(i) R is not reflexive, symmetric, vacuously antisymmetric, and not transitive.
(ii) It is important that S has at least two different elements because if S had only one element, then the power set P(S) would contain only two sets: the empty set and the set S itself.
(iii) If S was empty, there would be no elements in S, and hence the power set P(S) would only contain the empty set. The answers regarding reflexivity, symmetry, antisymmetry, and transitivity would all change, and the relation R would not possess any of these properties. If S had only one element, the power set P(S) would contain two sets: the empty set and the singleton set containing the one element of S. The relation R would be reflexive, symmetric, antisymmetric, and transitive, as it satisfies all these properties by definition.
(i)Let's analyze the properties of relation R on P(S):
Reflexive: A relation R is reflexive if for every element x in the set S, (x, x) belongs to R. In this case, since the intersection of any set with itself is never empty, the relation R is not reflexive.
Symmetric: A relation R is symmetric if for every pair (x, y) in R, (y, x) also belongs to R. In this case, since the intersection of two sets is commutative, if (X, Y) belongs to R, then (Y, X) also belongs to R. Thus, the relation R is symmetric.
Antisymmetric: A relation R is antisymmetric if for every distinct pair (x, y) in R, (y, x) does not belong to R. Since the relation R is defined by the condition X∩Y = φ, there are no distinct pairs (X, Y) that satisfy the condition. Therefore, the relation R is vacuously antisymmetric.
Transitive: A relation R is transitive if for every three sets X, Y, and Z such that (X, Y) belongs to R and (Y, Z) belongs to R, then (X, Z) also belongs to R. In this case, if X∩Y = φ and Y∩Z = φ, it does not imply that X∩Z = φ. Hence, the relation R is not transitive.
(ii) In this scenario, the relation R would not have any pairs (X, Y) where X and Y are non-empty subsets of S, because the intersection of any two non-empty subsets would never be empty. Thus, the relation R would be trivial and uninteresting.
(iii) In this case, since there are no non-empty subsets in P(S), the relation R would not have any pairs (X, Y) where X and Y are non-empty subsets of S.
In this case, the relation R would have only one possible pair (X, Y) with X and Y being the empty set, and their intersection would indeed be empty.
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Rotate point (-3, 2) about the origin 180 degrees clockwise. Where will the new point be?
Answer: the answer is (3,-2)
Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)
therefore
(-3,2) becomes (3,-2)
I'm pretty sure
2.
Harry pours 650 cubic centimeters of water into cylindrical glass with a diameter of 10
centimeters. He then pours the water from the first glass to another cylindrical glass with a
diameter of 8 cm. How much higher did the water reach in the second glass than in the first
glass? Round to the nearest tenth of a centimeter.
agures of the
Answer:
113.1 is the answer. I used the arbitory height of 4 so the volume of both are now 314.16 and 201.06
314.16-201.06=113.1
How would you describe the difference between the graphs of f (x) = 3x²
and g(x) = -2² ?
OA. g(x) is a reflection of f(x) over the line y = x.
B. g(x) is a reflection of f(x) over the line y = -1.
C. g(x) is a reflection of f(x) over the x-axis.
D. g(x) is a reflection of f(x) over the y-axis.
Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).
The given functions are f(x) = 3x² and g(x) = -2².
To understand the difference between their graphs, let's examine the characteristics of each function individually:
Function f(x) = 3x²:
The coefficient of x² is positive (3), indicating an upward-opening parabola.
The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.
The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.
Function g(x) = -2²:
The coefficient of x² is negative (-2), indicating a downward-opening parabola.
The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.
The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.
Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.
Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.
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Darla, Ellie, and Fran ate a whole container of ice cream. Darla ate half as much as Ellie ate, and Fran ate 5 times as much as Darla ate. If the container of ice cream cost $4.00, how much, in dollars, should each person pay?
