Determine the lateral area and the surface area of each triangular prism by determining the area of the shape’s net.
Answers
The lateral area and the surface area of the right prism are 540 square yards and 1152 square yards, respectively.
How to determine the lateral area and the surface area of a triangular prism
Herein we find the case of a right prism with a triangular base, whose lateral area (A) and surface area (A'), both in square yards, must be determined.
The lateral area is the sum of the areas of three rectangular faces and the surface area is the sum of the lateral area and the area of the two triangles. Area formulas for rectangles and triangles are shown below:
Rectangle
A = w · l
Triangle
A = 0.5 · w · l
Where:
w - Width, in yardsl - Length, in yardsNow we determine the lateral area and the surface area of the prism:
Lateral area
A = (37 yd) · (5 yd) + (20 yd) · (5 yd) + (51 yd) · (5 yd)
A = 540 yd²
Surface area
A' = 540 yd² + 2 · 0.5 · (51 yd) · (12 yd)
A' = 1152 yd²
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Related Questions
I Need help now please
Answers
In the congruent triangles; ΔABC and ΔBDE, ∠ABC = ∠DBE by CPCT that is Corresponding parts of Congruent Triangle.
Explain about the ASA congruence?The triangles are congruent if their including sides are congruent and two of their angles match two of the other triangle's angles called Angle - Side -Angle congruenceThe term "CPCT" stands for "Corresponding parts of Congruent Triangle," meaning that if two triangles are congruent, they are precisely mirror images of one another and their corresponding parts, such as side lengths and angles, can be assumed to be equal.So,
ΔABC and ΔBDE, are congruent triangles
Thus,
∠ABC = ∠DBE (Corresponding parts of Congruent Triangle) CPCT.
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The total number (in millions) of smartphone units shipped worldwide from 2009 to 2016 is given by
S(x)=-5.11x^2+243.57x+102.64, where x is the number of years after 2009. Assuming the trend continues, how many millions of smartphone units will be shipped worldwide in 2019? (Do not round your answer.)
Answers
Answer: 2027.34
Step-by-step explanation:
first you plug in 10 for x
after you squared and multiplied you add
then it should come out to be 2027.34
In linear equation, 2027 .34 millions of smartphone units will be shipped worldwide in 2019.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
S(x)=-5.11x^2+243.57x+102.64 ...............1
For smartphone skipped in 2019
x = 2019 - 2009
x = 10
putting x = 10 in (1)
S( 10 ) = -5.11 (10)² + 243.57 * 10 + 102.64
= -511 + 2435.7 + 102.64
= 2027 .34
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The complete question is -
The total number (in millions) of smartphone units shipped worldwide from 2009 to 2016 is given by S(x)=-5.11x^2+243.57x+102.64. where is the number of years after 2009. Assuming the trend continues, how many millions of smartphone units will be shipped worldwide in 2019? (Do not round your answer.)
(Source: Statista 2017)
solve the following equation \(2x < 6\)
Answers
Answer:
x < 3
Step-by-step explanation:
Divide both sides of the inequality by 2
*-*-*-*
บ
y=x
E(3.-3) F(5,-3)
H(2-5) G(4-5)
What are the coordinates of the image of vertex G after
a reflection across the line y = x?
O(-4,-5)
O (4, 5)
O(-5, 4)
(5,-4)
Answers
The coordinates of the image of vertex G after a reflection across the line y = x will be (-5, 4). Then the correct option is C.
What is a reflection of the point?It is the image of the point which is located in the opposite direction of a given point.
The rule of the refection given will be given as,
Firstly, the rule for reflecting a point about the line y = x is;
While reflecting on the line y = x, we get the reflected points by swapping the coordinates.
The coordinates are given below.
E(3, -3), F(5, -3), H(2, -5), G(4, -5)
The coordinates of the image of vertex G after a reflection across the line y = x are given as,
G(4, -5) ⇒ G'(-5, 4)
The coordinates of the image of vertex G after a reflection across the line y = x will be (-5, 4). Then the correct option is C.
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The deck of a bridge is suspended 225 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 225 – 16t2. (a) Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 3 and lasting the following amount of time. (i) 0.1 seconds ______ ft/s (ii) 0.05 seconds ______ft/s (iii) 0.01 seconds _______ ft/s (b) Estimate the instantaneous velocity (in ft/s) of the pebble after 3 seconds._______ ft/s
Answers
a) (i) Average velocity = -96.8 ft/s
(ii) Average velocity = -95.2 ft/s
(iii) Average velocity = -92.8 ft/s
b) The instantaneous velocity of the pebble after 3 seconds is approximately -96 ft/s.
