Question 2(Multiple Choice Worth 5 points)
(03.01 LC)
Triangle J'K'L' shown on the grid below is a dilation of triangle JKL using the origin as the center of dilation:
14
13
12
11
10
9
8
7
6
K
K
04
C
6 7 8 9 10 11 12 13 14
Which scale factor was used to create triangle J'K'L'?
6
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Answers
The dilation of the triangle JKL is with a scale factor of d = 1/2
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be represented as ΔJKL
Now , the coordinates of J = J ( 8 , 12 )
The coordinates of K = K ( 4 , 8 )
The coordinates of L = L ( 12 , 6 )
Now , let the dilated triangle be represented as ΔJ'K'L'
Now , the coordinates of J' = J' ( 4 , 6 )
The coordinates of K' = K' ( 2 , 4 )
The coordinates of L' = L' ( 6 , 3 )
So , the scale factor is given by d = y₂/y₁
Scale factor d = 1/2
Hence , the scale factor of the dilation is 1/2
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Related Questions
A lorry is travelling at 13.5 m/s along a stretch of road where the speed limit is 50 km/h. 1 kilometre = 1000 metres 1 hour = 3600 seconds Show that the lorry is travelling below the speed limit.
Answers
The lorry is travelling below the speed limit.
What is Unit of measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given that A lorry is travelling at 13.5 m/s along a stretch of road where the speed limit is 50 km/h
We know that 1 kilometre = 1000 metres
1 hour = 3600 seconds
It will do a lot more than that in an hour
13.5×3600 m/h
13.5×3600 / 1000 km/hour
= 48.6km/hour
That is definitely less than 50km/h
Hence, the lorry is travelling below the speed limit.
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The satellite Space Explorer flies 30400 miles in 19 hours. Find the rate of change.
Answers
The formula for the rate of change is R = D/T
So when you put that into the formula it will look like R=30400m/19h and the quotient will be 1600 roc.
The point where the lines containing the altitudes are concurrent is called the _____ of a triangle.
Answers
The point where the lines carrying the elevations intersect is the orthocenter of a triangle.
What is a triangle?A polygon with three edges and three vertices is called a triangle.
It is one of the fundamental geometric shapes.
The symbol for a triangle having vertices A, B, and C is ABC.
In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space).
In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.
All triangles are enclosed in a single plane if all of the geometry is the Euclidean plane, however, this is no longer true in higher-dimensional Euclidean spaces.
The orthocenter of a triangle is the intersection of the lines that carry the elevations.
Therefore, the point where the lines carrying the elevations intersect is the orthocenter of a triangle.
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Dana tried to evaluate an expression. Here is her work:
45 [(4 + 3) (60 ÷ 12 - 2)]
-
=
= 45 [7 (60+ 10)]
= 45 - [7.6]
= 45 - 42
= 3
Is Dana's work correct?
Step 1
Step 2
Step 3
Step 4
Answers
Dana is not correct, she has done mistake in the second step.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 45 [(4 + 3) (60 ÷ 12 - 2)]
45 [(4 + 3) (60 ÷ 12 - 2)]
The first step is 45 [7 (60÷ 10)], it is correct
The second step 45- [7.6] is wrong because 45 is a multiple of [7 (60÷ 10)]
45(42)
When we multiply 45 with 42 we get
1890
Hence, Dana is not correct, she has done mistake in the second step.
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to what decimal place should each answer be rounded? how many significant figures does the rounded answer have?
Answers
The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.
Rounding a number is important when providing an answer to a calculation or question. The number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required.
To calculate the number of decimal places and significant figures the answer should be rounded to, the general rule is to round to one more decimal place than the least accurate measurement. For example, if the least accurate measurement used in the calculation is rounded to two decimal places, the answer should be rounded to three decimal places.
The significant figures of the rounded answer can be determined by counting the number of digits in the number, excluding the decimal point. For example, the number 6,782 would have four significant figures, as there are four digits in the number.
In conclusion, the number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required. The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.
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of the 800 students at a certain college, 250 students live on campus and are more than 20 years old. how many of the 800 students live on campus and are 20 years old or less? (1) 640 students at the college are more than 20 years old. (2) 60 students at the college are 20 years old or less and live off campus.
Answers
As per the concept of permutation 100 out of the 800 students at the college live on campus and are 20 years old or less.
A permutation is the arrangement of objects in a specific order. In this problem, we are trying to find the number of students who live on campus and are 20 years old or less.
From the information given, we know that 250 students live on campus and are more than 20 years old. If there are 800 students in total at the college, then the number of students who are not living on campus is
=> 800 - 250 = 550.
