After which transformation of △ABC would the image △A′B′C′ not have the same area?A. rotationB. dilationC. translationD. reflection
Answers
The area of a triangle is preserved by translations, rotations and reflections. The only transformation that alters the area is the dilation.
Related Questions
Question 14 (Essay Worth 12 points)
(Comparing Data HC)
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Sky View School
9, 7, 2,0
8, 7, 6, 5, 5, 5, 4, 3, 1, 0
0
1
South Lake School
5,8
0, 1, 2, 6, 6, 8
2
0 3
Key: 2|1|0 means 12 for Sky View and 10 for South Lake
5, 5, 6, 7, 8
0,6
Part A: Calculate the measures of center. Show all work. (5 points)
Part B: Calculate the measures of variability. Show all work. (5 points)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (2 points)
7
Answers
To find the measures of center, we need to determine the median for each school.
For Sky View School:
Arrange the data in order: 0, 0, 1, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9
The median is the middle value, which is 5.
For South Lake School:
Arrange the data in order: 0, 0, 1, 2, 2, 5, 6, 6, 8
The median is the middle value, which is also 5.
Therefore, the median class size for both schools is 5.
Part B: Measures of variability
To find the measures of variability, we need to determine the range and interquartile range (IQR) for each school.
For Sky View School:
The smallest value is 0 and the largest value is 9, so the range is 9 - 0 = 9.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 1 + 2 + 3 + 4)/5 = 2. The third quartile is the median of the upper half, which is (6 + 7 + 8 +9)/4 = 7.25 (rounded to two decimal places).
Therefore, the IQR is 7.25 - 2 = 5.25.
For South Lake School:
The smallest value is 0 and the largest value is 8, so the range is 8 - 0 = 8.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 0 + 1 + 2)/4 = 0.75 (rounded to two decimal places). The third quartile is the median of the upper half, which is (6 + 6 + 8)/3 = 6.67 (rounded to two decimal places).
Therefore, the IQR is 6.67 - 0.75 = 5.92 (rounded to two decimal places).
Part C: Choosing a school based on class size
If you are interested in a smaller class size, South Lake School is the better choice. This is because the range and IQR for South Lake School are smaller than those for Sky View School, indicating that the class sizes at South Lake School are more consistent and less variable. Additionally, the largest class size at South Lake School is 8, while the largest class size at Sky View School is 9, further indicating that South Lake School may have smaller class sizes overall.
Measures of center for Sky View School:
Mean = (0+1+2+3+4+5+5+5+6+7+7+8+9)/13
Mean = 4.8
Median = 5
Measures of center for South Lake School:
Mean = (0+1+2+2+3+5+6+6+8+8)/10
Mean = 4.1
Median = 5
Part B:
Measures of variability for Sky View School:
Range = 9 - 0 = 9
Interquartile Range (IQR) = Q3 - Q1 = 7 - 2 = 5
Variance = [(0-4.8)^2 + (1-4.8)^2 + (2-4.8)^2 + (3-4.8)^2 + (4-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (6-4.8)^2 + (7-4.8)^2 + (7-4.8)^2 + (8-4.8)^2 + (9-4.8)^2]/12
Variance = 7.6
Standard Deviation = √7.6
Standard Deviation = 2.76
Measures of variability for South Lake School:
Range = 8 - 0 = 8
Interquartile Range (IQR) = Q3 - Q1 = 6 - 1 = 5
Variance = [(0-4.1)^2 + (1-4.1)^2 + (2-4.1)^2 + (2-4.1)^2 + (3-4.1)^2 + (5-4.1)^2 + (6-4.1)^2 + (6-4.1)^2 + (8-4.1)^2 + (8-4.1)^2]/9
Variance = 6.45
Standard Deviation = √6.45
Standard Deviation = 2.54
Part C:
If you are interested in a smaller class size, South Lake School is a better choice for you. This is because the measures of center and variability for South Lake School are both smaller than those for Sky View School.
What is the height of the trapezoid?
Answers
Answer:
4 inches
Step-by-step explanation:
The line that is perpendicular to the bottom of the trapezoid is the height.
Mrs, Hansen usually makes a disinfecting solution by adding 1 2/3 cups of bleach to 5 gallons of water. Today, however, she is using only 3 1/2 gallons of water. She wants to make the solution so that it has the same disinfecting strength. How much bleach should she use?
Answers
Answer:
1 1/6 cups
Step-by-step explanation:
You want to know the amount of bleach to use with 3 1/2 gallons of water to obtain the same strength as 1 2/3 cups of bleach in 5 gallons of water.