Determine the perimeter of a soccer field with a length of 97 metres and a width of 69 metres
Answer: Therefore, the perimeter of the soccer field is 332 meters.
Step-by-step explanation:
To determine the perimeter of a soccer field with a length of 97 meters and a width of 69 meters, we can use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2 * (length + width)
Plugging in the values, we have:
Perimeter = 2 * (97 + 69)
Perimeter = 2 * 166
Perimeter = 332 meters
Help I’m lost somebody please help me
Answer:
l
Step-by-step explanation:
GEOMETRY 30POINTS
find x to the nearest degree!
The calculated value of x to the nearest degree is 56
How to calculate x to the nearest degreeFrom the question, we have the following parameters that can be used in our computation:
The triangle
The value of x can be caluclated using the following cosine rule
So, we have
cos(x) = 5/9
Evaluate the quotient
cos(x) = 0.5556
Take the arc cos of both sides
x = 56
Hence, the value of x to the nearest degree is 56
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Hungry Harry is a giant ogre with an even bigger appetite. After Harry wakes up from hibernation, his daily hunger � ( � ) H(t)H, left parenthesis, t, right parenthesis (in kg kgstart text, k, g, end text of pigs) as a function of time � tt (in hours) can be modeled by a sinusoidal expression of the form � ⋅ cos ( � ⋅ � ) + � a⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d. When Harry wakes up at � = 0 t=0t, equals, 0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs. Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs. Find � ( � ) H(t)H, left parenthesis, t, right parenthesis.
The equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5
Given:Hunger of Harry as a function of time,H(t)H(t) can be modeled by a sinusoidal expression of the form,a⋅cos(b⋅t)+da⋅cos(b⋅t)+d, where Harry wakes up at t=0t=0t=0, his hunger is at a maximum, and he desires 30 kg 30 kg30, start text, space, k, g, end text of pigs.
Within 2 22 hours, his hunger subsides to its minimum, when he only desires 15 kg 15 kg15, start text, space, k, g, end text of pigs.
Therefore, the equation of the form for H(t)H(t) will be,H(t) = A.cos(B.t) + C where, A is the amplitude B is the frequency (number of cycles per unit time)C is the vertical shift (or phase shift)
Thus, the maximum and minimum hunger of Harry can be represented as,When t=0t=0t=0, Harry's hunger is at maximum, i.e., H(0)=30kgH(0)=30kg30, start text, space, k, g, end text.
When t=2t=2t=2, Harry's hunger is at the minimum, i.e., H(2)=15kgH(2)=15kg15, start text, space, k, g, end text.
According to the given formula,
H(t) = a.cos(b.t) + d ------(1)Where a is the amplitude, b is the angular frequency, d is the vertical shift.To find the value of a, subtract the minimum value from the maximum value.a = (Hmax - Hmin)/2= (30 - 15)/2= 15/2 = 7.5To find the value of b, we will use the formula,b = 2π/period = 2π/(time for one cycle)The time for one cycle is (2 - 0) = 2 hours.
As Harry's hunger cycle is a sinusoidal wave, it is periodic over a cycle of 2 hours.
Therefore, the angular frequency,b = 2π/2= π
Therefore, the equation for Harry's hunger in terms of time can be written as,H(t) = 7.5.cos(π.t) + 22.5
Answer: H(t) = 7.5.cos(π.t) + 22.5.
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45% of the Walton High School student body are male. 90% of Walton females love math, while only 60% of the males love math. What percentage of the student body loves math?
Approximately 76.5% of the student body at Walton High School loves math.
To determine the percentage of the student body that loves math, we need to consider the proportions of males and females in the Walton High School student body and their respective percentages of loving math.
Given that 45% of the student body are males, we can deduce that 55% are females (since the total percentage must add up to 100%). Now let's calculate the percentage of the student body that loves math:
For the females:
55% of the student body are females.
90% of the females love math.
So, the percentage of females who love math is 55% * 90% = 49.5% of the student body.
