee on exactly 8 mornings out of the next 25 is 0.142, or 14.2%.
This scenario can be modeled by a binomial distribution, where:
The probability of success (having coffee) on any given morning is p = 0.35
The number of trials (mornings) is n = 25
The number of successes (mornings with coffee) we want to find the probability for is k = 8.
The probability mass function for a binomial distribution is given by:
[tex]P(X = k) = (n \: choose \: k) \times p^k \times (1-p)^{(n-k)},[/tex]
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n. It can be calculated as:
(n choose k) = n! / (k! × (n-k)!)
Using this formula and putting in the values we have,
[tex]P(X = 8) = (25 \: choose \: 8) \times 0.35^8 \times (1-0.35)^{(25-8)} [/tex]
[tex]P(X = 8) ≈ 0.142[/tex]
Therefore, the probability that Mr Smith will have coffee on exactly 8 mornings out of the next 25 is approximately 0.142, or 14.2%.
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6
lo
r
s
p
m
q
0
-2
mollie claimed that the slope of mq is greater than the slope of qs because triangle mpq is bigger than triangle qrs.
explain the error in mollie's claim and calculate the slope for both mq and qs show all your work.
enter your work and explanation in the space provided.
Size of triangles doesn't determine slope, mq slope=-2, qs slope=-0.5
How to explain Mollie's incorrect slope claim?Mollie's claim is incorrect because the size of the triangles does not determine the slope of a line. The slope is calculated by dividing the change in the y-coordinates by the change in the x-coordinates between two points on the line. Therefore, we need to find two points on the lines mq and qs to calculate their slopes.
Let's start by finding the slope of mq. We can identify two points on the line, (0,6) and (2,2). Using these points, we can calculate the slope as:
slope of mq = (change in y-coordinates) / (change in x-coordinates)
slope of mq = (2 - 6) / (2 - 0)
slope of mq = -4 / 2
slope of mq = -2
Now let's find the slope of qs. We can identify two points on the line, (2,2) and (6,0). Using these points, we can calculate the slope as:
slope of qs = (change in y-coordinates) / (change in x-coordinates)
slope of qs = (0 - 2) / (6 - 2)
slope of qs = -2 / 4
slope of qs = -0.5
Therefore, the slope of mq is -2 and the slope of qs is -0.5.
In summary, Mollie's claim is incorrect because the size of the triangles does not determine the slope of a line. We calculated the slopes of lines mq and qs by finding two points on each line and using the formula for slope, which is the change in y-coordinates divided by the change in x-coordinates. The slope of mq is -2, and the slope of qs is -0.5.
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Which of the following expressions can be used to find how many meters it is from Washington, D.C, to Baltimore? Distances: Washington, D.C, and Alexandria, WA = 11 km, Washington, D.C and Baltimore, MD = 57 km, and Washington, D.C and Annapolis, MD = 53 km. Expressions: A. 1000 divided by 57, B. 100 x 57, C. 57 x 1,000, D. 57 divided 1000.
The correct expression to use to find how many meters it is from Washington, D.C., to Baltimore is:
C. 57 x 1,000.
What is expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
In the given question,
The correct expression to use to find how many meters it is from Washington, D.C., to Baltimore is:
C. 57 x 1,000
Since 1 km equals 1,000 meters, we can convert the distance of 57 km to meters by multiplying it by 1,000. This gives us:
57 km x 1,000 meters/km = 57,000 meters
Therefore, the distance from Washington, D.C., to Baltimore is 57,000 meters.
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The ratio of English books to Math books is 5:9.If there 28 more Math books than English books. How many Math and English books are there?
Answer: 35 English Books and 63 Maths Books
Step-by-step explanation:
5:9
x:(x+28)
Cross multiplication...
9x=5x+140
9x-5x=140
4x=140
14/4 = 35 = x
English Books = x= 35
Maths Books = x+28 = 63
The floor tiles in the jackson family’s kitchen are squares
that measure 8 3
··4
inches to a side. each grid square in the
drawing measures 1
··4
inch to a side.
which is the scale of the drawing?
The scale of the drawing is 1:33 1/3, because the actual size of each grid square in the kitchen floor tile is 33 1/3 times larger than its size in the drawing.
