AB is dilated by a scale factor of 3 to form A'B'. Point O, which lies on AB, is the center of dilation.
The slope of AB is 3. The slope of A'B' is 3. A'B' passes through point O.
What is dilation in mathematics?Dilation is a process of transformation used to resize an object.
The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. The size of the form does differ, though.
By multiplying the x and y coordinates of the original figure by the scale factor, you may locate locations on the dilated image when a dilation in the coordinate plane has the origin as the center of dilation.
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Brianna made a design with chalk on the playground in the shape of a triangle. Two sides of the triangle measuring 5 feet and 8 feet meet at a 40° angle. What is the area of the triangle? Round your answer to the nearest tenth.
Answer:
12.9 ft²
Step-by-step explanation:
sin = opp/hyp
sin 40 = height/ 5
5 * sin40 = height
h = 3.213938048432697
--------------------
area = (1/2)bh
a = (1/2) * 8 * 3.213938048432697
a = 12.9 ft²
which of the following is an area of mathematics that studies how competing parties interact
An area of mathematics that studies how competing parties interact is known as "game theory."
Game theory analyzes strategic decision-making in situations where multiple participants, known as players, make choices that affect each other's outcomes. It examines the interactions, strategies, and outcomes of these competitive or cooperative situations.
Game theory provides mathematical models and frameworks to analyze various scenarios, such as conflicts, negotiations, auctions, voting systems, and economic markets. It studies the behavior of rational players, their objectives, and the choices they make to maximize their own outcomes, considering the actions and reactions of other players.
The field of game theory explores concepts such as strategies, payoffs, Nash equilibrium, dominant strategies, and cooperative or non-cooperative games. It aims to predict and understand the behavior and outcomes of competitive situations and provides insights into decision-making, resource allocation, and the dynamics of interactions between individuals, organizations, or even nations.
Overall, game theory serves as a valuable tool in various disciplines, including economics, political science, psychology, and computer science, to analyze and model situations where competing parties interact.
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Miyo can make 5 origami figures in 3 minutes. How many origami figures can Miyo make in 18 minutes?
Answer:
Miyo can make 30 origami figures in 18 minutes
Step-by-step explanation:
tbh, i just counted up by 5's until i reached 18
Answer: 3
Step-by-step explanation: Because we know Miyo can make 5 origami figures in 3 minutes. and we want to know How many origami figures can Miyo make in 18 minutes? so, we know 5*3 is 15. right? well, then we take 18-15 and get 3 so, Miyo can make 3 origami figures in 18 mins.
all things algebra unit 5 homework 2
if a password is to have 4 digits, each from 0 to 9, what is the probability that there will be no repeats on the digits?
The probability that there will be no repeats on the digits is 0.504.
What is meaning of probability?
The ratio of favorable outcomes with the total number of outcomes is known as probability of that event.
The number of digits of the password is 4.
The numbers from 0 to 9 is 10.
If the digit can repeat, then we can chose first digit in 10 ways, the second digit in 10, third digit in 10 ways and fourth digit in 10 ways.
The total number of ways is 10 × 10 × 10 × 10 =10000.
If the digit can't repeat, then we can chose first digit in 10 ways, the second digit in 9 (because we can't use first digit) , third digit in 8 ways (because we can't use first digit and second digit) and fourth digit in 7 ways(because we can't use first digit, second digit, and third digit).
The total number of ways is 10 × 9 × 8 × 7 =5040.
The favorable outcomes for this event is 5040.
The total number of outcomes is 10000.
The required probability is 5040/10000 = 0.504.
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(4 - 3i) + (2 + i )(5 - 2i)
Answer:
16 - 2i
Step-by-step explanation:
If you simplify your answer will be: 16−2i
Hope i get brainlest
frances receives one dollar for every pound of worms she gives her grandfather. which reinforcement schedule is this? group of answer choices fixed interval fixed ratio variable interval variable ratio
Answer:fixed ratio
Step-by-step explanation: :)
This is an illustration of a fixed ratio reinforcement schedule: after a predetermined number of responses, Frances is given a reward (in this case, $1). (every pound of worms).