For the males:
45% of the student body are males.
60% of the males love math.
So, the percentage of males who love math is 45% * 60% = 27% of the student body.
To find the total percentage of the student body that loves math, we add the percentages of females who love math and males who love math:
49.5% + 27% = 76.5%
As a result, 76.5% of Walton High School's student body enjoys maths.
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You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally installed. Estimate the cost of having a 25 by 26 ft brick patio installed.
Answer:
$4929
Step-by-step explanation:
I assume the cost is proportional to the area.
15 ft × 20 ft = 300 ft²
25 ft × 26 ft = 650 ft²
650/300 = x/$2275
300x = 650 × $2275
x = $4929
Answer: $4929
please help!!!!!!!!!!!!!!!!!!!!!!
The systematic sample would be A. The city manager takes a list of the residents and selects every 6th resident until 54 residents are selected.
The random sample would be C. The botanist assigns each plant a different number. Using a random number table, he draws 80 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 80 plants is equally likely to be drawn using the random number table.
The cluster sample is C. The host forms groups of 13 passengers based on the passengers' ages. Then, he randomly chooses 6 groups and selects all of the passengers in these groups.
What are systematic, random and cluster samples ?A systematic sample involves selecting items from a larger population at uniform intervals. A random sample involves selecting items such that every individual item has an equal chance of being chosen.
A cluster sample involves dividing the population into distinct groups (clusters), then selecting entire clusters for inclusion in the sample.
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 Ex is tangent to circle O at point L, and IF is a secant line. If m_FLX = 104°, find
mLKF.
Answer:
arc LKF = 208°
Step-by-step explanation:
the angle FLX between the tangent and the secant is half the measure of the intercepted arc LKF , then intercepted arc is twice angle FLX , so
arc LKF = 2 × 104° = 208°
I need help with a question
The function for which f(x) is equal to f⁻¹(x) is: C. [tex]f(x) = \frac{x+1}{x-1}[/tex]
What is an inverse function?In this exercise, you are required to determine the inverse of the function f(x) with an equivalent inverse function f⁻¹(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;
[tex]f(x) = y = \frac{x+6}{x-6} \\\\x=\frac{y+6}{y-6}[/tex]
x(y - 6) = y + 6
y = xy - 6x - 6
f⁻¹(x) = (-6x - 6)/(x - 1) ⇒ Not equal.
Option B.
[tex]f(x) = y = \frac{x+2}{x-2} \\\\x=\frac{y+2}{y-2}[/tex]
x(y - 2) = y + 2
y = xy - 2x - 2
f⁻¹(x) = (-2x - 2)/(x - 1) ⇒ Not equal.
Option C.
[tex]f(x) = y = \frac{x+1}{x-1} \\\\x=\frac{y+1}{y-1}[/tex]
x(y - 1) = y + 1
y - xy = x + 1
f⁻¹(x) = (x + 1)/(x - 1) ⇒ equal.
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Triangle ABC has the following coordinates: A=(5,-5), B=(3,-3), C=(5,-3) What are the coordinates of triangle A'B'C' if it is created by dilating triangle ABC with the origin (0,0) as the center of dilation and with a scale factor of 3?
Answer:A' = (15, -15), B' = (9, -9), and C' = (15, -9)
Step-by-step explanation:
To dilate triangle ABC with a center of dilation at the origin (0,0) and a scale factor of 3, you need to multiply the coordinates of each vertex by the scale factor.