What is average velocity?
The change in position or displacement (x) divided by the time intervals (t) in which the displacement happens yields the average velocity. Depending on the sign of the displacement, the average velocity can be positive or negative.
(a)
(i) The time period from t = 3 to t = 3.1 is 0.1 seconds. The average velocity of the pebble during this time period can be found by taking the difference in position (y) divided by the difference in time (t).
Average velocity = (y(3.1) - y(3)) / (3.1 - 3)
Substituting [tex]y = 225 - 16t^2[/tex], we get:
[tex]Average\ velocity = [(225 - 16(3.1)^2) - (225 - 16(3)^2)] / (0.1)[/tex]
Average velocity = -96.8 ft/s (rounded to one decimal place)
(ii) The time period from t = 3 to t = 3.05 is 0.05 seconds. The average velocity of the pebble during this time period can be found using the same formula as above:
[tex]Average\ velocity = (y(3.05) - y(3)) / (3.05 - 3)[/tex]
Substituting [tex]y = 225 - 16t^2[/tex], we get:
[tex]Average\ velocity = [(225 - 16(3.05)^2) - (225 - 16(3)^2)] / (0.05)[/tex]
Average velocity = -95.2 ft/s (rounded to one decimal place)
(iii) The time period from t = 3 to t = 3.01 is 0.01 seconds. The average velocity of the pebble during this time period can be found using the same formula as above:
Average velocity = (y(3.01) - y(3)) / (3.01 - 3)
Substituting [tex]y = 225 - 16t^2[/tex], we get:
[tex]Average \ velocity = [(225 - 16(3.01)^2) - (225 - 16(3)^2)] / (0.01)[/tex]
Average velocity = -92.8 ft/s (rounded to one decimal place)
(b)
The instantaneous velocity of the pebble at any given time t can be found by taking the derivative of the position function y(t) with respect to time:
[tex]\frac{dy}{dt} =-32t\\[/tex]
Substituting t = 3, we get:
[tex]\frac{dy}{dt} =-96ft/s\\[/tex]
Therefore, the instantaneous velocity of the pebble after 3 seconds is approximately -96 ft/s.
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Bob can row 9 mph in still water. The total time to travel downstream and return upstream to the starting point is 9 hours. If the total distance downstream and back is 32 miles, determine the speed of the river (current speed).
Current Speed = ___________
Answers
Let's call the speed of the river "r". The speed of the current in the downstream direction is 9 + r mph, and the speed of the current in the upstream direction is 9 - r mph. The time it takes to travel downstream and return upstream is the same, so we can set up the following equation:
(32 miles) / (9 + r mph) + (32 miles) / (9 - r mph) = 9 hours
We can simplify this equation by converting hours to minutes and miles to feet, and then simplify further by multiplying both sides of the equation by the denominators:
32 * 60 * (9 + r) + 32 * 60 * (9 - r) = 9 * 60 * (9 + r) * (9 - r)
Expanding the right side of the equation and simplifying:
32 * 60 * (9 + r) + 32 * 60 * (9 - r) = 810 * (9 + r) * (9 - r)
Expanding the left side of the equation and simplifying:
32 * 60 * 9 + 32 * 60 * r + 32 * 60 * 9 - 32 * 60 * r = 810 * (9 + r) * (9 - r)
Combining like terms and solving for r:
32 * 60 * 9 * 2 = 810 * (9 + r) * (9 - r)
96720 = 810 * (9 + r) * (9 - r)
Dividing both sides by 810:
119 = (9 + r) * (9 - r)
Expanding the right side of the equation:
119 = 81 - r^2
Adding r^2 to both sides of the equation:
119 + r^2 = 81
Subtracting 81 from both sides of the equation:
38 + r^2 = 0
Taking the square root of both sides of the equation:
r = ± sqrt(38)
Since r is the speed of the current, it must be a positive value, so we take the positive square root:
r = sqrt(38) mph
The speed of the river (current speed) is approximately 6.17 mph.
Cheryl says that the system of equations at the right
MUST be solved by elimination rather than by substitution.
a. Explain why Cheryl is not correct.
b. Why might Cheryl think this is true?