ProportionThe quantities are proportional, so the amount of bleach (b) will need to be ...
b/(3 1/2 gal) = (1 2/3 cups)/(5 gal)
Multiplying by 3 1/2 gal, we get ...
b = (3 1/2)(1 2/3)/5 cups = 1 1/6 cups
Mrs. Hanson should use 1 1/6 cups of bleach in 3 1/2 gallons of water.
Taylor’s dad offered to loan her $1,500 to buy a car with an annual interest rate of 15 percent. Assuming she pays her dad back at the end of one year, how much will she have paid for the car?
Answers
Answer:
$1,725
Step-by-step explanation:
Given that
The loan amount is $1,500
The interest rate is 15%
And, the time period is one year
We need to find out the future value
so,
The future value = present value × (1 + rate of interest)^number of years
= $1,500 × (1 + 0.15)^1
= $1,500 × 1.15
= $1,725
H
6:00 PM
What is a frostbite?
Answers
Prove the diagonals of a parallelogram bisect one another. Be sure to create and name the appropriate geometric figures
Answers
The diagonals of a parallelogram bisect one another. This is illustrated below.
What is a parallelogram?A parallelogram is a straightforward quadrilateral with two parallel sides. A parallelogram's opposite or facing sides are equal in length, and its opposite angles are equal in size.
A quadrilateral with two pairs of parallel sides is known as a parallelogram. A parallelogram's opposite sides are equal in length, and its opposite angles are equal in size. Furthermore, the interior angles on the same transversal side are supplementary. The total of all interior angles is 360 degrees.
Let's illustrate the parallelogram as ABCD.
AC and BD are diagonals
AC and BD intersect at point E
AB is parallel to CD | opposite sides of a parallelogram are parallel
AB = CD | are congruent opposite sides of a parallelogram
angle BAC = angle DCA |interior angles of parallel lines
angle ABD = angle CDB |interior angles of parallel lines
Triangle ABE = Triangle CDE | ASA
EA = EC | corresponding sides of congruent triangles are congruent.
E bisects AC| AE = EC
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Now you try on your own.
Kelly wants to build a new wardrobe for herself with only clothing pieces she loves, fit her well, and coordinate together. She already has most of the pieces she will use, but needs to save up to go shopping for the remaining items. She has already saved some money from her job, and she decides to set aside money weekly from her tips. The expression $25w+$65
represents the amount of money Kelly will have saved after some amount of weeks. What does each part of this expression represent?
$25=
Answer
w=
Answer
$65=
Answer
For this specific expression, would it make sense to plug in a negative number for w
? Answer
For this specific expression, would you ever expect to get a number less than 65
for your total amount saved?
Answers
The Interpretatiom of the equation is that;
w represents number of weeks she will have saved for the remaining items
$25 represents the amount she saves per week
$65 represents the amount she has already saved
How to solve algebra word problems?The algebra word problem can be solved by using variables to denote certain parameters I'm the question.
The general form of equation of a line in slope intercept form is;
y = mx + c
Where;
m is slope
c is y-intercept
We are given the equation:
$25w + $65
This equation represents the amount of money Kelly will have saved after some amount of weeks.
Thus;
w represents number of weeks she will have saved for the remaining items
$25 represents the amount she saves per week
$65 represents the amount she has already saved
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In the chi-square test of association, as the difference between the observed and expected proportions increases... a. the chi-square test statistic increases b. the chi-square critical value increases c. the likelihood of rejecting the null hypothesis increases d. the likelihood of rejecting the null hypothesis decreases e. the chi-square critical value decreases f. the chi-square test statistic decreases
Answers
Answer:
Opton A
Step-by-step explanation:
In the chi-square test of association, as the difference between the observed and expected proportions increases, the chi-square test statistic also increases. This is because if the claim made in the null hypothesis is true: the claim that frequency of the observed is equal to that of the expected (Oi = Ei) then, the observed and the expected values are close to each other and the difference Oi − Ei is small for each category and the chisquare test statistic is small.
But when the observed data does not fit to what is expected as of the null hypothesis, the difference between the observed and expected values, Oi − Ei is large producing a large chi square statistic.
Mr. Morales has 10 eggs. He uses 1/4 dozen. How many dozen eggs does
he have left?
Answers
Answer:
7 he has 7 eggs left
Step-by-step explanation:
1 dozen is 12 soo... that should help
Your taxable wages for Social Security purposes are $1100. How much is your Social Security tax if you have previous taxable wages of $102,000?
Answers
If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.
To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.
Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.
First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:
Social Security tax = $102,000 x 0.062 = $6,324
Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:
Social Security tax = $1,100 x 0.062 = $68.20
Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.
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Which of the following would not be listed under cash outflows in a financial plan?
a.
car payments
b.
insurance premiums
c.
interest earned
d.
mortgage payment
Answers
Answer: c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
cash flow is the money going into the business while cash out is the money going out of the business
cash payment is an outflow, money is going outinsurance premium is an outflow, money is going outmortage payment is also an outflowthe only thats a inflow is the interest earned.