Let's calculate the coordinates of triangle A'B'C':
For point A:
x-coordinate of A' = scale factor * x-coordinate of A = 3 * 5 = 15
y-coordinate of A' = scale factor * y-coordinate of A = 3 * (-5) = -15
Therefore, A' = (15, -15)
For point B:
x-coordinate of B' = scale factor * x-coordinate of B = 3 * 3 = 9
y-coordinate of B' = scale factor * y-coordinate of B = 3 * (-3) = -9
Therefore, B' = (9, -9)
For point C:
x-coordinate of C' = scale factor * x-coordinate of C = 3 * 5 = 15
y-coordinate of C' = scale factor * y-coordinate of C = 3 * (-3) = -9
Therefore, C' = (15, -9)
Hence, the correct coordinates of triangle A'B'C' are A' = (15, -15), B' = (9, -9), and C' = (15, -9).
What else would need to be congruent to show that ABC=AXYZ by SAS?
A
B
OA. ZB=LY
B. BC = YZ
OC. C= LZ
OD. AC = XZ
с
X
Z
Given:
AB XY
BC=YZ
What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D
How to determine the statementGiven that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.
We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..
ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.
In ΔABC, side between ∠A and ∠C is AC,
in ΔXYZ, side between ∠X and ∠Z is XZ.
Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.
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GEOMETRY 100POINTSSS
Find x
Answer:
5.9
Step-by-step explanation:
sin Θ = opp/hyp
sin 36° = x/10
x = 10 × sin 36°
x = 5.88
Answer: 5.9
QUESTION IN PICTURE
Please explain your answer in steps, thank you.
We can complete the blanks with the following ratios:
(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags
Since we do not need a flag at the starting line, then 32 flags will be required in total.
How to obtain the number of flagsTo solve the problem, we would first convert 400 yds to feet and miles.
To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.
To convert to miles, we would have 0.227 miles.
Now, we divide the entire race distance by the number of miles divisions.
This gives us:
7.5 mi /0.227 mi
= 33 flags
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The pyramid and prism above have the same triangular base and height. The volume of the pyramid is 18 cubic inches. What is the volume of the prism?
A. 36 cubic inches
B. 72 cubic inches
C. 6 cubic inches
D. 54 cubic inches
Solve the missing element . use 3.14 for pi and Area = pi r2 ; C= pi D
We can solve for the missing elements as follows:
1. Radius - 10 inches
Diameter - 20
Circumference - 62.8
Area - 314
2. Radius - 6ft
Diameter - 12
Circumference - 37.68
Area - 113.04
3. Radius - 18
Diameter - 36 yards
Circumference - 113.04
Area - 1017.36
4. Radius 15
Diameter - 30 cm
Circumference 94.2
Area - 706.5
5. Radius - 5 mm
Diameter 10
Circumference 31.4
Area -78.5
6. Radius 20
Diameter - 40 inches
Circumference 125.6
Area -1256
How to solve for the valuesTo solve for the given values, we will use the formulas for area, circumference. Also, we can obtain the radius by dividing the diameter by 2 and the diameter is 2r. So we will solve for the values this way:
1. radius = 10 inches
diameter = 20
circumference = 2pie*r 2 *3.14*10 = 62.8
Area = 314
2. radius = 6ft
diameter = 12
circumference = 37.68
Area = 113.04
3. radius = 18
diameter = 36 yards
circumference = 113.04
Area = 1017.36
4. radius = 15
diameter = 30 cm
circumference = 94.2
Area = 706.5
5. radius = 5 mm
diameter = 10
circumference = 31.4
Area = 78.5
6. radius = 20 inches
diameter = 40 inches
circumference = 125.6
area = 1256
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which of the following are like radicals? Check all
of the boxes that apply.
3x√√xy
-12x√√xy
-2x√√xj
x-√4x2²
-x√x²y
2√xy
Answer:
the first 2
Step-by-step explanation:
let me know if it is wrong
Circumference of circle inscribed or circumscribed polygon
Hint: you will need to find the diameter of the circle, use Pythagorean Theorem)
ind then I out of the 3 problems.
Find the exact circumference of each circle by using the given inscribed or circumscribed polygon.
8 cm
15 cm
The exact circumferences of the inscribed and circumscribed circles for the given polygons are 8π cm and 15π cm, respectively.
