The solution is Option A.
The dilation scale factor is given by the equation D = 5
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 dilation scale factor be represented as D
Now , the equation will be
The coordinates of the triangle ΔABC is given as
A ( -3 , -3 ) , B ( 3 , 3 ), C ( 0 , 3 )
And , coordinates of the triangle ΔA'B'C' is given as
A′ ( -15 , -15) , B′ ( 15 , 15 ) , C′ ( 0 , 15 )
The dilation factor is given by D = x₂ / x₁ or D = y₂ / y₁
Substituting the values in the equation , we get
D = -15 / -3 = 5
And , D = 15 / 3 = 5
Hence , the dilation factor is 5
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is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?
(a) The sample size for the above sample is 15.
(b) The sample mean for these data is 3.8.
(c) The sample median is 3.6.
(d) To compute the 20% trimmed mean for the above data set is 3.7.
(e) The sample mean is less descriptive as the location's center (median) than the trimmed mean.
The following measurements were recorded for the drying time, in hours
3.4 2.5 4.8 2.9 3.6 is:
2.8 3.3 5.6 3.7 2.8
4.4 4.0 5.2 3.0 4.8
(a) We have to determine the sample size for the above sample.
The number of participants or observations included in a study is referred to as the sample size. This number is commonly represented by the symbol n.
Sample Size (n) = 15
(b) We have to calculate the sample mean for these data.
Sample Mean = Total Sum of data/Total Number
Sample Mean = (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.6 + 3.7 + 2.8 + 4.4 + 4.0 + 5.2 + 3.0 + 4.8)/15
Sample Mean = 56.8/15
Sample Mean = 3.8
(c) We have to calculate the sample median.
To define the sample median we first represent the data in ascending order.
2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6
Sample Size(n) = 15
So Median = (n+1)/2th term
Median = (15 + 1)/2th term
Median = 16/2th term
Median = 8th term
So the 8th term in the given data is 3.6. So,
Median = 3.6
(d) We have to compute the 20% trimmed mean for the above data set.
To compute the 20% termed mean, remove 20% of the largest and 20% of the smallest elements from the sample and compute the mean of the new sample.
New sample: 2.9 3.0 3.3 3.4 3.6 3.7 4.0 4.4 4.8
New Mean = 33.3/9
New Mean = 3.7
(e) We have to check is the sample mean for these data more or less descriptive as a center of location than the trimmed mean.
The mean value is 3.8, the median value is 3.6, and the trimmed mean value is 3.7. As a result, the sample mean is less descriptive as the location's center (median) than the trimmed mean.
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The complete question is:
The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint.
3.4 2.5 4.8 2.9 3.6
2.8 3.3 5.6 3.7 2.8
4.4 4.0 5.2 3.0 4.8
Assume that the measurements are a simple random
sample.
(a) What is the sample size for the above sample?
(b) Calculate the sample mean for these data.
(c) Calculate the sample median.
(d) Compute the 20% trimmed mean for the above data set.
(e) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?
A department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. What is the percent markup? A department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. What is the percent markup?
The percent markup of a department, if they sell 300 shirts at a cost of $9 each is 50%
According to the question, we learn that a department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. This means :
The selling price of 300 shirts = 300 × $9
The selling price of 300 shirts = $2700
Selling price > cost price i.e., 2700 > 1800
when selling price is greater than cost price it means department store made a profit.
Profit = selling price - cost price
Profit = 2700 - 1800 = $900
Profit percentage = profit/ cost price × 100
Profit % =[tex]\frac{900}{1800} \times 100[/tex]
Profit % = 50%
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PLSSSS HELP
Brian's mathematics test had 85 problems: 20 arithmetic, 30 algebra, and 35 geometry problems. Although he answered 70% of the arithmetic problems, 40% of the algebra problems, and 60% of the geometry problems correctly, he didn't pass the test because he got less than 60% of the problems right. How many more questions would he have needed to answer correctly to earn a 60% passing grade?
Answer:
4
Step-by-step explanation:
You want to know how many more questions Brian needed to answer correctly to get a passing grade of 60% on his 85-question test, given that he answered correctly 70% of the 20 arithmetic problems, 40% of the 30 algebra problems, and 60% of the 35 geometry problems.
Correct answersThe number of correct answers Brian supplied was ...
0.70·20 +0.40·30 +0.60·35 = 14 +12 +21 = 47
The number of correct answers Brian needed for a passing grace was ...
0.60·85 = 51
Brian needed to answer 51 -47 = 4 more questions correctly to earn a passing grade.
If C.P. of 100 pencils is Rs.250 and S.P. of 1 dozen pencils is Rs.33, find the gain or loss per cent.
