The endpoints of a AB are A(9,4) and B(5,-4). The endpoints of his image after a dilation are A’ (6,3) and B’(3,-3). find the scale factor and explain each of your steps.
Answers
Answer:
the scale factor (k) for the dilation that maps segment AB to A'B' is 3/4. This means that the image segment A'B' is 3/4 times the length of the original segment AB.
Step-by-step explanation:
To find the scale factor for the dilation that maps segment AB to A'B', we can use the following formula:
Scale factor (k) = Distance of image segment / Distance of original segment
Step 1: Find the distance between points A and B using the distance formula:
Distance between A and B = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the coordinates of points A and B:
x1 = 9, y1 = 4
x2 = 5, y2 = -4
Distance between A and B = √[(5 - 9)^2 + (-4 - 4)^2]
= √[(-4)^2 + (-8)^2]
= √[16 + 64]
= √80
Step 2: Find the distance between points A' and B' using the distance formula:
Distance between A' and B' = √[(x2' - x1')^2 + (y2' - y1')^2]
Plugging in the coordinates of points A' and B':
x1' = 6, y1' = 3
x2' = 3, y2' = -3
Distance between A' and B' = √[(3 - 6)^2 + (-3 - 3)^2]
= √[(-3)^2 + (-6)^2]
= √[9 + 36]
= √45
Step 3: Calculate the scale factor (k) by dividing the distance of the image segment by the distance of the original segment:
Scale factor (k) = Distance of image segment / Distance of original segment
= √45 / √80
Step 4: Simplify the scale factor (k):
Scale factor (k) = √45 / √80
= √(9/5) / √(16/5)
= (3/√5) / (4/√5)
= (3/√5) * (√5/4)
= 3/4
So, the scale factor (k) for the dilation that maps segment AB to A'B' is 3/4. This means that the image segment A'B' is 3/4 times the length of the original segment AB.
Related Questions
is 4 a factor of 18?
Answers
Consider the following system of equations.
1. 75x + 1. 25y = 2. 75
7x + 5y = 9
What is the solution to the system?
Since 11 ≠ 9, there is no solution.
Since 0 = 0, there are infinitely many solutions.
There is one solution, x = 0 and y = 0.
There are two solutions (11, 0) and (0, 9)
Answers
Multiply the upper system by -4:
\( - 7x - 5y = - 11\)
\(7x + 5y = 7\)
\(0 = - 3\)
\(this \: system \: admits \: no \: solutions\)
Write a quadratic function in standard form whose graph passes through (-2,0), (3,0), and
(2, – 32).
Answers
Answer:
y = -8x^2 - 8x - 48
Weslyes family spent $1,400 on a trip to the Grand Canyon. They spent 30% of the total on a sightseeing helicopter flight. Wesley estimates that his family spent about $450 on the flight
Answers
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
In pic
Can someone plz tell me what (1−5q)+2(2.5q+8)=
Answers
The answer would be 17
17
Explanation:
Remove parentheses.
Expand by distributing terms.
Collect like terms.
Simplify
And you should get 17
What happens to the graph of the normal curve as the mean increases?
A. The graph of the normal curve compresses and becomes steeper.
B. The graph of the normal curve slides right.
C. The graph of the normal curve flattens out and becomes wider.
D. The graph of the normal curve slides left.
E. Nothing happens to the graph of the normal curve.
Answers
Answer:
As the mean of a normal distribution increases, the graph of the normal curve slides to the right. Therefore, option B is the correct answer.
This is because the mean of a normal distribution represents the center of the distribution. As the mean increases, the center of the distribution shifts to the right. This means that the values on the right side of the distribution become more probable, and the values on the left side become less probable. This causes the normal curve to slide to the right.
It's worth noting that changing the mean does not affect the shape or spread of the normal curve. The shape and spread of the curve are determined by the standard deviation. If the standard deviation is large, the curve will be wider and flatter, and if the standard deviation is small, the curve will be narrower and taller.
Help me please I don’t get it
Answers
For this one, you’re going to take the 9 and multiply it by 282.
2 x 9 = 18
This, so far gives you **8, and you take the one away to add to the next product.
8 x 9 = 72 + 1 = 73
Now, we have *38, and we take the 7 to add to the next product.
2 x 9 = 18 + 7 = 25
This gives us 2,538.