To find the exact circumference of a circle inscribed or circumscribed by a polygon, we can use the Pythagorean theorem to determine the diameter of the circle.
In the case of an inscribed polygon, the diameter of the circle is equal to the diagonal of the polygon. Let's consider the polygon with a diagonal of 8 cm. If we draw a line connecting two non-adjacent vertices of the polygon, we get a diagonal that represents the diameter of the inscribed circle.
Using the Pythagorean theorem, we can find the length of this diagonal. Let's assume the sides of the polygon are a and b. Then the diagonal can be found using the equation: diagonal^2 = a^2 + b^2. Substituting the given values, we have 8^2 = a^2 + b^2. Solving this equation, we find that a^2 + b^2 = 64.
For the circumscribed polygon with a diagonal of 15 cm, the diameter of the circle is equal to the longest side of the polygon. Let's assume the longest side of the polygon is c. Therefore, the diameter of the circumscribed circle is 15 cm.
Once we have determined the diameter of the circle, we can calculate its circumference using the formula C = πd, where C is the circumference and d is the diameter.
For the inscribed circle, the circumference would be C = π(8) = 8π cm.
For the circumscribed circle, the circumference would be C = π(15) = 15π cm.
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Given ABCD, what is the measure of
145
A. 90°
B. 35°
C. 10°
D. 145°
E. 55°
F. 235°
Answer: D. 145°
Step-by-step explanation:
Since it is a parallelogram given by the symbol, then angle B is equal to angle D which is 145°.
I need help!! f(x)=-2(x-3)
Answer:
Step-by-step explanation:
Certainly! I'm here to assist you.
The given function is f(x) = -2(x - 3).
To simplify this expression, we can distribute the -2 to the terms inside the parentheses:
f(x) = -2 * x - (-2) * 3
Simplifying further:
f(x) = -2x + 6
Therefore, the simplified form of the function f(x) = -2(x - 3) is f(x) = -2x + 6.
Assume that each circle shown below represents one unit.express the shaded amount as a single fraction and as a mixed number
One fraction :
Mixed number:
The shape is represented as below
As one fraction = 9/4As a mixed number = 2 1/4How to represent the figure as a fractionThe figure is of three shapes, the firs two are whole numbers then the last is a fraction.
Adding them results to
shape 1 + shape 2 + shape 3
1 + 1 + 1/4
As one fraction
= 9/4
as a mixed number
= 2 1/4
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What is the average rate of change in f(x) on the interval [5,9]?
A)-1.5
B)6/4
C)4
D)-6
Answer:
A) -1.5
Step-by-step explanation:
We can find the average rate of change of a function over an interval using the formula:
(f(x2) - f(x1)) / (x2 - x1), where
(x2, f(x2)) is the rightmost part of the interval. In this problem, 9 is our x2 and f(x2) is 3 since 3 is the y-coordinate when you plug in 9 for f(x))(x1, f(x1)) is the leftmost part of the interval of the interval.In this case, 5 is our x1 and f(x1) is 9 since 9 is the y-coordinate when you plug in 5 for f(x).Thus, we can plug in (9, 3) for (x2, f(x2)) and (5, 9) for (x1, f(x1)) to find the average rate of change in f(x) on the interval [5,9].
(3 - 9) / (9 - 5)
(-6) / (4)
-3/2
is -3/2.
If we convert -3/2 into a normal number, we get -1.5
Thus, the average rate of change in f(x) on the interval [5,9] is -1.5
Answer:
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]
In this case, we need to find the average rate of change on the interval [5, 9], so a = 5 and b = 9.
From inspection of the given graph:
f(5) = 9f(9) = 3Substitute the values into the formula:
[tex]\textsf{Average rate of change}=\dfrac{f(9)-f(5)}{9-5}=\dfrac{3-9}{9-5}=\dfrac{-6}{4}=-1.5[/tex]
Therefore, the average rate of change of f(x) over the interval [5, 9] is -1.5.