CP of 100 pencils = Rs.250
CP of 1 pencil = 250/100 = 2.5
SP of 1 dozen pencils = Rs.33
SP of 12 pencils = Rs.33
SP of 1 pencil = \frac{33}{12}=2.75
SP>CP
So, Profit% = SP - CP/ CP × 100 = 2.75 - 2.5/2.5 × 100 = 10 %
Hence The profit % is 10%
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A triangle has a 60 degree angle, and the two adjacent sides are 12 and 12 square root 3. Find the radius of a circle with the same vertex as a center, if the arc inside the triangle divides it into two regions of equal area.
The radius of a circle with the same vertex as a center, if the arc inside the triangle divides it into two regions of equal area is (18 × ✓π) / π
How to calculate the radiusFrom the information, the triangle has a 60 degree angle, and the two adjacent sides are 12 and 12 square root 3.
The area of a triangle will be;
A = 1/2 × a × b × sin C
= 1/2 × 12 × 12✓3 × sin 60
= 108
Area of sector = πr² / 360 × 60.
r² = (108/2) × 6 ) π
r² = 324 / π
r = 18✓π / π
The radius is 18✓π / π.
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Solve.
320e=18
e= what?
Answer: e = 1/18
Step-by-step explanation:
e = 18/320
e = 1/18
Answer: 0.05625
Step-by-step explanation: So, you divide 18 by 320, and that gives you 0.05625, and you can double check by multiplying 0.05625 by 320, which gives you 18.
How do I solve this equation?
3(5)-3(4)•y
when y is 2
Answer:
-9
Step-by-step explanation:
3(5)-3(4)•y
3(5)-3(4)•2
15 - 12 · 2
15 - 24
-9
Answer:
To solve the equation 3(5) - 3(4)•2, we need to simplify each term and then substitute the value of 2 for y.
Starting with the first term:
3(5) = 15
Next, the second term:
-3(4)•2 = -24
So, putting it all together:
15 - 24 = -9
So when y is 2, the equation simplifies to -9.
Step-by-step explanation:
Marta’s jump rope is 10 inches shorter than three times the length of David’s rope.
If both of their ropes lay together end to end, they measure 120 inches long. How long is each person’s jump rope?
Marta's rope is 10 inches shorter than three times the length of David's rope and they measure 120 inches long together , then Marta's rope is 77.5 inches long and David's rope is 32.5 inches long.
Let's call the length of David's rope x.
According to the problem, Marta's rope is 10 inches shorter than three times the length of David's rope, so we can write an equation for Marta's rope:
length of Marta's rope = 3 * x - 10
And the combined length of both of their ropes is 120 inches, so we can write another equation:
x + (3 * x - 10) = 120
Expanding the second equation and solving for x, we get:
4x - 10 = 120
Adding 10 to both sides:
4x = 130
Dividing both sides by 4:
x = 32.5
So, David's rope is 32.5 inches long.
We can use the first equation to find the length of Marta's rope:
length of Marta's rope = 3 * x - 10 = 3 * 32.5 - 10 = 87.5 - 10 = 77.5 inches
So, Marta's rope is 77.5 inches long.
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A mathematical ________________ is a statement that contains _______________, _________________, and ___________________.
A mathematical theorem is a statement that contains hypotheses, conclusions, and proofs.
What in arithmetic is a theorem?Mathematics revolves around the theorems. A thorough proof is a specific kind of logical reasoning that has been used to demonstrate the truth of a claim, which is what a theorem is.
Which mathematical theorem is the hardest?"When n is higher than 2, there are no pretty much the entire number answers to the problem xn + yn = zn." This equation, also referred to as "Fermat's Last Theorem," was presented for the first time by French scientist Pierre de Fick in 1637 and had baffled the world's greatest minds for further than three centuries.
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Une enquête faite auprès des collégiens d'une ville a permis de recueillir les informations suivantes : 7
30 des élèves interrogés n'ont pas de téléphone portable;
400 élèves possèdent un téléphone portable et un ordinateur;
1 6 des élèves interrogés n'ont pas d'ordinateur;
1 15 des élèves interrogés n'ont ni téléphone portable
ni ordinateur.
Combien de collégiens ont été interrogés pour réaliser
cette enquête ?
600 élèves :
On sait que 7/30+1/6 ne font pas partie des 400 élèves qui possèdent téléphone portable et ordinateur . 7/30+1/6=12/30=2/5 mais parmi ces élèves figurent ceux qui n'ont ni l'un, ni l'autre. Ils font donc partie des 2/5 qui viennent d'être dénombrés
Il faut donc les retrancher, sinon ils seraient comptés deux fois
donc le nombre n'ayant ni l'un ni l'autre est : 2/5-1/15=5/15=1/3
Par conséquent 2/3 ont unt téléphone et un ordinateur
Comme ces 2/3 correspondent à 400 élèves, le nombre total d'élèves interrogés sera donc de 400*3/2=600 élèves.