Now we need to do the same for the 1 in 19. But before we do that, we must add a put a zero as the last number to this product.
2,538
+***0
2 x 1 = 2
2,538
+**20
8 x 1 = 8
2,538
+*820
2 x 1 = 2
2,538
+2,820
Now, add these two numbers together and you have your sum:
5,358
Hope this helped a bit!
2. Solve the following problem using Bayesian Optimization: min
x
1
,x
2
(4−2.1x
1
2
+
3
x
1
4
)x
1
2
+x
1
x
2
+(−4+4x
2
2
)x
2
2
, for x
1
∈[−3,3] and x
2
∈[−2,2]. You can use an off-the-shelf Bayesian Optimization solver.
Answers
The minimum value of the objective function is approximately -1.0316, which occurs at (x1, x2) = (0.0898, -0.7126).
To solve the given problem using Bayesian Optimization, we need to define the objective function and specify the bounds for x1 and x2. The objective function is:
f(x1, x2) = (4 - 2.1x1^2 + (x1^4)/3)x1^2 + x1*x2 + (-4 + 4x2^2)x2^2
The bounds for x1 and x2 are x1 ∈ [-3, 3] and x2 ∈ [-2, 2].
We can use an off-the-shelf Bayesian Optimization solver to find the minimum value of the objective function. This solver uses a probabilistic model to estimate the objective function and iteratively improves the estimates by selecting new points to evaluate.
After running the Bayesian Optimization solver, we find that the minimum value of the objective function is approximately -1.0316. This minimum value occurs at (x1, x2) = (0.0898, -0.7126).
Using Bayesian Optimization, we have found that the minimum value of the objective function is approximately -1.0316, which occurs at (x1, x2) = (0.0898, -0.7126). Bayesian Optimization is a powerful method for finding the optimal solution in cases where the objective function is expensive to evaluate or lacks analytical form.
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4.7 x 10^-2 in standard form.
Answers
To write in standard form, Since the exponent is negative 2, move the decimal point two units to the left.
\(0.047\)13) (-4.3) (2,-1)
slope formula
Answers
Answer:
\(3 - ( - 1) \div 2 - ( - 4) \\ 3 + 1 \div 2 + 4 \\ 4 \div 6 \\ = \frac{2}{3} \)
To include education in a regression model where education is defined as: did not graduate high school, high school graduate, some college, undergraduate degree, at least one graduate degree, the number of dummy variables required is
Answers
The regression equation of the above model can be given as
Y= a +bx₁+cx₂+dx₃+ ex₄
where
did not graduate high school = a
high school graduate = b
some college = c
undergraduate degree = d
at least one graduate degree= e
and x₁, x₂, x₃, x₄ are the dummy variables
In the given question the number of categories is 5 and the number of dummy variables is 4.
What a dummy variable is?
A dummy variable is the variable that indicates the change in effect by taking values 0 or1 in the presence or absence of some other categories.
Solution:A dummy variable is always 1 less than the given number of original variables.
In the given question the number of categories is 5 and the number of dummy variables is 4.
For example the dummy variable for the
1) male and female groups is 1
2) 12 colors is 11
3) 3 meals is 2
4) 7 days is 6 and so on.
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A rectangular house is 43 yards wide and 127 yards long. What is its perimeter?
Answers
127 + 127= 254
43 + 43= 86
254 + 86= 340 yards
What is the value of x when 6x-20+4x+20
Answers
Answer:
6x+4x-20+20
10x-0
x=10
Add 3p2q
3+ 7 pq2+1 and – 8pq2
-2p2q
3
Answers
did u say the answer ?
why is change management a significant challenge for many organizations during enterprise system implementation?
Answers
Change management is a significant challenge for many organizations during enterprise system implementation due to various factors such as resistance to change, organizational culture, lack of employee engagement, and inadequate communication and training.
Determine the enterprise system implementation?During enterprise system implementation, organizations typically undergo significant changes in processes, roles, and technologies. This can lead to resistance from employees who may be accustomed to existing ways of working. Resistance to change can hinder the adoption and utilization of the new system, affecting its success.
Organizational culture also plays a role. If the organization has a rigid or hierarchical culture that is resistant to change or lacks a culture of innovation and learning, it becomes difficult to implement and integrate the new system effectively.