-7x+12y=13
7x-11y--9
Answers
Answer: look at the image for the answer
Step-by-step explanation:
You pick a card at random. 3 4 5 6 What is P(5)? Write your answer as a perc
Answers
Answer: 5 is 1/4 meaning 25%
Step-by-step explanation:
I think this is what you meant to ask... HOPE THIS HELPS U
Miss oliverie class plays a game in teams. Each team has the same number of students. The ratio of teams to players is 8 : 32. how many students are in Miss Oliver’s class? How many students are in each team?
Answers
The solution is, 128 students are in Miss Oliver’s class. 4 students are in each team.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
here, we have,
given that,
Each team has the same number of students.
let , each team has x students.
The ratio of teams to players is 8 : 32.
again, let, no. of teams = 8y
no. of players = 32y
so, we get,
8y*x = 32y
so, x = 4
Hence, The solution is, 128 students are in Miss Oliver’s class. 4 students are in each team.
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The water company has a different monthly pricing plan for residential customers than for business customers. For each pricing plan, cost (in dollars) depends on water used (in hundreds of cubic feet, HCF), as shown below. Residential Plan Cost (in dollars) 33 Business Plan 34 4 14 16 18 23 34 Monthly water usage (in HCF) X $ ? (a) If the monthly water usage is 22 HCF, which plan costs less? Residential Plan Business Plan How much less does it cost than the other plan? sa (b) For what amount of monthly water usage do the plans cost the same? If the monthly water usage is more than this amount, which plan costs more? Residential Plan Business Plan
Answers
The cost than the other plan is 215 money and the plans cost the same when the monthly water usage is 0.1 HCF.
(a) If a monthly water consumption of 22 HCF is used, the cost of the residential plan is:
33 + 14(22) = 341 cash
The Business Plan has an expense of:
34+4(22)=126 pounds
Consequently, the Residential Plan is less expensive than the Commercial Plan by
340 - 126 equals 215 money.
(b) The following equation must be solved in order to determine the monthly water usage at which the plans are equally expensive:
33 + 14X = 34 + 4X
When we simplify and find X, we obtain:
10X = 1 \sX = 0.1
Therefore, when the monthly water usage is 0.1 HCF, the plans are priced the same. The Business Plan is less expensive than the Residential Plan for water consumption above 0.1 HCF per month.
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identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x or y (2y^3 2y^2)dx (3y^2x 2xy)dy
Answers
The given equation is exact. An equation is said to be exact if it can be written in the form
M(x,y)dx + N(x,y)dy = 0
where M and N are functions of x and y, and their partial derivatives with respect to y and x, respectively, are equal.
In this case, we have:
M(x,y) = 2y^3
N(x,y) = 3y^2x + 2xy^2
Taking the partial derivative of M with respect to y gives:
∂M/∂y = 6y^2
Taking the partial derivative of N with respect to x gives:
∂N/∂x = 3y^2
Since ∂M/∂y = ∂N/∂x, the equation is exact.
To solve the equation, we need to find a function F(x,y) such that ∂F/∂x = M and ∂F/∂y = N.
Integrating M with respect to x gives:
F(x,y) = y^2x^2 + g(y)
where g(y) is an arbitrary function of y.
Taking the partial derivative of F with respect to y and comparing it with N, we get:
∂F/∂y = 2xy + g'(y) = N
Comparing the coefficients of y and the constant terms, we get:
2x = 3y^2, g'(y) = 2y^2
Solving these equations gives:
x = (3/2)y^2 and g(y) = (2/3)y^3 + C
where C is an arbitrary constant.
Substituting these values in F(x,y), we get:
F(x,y) = (2/3)y^3 + y^2x^2 + C
Therefore, the general solution of the given equation is:
(2/3)y^3 + y^2x^2 = C
where C is an arbitrary constant.
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Let p = "x > 7," q = "x = 7," and r = "11 > x."Select the symbol form for each of the following statement.(a). x ≥ 7p v qp ~ qp v rq ~ rp ^ q(b) 11 > x > 7p ~ qr ~ pr ^ pr v pp ^ q(c) 11 > x ≥ 7r ~ (p v q)r ^ (p ~ q)p ^ (q v r)r ^ (p v q)r v (p ^ q)
Answers
The correct symbol forms are:
a) x ≥ 7 is equivalent to p v q
b) 11 > x > 7 is equivalent to p ∧ r
c) 11 > x ≥ 7 is equivalent to ( p v q) ∧ r
We have the following definitions:
p = "x > 7"
q = "x = 7"
r = "11 > x"
a) The statement "x ≥ 7" is true if x is greater than 7 or if x is equal to 7. In other words, "x > 7 or x = 7" must be true. Using the given definitions, we can see that this is equivalent to p v q.