What is a fixed ratio reinforcement schedule?An example of a reinforcement plan utilized in the behavioral psychology concept of operant conditioning is a fixed ratio reinforcement schedule. A reward or reinforcement is delivered according to this schedule after a predetermined number of actions or responses. As an illustration, a rat might receive a food pellet after every 10 lever presses.
Fixed ratio schedules work well for encouraging high response rates since the subject is driven to keep up the activity in order to earn the reward. Yet, if the reinforcement is stopped, the behavior can become less frequent or cease entirely.
Fixed ratio schedules can also cause behaviors to become rigid or stereotyped because the subject may start concentrating only on the number of responses required to earn the reward and stop considering other options or actions.
Overall, fixed ratio reinforcement regimens can be helpful in teaching both humans and animals to carry out particular tasks, but they should be utilized with caution and consideration for any unexpected consequences.
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find the point on the plane 4x − y + 4z = 40 nearest the origin.(x,y,z)=
The point on the plane 4x - y + 4z = 40 nearest the origin is (-3.048, -0.762, 6.467)
Given data ,
To find the point on the plane 4x - y + 4z = 40 nearest the origin, we need to minimize the distance between the origin and the point on the plane.
The normal vector to the plane 4x - y + 4z = 40 is given by (4,-1,4). To find the perpendicular distance from the origin to the plane, we need to project the vector from the origin to any point on the plane onto the normal vector. Let's choose the point (0,0,10) on the plane:
Vector from origin to (0,0,10) on the plane = <0-0, 0-0, 10-0> = <0,0,10>
Perpendicular distance from the origin to the plane = Projection of <0,0,10> onto (4,-1,4)
= (dot product of <0,0,10> and (4,-1,4)) / (magnitude of (4,-1,4))
= (0 + 0 + 40) / √(4^2 + (-1)^2 + 4^2)
= 40 / √(33)
To find the point on the plane nearest the origin, we need to scale the normal vector by this distance and subtract the result from any point on the plane. Let's use the point (0,0,10) again:
Point on the plane nearest the origin = (0,0,10) - [(40 / √(33)) / √(4^2 + (-1)^2 + 4^2)] * (4,-1,4)
= (0,0,10) - (40 / √(33)) * (4/9,-1/9,4/9)
= (0,0,10) - (160/9√(33), -40/9√(33), 160/9√(33))
= (-160/9√(33), -40/9√(33), 340/9√(33))
Hence , the point on the plane 4x - y + 4z = 40 nearest the origin is approximately (-3.048, -0.762, 6.467)
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Sally want to open a bakery. One of the things that she is going to sell is bagels. Sally asked people what type of bagels are their favorite. Out of the 200 people that she asked, 23 said that raisin cinnamon was their favorite. Sally plans bake 1200 bagels a day. How many should be raisin cinnamon?
Answer:
138
Step-by-step explanation:
200 x 6 = 1200
23 x 6 = 138
Answer:
138
Step-by-step explanation:
Divide 23 by 20023÷200=0.115
Multiply 0.115 by 12000.115*1200=138
a sphere has a volume of 36 pie inches cube. What is the radius of the sphere?
A. 3 in
B. 4 in
C. 6 in
D. 12 in
E. 27 in
Answer:
3 in
Step-by-step explanation:
help asap
short its an MCQ
If the diameter of 3 circles is in the ratio 4: 2: 1. The perimeter of the smallest circle is 8 cm. Then the area of
the shaded region is
Answer:
216\(\pi\)
Step-by-step explanation:
Given the figure.
And the perimeter in the ratio 4: 2: 1.
Perimeter of smallest circle = \(8\pi\)
To find:
Area of shaded region.
Solution:
To find the area, we need to have radius first.
And radius can be calculated by the given perimeter.