.
At a meat packing plant in Green Bay, the owners want to begin a continuing education program so their 186 employees can get a college education online if they desire. The following table represents an incomplete picture of the results. Use the following two-way frequency table for the questions below:
Men Women Total
No College Credit 28 A B
Some College C D 81
College Graduate 15 22 E
Total 79 F 186
a. Fill in the missing data in the table for values A through F. Explain the strategies you used to get each answer.
b. Describe a few pieces of data in terms of joint relative frequency. Explain why these data are both joint and relative.
c. Explain a few ways we can summarize pieces of this table using conditional relative and marginal relative frequency.
d. Are the data independent or dependent? Why?
Answer:
a. To fill in the missing data in the table, we can use the information given in the table along with the fact that the total number of employees is 186.
For value A: Since the total number of employees with no college credit is 28, and the total number of men is 79, we can subtract the number of men with some college (C) and college graduates (15) from the total number of men to find the missing value A. So A = 79 - C - 15.
For value B: Since the total number of women is 186, we can subtract the number of women with some college (D) and college graduates (22) from the total number of women to find the missing value B. So B = 186 - D - 22.
For value C: Since the total number of employees with some college is 81, and we have already determined the values A and D, we can subtract A and D from the total number of employees with some college to find the missing value C. So C = 81 - A - D.
For value D: Similarly, we can subtract B and E from the total number of women to find the missing value D. So D = 186 - B - E.
For value E: Since the total number of college graduates is 37 (15 men + 22 women), we can subtract the number of college graduates among men (15) from the total to find the missing value E. So E = 37 - 15.
For value F: Since the total number of employees is 186, we can subtract the total number of men (79) from the total to find the missing value F. So F = 186 - 79.
b. Joint relative frequency refers to the proportion of individuals that fall into a particular combination of categories. For example, the joint relative frequency of men with no college credit is the number of men with no college credit divided by the total number of employees (28/186). These data are joint and relative because they represent the proportion of individuals in a specific category combination relative to the total population.
c. To summarize the data using conditional relative frequency, we can calculate the proportion of individuals in each category given a specific condition. For example, we can calculate the conditional relative frequency of women who are college graduates by dividing the number of women who are college graduates (22) by the total number of women (186). Similarly, we can calculate the conditional relative frequency of men with some college by dividing the number of men with some college (C) by the total number of men (79).
To summarize the data using marginal relative frequency, we can calculate the proportion of individuals in each category by dividing the number of individuals in that category by the total number of individuals. For example, we can calculate the marginal relative frequency of men by dividing the total number of men (79) by the total number of employees (186). Similarly, we can calculate the marginal relative frequency of college graduates by dividing the total number of college graduates (37) by the total number of employees (186).
d. The data in the table can be analyzed to determine if there is an association or relationship between the variables. If the values in the table change depending on the categories of the other variable, then the variables are dependent. In this case, the data is dependent because the number of individuals with certain educational levels (no college credit, some college, college graduate) varies based on their gender. For example, there are different proportions of men and women in each educational category, indicating a relationship between gender and education level.
Step-by-step explanation:
The missing values in the two-way frequency table are filled based on the given values and the composition of the table. The table represents joint relative frequency, which is the proportion of specific groups in the total population. We can summarize the data using marginal and conditional relative frequencies, and the data are considered dependent because an employee's education level depends on their gender.
Explanation:To fill in the missing values of the two-way frequency table, we need to use the given numbers and the rules of the two-way frequency table. Here are the strategies used for filling in the values for A through F:
A = Total number of women - Total number of women with some college and college graduate education (in this case A = F - D - 22, because we know the number of total women F and the number of women college graduates 22, but D is still unknown).B = Total number of employees - Total number of men - Total number of women (B = 186 - 79 - F).C = Total number of some college - Number of women with some college (C = 81 - D)D = Total number of some college - Number of men with some college (D = 81 - C).E = Total number of employees - Total of men and women with and without college (E = 186 - B - 81 - 37F = Total number of employees - Total number of men (F = 186 - 79).The table will also represent joint relative frequency because each cell represents the joint occurrence of two categories (gender and education level). For example, the number of male employees with no college credit (28) divided by the total number of employees (186) is a joint relative frequency.