We also know that 640 students at the college are more than 20 years old. This means that the number of students who are 20 years old or less is
=> 800 - 640 = 160.
Finally, we know that 60 students at the college are 20 years old or less and live off campus.
So, the number of students who live on campus and are 20 years old or less is
=> 160 - 60 = 100.
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Both trapezoids are similar. The area of the larger trapezoid is 61 ft? Which is the best approximation for the area of the smaller trapezoid?
Answers
The area of the smaller trapezoid is 39 ft².
What is Similarity?Two figures are said to be similar if they share the same shape. Congruent objects are those that are precisely the same size and shape.
Given:
The area of the larger trapezoid is 61 ft².
and, side of smaller trapezium, a = 24 feet
side of larger trapezium, b = 30 feet
So, Area of the larger trapezoid / Area of the smaller trapezoid = b² /a²
61 / Area of the smaller trapezoid = 30² / 24²
Area of the smaller trapezoid = 39 ft²
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In the sport competition, France won more gold medals than Italy, who won more gold medals than Korea. If the total
number of gold medals won by these three countries is three consecutive integers whose sum is 39, find the number of
gold medals won by each.
Answers
The number of gold won by Korea is 12
The number of gold won by Italy is 13
The number of gold won by France is 15
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of gold won by Korea = x
Number of gold won by Italy = x + 1
Number of gold won by France = x + 2
Now,
The total number of gold medals won by these three countries is three consecutive integers whose sum is 39.
This means,
x + x + 1 + x + 2 = 39
3x + 3 = 39
3x = 39 - 3
3x = 36
x = 12
Thus,
Number of gold won by Korea = 12
Number of gold won by Italy = 13
Number of gold won by France = 15
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evaluate the function when x = -2,0, and 5
f(x) = x + 6
Answers
The value of function at x = - 2 is, 4
The value of function at x = 0 is, 6
The value of function at x = 5 is, 11
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The function is,
⇒ f (x) = x + 6
Now, Substitute x = -2 in above equation,
⇒ f (x) = x + 6
⇒ f (-2) = -2 + 6
⇒ f (-2) = 4
Substitute x = 0 in above equation,
⇒ f (x) = x + 6
⇒ f (0) = 0 + 6
⇒ f (0) = 6
Substitute x = 5 in above equation,
⇒ f (x) = x + 6
⇒ f (5) = 5 + 6
⇒ f (5) = 11
Thus, The value of function at x = - 2 is, 4
The value of function at x = 0 is, 6
The value of function at x = 5 is, 11
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which algebraic expression is represented by the model
Answers
The algebraic expression that is represented by the model is 3x + 2y + 5
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
From the model:
Each yellow box, represent x, each blue box represent y and each maroon box represent 1. Hence:
The expression = (x + x + x) + (y + y) + (1 + 1 + 1 + 1 + 1) = 3x + 2y + 5
The algebraic expression is 3x + 2y + 5
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9 subtracted from twice of x gives 5 time x
Answers
Answer:
x = -3.
Step-by-step explanation:
2x - 9 = 5x
2x - 5x = 9
-3x = 9
x = -3.
suppose max owns a light bulb manufacturing company and deter- mines that 3 out of every 75 bulbs are defective. let x be the number of light bulbs tested until he gets a defective for the first time. (a) determine the pmf of x. (b) find the expected number of the light bulbs tested until he gets a defective for the first time.
Answers
a) The pmf of x is a geometric distribution,[tex]p(x) = (3/75)(72/75)^(x-1).[/tex]
b) The expected number of bulbs tested until he gets a defective for the first time is 25.
a) The probability of success (getting a non-defective bulb) is 72/75 and the probability of failure (getting a defective bulb) is 3/75. The pmf of x is a geometric distribution, [tex]p(x) = (3/75)(72/75)^(x-1)[/tex]. This means that the probability of success P is multiplied by [tex](1-P)^(x-1)[/tex] for each x value. b) The expected number of bulbs tested until he gets a defective for the first time is 25. This can be calculated as the sum of all x values multiplied by the corresponding pmf values: [tex]E(x) = Σ x p(x) = 3/75 + 24/75 + 48/75 + 72/75 + ... = 25[/tex].
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5 is more than a number is greater than or equal to 27
Answers
5 more than a number is greater or equal to 27
The "number" can be represented as x.
[tex]\boxed{x+5\geq 27}[/tex]
Which statement is true about the triangle? Question 8 options: w = 99°, because 42 + 39 = 81 and 180 – 81 = 99. w = 261°, because 42 + 39 = 81 and 18 + 81 = 261. w = 81°, because 180 – (42 + 39) = 99 and 180 – 99 = 81. None of the above.
Answers
Answer c
w = 81°, because 180 – (42 + 39) = 99 and 180 – 99 = 81
Step-by-step explanation:
The statement which true about the triangle is a) w = 99°, because 42 + 39 = 81 and 180 – 81 = 99.
What is TriangleA triangle is a shape consisting of 3 sides and 3 vertices (180º total) of a straight line. As early as 300 BC, Euclid had come up with the concept that the sum of three angles is 180°. This makes great contributions to the concept of shapes, such as finding the lengths of their sides and angles.
A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry with vertices A, B and C represented as triangle ABC.
In Euclidean geometry, every three points define a unique triangle and a unique plane (that is, two-dimensional Euclidean space) when they do not collide. In other words, only one plane contains its sides, and every triangle contains many faces. If the whole geometry is just Euclidean planes, there is only one plane and everything is contained within it; however, in high-dimensional Euclidean space, this is no longer true.
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A survey of statistics undergraduate at prosperity university completed a survey that asked for their verbal and math sat scores. they wanted to predict the verbal score based on the math score. interpret the slope12.78% of the variability of verbal score can be explained by the variation in the math score.A.12.78% of the variability of math score can be explained by the variation in the verbal score.B.As the math score increases by 1 point, the verbal score increases by 12.78 points on average.C.As the verbal score increases by 1 point, the math score increases by 12.78 points on average.D.As the math score increases by 1 point, the verbal score increases by 0.3480 points on average.E.As the verbal score increases by 1 point, the math score increases by 0.3480 points on average.
Answers
The correct option: A. 12.78% of the variability of verbal score that can be explained by the linear regression on the math score.
Correlation coefficient: What is it?A "Statistical measurement" that determines the strength of the correlation between the relative movements for two variables is the correlation coefficient. R is used to denote it, and its range is somewhere between (-1 , 1).Students majoring in statistics at Prosperity University responded to a survey that requested their Verbal as well as Math SAT scores. Depending on the math score, they sought to anticipate the verbal score.
Stated values:
R-Squared was initially 12.78%.The verbal score increases up 12.78 points on average for every point in math scored higher, and vice versa.We must first comprehend what a correlation coefficient is, claims the assertion.
Here, depending on the survey results, they seek to determine the verbal score using the math number (independent variable).
The dependent variable is verbal score.Score in math is an independent variable.r² = 0.1278
r = √0.1278
Statement(1): - 12.78% of the verbal score variability that the linear regression on the mathematics score can account for.
TRUE. The provided model accounts for 12.78% of the variability and the verbal and mathematical scores.
Statement #2: A linear regression just on verbal score can account for 12.78% of the variance in math scores.
FALSE, Since the verbal score rather than the numerical score is the dependent variable.
Statement 3: The verbal significant dimension by 12.78 points for every 1 point improvement in math scores.
FALSE, the determination coefficient does not accurately capture the slope of the a linear model.
Statement (4): A math score increases up 12.78 points for every 1 point that the verbal score goes up on average.
FALSE—the determination coefficient does not accurately capture the slope of the a linear model.
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The correct question is-
A survey of Statistics undergraduate at Prosperity University completed a survey that asked for their Verbal and Math SAT scores. They wanted to predict the verbal score based on the math score. The value of R-Squared was 12.78%. Interpret R-squared.
Group of answer choices
A. 12.78% of the variability of verbal score that can be explained by the linear regression on the math score.
B. 12.78% of the variability of math score that can be explained by the linear regression on the verbal score.
C. As the math score increases by 1 point on average, the verbal score increases by 12.78 points.
D. As the verbal score increases by 1 point on average, the math score increases by 12.78 points.
a bag contains 9 blue marbles and 1 green marble. what is the probability of drawing a blue marble (no replacement) followed by a green marble?
Answers
The probability of drawing a blue marble (no replacement) followed by a green marble is 2/207
Total marbles: 2 + 9 + 18 + 10 + 7 = 46
In the first scenario, the likelihood of getting a red marble is 2/46=1/23.
Since there are now 45 marbles, the probability of drawing a purple marble in the second scenario is 10/45, or 2/9.
Therefore, the likelihood of taking out a red marble in the first scenario, failing to replace it, and taking out a purple marble in the second scenario is 1/23 * 2/9.
Therefore, the likelihood of removing a red marble in the first scenario, choosing not to replace it and removing a purple marble in the second scenario
=2/46 x 10/45
=1/23 x 2/9
=2/207
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The assets and liabilities of a doctor are listed below.