The graph of a pair of linear equations is shown in the coordinate plane below.
Which value is the x-coordinate of the solution?
-5
-3
-2
0
The value of the x-coordinate of the solution will be -2. Then the correct option is C.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equations are given below.
y = (5/2)x + 2 ...1
y = - x - 5 ...2
From equations 1 and 2, then we have
(5/2)x + 2 = - x - 5
(7/2)x = -7
x = -2
The value of the x-coordinate of the solution will be -2. Then the correct option is C.
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find the inverse function of f(x) = 2x +3
Answer:
So the inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x - 3) / 2.
Step-by-step explanation:
To find the inverse of a function, we switch the x and y variables and solve for y. So, we start with:
y = 2x + 3
Switching x and y, we get:
x = 2y + 3
Now, we solve for y:
x - 3 = 2y
y = (x - 3) / 2
So the inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x - 3) / 2.
Answer & Step-by-step explanation:
To determine f's inverse function (x)= 2x + 3, we can follow these steps:
Step 1: Replace f(x) with y: y = 2x + 3
Step 2: Solve for x in terms of y:
y = 2x + 3
y - 3 = 2x
x = (y - 3) / 2
Step 3: Replace x with f^(-1)(x):
f^(-1)(x) = (x - 3) / 2
Therefore, the inverse function of f(x) = 2x + 3 is f^(-1)(x) = (x - 3) / 2.
Hope it helps!A scale drawing of Julie's living room is shown below: A rectangle is shown. The length of the rectangle is labeled as length equal to 8 cm, and the width is labeled as width equal to 6 cm. If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room? (5 points) a Length = 16 feet, width = 12 feet b Length = 10 feet, width = 8 feet c Length = 32 feet, width = 24 feet d Length = 14 feet, width = 12 feet
A man keeps birds in a big cage in his garden
2/5 of the birds are brown
4 of the birds of black
the rest of the birds are white
the man takes a bird out the cage at random
the probability that this bird is black is 0.2
how many of the birds in the cage are white
You are a bookstore owner and want to calculate the usual amount of money
made each day, but you know that you make four times more on Mondays
than any other day. Which measure of central tendency should you use?
A. All measures of center work equally well.
B. Mode
C. Median
D. Mean
Answer:
Median
Step-by-step explanation:
I took the test myself.
Calculate
-73 - 110
Answer:
Step-by-step explanation:
-183
Answer:
Any negative minus a positive is a negative:
-183
Step-by-step explanation:
Hope it helps! =D
me pueden decir los múltiplos de 5? porfas:(
Los múltiplos de 5 son 5,10,15,20,25,30,35,40,45,50,..........
Definición de múltiplosLos múltiplos son números que se multiplican por un número con un entero positivo (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, etc.). En términos simples, un múltiplo es el producto de un número con otro número (enteros enteros, no fracciones ni decimales).
Los números múltiples son mayores o iguales que el número en sí. Esto se debe a que el primer múltiplo se multiplica por 1. Entonces, el primer múltiplo es el número mismo. Un número o números pueden tener múltiplos de una lista ilimitada de múltiplos. Porque los números se pueden multiplicar continuamente por otros enteros más grandes.
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which equation is standard form has a slope of -2/5 and passes through the point (5,-8)
The equation of the line with a slope of -2/5 and passing through the point (5, -8) in standard, slope-intercept, form is; y = -0.4·x - 6
What is an equation?An equation consists of expressions and or numbers, expressed to be equivalent, by joining them with an '=' sign.
A standard form of the equation of a straight line is the slope-intercept form, which can be presented as follows; y = m·x + c
Where;
m = The slope of the graph of the equation
c = The y-intercept
The equation in the slope-intercept form can be obtained from the point-slope form, using the details of the slope of the graph of the equation (-2/5), and the point through which the graph of the equation passes (5, -8)
The point-slope of the equation is therefore;
y - (-8) = (-2/5)×(x - 5)
y + 8 = -2·x/5 + 2
y = -2·x/5 + 2 - 8 = -2·x/5 - 6 = -0.4·x - 6
The equation with a slope of -2/5 and passing through the point (5, -8), therefore is; y = -0.4·x - 6
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A composite figure is shown.
Which of the following represents the total area of the figure?
The total area of the composite figure is 484 square feet.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
Given:
A composite figure is shown.
To find the complete area:
Here, we have dissected three figures separately.
So, the complete area,
= The area of the triangle with a height 22 feet and base 8 feet +
the area of the rectangle with a length 16 feet and width 22 feet +
the area of the triangle with a height 4 feet and base 22 feet
= (1/2 x 22 x 8) + (16 x 22) + (1/2 x 4 x 22)
= 88 + 44 + 352
= 484 square feet.