We may summarize the table data using conditional relative frequency and marginal relative frequency. The marginal relative frequency is the total of each row or column divided by the grand total. The conditional relative frequency would be, for example, the proportion of women among those with no college credit.
The data are dependent because the education level depends on whether the employee is a man or a woman.
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Please help me with this question
An estimate for the mean is 47.6 kg.
How to calculate the mean for the set of data?In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:
Mean = [F(x)]/n
Cumulative frequency = 10 + 7 + 2 + 8 + 3
Cumulative frequency = 30
For the total number of data based on the frequency, we have;
Total weight, F(x) = 10(40) + 7(52.5) + 2(65) + 8(77.5) + 3(90)
Total weight, F(x) = 40 + 367.5 + 130 + 620 + 270
Total weight, F(x) = 1427.5
Now, we can calculate the mean weight as follows;
Mean = 1427.5/30
Mean = 47.6 kg.
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Which of the following are necessary when proving that the opposite sides of
a parallelogram are congruent? Check all that apply.
A. Opposite sides are parallel.
B. Corresponding parts of congruent triangles are congruent.
C. Opposite sides are perpendicular.
D. Corresponding parts of similar triangles are similar.
SUBMIT
Answer:
It's A and B: Opposite sides are parallel and Corresponding parts of congruent triangles are congruent.
Step-by-step explanation:
Determine the equation of the ellipse with foci... 100points
The equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is[tex](x^2/289) + (y^2/225) = 1.[/tex]
To determine the equation of an ellipse given its foci and the length of its major axis, we need to use the standard form equation for an ellipse. The standard form equation for an ellipse centered at the origin is:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.
In this case, we know that the distance between the foci is equal to 2a, which means a = 34/2 = 17. The foci of the ellipse are given as (7, 17) and (7, -13). The foci lie on the major axis of the ellipse, and since their y-coordinates differ by 30 (17 - (-13) = 30), the length of the major axis is equal to 2b, which means b = 30/2 = 15.
Now we have the values of a and b, so we can substitute them into the standard form equation:
[tex](x^2/17^2) + (y^2/15^2) = 1[/tex]
Simplifying further, we have:
[tex](x^2/289) + (y^2/225) = 1[/tex]
Therefore, the equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is:
[tex](x^2/289) + (y^2/225) = 1.[/tex]
This equation represents an ellipse centered at the point (0, 0) with a semi-major axis of length 17 and a semi-minor axis of length 15.
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Answer:
The equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is
To determine the equation of an ellipse given its foci and the length of its major axis, we need to use the standard form equation for an ellipse. The standard form equation for an ellipse centered at the origin is:
where 'a' represents the semi-major axis and 'b' represents the semi-minor axis.
In this case, we know that the distance between the foci is equal to 2a, which means a = 34/2 = 17. The foci of the ellipse are given as (7, 17) and (7, -13). The foci lie on the major axis of the ellipse, and since their y-coordinates differ by 30 (17 - (-13) = 30), the length of the major axis is equal to 2b, which means b = 30/2 = 15.
Now we have the values of a and b, so we can substitute them into the standard form equation:
Simplifying further, we have:
Therefore, the equation of the ellipse with foci (7, 17) and (7, -13), and a major axis of length 34 is:
This equation represents an ellipse centered at the point (0, 0) with a semi-major axis of length 17 and a semi-minor axis of length 15.
What is -2.93(b + 12) = -11.72
What is b
(Solve two-step linear equations)