b) 11 > x > 7. The statement "7 < x < 11" means that x is greater than 7 and less than 11. In other words, both "x > 7" and "x < 11" must be true. hence, it can be expressed as the conjunction of "x > 7" and "x < 11," which is equivalent to p ∧ r.
c) 11 > x ≥ 7. Combining answer from part a and b, this is equivalent to:
( p v q) ∧ r
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Larry wants to do everything possible to be in a position to detect that a treatment he has designed is effective given that it is actually effective. Which of the following should he do?
a. decrease the sample size
b. decrease the population standard deviation
c. use an alpha (a) of .01 instead of .05
d. use an alpha (a) of .05 instead of .01
Answers
Larry wants to do everything possible to be in a position to detect that a treatment he has designed is effective given that it is actually effective. use an alpha (a) of .05 instead of .01 and decrease the population standard deviation. Option B and C are correct .
How to interpret a standard deviation?
With a standard deviation of 1, 68% of the population is within the average plus or minus the standard deviation. Consider a scenario where the standard deviation is three inches and the average male height is 5 feet 9 inches. As a result, 68% of all guys are between 5' 6" and 6', 5'9" plus or minus 3 inches.
What makes standard deviation so special?
Karl Pearson is credited with giving SD the name "standard deviation". I wouldn't imagine anything more than that he intended to suggest it as a benchmark. If anything, standardization-related references either stand alone or make references to SD itself.
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42 is an integer and should be printed using %d. the character 'j' can be printed using %c. floating point numbers use %f. 3.141590 is an example of
Answers
3.141590 is an example of floating-point number, which is printed using %f.
Floating-point numbers are a way to represent real numbers in a computer. They are used to store values that have a fractional component, such as 3.14159. Unlike integers, which can be stored precisely in a fixed amount of memory, floating-point numbers use a fixed number of bits to represent the number's significant digits and its exponent. This allows them to represent a wide range of values, but can also result in some loss of precision. When printing a floating-point number, the %f format specifier is used to specify the number of decimal places to display.
For example, the number 3.141590 can be printed using the format specifier %f as follows:
printf("%f", 3.141590);
This will output:
3.141590
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Suppose that when tomorrow (time t + 1) arrives, an individual will order food to be eaten tomorrow as if he is maximizing a utility function U(ft+1I ht+1) = −(ft+1 − ht+1)2
where ft+1 stands for food at time t + 1 and ht+1 stands for how hungry she is at time t + 1. Solve for the amount of food that he will order tomorrow, for tomorrow.
(b) Now suppose that when ordering food today to be eaten tomorrow, the same individual behaves as if she has the following utility function:
U(ft+1| ht+1, ht) = −(1 − α)(ft+1 − ht+1) 2 − α(ft+1 − ht) 2
where α ∈ [0, 1]. Thus, the amount she orders for tomorrow depends on how hungry she is today, and how hungry she will be tomorrow (which you can assume she forecasts with perfect accuracy). Solve for the optimal amount of food that she will order today, for tomorrow.
(c) How might we interpret the parameter α in terms of projection bias?
(d) If α = 1, how much food does the individual order today, for tomorrow?
(e) Suppose the individual orders food today for tomorrow. Under what conditions would she prefer, once tomorrow arrives, to throw all of the food away rather than eat everything she ordered?
(f) Describe a real-life example of where such projection bias may lead to economic inefficiency or misallocated resources. This example can be from a paper we discussed in lecture, or you may think of another application.
Answers
a) Food with the greatest possible utility will be ordered tomorrow is [tex]f_{t+1}[/tex] = [tex]h_{t+1}[/tex].
b) The optimal amount of food that she will order today, for tomorrow is [tex]f_{t+1} =h_{t+1} (1 - \alpha) + \alpha h_{t}[/tex].
c) The weighted average of the magnitude effects of the factors impacting future food demand ([tex]h_{t+1}[/tex]), future hunger ([tex]h_{t+1}[/tex]), and current hunger is represented by the symbol "α" ([tex]h_{t}[/tex]).
d) [tex]U(f_{t+1}| h_{t+1}, h_{t}) = - 1(f_{t+1} - h_{t})^2[/tex] indicates that the amount of food ordered depends only on how hungry you are right now ([tex]h_{t}[/tex]), not how hungry you will be in the future ([tex]h_{t+1}[/tex]).