Home Value $492,456
Mortgage $287,763
Credit Card Balance $3,458
Owned Work Equipment $20,267
Car Value $15,981
Investments $62,309
Personal Loan $38,924
What is the total value of the doctor's capital assets?
$20,267
$62,309
$528,704
$591,013
Answers
Answer:
Hi! The answer is $591,013
aka D!
Step-by-step explanation:
A capital asset is property that is expected to generate value over a long period of time, such as a building, machinery, and vehicles.
In a class of 25 students, 24 of them took an exam in class and 1 student took a make-up exam the following day. The professor graded the first batch of 24 exams and found an average score of 74 points with a standard deviation of 8.9 points. The student who took the make-up the following day scored 64 points on the exam.1. Does the new student's score increase or decrease the average score? ? Increase Decrease2. What is the new average? Answer to four decimal places.3. Does the new student's score increase or decrease the standard deviation of the scores? ? Increase Decrease
Answers
Since the new score is below the current average score, it sure decreases the average score.
What is the probability of a score falling above or below the mean?Regardless of what a normal distribution looks like or how big or small the standard deviation is, approximately 68 percent of the observations (or 68 percent of the area under the curve) will always fall within two standard deviations (one above and one below) of the meanOne approach is the percentile rank. The percentile rank of a score is the percentage of scores in the distribution that are lower than that score. Percentiles are useful for comparing values.Soft inquiries such as viewing your own credit report will not affect your FICO Score. Hard inquiries such as actively applying for a new credit card or mortgage will affect your score
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a friend tells you that she has a total of three hours available to study for an exam next week. you should advise her to
Answers
You should advise her to divide the three hours into smaller, more manageable study sessions with breaks in between for maximum productivity and retention.
When studying for an exam, it's important to prioritize effectiveness over efficiency. Spending three hours straight on studying can lead to burnout and decreased retention. Instead, you can suggest dividing the time into shorter, more manageable study sessions of 50–60 minutes with 10-15 minute breaks in between. This way, your friend can focus on one topic at a time, recharge during the break, and avoid mental fatigue.
It's important to encourage your friend to take care of their physical and emotional well-being by eating well, getting enough sleep, and finding ways to reduce stress. These habits can help improve their overall focus and performance during their study sessions.
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a marketing research company records the consumer habits of a sample of families from a certain community. the table below summarizes the number of gallons of milk consumed by these families during the last month. number of families gallons of milk for these families, what is the mean number of gallons of milk consumed last month? round your answer to at least one decimal place.
Answers
Answer:
The mean is 11.3 to one decimal place.
Step-by-step explanation:
PLS HELP ASAP
D = Drawing
W = Writing
Jordan spends 75 minutes drawing and writing his comic book every day. He draws for 25 minutes longer than he writes.
D + W = 75
W + 25 = D
How much time does Jordan spend writing each day? Show All Work
Is it possible for Jordan to have spent 30 minutes writing if he spends exactly 75 minutes working on his comic book and draws for 25 minutes longer than he writes.
Yes or No?
To support your answer
_ + _ _ 75
Answers
Jordan spend 25 minutes writing each day
No
How much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:
D + W = 75
W + 25 = D
So, we have
W + W + 25 = 75
Evaluate
W = 25
This means that Jordan spends 25 minutes on writing
is it possible?Based on the answer in (a), the truth statement is No
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Find the degree of this polynomial. 4q
Answers
The degree of the polynomial is 9
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of terms, variables, constants, coefficients, and factors.
They are also made up of some mathematical operations, such as;
AdditionSubtractionMultiplicationDivisionBracketParentheses, etcTo determine the degree of a polynomial which is also an example of algebraic expressions, we need to take note of the sum of the exponents.
From the information given,we have that
4q^2rs^6
The degree would be;
= 2 + 1 + 6
Add values
= 9
Hence, the value is 9
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The complete question:
Find the degree of this polynomial. 4q^2rs^6
I need help with this question
Answers
The mean absolute deviation of the numbers will be 3.5.
What is a mean absolute deviation?The average distance between the data points and a centre point is referred to as absolute deviation. (|xi - x|)/N is the formula for mean absolute deviation. N is the number of terms in the sample, where xi is the sample's individual value and x is the sample's mean or average.
Mean = ( 4 + 15 + 8 +4 + 6 + 11 + 1 + 7 + 3 1 ) / 10
Mean = 57 / 10
Mean = 5.7
The mean absolute deviations are calculated as:-
[tex]MAD = \dfrac{\sum{(X - \bar X)}}{n}[/tex]
MAD = 34 / 10
MAD = 3.4
Hence, the value of the mean absolute deviation is 3.4.
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a company has given you the task to research the amount of snowfall in cleveland from december to february. would you be more interested in looking at the mean, median, or mode?
Answers
The number of measurements, and the mode being the most frequently occurring value among the snowfall measurements.
The mean, median, and mode are all useful measures of central tendency when researching the amount of snowfall in Cleveland from December to February. The mean is calculated by adding up all of the snowfall measurements and dividing that by the number of measurements. For example, if there were 4 snowfall measurements of 10, 20, 30 and 40 inches, the mean would be 25 inches (10+20+30+40 / 4). The median is the middle value of the snowfall measurements when they are arranged from least to greatest. In this example, the median would be 25 inches as well. The mode is the most frequently occurring value among the snowfall measurements. In this example, the mode is also 25 inches.
The mean, median and mode are all useful measures of central tendency when researching the amount of snowfall in Cleveland from December to February, with the mean and median being calculated by adding up all of the snowfall measurements and dividing that by the number of measurements, and the mode being the most frequently occurring value among the snowfall measurements.
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PLEASE HELP I DONT UNDERSTAND
Answers
Answer:
18
Step-by-step explanation:
X= -6 which is x≤2
So,
f(-6) = -2(-6)+6
= 18
qualitative research relies on numerical data and statistical tests as the bases for reporting results. true or false
Answers
The statement "qualitative research relies on numerical data and statistical tests as the bases for reporting results." is False.
Qualitative research does not rely on numerical data and statistical tests as the bases for reporting results.
Qualitative research is a type of research that focuses on understanding and describing the experiences, behaviors, and motivations of individuals and groups.
This type of research typically involves collecting numerical data through methods such as surveys, experiments, and statistical analyses, and using statistical tests to analyze the data and make inferences about the population being studied.
Therefore, it is false that qualitative research relies on numerical data and statistical tests as the bases for reporting results.
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4. Ron is using the following formula to predict
the population of dolphins in the Galapagos
P = 2000(1.2)^t
Islands each year:
Question a): What is the initial value of this
exponential equation?
Question b): What is the constant percentage
growth rate of the loan per year?
Question c): What is the growth factor of the
loan per year?
Answers
The initial value is 2000
The constant percentage growth rate is 20%
The growth factor is 1.2
How to find the initial valueExponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting or initial value
b = the base function
x = the exponents
Considering the given problem, P = 2000(1.2)^t
the initial value = 2000
the base = 1.2
the exponents = t
The base is what says whether it will be an exponential growth or decay. For values of the base greater than 1 is exponential growth
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a survey of consumers in a particular community showed that 10% were dissatisfied with plumbing jobs done in their homes. half the complaints dealt with plumber a, who does 40% of the plumbing jobs in the town. find the probability that a consumer will obtain a an unsatisfactory plumbing job, given that the plumber was a. b a satisfactory plumbing job, given that the plumber was a.
Answers
The probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75.
To find the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A, we first need to determine the proportion of plumbing jobs done by Plumber A that result in consumer dissatisfaction.
Given that half the complaints dealt with Plumber A and that Plumber A does 40% of the plumbing jobs in the town, we can calculate this proportion as follows:
Proportion of unsatisfactory plumbing jobs done by Plumber A = (Half the complaints / Total number of plumbing jobs done by Plumber A)
= (Half the complaints / 40% of the total plumbing jobs in the town)
= (Half of 10% / 40%)
= 10% / 2 / 40% = 1 / 4 = 0.25
Therefore, the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A is 0.25.
To find the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A, we subtract the probability of obtaining an unsatisfactory plumbing job from 1:
Probability of a satisfactory plumbing job given that the plumber was Plumber A = 1 - Probability of an unsatisfactory plumbing job
= 1 - 0.25
= 0.75
Therefore, the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75.
In conclusion, given that Plumber A does 40% of the plumbing jobs in the town and that half the complaints dealt with Plumber A, the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A is 0.25, and the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75. These probabilities can be used to make informed decisions about which plumber to choose for plumbing jobs in the community.
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If 55% of a number is 176 and 35% of the same number is 112, find 90% of that number.
Answers
Answer:
288
Step-by-step explanation:
175 times 100 divided by 55 = 320
320 times .9 = 288
Answer: your answer would be 288
Step-by-step explanation:
Why do you think it is important to consider both salary and benefits when applying for a job? Dave Ramsey video notes
Answers
Answer:
Ramsey Solutions pays an average salary of $84,233 and salaries range from a low of $72,978 to a high of $96,811. Individual salaries will, of course, vary depending on the job, department, location, as well as the individual skills and education of each employee.