Hence, the area is 484 square feet.
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or A line passes through the points (1,1) and (2,7). Write its equation in slope-intercept form.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 1 } \implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 6}(x-\stackrel{x_1}{1}) \\\\\\ y-1=6x-6\implies {\Large \begin{array}{llll} y=6x-5 \end{array}}[/tex]
3c + b² + (27a) - d
a = 1/3
b = 9
c = 5
d = -10
Answer:
Step-by-step explanation:
Rephrase it.
3(5) + 9² + (27 x 1/3) - (-10)
15 + 9x9 + 9 - (-10)
15 + 81 + 9 - (-10)
96 + 9 - (-10)
115
6300000 in standard form
Answer:
6.3×10^6
Step-by-step explanation:
6.3×10^6
in standard form
Which combined inequality has the same solution set shown in the graph of x?
Number line ranging from negative four to four, with a line beginning with an open point at negative three and ending with a closed point at negative one
Responses
–3 ≤ x > –1
–3 ≤ x > –1
–3 ≤ x < –1
–3 ≤ x < –1
–3 < x ≤ –1
–3 < x ≤ –1
–3 > x ≥ –1
A caterer charges $110 to cater a party for 10 people and $220 for 20 people. Assume the cost, y, is a linear function of the number of x people. Write an equation in slope-intercept form for this function. What does the slope represent? How much would a party for 60 people cost?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the cost per people.b is the intercept, representing the fixed cost.Two points on the function are given as follows:
(10, 110) and (20, 220).
The slope is given by the change in the output divided by the change in the input, hence:
m = (220 - 110)/10
m = 11.
Hence:
y = 11x + b.
When x = 10, y = 110, hence the intercept b is given as follows:
110 = 11(10) + b
b = 0.
Hence the function giving the cost for x people is of;
y = 11x.
The cost for 60 people would be of:
y = 11(60)
y = $660.
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how do i solve this problem
Answer:
No, it is not.
Step-by-step explanation:
remember PEMDAS (parenthesis, exponents, mult., etc)
use distributive property, but solve parenthesis first
3x(x+4)²
(x+4)(x+4) = x² + 8x + 16
3x(x² + 8x + 16) >>> 3x³ + 24x² + 48x
so the equation is not equal
Pls help me with this! I keep getting this one wrong
Tysm!
Answer:
31.4 in^2
Step-by-step explanation:
Circumference formula: pi times 2 times radius
so equation would be 3.14 (pi value) times 2 times 5 and you get your answer
which measurement is equivalent to 2.34 meters? responses 0.0234 cm 0.0234 cm 23.4 cm 23.4 cm 234 cm 234 cm 2340 cm
Option 234 cm is the correct option.
The measurement equivalent to 2.34 meters is: 234 cm
To convert meters to centimeters,
you multiply the number of meters by
100.
So, 2.34 meters multiplied by 100 is equal to 234 centimeters.
An object is only identified or classified using numbers on a nominal scale, which is a measuring scale. Only non-numeric (quantitative) factors or situations where numbers have no meaning are often addressed by this assessment.
By increasing the number of metres by 100, one may convert measurements from metres to centimetres. One metre equals one hundred centimetres, or 1 m = 100 cm, as is common knowledge.
Cm is used to represent it in writing. It may also be described as the unit of length in the current metric system, the International System of Units (SI). It is equal to one hundredth of a metre.
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27 children sit at table of 6, fillling where possible. Express how are filled using mixed number.
The number of table in the form of mixed number will be 4 ¹/₂ tables.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
27 children sit at table of 6, fillling where possible. Then the number of table is given as,
⇒ 27 / 6
⇒ 4 ³/₆
⇒ 4 ¹/₂ tables
The number of table in the form of mixed number will be 4 ¹/₂ tables.
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the rocket coaster has 15 cars, some that hold 3 people and some that hold 5 people. there is room for 63 people altogether. how many 3-passenger cars are there? how many 5-passenger cars are there?
There are 6 cars that hold 3 people and 9 cars that hold 5 people.
How to determine the number of passengersLet's call the number of 3-passenger cars "x" and the number of 5-passenger cars "y".
We know the total number of cars is 15, so:
x + y = 15
We also know that the total number of passengers is 63, so:
3x + 5y = 63
Now we can use the first equation to solve for one of the variables in terms of the other:
y = 15 - x
Substitute this expression for y into the second equation:
3x + 5(15 - x) = 63
Expand
3x + 75 - 5x = 63
Evaluate like terms:
2x = 12
Divide both sides by 2:
x = 6
Recall that
y = 15 - x
So, we have
y = 15 - 9
y = 6
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The square rootof 144xsquareduvuded by 4