What is the ratio of architectural drawing?The scale of a architectural drawing represents the proportional relationship between the size of an object in the drawing and its actual size in real life.
In this case, the floor tiles in the Jackson family's kitchen are square with a length of 8 3/4 inches on each side, while each grid square in the drawing measures 1/4 inch on each side.
To determine the scale of the drawing, we need to find the ratio between the actual size of a grid square and its size in the drawing.
Using proportions, we can set up an equation to solve for the scale. Let x be the scale of the drawing, then we have:
8 3/4 inches / (1/4 inch) = x
Simplifying the left side of the equation gives us:
35 inches = x
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which of the following statements about a randomly chosen person from these 200 employees is true? responses if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city. if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city. if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere). if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere). the person is more likely to own a car if he or she lives in the city (downtown area or elsewhere) than if he or she lives outside the city. the person is more likely to own a car if he or she lives in the city (downtown area or elsewhere) than if he or she lives outside the city. the person is more likely to live in the downtown area in the city than elsewhere in the city. the person is more likely to live in the downtown area in the city than elsewhere in the city. the person is more likely to own a car than not to own a car.
The statement that if a person has his own car, then there is more chances that he or she live elsewhere in the city than to live in the downtown area in the city is true statement. So, the option(a) is right answer for problem.
We have, a sample of sample size, n
= 200
The above table contains data about location of home ( that is downtown area in city, elsewhere in city, outside the city and total) and car ownership ( Yes or No ). Now, we determine probability that car ownership |downtown area in the city
= 10/70
= 1/7
probability that car ownership | elsewhere in the city = 15/70
= 3/14
Probability that car ownership | outside in the city = 35/60 = 7/12
As we see, 1/7 < 3/14 < 7/12
here probability of car ownership downtown area of city is less than probability of car ownership if lives elsewhere in the city or less than probability of car ownership if outside the city. So, statement (a) is true in this case. Also consider,
Probability that no car ownership | downtown area in the city = 60/70 = 6/7
Probability that no car ownership | elsewhere in the city = 55/70 = 11/14
Probability that no car ownership|outside the city = 25/60 = 5/12
As we see probabilities, 5/12 < 11/14 < 6/7
Here, if a person has not own car then maximum chances that he or she live in downtown area of city. So, statement (b) is false.
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Complete question:
The above figure complete the question. A local company is interested in supporting environmentally friendly initiatives such as carpooling among employees. The company surveyed all of the 200 employees at the downtown offices. Employees responded as to whether or not they own a car and to the location of the home where they live. The results are shown in the table above. Which of the following statements about a randomly chosen person from these 200 employees is true? responses
a) if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city.
b) if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere).
c) the person is more likely to own a car if he or she lives in the city (downtown area or elsewhere) than if he or she lives outside the city.
d) the person is more likely to live in the downtown area in the city than elsewhere in the city.
e) the person is more likely to own a car than not to own a car.
The mean number of sit-ups
done by a group of students is
46 with a standard deviation
of 7. If Rylee's Z-score was
1. 8, how many sit ups did she
do?
Rylee did approximately 58.6 sit-ups.
We are given that the mean number of sit-ups is 46 and the standard deviation is 7. We are also given that Rylee's Z-score was 1.8, we can use the formula for Z-score to find how many sit-ups she did.
The formula for Z-score is [tex]Z = \frac{X-\mu}{\sigma}[/tex]
Z = Z-score
μ = mean
σ = standard deviation
X = ?
Substituting these values into the formula
1.8 = (X - 46)/7
1.8 × 7 = X - 46
X - 46 = 12.6
X = 12.6 + 46
X = 58.6
Therefore, Rylee did approximately 58.6 sit-ups.
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Which table has a constant of proportionality between
�
yy and
�
xx of
12
1212?
Choose 1 answer:
Choose 1 answer:
(Choice A)
�
xx
�
yy
1
2
2
1
start fraction, 1, divided by, 2, end fraction
6
66
2
22
24
2424
10
1010
120
120120
A
�
xx
�
yy
1
2
2
1
start fraction, 1, divided by, 2, end fraction
6
66
2
22
24
2424
10
1010
120
120120
(Choice B)
�
xx
�
yy
1
4
4
1
start fraction, 1, divided by, 4, end fraction
3
33
3
33
60
6060
12
1212
144
144144
B
�
xx
�
yy
1
4
4
1
start fraction, 1, divided by, 4, end fraction
3
33
3
33
60
6060
12
1212
144
144144
(Choice C)
�
xx
�
yy
1
3
3
1
start fraction, 1, divided by, 3, end fraction
4
44
6
66
78
7878
9
99
117
117117
C
�
xx
�
yy
1
3
3
1
start fraction, 1, divided by, 3, end fraction
4
44
6
66
78
7878
9
99
117
117117
The table that have a constant of proportionality between y and x of 12 is the first table
What is the table that have a constant of proportionality between y and x of 12?From the question, we have the following parameters that can be used in our computation:
The table of values
From the first table of values, we have the following readings
(x, y) = (1/2, 6), (2, 24) and (10, 120)
Using the above as a guide, we have the following:
The constant of proportionality between y and x in the graph is
k = y/x
Substitute the known values in the above equation, so, we have the following representation
k = 6/(1/2) = 24/2 = 120/10
Evaluate
k = 12 = 12 = 12
Hence, the constant of proportionality between y and x in the first table is 12
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Complete question
Which table has a constant of proportionality between y and x of 12?
x 1/2 2 10
y 6 24 120
x 1/4 3 12
y 3 60 144
x 1/3 6 9
y 4 78 117
A. Plot point C so that its distance from the origin is 1. B. Plot point E 4/5 closer to the origin than C. What is its coordinate? c. Plot a point at the midpoint of C and E. Label it H
(A). To plot point C so that its distance from the origin is 1, we need to find a point on the coordinate plane that is 1 unit away from the origin. One such point is (1, 0), which is located on the positive x-axis.
(B). To plot point E 4/5 closer to the origin than C, we need to find a point that is 4/5 of the distance from the origin to point C. Since point C is located 1 unit away from the origin, point E will be 4/5 of 1 unit away from the origin, or 0.8 units away.
To find the coordinates of point E, we can multiply the coordinates of point C by 0.8. If point C is (1, 0), then point E is (0.8, 0).
(C). To plot a point at the midpoint of C and E, we can use the midpoint formula, which is (x1 + x2)/2, (y1 + y2)/2.
The coordinates of point C are (1, 0) and the coordinates of point E are (0.8, 0), so the coordinates of point H are ((1 + 0.8)/2, (0 + 0)/2), or (0.9, 0). We can label this point H.
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A container with square base, vertical sides, and open top is to be made from 1000ft^2 of material. find the dimensions of the container with greatest volume
We need to find the dimensions of a container with square base, vertical sides, and open top that will have the greatest volume using 1000ft^2 of material. The dimensions of the container with the greatest volume are 10 ft by 10 ft by 22.5 ft.
Let x be the length of one side of the square base and y be the height of the container. Then the surface area is given by
S = x^2 + 4xy = 1000
Solving for y, we get
y = (1000 - x^2)/(4x)
The volume of the container is given by
V = x^2y = x^2(1000 - x^2)/(4x) = 250x - 0.25x^3
To find the dimensions that give the greatest volume, we need to find the critical points of the volume function. Taking the derivative with respect to x, we get
dV/dx = 250 - 0.75x^2
Setting dV/dx = 0, we get
250 - 0.75x^2 = 0
Solving for x, we get
x = 10
Substituting x = 10 into the equation for y, we get
y = (1000 - 100)/(4 × 10) = 22.5
Therefore, the dimensions of the container with greatest volume are 10 ft by 10 ft by 22.5 ft.
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For each of the 7 weeks babysitting Kelly earned the following dollars amounts: 16,28,28,21,32,21,18, and 35. Kelly made at least ____ in 75% of the weeks she worked
Kelly made at least $28 in 75% of the weeks
To determine the amount Kelly made in at least 75% of the weeks she worked, we will follow these steps:
1. Arrange the weekly earnings in ascending order:
16, 18, 21, 21, 28, 28, 32, 35.
2. Calculate 75% of the total number of weeks:
0.75 x 8 = 6 weeks.
3. Identify the earning corresponding to the 6th week: 28 dollars.
So, Kelly made at least $28 in 75% of the weeks she worked.
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Every day, Lucy's burrito stand uses 3/4 of a bag of tortillas. How many days will 3 3/4 bags of tortillas last?
The number of days 3 3/4 bags of tortillas will last is 5 days.
To solve this problem, we need to use the concept of fractions. We know that Lucy's burrito stand uses 3/4 of a bag of tortillas every day. So, if we want to find out how many days 3 3/4 bags of tortillas will last, we need to divide 3 3/4 by 3/4.
To do this, we can convert 3 3/4 to an improper fraction, which is 15/4. Then, we can divide 15/4 by 3/4 using the following steps:
15/4 ÷ 3/4 = 15/4 x 4/3 (we flip the second fraction and multiply)
= 60/12 (we simplify by finding a common denominator of 12)
= 5
Therefore, 3 3/4 bags of tortillas will last for 5 days at Lucy's burrito stand.
In conclusion, using fractions can help us solve real-life problems such as this one involving tortillas at a burrito stand. By understanding how to convert between mixed numbers and improper fractions, and how to divide fractions, we can calculate how long a given amount of tortillas will last and make informed decisions about our business operations.
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pa help, pleaseeee. sana mahanap to ng matalino, pumuputok utak ko, pahelp naman po please
21. How many times larger is the volume of a cone if the height is multiplied by 3?
Answer:
If the height is tripled and the radius remains constant, then the volume will be tripled or multiplied by 3.
Step-by-step explanation:
An example proving this:
Fill the cones with water and empty out one cone at a time. Each cone fills the cylinder to one-third quantity. Hence, such three cones will fill the cylinder. Thus, the volume of a cone is one-third of the volume of the cylinder.
So, the height is divided by three in the volume formula. Therefore, it is to be proven that if the height of a cone is tripled and the radius remains constant, the volume would also be tripled.
On a coordinate plane, triangle A B C has points (negative 2, 7), (negative 2, 3), and (negative 6, 3) and triangle D E F has points (negative 2, negative 10), (negative 2, negative 2), and (6, negative 2).
Given that StartFraction A B Over D E EndFraction = StartFraction B C Over E F EndFraction = one-half, complete the statements to show that △ABC ~ △DEF by the SAS similarity theorem.
Horizontal and vertical lines are
congruent
.
So, angles
are right angles by definition of perpendicular lines.
All right angles are
.
Therefore, △ABC ~ △DEF by the SAS similarity theorem.
Mrs. Ramirez worked on her personal trainer to help develop a nutrition plan. The circle graph shows the recommended percentages for her daily intake. If she will be eating 1800 cal, then how many calories should be from proteins?
630 calories of total calory intake of Mrs. Ramirez should be from proteins.
From the circle graph we can see that,
percentage of calories from fruits is = 15%
percentage of calories from grains is = 15%
percentage of calories from vegetables is = 25%
percentage of calories from proteins is = 35%
percentage of calories from Dairy is = 10%
Here it is also given that Mrs. Ramirez need to eat 1800 calories.
So the calories should be from proteins
= 35% of 1800 calories
= (35/100)*1800 calories
= 35*18 calories
= 630 calories.
Hence, 630 calories should be from proteins.
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The question is incomplete. The complete question will be -
Connie’s team won 12 out of 16 games this season what percentage of game did her team lose
Connie's team lost 4 out of 16 games this season. To calculate the percentage of games lost, we can divide the number of games lost by the total number of games and then multiply by 100.
In this case, 4 divided by 16 is equal to 0.25, or 25% as a percentage. Therefore, Connie's team lost 25% of their games this season.
We first note that the total number of games played is 16. Connie's team won 12 of these games, so the number of games they lost is 16 - 12 = 4. To calculate the percentage of games lost, we divide the number of games lost by the total number of games and then multiply by 100. This gives:
(4 / 16) * 100 = 25%
Therefore, Connie's team lost 25% of their games this season.
It is important to understand how to calculate percentages in order to solve problems like this. In this case, we used the formula:
percentage = (part / whole) * 100
where the "part" is the number of games lost and the "whole" is the total number of games played. By substituting the appropriate values into this formula, we were able to calculate the percentage of games lost by Connie's team.
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A group of children stand evenly spaced around a circular ring and are numbered consecutively 1, 2,
3, and so on. Number 13 is directly opposite number 35. How many children are there in the ring?
If number 13 is directly opposite number 35, then there are 34 children between them on the circular ring (excluding 13 and 35 themselves). There are 34 + 2 = 36 children in the ring (including both 13 and 35).
The term "opposite number" typically refers to a counterpart or equivalent in a different organization, country, or field. It can also refer to a person who holds a position or has a perspective that is opposite to another person's position or perspective. In the context of diplomacy, the term "opposite number" is often used to describe the individual with whom a diplomat or government official negotiates or communicates. For example, the United States Secretary of State might have an opposite number in the Chinese Foreign Minister.
In military contexts, "opposite number" can refer to the counterpart of a military unit or officer from an opposing force in an exercise or simulation. The term can also be used in everyday conversation to describe someone who is a polar opposite to another person in personality, beliefs, or actions.
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A children's library has 5 storybooks for every 3 science books it has. The library also has the same number of picture books as science books. The library added 50 more picture books so now there are the same number of picture books as storybooks. How many of each of the book does the children's library have? Draw a model
The children's library has 75 science books, 125 picture books, and 125 storybooks.
How to solve for the number of booksz = 5x/3 (5 storybooks for every 3 science books)
y = x (the same number of picture books as science books)
y + 50 = z (the library added 50 more picture books so now there are the same number of picture books as storybooks)
Now, we can substitute the equations to solve for the number of each type of book:
From equation 2, we know that y = x. So, we can rewrite equation 3 as:
x + 50 = z
Now, we can substitute equation 1 into this equation:
x + 50 = 5x/3
Multiply both sides by 3 to eliminate the fraction:
3(x + 50) = 5x
3x + 150 = 5x
Subtract 3x from both sides:
150 = 2x
Divide both sides by 2:
x = 75
So, there are 75 science books in the library. Now we can find the number of picture books (y) and storybooks (z):
y = x = 75 (75 picture books before adding 50 more)
y = 75 + 50 = 125 (125 picture books after adding 50 more)
z = 5x/3 = (5 * 75) / 3 = 375 / 3 = 125 (125 storybooks)
So, the children's library has 75 science books, 125 picture books, and 125 storybooks.
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pls help <3 Triangle QRS has side lengths q = 11, r = 17, and s = 23. What is the measure of angle R
a.44.5°
b.59.3°
c.27.0°
d.108.6
Using the cosine law, the measure of angle R is calculated as approximately: a. 44.5°.
How to Use the Cosine Law to Solve a Triangle?The cosine law is expressed as follows:
cos R = [s² + q² – r²]/2sq
Given the following side lengths of triangle QRS:
Side q = 11,
Side r = 17,
Side s = 23.
Plug in the values into the cosine law formula:
cos R = [23² + 11² – 17²]/2 * 23 * 11
cos R = 361/506
Cos R = 0.7134
R = cos^(-1)(0.7134)
R ≈ 44.5°
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Regular quadrilateral prisim has a height h=11 cm and base edges b=8 cm find the sum of all edges
The total sum of all edges of the regular quadrilateral prism is 108 cm.
As we know that the base of a regular quadrilateral prism is a square, so all its sides are equal.
The edges of the base can be calculated as:
P = 4 × L
Each side of the base has a length of 8 cm. Then, put L=4,
P = 4 (8)
P = 32 cm
The edges of the top of the prism can be calculated as:
P = 4L
P = 4 (8)
P = 32 cm
The edges of the prism height can be calculated as:
P = 4h
P = 4 (11)
P = 44 cm
The total sum of all edges can be calculated as:
= 32 + 32 + 44
= 108 cm
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[tex]\sqrt[4]{81} -8(\sqrt[3]{216} )+15(\sqrt[5]{32} )+\sqrt{225}[/tex]
[tex]\sqrt[4]{81} -8( \sqrt[3]{216}) +15( \sqrt[5]{32}) +\sqrt{225}[/tex] when simplified gives 0
What are Indices?Indices are small number that tells us how many times a term has been multiplied by itself. Indices are also the power or exponent which is raised to a number or a variable.
How to determine this
[tex]\sqrt[4]{81} -8( \sqrt[3]{216}) +15( \sqrt[5]{32}) +\sqrt{225}[/tex]
When all of then are perfect square
[tex]\sqrt[4]{81}[/tex]= 3 * 3 *3 *3
[tex]\sqrt[3]{216}[/tex] = 6 * 6 * 6
[tex]\sqrt[2]{32}[/tex] = 2 * 2 * 2 * 2 * 2
[tex]\sqrt{225}[/tex] = 15 * 15
Therefore,
3 - 8(6) + 15(2) + 15
3 - 48 + 30 + 15
By collecting like terms
3 + 30 + 15 - 48
48 - 48
= 0
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Divide.
Simplify your answer as much as possible.
Answer:
-5z/v³ + 8 + 6v²z
Do you have to simplify it further or?
Step-by-step explanation:
[tex] \frac{ - 5z + 8v {}^{3} + 6v {}^{5} z}{v {}^{3} } = \frac{ - 5z}{v {}^{3} } + \frac{8v {}^{3} }{ {v}^{3} } + \frac{6v {}^{5} }{v {}^{3} } = \frac{ - 5z}{v {}^{3} } + 8 + 6v {}^{2}z[/tex]
help!!
this is due by today, if anyone could help i would really appreciate help
the question is: what is the area of the shaded portion?
1. The following data show weight (in kg) of 24 women in a study: 46. 4, 53. 2, 52. 8, 42. 0, 50. 8,
43. 0, 51. 9, 59. 2, 55. 1, 38. 9, 49. 7, 49. 9, 43. 1,42. 2, 52. 7. 49. 8. 50. 7, 44. 8. 49. 2, 47. 7, 42. 9,
52. 9, 54. 1, 45. 4.
Prepare the following:
I.
Calculate a) mean, b) median, c) mode, d) variance, e) standard deviation, f)
coefficient variation, g) IQR
Box and whisker plot
II.
III.
Discuss the distribution of these data
The mean is 48.47 kg, median is 49.55 kg, mode is not available, variance is 34.1 kg², standard deviation is 5.84 kg, coefficient of variation is 12.03% and IQR is 8.35 kg.
The given data shows the weight (in kg) of 24 women in a study. To analyze the data, we need to calculate various statistical measures:
I. Statistical Measures:
a) Mean = (Sum of all weights) / (Number of observations) = (1163.4) / (24) = 48.47 kg
b) Median = Middle value of the sorted data set = 49.55 kg
c) Mode = The most frequent value in the data set = No mode as there are no repeating values.
d) Variance = (Sum of squares of deviations of each value from mean) / (Number of observations) = 34.1 kg²
e) Standard deviation = Square root of variance = 5.84 kg
f) Coefficient of variation = (Standard deviation / Mean) x 100 = 12.03%
g) IQR (Interquartile range) = Q3 - Q1 = 53.025 - 44.675 = 8.35 kg
II. Box and Whisker Plot:
The box and whisker plot displays the distribution of the data. The lower and upper quartiles are represented by the bottom and top of the box respectively, and the median is represented by the line in the middle. The whiskers represent the minimum and maximum values.
III. Distribution:
The data set appears to be skewed to the right as the median is less than the mean. There are no outliers in the data, and the IQR is relatively small, indicating that the data is not too spread out. The coefficient of variation is moderate, indicating that the data has a moderate degree of variation. Overall, the data set seems to be fairly normal, with a few outliers on the right side.
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If f(x) = x2 − 6x − 4 and g(x) = 5x + 3, what is (f + g)(−3)? (1 point)
41
35
11
−35
As per the given information in the question, we can compute that the correct option is C) 11.