a) [tex]U(f_{t+1} | h_{t+1} ) = -(f_{t+1} - h_{t+1})^2[/tex]
To maximize utility:
[tex]\frac{du}{dx} f_{t+1} = -2 (f_{t+1}-h_{t+1})[/tex]
du/dt [tex]f_{t+1}[/tex] = 0
[tex]-2 (f_{t+1} - h_{t+1}) = 0[/tex]
[tex]f_{t+1}[/tex] = [tex]h_{t+1}[/tex]
Food with the greatest possible utility will be ordered tomorrow.
b) [tex]U(f_{t+1}| h_{t+1}, h_{t}) = -(1 - \alpha)(f_{t+1} - h_{t+1})^2 - \alpha(f_{t+1} - h_{t})^2[/tex]
[tex]\frac{d}{dt}f t+1 = -2 (1 - \alpha)(f_{t+1} - h_{t+1}) - 2\alpha (f_{t+1} - h_{t})[/tex]
[tex]\frac{d}{dt}f t+1 = (2\alpha - 2) (f_{t+1} - h_{t+1}) - 2\alpha(f_{t+1} - h_{t})[/tex]
[tex]\frac{d}{dt}f_{t+1} = 2\alpha f_{t+1} - 2\alpha h_{t+1}- 2 f_{t+1} + 2h_{t+1} -2\alpha f_{t+1}+ 2\alpha h_{t}[/tex]
[tex]\frac{d}{dt} f_{t+1} = - 2\aplha h_{t+1} - 2 f_{t+1} + 2h_{t+1} + 2\alpha h_{t} =0[/tex]
[tex]2 f_{t+1} =2h_{t+1} - 2\alpha h_{t+1} -2\alpha h_{t}[/tex]
[tex]f_{t+1} =h_{t+1} - \alpha h_{t+6}- \alpha h_{t}[/tex]
[tex]f_{t+1} =h_{t+1} (1 - \alpha) + \alpha h_{t}[/tex]
c) The weighted average of the magnitude effects of the factors impacting future food demand ([tex]h_{t+1}[/tex]), future hunger ([tex]h_{t+1}[/tex]), and current hunger is represented by the symbol "α" ([tex]h_{t}[/tex]).
d) [tex]U(f_{t+1}| h_{t+1}, h_{t}) = -(1 - \alpha)(f_{t+1} - h_{t+1})^2 - \alpha(f_{t+1} - h_{t})^2[/tex]
If α = 1 , putting value :
[tex]= - (1-1) (f_{t+1} - h_{t+1}) - 1(f_{t+1} - h_{t})^2\\= 0 - 1(f_{t+1} - h_{t})^2[/tex]
[tex]U(f_{t+1}| h_{t+1}, h_{t}) = - 1(f_{t+1} - h_{t})^2[/tex]
It indicates that the amount of food ordered depends only on how hungry you are right now ([tex]h_{t}[/tex]), not how hungry you will be in the future ([tex]h_{t+1}[/tex]).
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an event coordinator for a particular marathon held yearly is reviewing the data from the top 30 race finish times from the last race. using excel, calculate the mode(s) of the dataset provided below. finish times (hours) 2.45 2.47 2.47 2.49 2.47 2.77 2.97 3.22 3.42 select the correct answer below: A. there are two modes. the modes are 2.47 and 4.14. B. there is one mode. the mode is 2.47. C. there is one mode. the mode is 4.14. D. there is no mode.
Answers
The correct statement regarding the mode of the data-set is given as follows:
B. there is one mode. the mode is 2.47.
What is the mode?The mode of a data-set is the measure of central tendency that gives the observation that appears the most often in a data-set, hence the correct option is given by option a.
From the observations in this problem, a finish time of 2.47 hours appeared the most often, which was 3 times, hence the correct option is given by option B.
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Find x from given triangle
Answers
The value of x is 2.
Describe Triangles?Triangles are one of the most basic shapes in geometry and have a wide range of applications in mathematics, science, and engineering.
The three sides of a triangle are called edges, and the three angles are called vertices. Triangles can be classified based on the lengths of their sides and the measures of their angles.
Since DE is parallel to AC, we can use the intercept theorem to relate the lengths of the corresponding sides of triangles ABD and CBE.
In triangle ABD and CBE, we have:
AD/CE = AB/BC
Substituting the given values, we get:
2/1 = (x+2)/4
Cross-multiplying, we get:
8 = 2(x+2)
Simplifying, we get:
x+2 = 4
x = 2
Therefore, the value of DB is 2.
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need help asap 25 pointd
Answers
Answer:
x= 7 ;
y+x=18
y=18-x
y=18-7
y=11
Consider your eight-digit student ID as a set of single-digit integers. For example, if your student ID is the number 01238586, then it represents the set S = {0, 1, 2, 3, 5, 6, 8}. Now consider your student ID as a sequence of eight digits. For example, if your student ID is the number 01238586, then it represents the sequence D = (0, 1, 2, 3, 8, 5, 8, 6). The sequence can be used to define a relation r:S -→ S by creating the elements of r as follows, r = {(d1, d2), (d3, d4), (d5, do), (d7, dz)} = > > The di, 1 < i < 8 are the digits in the sequence read left to right. For example, if your student ID is the number 01238586, then r = {(0, 1), (2, 3), (8,5), (8, 6)} 2 Questions to Answer a. Create the relation r using your student ID. Record the relation in roster notation as a set of 2- tuples (see example).
b. Extend your relation by adding the 2-tuple (d2, dị) to r, creating the relation R. That is, , R= r U {(d2, d])} Record the relation Ras a set of 2-tuples c. Find the transitive closure, T, of the relation R. Record the relation T as a set of 2-tuples.
Answers
The relation r in roster notation as a set of 2-tuples is: r = {(1, 0), (6, 9), (9, 9), (8, 4)} The relation R in roster notation as a set of 2-tuples is: R = {(1, 0), (6, 9), (9, 9), (8, 4), (0, 1)}. The transitive closure T of the relation R is the set of tuples above. T = {(1, 0), (1, 1), (1, 4), (1, 8), (6, 9), (6, 4), (6, 8), (9, 9), (9, 4), (9, 8), (8, 4)}.
To create the relation r using your student ID, we first represent the student ID as a set of single-digit integers:
S = {1, 0, 6, 9, 9, 8, 4, 7}
Then we use the sequence D = (1, 0, 6, 9, 9, 8, 4, 7) to create the relation r as follows: r = {(1, 0), (6, 9), (9, 9), (8, 4)}
So the relation r in roster notation as a set of 2-tuples is:
r = {(1, 0), (6, 9), (9, 9), (8, 4)}
To extend the relation r by adding the 2-tuple (d2, dị) to r, we first need to identify the values of d2 and d1 from our student ID:
d2 = 0
d1 = 1
Then we add the tuple (d2, d1) to r to create the new relation R:
R = r U {(0, 1)}
So the relation R in roster notation as a set of 2-tuples is:
R = {(1, 0), (6, 9), (9, 9), (8, 4), (0, 1)}
To find the transitive closure of the relation R, we need to find all pairs of elements that are related transitively. We can do this by repeatedly applying the rule that if (a, b) and (b, c) are in the relation, then (a, c) is also in the relation.
Starting with the relation R, we can see that (1, 0) is related to (0, 1), so we add (1, 1) to the relation. Then we can add (1, 4) and (1, 8) to the relation, based on the pairs (1, 0) and (0, 4) and (0, 8), respectively.
Next, we can add (6, 9) and (9, 9) to the relation, based on the pair (6, 9). We can also add (6, 4) and (6, 8) to the relation, based on the pairs (6, 9) and (9, 4) and (9, 8), respectively.
We can also add (9, 4) and (9, 8) to the relation, based on the pair (9, 9). Finally, we can add (8, 4) to the relation, based on the pair (8, 4).
Applying these rules, we get the transitive closure T of the relation R:
T = {(1, 0), (1, 1), (1, 4), (1, 8), (6, 9), (6, 4), (6, 8), (9, 9), (9, 4), (9, 8), (8, 4)}
So the relation T in roster notation as a set of 2-tuples is:
T = {(1, 0), (1, 1), (1, 4), (1, 8), (6, 9), (6, 4), (6, 8), (9, 9), (9, 4), (9, 8), (8, 4)}
The transitive closure T of the relation R is the set of tuples above.
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How to get the equation
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The equation of the line passing through the points (-4, -3) and (2, -1) is y = (1/3)x - (5/3).
What is the point-slope form of a line?To find the equation of a line given two points, we can use the point-slope form of the equation.
y - y₁₁ = m(x - x₁)
where m is the slope of the line, and (x₁, y₁) is one of the given points.
First, we need to find the slope of the line. We can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the two given points.
m = (-1 - (-3)) / (2 - (-4))
m = 2/6
m = 1/3
Now we can choose one of the given points and substitute its coordinates into the point-slope form, along with the slope we just found:
y - (-3) = (1/3)(x - (-4))
Simplifying this equation, we get:
y + 3 = (1/3)(x + 4)
y = (1/3)x - (5/3)
Therefore, the equation of the line passing through the points (-4, -3) and (2, -1) is y = (1/3)x - (5/3).
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The Smith family went out to dinner. The total cost for the meal, including tax, was $87.98. The family left a 15% tip. What was the final cost of the meal, including the tip? Round to the nearest hundredths.
Answers
Answer:
36.39 hope this helps
Step-by-step explanation:
two dice (one red and one green) are to be rolled. the sample space consists of the 36 outcomes listed below. the first number is what is rolled on the red die and the second number is what is rolled on the green. determine: [ 1,1 1,2 1,3 1,4 1,5 1,6 ][ 2,1 2,2 2,3 2,4 2,5 2,6 ]S = [ 3,1 3,2 3,3 3,4 3,5 3,6 ][ 4,1 4,2 4,3 4,4 4,5 4,6 ][ 5,1 5,2 5,3 5,4 5,5 5,6 ][ 6,1 6,2 6,3 6,4 6,5 6,6 ]a) p(at least one of the dice is a 5) b) p(sum of the dice is equal to 7) c) p(sum of the dice is 11 or more) d) p(both are less than 3) e) p(red is larger than green) f) p(sum is greater than 9) g) p(red = 6)h) P(largest number is a 5)i) P(smallest number is a 5)
Answers
a) To find the probability that at least one of the dice is a 5, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 11 outcomes where at least one die is a 5: (1,5), (2,5), (3,5), (4,5), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,5). Therefore, the probability is:
P(at least one 5) = 11/36
b) To find the probability that the sum of the dice is equal to 7, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 6 outcomes where the sum is 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Therefore, the probability is:
P(sum is 7) = 6/36 = 1/6
c) To find the probability that the sum of the dice is 11 or more, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 2 outcomes where the sum is 11 or more: (5,6), (6,5). Therefore, the probability is:
P(sum is 11 or more) = 2/36 = 1/18
d) To find the probability that both dice are less than 3, we can count the number of outcomes where this is true and divide by the total number of outcomes. There is only 1 outcome where both dice are less than 3: (1,1). Therefore, the probability is:
P(both less than 3) = 1/36
e) To find the probability that the red die is larger than the green die, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 15 outcomes where the red die is larger than the green die: (2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3), (6,4), (6,5). Therefore, the probability is:
P(red is larger) = 15/36 = 5/12
f) To find the probability that the sum of the dice is greater than 9, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 4 outcomes where the sum is greater than 9: (4,6), (5,5), (5,6), (6,4), (6,5), (6,6). Therefore, the probability is:
P(sum is greater than 9) = 6/36 = 1/6
g) To find the probability that the red die is 6, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 6 outcomes where the red die is 6: (6,1), (6,2), (6,3), (6,4), (6,5), (6,6). Therefore, the probability is:
P(red = 6) = 6/36 = 1/6
h) To find the probability that the largest number rolled is 5, we can count
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on june 1 mario sent out texts offering to sell his 2002 ford f-150 for $10,000 and asking for text acceptances. on june 7, andretti texted mario accepting his offer. however, andretti's text was not received by mario until june 10 due to connection problems. the text from andretti created an enforceable agreement between mario and andretti the moment it was sent.T/F
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The statement "the text from andretti created an enforceable agreement between mario and andretti the moment it was sent" is generally true.
In contract law, an agreement is formed when there is an offer from one party and an acceptance of that offer by the other party. An acceptance is typically effective upon communication to the offeror.
In this case, Mario made an offer to sell his 2002 Ford F-150 for $10,000 through a text message. Andretti responded to the offer with a text message accepting it.
The general rule is that an acceptance is effective upon communication to the offeror. Therefore, Andretti's acceptance of the offer was effective as soon as he sent the text message. It doesn't matter if the message was not received by Mario until later due to connection problems.
As long as Andretti sent the acceptance text message, it created an enforceable agreement between the two parties, assuming that there were no other legal issues that might affect the validity of the agreement.
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Consider the following two loans for P0=$10,000.
Loan A: 3 year loan, monthly installments, annual interest rate of 5%.
Loan B: 5 year loan, monthly installments, annual interest rate of 8%.
On which loan will you pay the least interest?
Answers
The Interest (simple interest) will be less on Loan A.
What exactly is simple interest?
Simple Interest is a simple way for computing interest on a loan or principle amount. Simple interest is a concept that is employed in numerous industries, including banking, finance, and automobiles. When you make a loan payment, the monthly interest is deducted first, followed by the principle amount.
The simple interest formula is as follows:
SI=P*R*T/100
SI stands for simple interest.
P stands for principal.
R is the interest rate (in percentage)
T denotes the length of time (in years)
The following formula is used to compute the total amount:
Amount (A) = Principal (P) x Simple Interest (SI)
Now,
For A Principal=$10000, Time = 3 years, Rate=5%
then interest paid=10000*3*5/100
=300*5=$1500
For B Principal=$10000, Time = 5 years, Rate=8%
Interest=10000*5*8/100
=500*8
=$4000
That means SI(B)>SI(A)
Hence,
The Interest will be less on Loan A.
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Which of the equations below could be the equation of this parabola? ASAP
Answers
Answer: A
hope this helped
g write a function called changelettercase that takes one string as a parameter and changes all the upper case letters to lower case and vice versa. the function returns the updated string with the cases swapped.
Answers
Here is a Python example of how to use the changelettercase function:
def changelettercase(string):
updated_string = ""
for char in string:
if char.isupper():
updated_string += char.lower()
elif char.islower():
updated_string += char.upper()
else:
updated_string += char
return updated_string
To hold the updated version of the input string, we initialize an empty string called the updated string in this function.
If so, we use the lower() method to make it lowercase and add it to the updated string. In the event that the character is not a letter, we merely add it to the updated string without altering its case.
The updated string, which now contains the input string with the letters' cases switched, is what we return at the end.
Here's an example usage of the function:
my_string = "Hello, World!"
new_string = changelettercase(my_string)
print(new_string)
output: "hELLO, wORLD!"
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Which expression is equivalent to
(3x2 + 2x - 4) + (5x2 - 4x + 5) ?
Question 2 options:
8x2 + 6x + 9
8x2 - 2x + 1
8x2 + 6x + 9
8x2 + 2x + 1
Answers
Answer:
D - 8x^2 - 2x + 1
Step-by-step explanation:
This is only if your questions is actually (3x^2 + 2x - 4) + (5x^2 - 4x + 5)
It really helps if you put the ^# so they know its meant to be an exponent
3) Flying with the wind a plane went 359 km/h. Flying into the same wind the plane only went 337
km/h. Find the speed of the plane in still air and the speed of the wind.
Answers
Answer: Let's call the speed of the plane in still air "p" and the speed of the wind "w".
When flying with the wind, the plane's speed is increased by the wind speed, so the equation is:
359 = p + w
When flying against the wind, the plane's speed is decreased by the wind speed, so the equation is:
337 = p - w
We can add these two equations to eliminate "p":
696 = 2p
So,
p = 348
Now that we know the speed of the plane in still air, we can use either equation to find the speed of the wind:
w = 359 - p = 359 - 348 = 11 km/h.
So, the speed of the plane in still air is 348 km/h and the speed of the wind is 11 km/h.
Step-by-step explanation:
What is the area, in square meters, of the trapezoid below?
Answers
this is split into three shapes
the middle is a rectangle
5.8 x 9.5 = 55.1
find width of left triangle
18 - 9.5 = 8.5
area of triangle is 1/2 base x height
8.5 x 5.8 / 2 = 24.65
5.1 x 5.8 /2 = 14.79
add all 3
99.47 is total area
Hope this helps : -)
- Jeron
let x be a random variable that takes values from 0 to 9 with equal probability 1/10
Answers
The probability of getting a number greater than zero is 9/10.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, 'x' be a random variable that takes values from 0 to 9 with an equal probability of 1/10.
We know, The total probability is 1.
Therefore, The probability of getting a number greater than zero is,
(1 - the probability of getting zero).
= 1 - 1/10.
= 9/10.
Some more concepts related to probability is a conditional probability which states,
The likelihood that one event will follow another given the occurrence of another event.
Q. let x be a random variable that takes values from 0 to 9 with equal probability 1/10, Find the probability of getting a number greater than zero.
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