Formula for Perimeter is given as:
Perimeter = \(2\pi r\)
\(8\pi = 2\pi r\\\Rightarrow r = 4\ cm\)
Radius of smallest circle = 4 cm
Ratio of perimeter is equal to the ratio of the radii.
Radius of 2nd smallest circle by the given ratio = 8 cm
Radius of largest circle = 16 cm
Area of a circle is given the formula:
\(A = \pi r^2\)
Area of the smallest circle = \(\pi 4^2 = 16\pi\ cm^2\)
Area of the 2nd smallest circle = \(\pi 8^2 = 64\pi\ cm^2\)
Area of the largest circle = \(\pi 16^2 = 256\pi\ cm^2\)
Area of the shaded region = Area of largest circle + 2 \(\times\) Area of 2nd smallest circle + 3 \(\times\) Area of smallest circle - 2 \(\times\) Area of smallest circle - 3 \(\times\) Area of 2nd smallest circle
Area of the shaded region = Area of largest circle - Area of 2nd smallest circle + Area of smallest circle = \(256\pi - 64\pi +16\pi = 216\pi\)
a college professor wants to survey a sample of students taking his course. here are some details about his course: he teaches 5 55 sections of the course. there are 250 250250 total students across those sections. there are 50 5050 graduate students and 200 200200 undergraduate students taking the course. each section has about 50 5050 students (some graduate and some undergraduate). the professor wants to take a sample of 30 3030 students for a survey. he suspects that opinions on the survey may differ the most based on student type (graduate or undergraduate), so he wants to design his sample to take that into account. which of these strategies will accomplish his intended design? choose 1 answer:
a. Randomly select 6 students from each section for the survey. b. Randomly select 6 graduate students and 24 undergraduate students for the survey C. For each section, randomly select one of the first 8 students to arrive to class, and every 8th student thereafter to take the survey. d. Randomly select one of the sections and give the survey to every student in that section
The strategy that will accomplish the intended design is Randomly select 6 graduate students and 24 undergraduate students for the survey. So, option b. is correct.
A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.
Based on the given information, the college professor wants to survey a sample of 30 students from his course, considering the differences between graduate and undergraduate students. The best strategy to accomplish his intended design is: Randomly select 6 graduate students and 24 undergraduate students for the survey.
This approach ensures that the sample includes a proportional representation of both graduate and undergraduate students, taking into account the difference in their numbers (50 graduate students and 200 undergraduate students) within the 250 total students.
So, option b. is correct.
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seriously high quality answers plus brainliest
Answer:
See below
Step-by-step explanation:
let e be exercising hours
let c be cleaning stalls hours
Here is the inequality system per week:
\(e + c \leq 12\\5e + 10c \geq 60\\condition: 0\leq e,c\leq 12\)
Two possible solutions:
\(c = 0, e = 12\\c = 1, e = 11\)
Answer:
a) see attached graph
b) (2,8) (3,7)
Step-by-step explanation:
Part a
let x = number of hours exercising horses
let y = number of hours cleaning stalls
As he must earn at least $60 per week: 5x + 10y ≥ 60
As he can work no more than 12 hours per week: x + y ≤ 12
Rearrange each equation to make y the subject:
5x + 10y ≥ 60
⇒ 10y ≥ 60 - 5x
⇒ y ≥ 6 - (1/2)x
Therefore, graph the line \(y=-\frac{1}{2}x+6\) with a solid line, and shade above the line (shown in blue on the attached diagram)
x + y ≤ 12
⇒ y ≤ 12 - x
Graph the line \(y=-x+12\) with a solid line, and shade below the line (shown in red on the attached diagram)
Part b
Possible solutions are any points found within the overlapping shaded region (shown in purple on the attached diagram) including the points on the lines:
e.g. (2, 8) or (3, 7) or (4, 6) or (5, 5) or (5, 7) etc.
Mary measures the weights of five newly hatched pythons in ounces. John converts Mary's measurements to grams. There are 28.35 grams in an ounce. Here are Mary's results: (a) Calculate the mean and standard deviation of Mary's measurements using the formula for each. 2. Use graphs and numerical summaries to describe how the following three datasets are similar and how they are different. A: 5,7,9,11,13,15,17 B: 5,6,7,11,15,16,17 C: 5,5,5,11,17,17,17
(a) Calculation of Mean and Standard Deviation: Mary's results in ounces are: 5, 6, 6, 7, and 8 ounces. Let's calculate the mean and standard deviation of Mary's measurements using the formula for each.
Mean Calculation:
Mean =\($\frac{\text{sum of values}}{\text{number of values}}$Mean = $\frac{5 + 6 + 6 + 7 + 8}{5}$Mean = 6.4 ounces\\\)
To calculate the standard deviation, we will need to use the following formula:
\($$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2}$$\)
The mean weight of the newly hatched pythons in ounces is 6.4 ounces, and the standard deviation is 1.02 ounces.
Dataset B has a mean of 10.29 and a standard deviation of 4.36.
Dataset C has a mean of 12 and a standard deviation of 5.23.
The datasets differ in terms of their mean and standard deviation. Dataset C has the highest mean and standard deviation, while dataset B has the lowest mean but a similar standard deviation to dataset A.
the datasets differ in terms of their variability, with dataset C having the highest variability and dataset B having the lowest.
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What is 6x + 5x - 6 = 32 + 9x
Answer:
x = 19
Step-by-step explanation:
I hope this helps!!
Step-by-step explanation:
6x + 5x - 6 = 32 + 9x
COMBINE LIKE TERMS:
11x - 6 = 32 + 9x
SUBTRACT 9X FROM BOTH SIDES:
2x - 6 = 32
ADD 6 TO BOTH SIDES
2x = 38
DIVIDE 2 FROM BOTH SIDES:
x = 19
ANSWER:
x = 19
There are 5 pencils in a pack.
Catalina has 2 packs. How many
pencils in all?
(unit)
Reese has 20 packs. How many
pencils in all?
(unit)
Answer:
Catalina has 10 pencils total. (2 x 5 = 10)
Reese has 100 pencils total. (20 x 5 = 100)
Answer:
1. 10 2. 100
Step-by-step explanation
5 x 2= 10
20x 5= 100
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
Domain > 0, Range C(x) > 2
Step-by-step explanation:
x is the distance, distance is always large than 0 => x > 0
=> Domain x > 0
Multiply both sides by 0.75
=> 0.75x > 0
Add both sides by 2
=> 0.75x + 2 > 0 + 2
=> 0.75x + 2 > 2
=> Range C(x) = 0.75x + 2 > 2
Write an equation and solve. Round to the nearest hundredth where necessary.
58 is 100% of what number?
A.) 1 = 58 • x; 39.4
B.) 58 = 1 • x; 60.3
C.) 58 = 1 • x; 58
D.) x = 58 • 1; 58
Answer:
The REAL answer is C.) 58 = 1 • x; 58
Step-by-step explanation:
once you solve the right answer the you can limit options down some and the answer is 58 and so you have to solve the problem backwards that's I got my answer.
5. Two forest fire towers, A and B, are 20.3 km apart. The bearing from A to B is N70°E. The ranger
in each tower observes a fire and radios the fire's bearing from the tower. The bearing from tower A is
N25°E. From Tower B, the bearing is N15°W. How far is the fire from each tower?
The distance between tower A and the fire, x, is approximately 3.992 km, and the distance between tower B and the fire, y, is approximately 14.898 km.
To solve this problem, we can use the law of sines and trigonometric ratios to set up a system of equations that can be solved to find the distances from each tower to the fire.
We know that the distance between the two towers, AB, is 20.3 km, and that the bearing from tower A to tower B is N70°E. From this, we can infer that the bearing from tower B to tower A is S70°W, which is the opposite direction.
We can draw a triangle with vertices at A, B, and the fire. Let x be the distance from tower A to the fire, and y be the distance from tower B to the fire. We can use the law of sines to write:
sin(70°)/y = sin(25°)/x
sin(70°)/x = sin(15°)/y
We can then solve this system of equations to find x and y. Multiplying both sides of both equations by xy, we get:
x*sin(70°) = y*sin(25°)
y*sin(70°) = x*sin(15°)
We can then isolate y in the first equation and substitute into the second equation:
y = x*sin(15°)/sin(70°)
y*sin(70°) = x*sin(15°)
Solving for x, we get:
x = (y*sin(70°))/sin(15°)
Substituting the expression for y, we get:
x = (x*sin(70°)*sin(15°))/sin(70°)
x = sin(15°)*y
We can then solve for y using the first equation:
sin(70°)/y = sin(25°)/(sin(15°)*y)
y = (sin(15°)*sin(70°))/sin(25°)
Substituting y into the earlier expression for x, we get:
x = (sin(15°)*sin(70°))/sin(25°)
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Calculate s2:n1 = 11n2 = 21df1 = 10df2 = 20s1 = 5.4SS1 = 291.6SS2 = 12482
The pooled variance, s_p^2, is 368.6957.
To calculate s2, we first need to calculate the pooled variance using the given formula:
s_p^2 = ((n1 - 1)*s1^2 + (n2 - 1)*s2^2) / (df1 + df2)
We know the values of n1, n2, df1, df2, s1, and SS1. We can use SS1 to calculate the sample variance for the first sample, s1^2, as follows:
s1^2 = SS1 / (n1 - 1) = 291.6 / 10 = 29.16
Similarly, we can use SS2 to calculate the sample variance for the second sample, s2^2, as follows:
s2^2 = SS2 / (n2 - 1) = 12482 / 20 = 624.1
Now, substituting the values in the formula for pooled variance, we get:
s_p^2 = ((11 - 1)*29.16 + (21 - 1)*624.1) / (10 + 20) = 368.6957
Therefore, the pooled variance, s_p^2, is 368.6957.
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What are mathematical formulas placed in software that performs an analysis on a dataset?
Algorithms are the mathematical formulas placed in software that performs an analysis on a dataset.
What is an algorithm?An algorithm in math is a procedure, a description of a set of steps that can be used to solve a mathematical computation.
Now,
The mathematical formulae are placed in a software for analysis in order to obtain results.For this process, an algorithm is followed, with the help of which, the results are derived and obtained.Hence, Algorithms are the mathematical formulas placed in software that performs an analysis on a dataset.
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please help me! Bethany incorrectly simplified the following expression: (4 x 10^11) (3 x 10^-14) + 0.000005 Which of Bethany’s steps show an error based solely on her previous step? Choose all that apply: A. Step one: (4 x 10^11) (3 x 10^-14) + (5 x 10^-5) B. Step two: (12 x 10^-3) + (5 x 10^-5) C. Step three: (120 x 10^-4) + (5 x 10^-5) D. Step four: (120 x 10^-4) + (50 x 10^-4) E. Step five: 170 x 10^-8 F. Step six: 1.7 x 10^-6
Answer:
Below.
Step-by-step explanation:
Step 1: it is 5 x 10^-6 not 5 x 10^-5.
Step 5 : the result of the addition is 170 x 10^-4 not 170 x 10^-8.
Answer: yes that is correct explanation:
Please help me work this out, it's not multiple choice. I'll mark you brainliest.
Answer:
the correct one is c
Step-by-step explanation:
pls mark me as brainliest
Lisa Has $ 7.80 to spend on some tomatoes and loaf of bread. Tomatoes cost $1.20 per pound, and a loaf of bread costs $1.80.
The inequality 1.20x + 1.80 ≤ 7.80 models this situation, where x is the number of pounds of tomatoes
solve the inequality how many piunds of tomatoes can lisa buy?
The perimeter of a rectangle is 48 in. If the length is twice
the width, what is the length of the rectangle?
A) 64 in.
B) 16 in.
C) 8 in.
D) 4 in.
Answer:
\( \boxed{\sf Length \ of \ the \ rectangle = 16 \ in} \)
Given:
Perimeter of rectangle = 48 in
Length = Twice the width
To Find:
Length of the rectangle
Step-by-step explanation:
Let width of the rectangle be 'w'.
So,
Length of the rectangle = 2w
\(\sf \implies Perimeter \ of \ rectangle = 2(Length + Width \\ \\ \sf \implies 48 = 2(2w + w) \\ \\ \sf \implies 48 = 2(3w) \\ \\ \sf \implies 48 = 6w \\ \\ \sf \implies 6w = 48 \\ \\ \sf \implies \frac{ \cancel{6}w}{ \cancel{6}} = \frac{48}{6} \\ \\ \sf \implies w = \frac{48}{6} \\ \\ \sf \implies w = \frac{8 \times \cancel{6}}{ \cancel{6}} \\ \\ \sf \implies w = 8 \: in\)
Width of the rectangle (w) = 8 in
Length of the rectangle = 2w
= 2 × 8
= 16 in
distribute -4(5x ²-2x).
Answer:
-20x^2+8x
Step-by-step explanation:
That is -20x squared by the way
You’re welcome :)
There are 4 floors of classrooms in a school. One classroom takes 16 of each floor. How many classrooms are there in all on the 4 floors?
Answer:
takes 16 what??
if u tell me i can help u x
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
If there are 4 floors and each classroom takes 1/6 of a floor, there are 6 classrooms per floor. Then, since there are 4 floors, you do 6 classrooms X 4 floors, which equals 24 classrooms.
What is scale factor of dilation that transform triangles PQR to triangle PQR explain your answer
Answer:
need coordinates of each or side lengths of each to solve
If a random variable X has the gamma distribution with α=2 and β=1, find P(2.2 P = (2.2 < X < 2.9)
The probability that 2.2 < X < 2.9 for a random variable X with a gamma distribution with α = 2 and β = 1 is approximately 0.0862
Given that X has the gamma distribution with α = 2 and β = 1, we are to find the value of P(2.2 < X < 2.9)
Using the gamma distribution, the pdf can be given as\(\[f(x) = \frac{1}{{\beta ^\alpha }\Gamma (\alpha )}x^{\alpha - 1}{e^{ - x/\beta }}\]\)
Where α = 2 and β = 1.
Substituting these values in the above pdf, we get\(\[f(x) = \frac{1}{{{\text{e}}\Gamma (2)}}{x^1}{e^{ - x}} = xe^{ - x}\]\)
Therefore, P(2.2 < X < 2.9) can be found using the cumulative distribution function as
P(2.2 < X < 2.9) = F(2.9) - F(2.2)
The cumulative distribution function can be given as\(\[F(x) = \int\limits_0^x {f(t)} dt = \int\limits_0^x {te^{ - t} dt} \]\)
Integrating by parts, we get
\(\[\begin{array}{l} u = t\hspace{0.33em}\Rightarrow du = dt \\ dv = {e^{ - t}}\hspace{0.33em}\Rightarrow v = - {e^{ - t}} \end{array}\]\)
Therefore, the integration of F(x) will be\(\[\begin{array}{l} F(x) = - xe^{ - x} - \int { - {e^{ - x}}dt} = - xe^{ - x} + {e^{ - x}} \\ F(x) = (1 - x){e^{ - x}} \end{array}\]\)
Putting the values of 2.2 and 2.9 in F(x), we get
\(\[\begin{array}{l} P(2.2 < X < 2.9) = F(2.9) - F(2.2) \\ P(2.2 < X < 2.9) = (1 - 2.9){e^{ - 2.9}} - (1 - 2.2){e^{ - 2.2}} \\ P(2.2 < X < 2.9) \approx 0.0862 \end{array}\]\)
Hence, the required probability is approximately equal to 0.0862.
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2. What is the value of win this equation?
5w+ 3 = 9
Answer:
w = 1.2 or 6/5
Step-by-step explanation:
math