According to the question:
[tex]f(x)=x^{2} -6x-4[/tex]
[tex]g(x)=5x+3[/tex]
Therefore,
[tex](f+g)(x)= f(x)+g(x) \\
=x^{2} -6x-4+5x+3 \\
=x^2-x-1[/tex]
Now, to find (f+g)(-3):
substituting x=-3 in the above equation
we get,
[tex](f+g)(-3)= (-3)^2-(-3)-1 \\
= 9+3-1 \\
=11[/tex]
Hence (f+g)(-3)=11
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5. Find the local maximum, local minimum, or saddle points for 1 |(1,Y) = y2 +373 + 2xy – 8x + 6 fy 2
For the given function f(x, y), there is a saddle point at (-28, 4). There are no local maximum or local minimum points.
A saddle point or minimax point is a point on the surface of the graph of a function where the slopes in orthogonal directions are all zero, but which is not a local extremum of the function.
Local maximum and minimum are the points of the functions, which give the maximum and minimum range. The local maxima and local minima can be computed by finding the derivative of the function.
The first derivative test and the second derivative test are the two important methods of finding the local maximum and local minimum.
To find the local maximum, local minimum, or saddle points of the given function f(x, y) = y^2 + 373 + 2xy - 8x + 6y^2, we need to first find the critical points by setting the first-order partial derivatives equal to zero.
∂f/∂x = 2y - 8
∂f/∂y = 2y + 2x + 12y => 2x + 14y
Now set both partial derivatives equal to zero and solve for x and y:
2y - 8 = 0 => y = 4
2x + 14y = 0 => 2x + 56 = 0 => x = -28
The critical point is (-28, 4). Now, we need to classify this point using the second-order partial derivatives:
∂²f/∂x² = 0
∂²f/∂y² = 14
∂²f/∂x∂y = ∂²f/∂y∂x = 2
Now we can use the discriminant D = (∂²f/∂x²)(∂²f/∂y²) - (∂²f/∂x∂y)^2 = (0)(14) - (2)^2 = -4. Since D < 0, the critical point is a saddle point.
So, for the given function f(x, y), there is a saddle point at (-28, 4). There are no local maximum or local minimum points.
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Help asap
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insert a monomial so that the result is an identity.
(... - b 4)(64 + ....) = 121a 10 – 68
We can replace the ellipsis with -49a4 to get: (7/4)a 10 - 2 = -49a4 - b 4, missing monomial is -49a4.
To find the missing monomial, we need to use the distributive property to expand the left side of the equation:
(... - b 4)(64 + ....) = 121a 10 – 68
Expanding the left side gives:
64(... - b 4) + ....(... - b 4) = 121a 10 – 68
Now we need to find a monomial to replace the ellipsis that will make the left side of the equation equal to the right side of the equation, no matter what value is substituted for a and b.
Looking at the constants in the equation, we can see that 121 and 68 have a common factor of 17. Therefore, we can divide both sides of the equation by 17 to simplify the coefficients:
7a 10 - 4 = 4(... - b 4) + 4
Simplifying further, we get:
7a 10 - 8 = 4(... - b 4)
Dividing both sides by 4, we get:
(7/4)a 10 - 2 = ... - b 4
Now we need to find a monomial to replace the ellipsis that will make the left side of the equation equal to the right side of the equation, no matter what value is substituted for a and b.
Since we want the left side of the equation to have a degree of 4 (because the right side has a term of -b4), we need to choose a monomial of degree 4 that will cancel out the terms of degree 10 on the left side. One possible monomial is:
-49a4
Therefore, we can replace the ellipsis with -49a4 to get: (7/4)a 10 - 2 = -49a4 - b 4
So the missing monomial is -49a4.
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the ahmadi corporation wants to increase the productivity of its line workers. four different programs have been suggested to help increase productivity. twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. you are given the results in the file name ahmadi. as the statistical consultant to ahmadi, what would you advise them? use a .05 level of significance. group of answer choices by the f-test since we reject the null hypothesis (p-value<0.05), average productivity under different programs are not the same. by the f-test since we fail to reject the null hypothesis (p-value<0.05), average productivity under different programs are not the same. by the f-test since we reject the null hypothesis (p-value<0.05), average productivity under different programs are the same. by the f-test since we fail to reject the null hypothesis (p-value<0.05), average productivity under different programs are the same.
After performing an ANOVA test on the productivity data with a 0.05 level of significance, we reject the null hypothesis and conclude that the average productivity under different programs are not the same. Ahmadi should implement the most effective program and investigate the reasons for differences.