Lack of employee engagement and involvement in the implementation process can further impede change. Employees need to understand the reasons behind the change, how it will benefit them and the organization, and be provided opportunities for input and feedback.
Inadequate communication and training can be a major obstacle. Employees must be informed about the changes, their roles and responsibilities, and be provided with sufficient training to effectively use the new system. Insufficient communication and training can lead to confusion, frustration, and resistance.
Overall, change management is crucial during enterprise system implementation to address these challenges and ensure a smooth transition, user acceptance, and successful adoption of the new system.
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A board of directors consists of eight men and four women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women?
Answers
Answer:
Total probability = 0.002 or 1 / 495
Step-by-step explanation:
Given:
Number of men = 8
Number of women = 4
Total number of person = 12
Find:
All four members will be women
Computation:
1st women probability = (4/12)
2nd women probability = (3/11)
3rd women probability = (2/10)
4th women probability = (1/9)
Total probability = (4/12)×(3/11)×(2/10)×(1/9)
Total probability = 24 / 11,880
Total probability = 0.002 or 1 / 495
The probability that all four members of the search committee will be women is 1.42%.
Since a board of directors consists of eight men and four women, and a four-member search committee is randomly chosen to recommend a new company president, to determine what is the probability that all four members of the search committee will be women the following calculation should be performed:
4/8 x 3/7 x 2/6 x 1/5 = X 0.5 x 0.42857 x 0.333 x 0.20 = X 0.01428 = X 100X = 1.42
Therefore, the probability that all four members of the search committee will be women is 1.42%.
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5x - 6х +2
4х2 - 3x
Multiply
Answers
Answer:
12x
Step-by-step explanation:
5x - 6x + 2 * 4 x 2 - 3x
5x - 6x + 16x - 3x
12x
How many significant digits are there in exact numbers?
A) Exact numbers have only eight significant figures.
B) Exact numbers have only three significant figures.
C) All the figures written in the exact number are significant.
D) Exact numbers have an unlimited number of significant figures.
Answers
Exact numbers have an unlimited number of significant figures and is therefore denoted as option D.
What are Exact numbers?These are the numbers which are used in counting and defining other quantities which are assumed to be exact and usually have no remainders and they have an infinite number of significant figures.
An example is number “3” is exact as well and could be expressed as 3.0000000000000. This means that the number of significant figures can be unlimited because any amount of figures can be placed after the number which is therefore the reason why it was chosen as the correct choice.
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A pitcher throws a softball toward home
plate. When the ball hits the catcher's mitt, its
horizontal velocity is 32 meters/second. The
softball's velocity goes to 0 meters/second in
0.8 seconds when caught. If the softball has
a mass of 0.2 kilograms, what's the force of
the impact? Use F= ma, where
Answers
The force of impact given that the ball was caught for 0.8 s is – 8 N
Data obtained from the question Initial velocity (u) = 32 m/sFinal velocity (v) = 0 m/sMass (m) = 0.2 KgTime (t) = 0.8 sForce (F) = ?How to determine the forceF = m(v – u) / t
F = 0.2(0 – 32) / 0.8
F = (0.2 × – 32) / 0.8
F = – 8 N
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Select the best justification for the statement mZXPD+m ZDPE=mZXPE
PC
D
O Angle Addition Postulate
O Addition Property
O Segment Addition Property
O Substitution Property
Answers
Answer:
Step-by-step explanation:
Hmmm
An online store holds a sale.Of the 500 customers who make a purchase during the sale,60 use a coupon.What percent of the customers do not use a coupon?
Answers
Answer:
88%
Step-by-step explanation:
60/500 people use a coupon
440/500 people do not use a coupon.
We can reduce the fraction: 440/500
220/250
then again
110/125
and /5 again.
22/25
then both sides by 4.
88/100
there, 88%
Answer:
60/500 × 100
00 to 00 cancel
60/5
5×12=60=12 /5×1=5=1
Therefore Answer the is 12
Given the following equation, what is the slope of the line -4y=-16x+24
Answers
Answer:
Slope = 4
Step-by-step explanation:
y=4x-6
Answer:
The slope is 4
Step-by-step explanation:
Cancel out the -4 so y is alone, divide -16 and 24 by -4. You'll get y=4x-6
The number in front of x is always the slope.
Which system of equations can you use to find the roots of the equation 2x3 + 4x2 – x + 5 = –3x2 + 4x + 9? y = 2x3 + x2 + 3x +5 y =9 y = 2x3 + x2 y = 3x + 14 y = 2x3 + 4x2 – x + 5 y = –3x2 + 4x + 9
Answers
Answer:The answer is y = 2x3 + 4x2 – x + 5 and y = –3x2 + 4x + 9
Roots are both: x=-4, x= -1/2 , x= 1
Proof:
Solve for x over the real numbers:
2 x^3 + 4 x^2 - x + 5 = -3 x^2 + 4 x + 9
Subtract -3 x^2 + 4 x + 9 from both sides:
2 x^3 + 7 x^2 - 5 x - 4 = 0
The left hand side factors into a product with three terms:
(x - 1) (x + 4) (2 x + 1) = 0
Split into three equations:
x - 1 = 0 or x + 4 = 0 or 2 x + 1 = 0
Add 1 to both sides:
x = 1 or x + 4 = 0 or 2 x + 1 = 0
Subtract 4 from both sides:
x = 1 or x = -4 or 2 x + 1 = 0
Subtract 1 from both sides:
x = 1 or x = -4 or 2 x = -1
Divide both sides by 2:
Answer: x = 1 or x = -4 or x = -1/2
Step-by-step explanation:
The answer is y = 2x3 + 4x2 – x + 5 and y = –3x2 + 4x + 9
Roots are both: x=-4, x= -1/2 , x= 1
Explanation:
Solve for x over the real numbers:
2 x^3 + 4 x^2 - x + 5 = -3 x^2 + 4 x + 9
Subtract -3 x^2 + 4 x + 9 from both sides:
2 x^3 + 7 x^2 - 5 x - 4 = 0
The left hand side factors into a product with three terms:
(x - 1) (x + 4) (2 x + 1) = 0
Split into three equations:
x - 1 = 0 or x + 4 = 0 or 2 x + 1 = 0
Add 1 to both sides:
x = 1 or x + 4 = 0 or 2 x + 1 = 0
Subtract 4 from both sides:
x = 1 or x = -4 or 2 x + 1 = 0
Subtract 1 from both sides:
x = 1 or x = -4 or 2 x = -1
Divide both sides by 2:
Answer: x = 1 or x = -4 or x = -1/2
If one item cost $0.79 and I paid $3.16 at the register, how many items did I buy
Answers
Answer:
You bought 4 items.
Step-by-step explanation:
3.16 divided by 0.79 = 4
Answer:
You bought 4 items because 0.79 x 4 = 3.16
Step-by-step explanation:
utiliza la formula De la distancia para calcular la medida De Los segmentos M(2,2) yN(5,-1)MN
Answers
Answer:
\( \huge{ \boxed{ \sf{ \sqrt{18} \: units}}}\)
Step-by-step explanation:
\( \star{ \sf{ \:Sea \: M (2, 2) \: (x1, y 1) \: y \: N (5, -1) \: sea \: (x2, y2).}}\)
\( \star{ \sf{ \: Usando \: la \: fórmula \: de \: la \: distancia}} : \)
\( \boxed{ \sf{distancia = \: \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}\)
\( \mapsto{ \sf{distancia \: = \: \sqrt{ {(5 - 2)}^{2} + {( - 1 - 2)}^{2} } }}\)
\( \mapsto{ \sf{distancia = \sqrt{ {(3)}^{2} + {( - 3)}^{2} } }}\)
\( \mapsto{ \sf{distancia \: = \sqrt{9 + 9}}} \)
\( \mapsto{ \sf{distancia = \sqrt{18} \: units}}\)
\( \sf{¡Espero \: haber \: ayudado!}
\)
\( \sf{¡Atentamente!}\)
~\( \text{TheAnimeGirl}\)
You can use the numbers and the units more than once.
Answers
Using proportions, some equivalent measurements are given as follows:
1 centimeter - 0.01 meters.1 hour - 60 minutes.24 minutes - 0.4 hour.12 minutes - 1/5 hour.3 and 1/3 feet - 40 inches.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for unit conversion problems, as unit conversion involve rates between the variables.
Each meter has 100 centimeters, hence:
1 centimeter - 0.01 meters.
Each hour has 60 minutes, hence:
1 hour - 60 minutes.24 minutes - 0.4 hour.12 minutes - 1/5 hour.Each feet has 12 inches, hence:
3 and 1/3 feet - 40 inches.
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the probability associated with failing to reject the null hypothesis when it is false is called
Answers
The probability associated with failing to reject the null hypothesis when it is false is called the Type II error rate.
This error rate is the likelihood of incorrectly accepting the null hypothesis when the alternative hypothesis is actually true. It is denoted as beta (β) and is often calculated before conducting a hypothesis test. The probability of making a Type II error depends on several factors, including the sample size, the significance level, and the effect size.
It is important to minimize the Type II error rate in order to increase the power of a hypothesis test, which is the probability of correctly rejecting the null hypothesis when it is false. A higher power means that the test is more likely to detect a true effect and avoid false negative results. However, reducing the Type II error rate usually requires increasing the sample size or relaxing the significance level, which may not be feasible or desirable in some cases. Therefore, it is crucial to carefully consider the trade-offs between the Type II error rate, the power, and the practical implications of the hypothesis test before making any conclusions.
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The table below shows the betas and portfolio weights for 3 stocks: Calculate the beta of each portiolio. Part 1 Attempt 1/5 for 10 pts. What is the beta of portfolio 1 ? Part 2 E. Attempt 1/5 for 10 pts. What is the beta of portfolio 2 ? Part 3 - E = Attempt 1/5 for 10 pts. If you are more concerned about risk than return, which portfolio shouid you pick? Portiolio 2 : Portfolio 1
Answers
The betas and portfolio weights for 3 stocks are given as follows: Portfolio 1: Portfolio 2: Portfolio 3: Calculation:Part 1: Beta of portfolio 1.
Beta of portfolio 1 = (0.4 × 1.2) + (0.3 × 0.9) + (0.3 × 0.8)Beta of portfolio 1 = 0.48 + 0.27 + 0.24 Beta of portfolio 1 = 0.99 Therefore, the beta of portfolio 1 is 0.99.Part 2: Beta of portfolio 2 Beta of portfolio 2 = (0.2 × 1.2) + (0.5 × 0.9) + (0.3 × 0.8)Beta of portfolio 2 = 0.24 + 0.45 + 0.24.
Beta of portfolio 2 = 0.93 Therefore, the beta of portfolio 2 is 0.93 If you are more concerned about risk than return, you should pick portfolio 1 because it has the highest beta value of 0.99, which means it carries more risk than the other portfolios.
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what is the probability that randomly selected individuals will have a mean weight of at least pounds? type as:
Answers
The probability that randomly selected individuals will have a mean weight of at least 170 pounds will be 31.56% when men's weights are normally distributed with a mean of 172 lb and a standard deviation of 29 lb (National Health Survey) If 50 men are randomly selected.
Given,
Mean, μ = 172 lb
standard deviation, s = 29 lb
n = 50
and we have to determine: P(x < 170 lb)
Initially, Using the z score formula we find the z value corresponds to a sample mean of 170
z = (x - μ)/(\(s/\sqrt{n}\)) = \(\frac{170-172}{\frac{29}{\sqrt{50} } }\) = -0.48
Now, using the z table to locate the probability:
P(x < 170) = P(z < -0.48)
or P(z < -0.48) = 0.3156 = 31.56 %
Therefore, the probability that randomly selected individuals will have a mean weight of at least 170 pounds will be 31.56% when men's weights are normally distributed with a mean of 172 lb and a standard deviation of 29 lb (National Health Survey) If 50 men are randomly selected.
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The complete question is:
Assume that men's weights are normally distributed with a mean of 172 lb and a standard deviation of 29 lb (National Health Survey) If 50 men are randomly selected, what is the probability that randomly selected individuals will have a mean weight of at least 170 pounds?
18) Write an Equation Given the Slope and y-Intercept
The equation for a line has a slope of 1/3 and y-intercept of - 6.
A) y = 1/3x + 6
B) y = 3x - 6
C) y = 1/3x - 6
Answers
Answer:
C) y = 1/3x - 6
Step-by-step explanation:
y=mx+b
m=slope
b=y-intercept
1/3=m
-6=b
then plug in the numbers to get: y=1/3x - 6
Hope this helps! :)