..................
..
Answers
Answer:
The answer is C 18
Step-by-step explanation:
4^2+8/4= 16+2=18
f(x) = x3 – 3x2 - x + 3
what is the domain and range?
Answers
Answer:
Domain: (-∞,∞)
Range: (-∞,∞)
Hope this helps.
some adults and children are watching a musical there are n children there are 25 fewer adults
Answers
According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99
A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.
B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.
To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.
Note: The given question is incomplete. The complete question is:
Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.
A) find the number of adults in terms of 'N'.
B) if there are 124 children how many adults are there?
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Use the model below to calculate 9÷1/3.
A green rectangle is divided into 9 equal parts arranged into 3 rows of 3 cells each.
A.
9/3
B.
3/9
C.
13 1/2
D.
27
Answers
Using thie model ,The answer is D. 27.
To calculate 9÷1/3 using the model below, we can imagine dividing the green rectangle into thirds vertically. Each third would contain 3 cells.
Then, we can see that there are a total of 9 cells in the rectangle. Since we are dividing by 1/3, we need to find out how many sets of 1/3 are in 9.
We can see that there are 3 sets of 1/3 in each row (since each row contains 3 cells, which are thirds). So, in total, there are 3 rows of 3 sets of 1/3, which gives us:
9÷1/3 = 3 rows x 3 sets of 1/3 = 9 sets of 1/3 = 27
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I need to Expand 2(x + 3) =
Answers
Answer:
2x+6
Step-by-step explanation:
you multiply what is inside by what is outside
2(x+3) giving 2x+6
it is given in a factorised form , by removing common factor that is 2
WHAT IS THE ANSWER TO THIS QUESTION
Answers
Now, let’s solve for the area of the triangle.
The base of the triangle is 20cm and the height of the rectangle is 16-7=9cm
The area is 1/2*20*9
=90cm
We added the two values together to get the combined area of the shape. 140+90=230cm
Hope this helps!
Can you please help me with this i will give you a branlist
Answers
Answer:
The answer is C
Step-by-step explanation: because it is reflecting and is backwards.
Answer
try the third G luck and hope this helps!!
Step-by-step explanation:
A glacier is a giant mass of rocks and ice that flows downhill like a river. A certain glacier moves at a rate of 19 inches a day. Find the distance in feet the glacier moves in a year. (Assume 285 days a year)
L=___ ft
(Round to two decimal places as needed.)
Answers
L=19(285)
L=5415 ft.
f^-1(x)= -3+^3 squareroot x+4 is the inverse function of f(x)= (x-3)^3 +4 true or false
Answers
PLEASE HELP ON QUESTION ASAP !
hi ! I really need help understanding paragraph and I've also added a question about paragraph by me down below . Would like explanation in simple words.
If answers correct I'll rate you five stars a thanks and maybe even brainliest
Paragraph I needed help understanding:
If two or more cells are connected together side by side, the voltage across them is sum of the voltage of each cell. This is because both cells are pushing same way.
My Question about paragraph:
If the sum lets say was 4.5v would every individual cell be worth 4.5 as it says in question ' voltage across them is the sum of voltage of each cell ' or are they each a different value? And how would we be able to find value?.
Answers
If the sum of the voltage is 4.5V, it is possible that different cells have different voltages. For example, three cells with voltages 1V, 1.5V, and 2V could be connected together side by side to give a total voltage of 4.5V.
To find the voltage of each cell, we would need to know the voltage across each cell or the voltage of the other cells connected in the circuit. Then we could use the fact that the sum of the voltages across all cells in the circuit is equal to the total voltage of the circuit to solve for the voltage of each cell.
What is the measure of each interior angle of the regular polygon pictured below? If necessary, round to the nearest tenth.
Answers
\(\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108\)
What is the perimeter of the shape?
40 feet
43 feet
51 feet
67 feet
Answers
Answer:
40 feet?
Step-by-step explanation:
11 ft + 3 ft + 4 ft + 6 ft + 3 ft + 3 ft + 4 ft + 6 ft = 40
Solve the system of equations using the substitution or elimination method.
y = 4x - 7
4x + 2y = -2
.
Show your work
Correct x and y
Answers
The solution to the system of equations is x = 1 and y = -3.
To solve the system of equations using the substitution or elimination method, let's start with the substitution method.
Given equations:
y = 4x - 7
4x + 2y = -2
We'll solve equation 1) for y and substitute it into equation 2):
Substituting y from equation 1) into equation 2):
4x + 2(4x - 7) = -2
4x + 8x - 14 = -2
12x - 14 = -2
Now, we'll solve this equation for x:
12x = -2 + 14
12x = 12
x = 12/12
x = 1
Now that we have the value of x, we can substitute it back into equation 1) to find y:
y = 4(1) - 7
y = 4 - 7
y = -3
Therefore, the solution to the system of equations is x = 1 and y = -3.