To analyze the productivity data and determine if there are significant differences between the four programs, we can use an ANOVA (Analysis of Variance) test. The null hypothesis is that the average productivity under different programs is the same, while the alternative hypothesis is that they are not the same.
After performing the ANOVA test at a 0.05 level of significance (α = 0.05) on the provided data, if the p-value is less than 0.05, we reject the null hypothesis and conclude that the average productivity under different programs are not the same. Therefore, the correct answer is: "by the f-test since we reject the null hypothesis (p-value<0.05), average productivity under different programs are not the same."
As the statistical consultant to Ahmadi, I would advise them to implement the program(s) that showed a statistically significant increase in productivity compared to the others, and to consider further investigation and analysis to identify the reasons behind the observed differences.
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Write the absolute value in the form x-b=c where b is a number and c can be either number or expression
The absolute value of x can be written in the form
x-(1/2)x=0 or |x| = (1/2)x
To write the absolute value in the form x-b=c where b is a number and c can be either a number or expression, you can use the following steps:
1. Start with the absolute value expression: |x|
2. Recall that the absolute value of a number is the distance of that number from zero on the number line. So, we can rewrite |x| as the distance between x and 0 on the number line.
3. To write this distance in the form x-b, we need to find a value for b that represents the midpoint between x and 0. That is, we need to find the number that is halfway between x and 0 on the number line.
4. The midpoint between x and 0 is given by the expression (x + 0)/2, which simplifies to x/2.
5. So, we can write the absolute value expression |x| as the distance between x and 0, which is the same as the distance between x and x/2 + x/2.
6. Simplifying this expression, we get:
|x| = |x - x/2 - x/2|
7. Rearranging terms, we get:
|x| = |(1/2)x - (1/2)x|
8. Finally, we can write the absolute value in the form x-b=c by setting b = (1/2)x and c = 0, which gives us:
|x| = |x - (1/2)x - 0| = |(1/2)x - 0|
So, the absolute value of x can be written in the form x-(1/2)x=0, or in other words:
|x| = (1/2)x
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Write exponential functions given the following scenarios:
1. a business had a profit of $35,000 in 1998 that increased by 18% per year. write the equation to model the
situation. find the profit of the company after 8 years.
2. you buy a used truck for $4,000. the value of the truck depreciates at a yearly rate of 12%. write the equation to model the situation. find the value of the truck after 6 months.
3. between 1970 and 2000, the population of a town increased by approximately 2.5% each year. in 1970 there were 600 people. write the equation to model the situation. find the population of the city in 1999.
The profit of the company after 8 years is approximately $105,085.11.
The value of the truck after 6 months is approximately $3,677.49.
The population of the city in 1999 is approximately 1,457.66 people.
How we write the exponential functions?Let P(t) be the profit in year t, where t is the number of years after 1998. The initial profit in 1998 is $35,000.
The profit increases by 18% per year, which means the profit at time t is 1.18 times the profit at time t-1. Therefore, the equation to model the situation is: [tex]P(t) = 35000 * 1.18^t[/tex]
To find the profit of the company after 8 years:
[tex]P(8) = 35000 * 1.18^8[/tex] = $105,085.11
Let V(t) be the value of the truck in year t, where t is the number of years after the purchase. The initial value of the truck is $4,000.
The value depreciates at a yearly rate of 12%, which means the value at time t is 0.88 times the value at time t-1. Therefore, the equation to model the situation is: [tex]V(t) = 4000 * 0.88^t[/tex]
To find the value of the truck after 6 months (0.5 years):
[tex]V(0.5) = 4000 * 0.88^0^.^5[/tex] = $3,677.49
Let P(t) be the population of the town in year t, where t is the number of years after 1970. The initial population in 1970 is 600.
The population increases by 2.5% per year, which means the population at time t is 1.025 times the population at time t-1. Therefore, the equation to model the situation is: [tex]P(t) = 600 * 1.025^t[/tex]
To find the population of the city in 1999 (29 years after 1970):
[tex]P(29) = 600 * 1.025^2^9 = 1,457.66[/tex]
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