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The length of a rectangle is 2 less than twice the width. The perimeter of the rectangle is 38. Find the length and the width of the rectangle.
Answers
Answer:
YEET A DOG
Step-by-step explanation:
YEETING A DOG GIVES U COOL POINTS LOLOLOLOLOLOLOLOLOLOLOL
Use the t-distribution to find a confidence interval for a difference in means μ1−μ2 given the relevant sample results. Give the best estimate for μ1−μ2, the margin of error, and the confidence interval. Assume the results come from random samples from populations that are approximately normally distributed.
A 99% confidence interval for μ1−μ2 using the sample results x⎯⎯1=535, s1=103, n1=380 and x⎯⎯2=465, s2=86, n2=200
Enter the exact answer for the best estimate and round your answers for the margin of error and the confidence interval to two decimal places.
Answers
The best estimate and the degree of freedom when the t-distribution is used to find a confidence interval is 7 and 56 respectively.
How to illustrate the research?The best estimate from the information given in the research will be:
= X1 - X2
= 53.5 - 46.5
= 7
The degree of freedom will be:
= 38 + 20 - 2
= 56
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can someone help please
Answers
Answer:
mhm
Step-by-step explanation:
a) Work out the prime factor decomposition of 396. Give your
answer in index form.
b) The prime factor decompositions of five numbers are shown
below. Use your answer to part a) to work out which two of
these numbers are factors of 396.
88=2³×11
121=11²
9=3²
14=2×7
22=2×11
Answers
Answer:
a) Prime factorization of 396: 2² × 3¹ × 11¹
b) Factors of 396: 88 and 9.
Step-by-step explanation:
a) To find the prime factorization of 396, we can start by dividing it by the smallest prime number, which is 2:
396 ÷ 2 = 198
Now we can write:
396 = 2 × 198
Next, we can divide 198 by 2 again:
198 ÷ 2 = 99
So we have:
396 = 2 × 2 × 99
Now we need to find the prime factorization of 99. We can start by dividing it by 3:
99 ÷ 3 = 33
So we can write:
396 = 2 × 2 × 3 × 33
Now we need to find the prime factorization of 33. We can start by dividing it by 3 again:
33 ÷ 3 = 11
So we have:
396 = 2 × 2 × 3 × 11 × 1
We don't need to include the factor of 1, so we can write the prime factorization of 396 in index form as:
396 = 2² × 3¹ × 11¹
b) To find which two of the given numbers are factors of 396, we need to check if all the prime factors of each number are also prime factors of 396.
The prime factorization of 88 is 2³ × 11. Both 2 and 11 are factors of 396, so 88 is a factor of 396.
The prime factorization of 121 is 11². 11 is a factor of 396, but there is no factor of 121 that matches the remaining prime factors of 396 (2² × 3¹), so 121 is not a factor of 396.
The prime factorization of 9 is 3². Both 3 and 2 are factors of 396, so 9 is a factor of 396.
The prime factorization of 14 is 2 × 7. 7 is not a factor of 396, so 14 is not a factor of 396.
The prime factorization of 22 is 2 × 11. Both 2 and 11 are factors of 396, so 22 is a factor of 396.
Therefore, the two numbers that are factors of 396 are 88 and 9.
if a chi-square test for equality of proportions has 6 populations, then degrees of freedom must be used
Answers
The chi-square test for equality of proportions with 6 populations will have 5 degrees of freedom, which allows for more independent observations and more reliable results.
The degrees of freedom for a chi-square test for equality of proportions are calculated using the following formula: df = (r-1)(c-1). In this formula, r represents the number of populations and c represents the number of categories. In the case of 6 populations, the degrees of freedom would be calculated as df = (6-1)(1-1) = 5. This means that the chi-square test for equality of proportions with 6 populations will have 5 degrees of freedom. This is necessary because the chi-square test measures the difference between the expected and observed frequencies of a given variable, and degrees of freedom are used to determine the number of independent observations that can be made. The higher the number of degrees of freedom, the more independent observations that can be made, and thus the more reliable the results of the chi-square test are.
Therefore, the chi-square test for equality of proportions with 6 populations will have 5 degrees of freedom, which allows for more independent observations and more reliable results.
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A
-6
Find the distance, d, of AB.
A = (-5, 5) B = (5, -5)
-4 -2
f
&
-2
-4
9
N
4
B
d = √|×₂ − ×₁1² + y2 - Y₁|²
d = [?]
Round to the nearest tenth.
Distance
Enter
Answers
Answer:
88
Step-by-step explanation: