To draw a dilation with a scale factor 1/2 , multiple every coordinates of pre-image with 1/2 and join the obtained points
A dilation is a transformation that alters the size of an image.
There is a centre and a scale factor in all dilations. The centre serves as the dilation's reference point (like the vanishing point in a perspective drawing)
The scale factor indicates how much the figure expands or contracts. A scale factor is usually denoted by the letter "k," and it is always greater than zero.
To draw a dilation with a scale factor of 1/2, follow these steps:
Step 1: Determine the scale factor and the dilation centre.
Step 2: Identify an image vertex. Draw a line through one of the image's vertices from the center of dilation.
Step 3: Find the horizontal distance and the vertical distance between the center of dilation and the vertex.
To find the horizontal and vertical distances from the centre of dilation to a new vertex, multiply the distances by the scale factor 1/2.
Step 4: Determine the new horizontal and vertical distances from the centre of dilation. Make a point plot.
Step 5: Join the new vertices together to create the dilated image.
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A rectangle has a height of 2x^42x 4 2, x, start superscript, 4, end superscript and a width of x^2+8x+15x 2 +8x+15x, squared, plus, 8, x, plus, 15. Express the area of the entire rectangle. Your answer should be a polynomial in standard form.
Area of rectangle is 2x⁶ + 16x⁵ + 30x⁴ when A rectangle has a height of 2x^42x 4 2, x, start superscript, 4, end superscript and a width of x^2+8x+15x 2 +8x+15x, squared, plus, 8, x, plus, 15.
Define area of rectangle.The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. When calculating a rectangle's area, we multiply the length by the width of the rectangle. The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Given
Rectangle's height = 2x⁴
Rectangle's width = x² + 8x + 15
Area of rectangle
Height × Width
2x⁴ × x² + 8x + 15
2x⁶ + 16x⁵ + 30x⁴
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A fast-food restaurant runs a promotion in which certain food items come with game pieces. According to the restaurant, 1 in 4 game pieces is a winner. If jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize?.
The probability that Jeff wins exactly 1 prize is (3/4)³
According to the question,
A fast-food restaurant runs a promotion in which certain food items come with game pieces
Let the event of winning the game piece be A and x be the random variable for winning prize
So, Probability of Winning the game = P(A) = p = 1/4
Probability of not winning = q = 1 - 1/4
=> q = 3/4
Using Binomial distribution,
The Probability that he wins exactly 1 prize = P(x = 1)
=> P(x) = ⁿCₓ pˣ qⁿ⁻ˣ
Here, n = 4 , x = 1
P(1) = ⁴C₁ p¹ q³
=> 4 × (1/4)( 3/4)³
=> (3/4)³ is probability that jeff wins exactly 1 prize
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If it took 4.2 hours for marianne to drive 226.8 miles. what was her average speed for the trip?
Answer:
54 mi/hr
Step-by-step explanation:
[tex]\frac{226.8}{4.2}=54[/tex] mi/hr
find the number of different ways that 570 contestants can win different first, second and third prizes.
184,219,440 ways.
What is contestant?
A participant in a contest or competition is known as a contestant. A contestant is someone who challenges election results.
There are 570 contestants, and any one of them can win the first prize.
One of the remaining 569 people can receive the second prize.
Third may be assigned to any of the remaining 568.
We can accomplish this in 570*569*568 ways
= 184,219,440 ways.
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The rectangular prism below is not
complete. When it is complete, it will
be a total of 27 cubic units. What will
the length, width, and height of the
cube below be once it is completely
filled in?
L x W x H
L=3
W=3
H=3
3x3x3=27
The picturegram shows information about CDs sold in a shop.
1 . How manny CDs were sold on Wednesday | Key = 3 |
2. How manny more CDs were sold on Thursday than Wednesday?
**If you know the answer let me know!**
Answer:
i believe number 1 is 18 and number 2 is 9.
Step-by-step explanation:
if one full circle represents 6 CDs then on wednesday 18 Cds were sold because 6+6+6=18 and on thursday they sold 9 more Cds than on wednesday because they sold 6+6+6+6+3 which equals 9.
Last year Raina biked n miles . This year She biked 575 miles . Using n , write an expression for the total number in of miles she Biked
Answer: n+575= total
or n+575=t
Step-by-step explanation:
n is what we start with, plus what she has this year. the total is unknown.
a section of a circular design. the drawing shows the measurements in a section of a circular design. how long is the radius of the circle? f 8.7 cm g 10 cm h 7 cm j 4.3 cm
10 cm length is the circle's radius when the measurements are depicted in a segment of a circular design on the drawing.
Given that,
The measurements are depicted in a segment of a circular design on the drawing.
We have to find what length is the circle's radius.
We know that,
Let us take the up line as AB and the perpendicular line is OP.
So,
In ΔOPB
∠P=90°
PB=5cm
OP is perpendicular to AB.
Sin30° = PB/OB
1/2=5/OB
OB=5×2
OB=10
Therefore, 10 cm length is the circle's radius when the measurements are depicted in a segment of a circular design on the drawing.
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Given h(x)=4x-5 find h(4)
Step-by-step explanation:
16-5= 11
hope it's helpful
Y/y-5+5/5-y= step bye step
The solution of the given equation is, y = -3.
what is solving an equation?
An effective method for solving linear equations can be found in the steps that follow. By deleting parentheses and combining like terms, each side of the equation can be made simpler. The variable term on one side of the equation can be separated using addition or subtraction. To find the variable, use multiplication or division.
Consider, the given equation
[tex]\frac{y}{y}-5 + \frac{5}{5}-y =0[/tex]
Since, If a/a then it is 1.
⇒ 1 - 5 + 1 - y = 0
-3 - y = 0
Add y on both sides,
-3 - y + y = 0 + y
-3 = y
y = -3
Hence, the solution of the given equation is, y = -3.
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The volume of a cone is 16π in³ and its height is
12 in. Find the radius of the cone.
Answer:
2 inches
Step-by-step explanation:
volume of a cone: 1/3 π r^2 h
h = 12
1/3 π r^2 (12) = 16π
4πr^2 = 16π
r^2 = 16π/4π
r^2 = 4
r = 2
help help help help help help help
Answer: 1. 2, 4, 8, 16, 32, 64, and 128,...... I don't know if I should keep going.
2. 5, 11, 17, 23, 29, 35, 41, and 47
Answer: 2.
Step-by-step explanation:
11+3=14
14+3=17
17+3=20
20+3=23
2. 5,11,17,23
1. the best / most precise estimate of the mean value of y is located at the mean of the x values. true false -select- 2. if you were thinking about opening up several new pizza places near colleges with 20,000 students, would you feel 95% confident that mean sales for those stores would be $175,000? yes no -select-
The first statement is false and answer to second statement is no.
The mentioned information does not state that x and y are linearly related or not. If they are not related in linear way, the mean value of y would not be located at the mean of the x values.
Confidence intervals indicate the mean or population of the sample. For the confidence interval of sales of pizza stores, the similar data would be required for comparison using statistics tool. Hence, the relevant data should be sales of nearby pizza stores till now. Thus, the mentioned statement is irrelevant.
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Diego charges $60 for the first hour of consulting and $30 for each additional hour or fraction of an hour.
What is the slope of the line passing through the points P1 x1 y1 and P2 x2 y2?
(y2 - y1) / (x2 - x1) is the slope of the line passing through the points P1 x1 y1 and P2 x2 y2.
The slope of the line passing through the points P1 (x1, y1) and P2 (x2, y2) is calculated by: (y2 - y1) / (x2 - x1).
1. Subtract the y-coordinates of the two points: y2 - y1.
2. Subtract the x-coordinates of the two points: x2 - x1.
3. Divide the two results from steps 1 and 2: (y2 - y1) / (x2 - x1).
For example, if the two points are P1 (1, 5) and P2 (3, 8), then the slope is calculated by: (8 - 5) / (3 - 1) = 3 / 2 = 1.5. This means that the line has a slope of 1.5, which means that for every 1 unit increase in x, the y-coordinate increases by 1.5 units. So, for every 2 units increase in x, the y-coordinate increases by 3 units.
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What expression shows the relationship between the value of any term and, its position in the sequence for the given sequence?
3, 5, 7, 9, 11, ...
A.2n
B.2n-2
C.2n+1
D.-3n-2
E.-n+3
The position in the sequence for the given sequence will be 2n + 1. Then the correct option is C.
What is an arithmetic sequence?Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The sequence is given below.
3, 5, 7, 9, 11, ...
The first term is 3. And the common difference is given as,
d = 5 - 3
d = 2
Then the position in the sequence for the given sequence will be given as,
aₙ = 3 + (n - 1) · 2
aₙ = 3 + 2n - 2
aₙ = 1 + 2n
The position in the sequence for the given sequence will be 2n + 1. Then the correct option is C.
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a restaurant menu lists 7 appetizers, 10 entrees, and 4 desserts. how many ways can a diner select a three-course meal?
From the given combination, there are 280 ways to select a three-course meal.
What is the combination?
Combinations are ways of choosing things from a collection when the order of the choices does not matter. The number of selections is denoted by [tex]^{n} C_{r}[/tex] if you have to choose "r" items from "n" things.
Given, 7 appetizers, 10 entrees, and 4 desserts
To select a three-course meal, we will choose 1 item from each course.
i.e. 1 appetizer from 7 appetizers
AND
1 enter from 10 entrees
AND
1 dessert from 4 desserts
So, For appetizers, selections = [tex]^{7} C_{1}[/tex]
For entrees, selections = [tex]^{10} C_{1}[/tex]
For desserts, selections = [tex]^{4} C_{1}[/tex]
Total possibilities = [tex]^{7} C_{1}[/tex] * [tex]^{10} C_{1}[/tex]* [tex]^{4} C_{1}[/tex] = 7*10*4 = 280
Hence, there are 280 ways to select a three-course meal.
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Elizabeth is going to roll a fair 666-sided die 600600600 times. Complete the following statement with the best prediction. Elizabeth will roll an even number.
The number of times getting an even number on the top of dice if dice is rolled 600 times is 300.
We know that probability is defined as the division of number of favorable outcomes to the total number of outcomes.
Here, favorable outcomes are even number from 6 possible numbers and those are =2,4,6
So, favorable outcomes are={2,4,6)
So, count of favorable outcomes is 3
Total number of outcomes are ={1,2,3,4,5,6}
So, count of total number of outcomes are =6
Therefore, probability of getting an even number on top of dice is =number of favorable outcomes/total number of outcomes
=>P(E) = 3/6
=>P(E)=1/2
Now, dice is rolled 600 times and probability of getting even number is 1/2,so total number of times even number comes on topo of dice is =(1/2)×600=300.
Hence, even number appearance is 300.
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find a formula for the exponential function that gives the value of an item initially worth $5000 that loses half its value every 5 years.
The formula for the exponential function is V = 5000 (2)^(−t/4).
What is an exponential function?
A function whose value is a constant raised to the power of an argument is called an exponential function.
Here, we have
The value of an item initially worth $5000 loses half its value every 5 years.
V = V₀eˣⁿ
At t = 0,V = V₀
So, V = 5000eˣⁿ
At t = 4,V = V₀/2 = 2500
Substituting these into our equation, we have
5000e^(4k) = 2500
e^(4k) = 12
4k = −ln2
k = −ln2/4
Finally, we have our equation
V = 5000e^(−tln2/4 )
V = 5000(e^ln2)^(−t/4)
V = 5000 (2)^(−t/4)
Hence, the formula for the exponential function is V = 5000 (2)^(−t/4).
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What are the coordinates of the image of the point (-3, 6) after a dilation with a center of (0, 0) and scale factor of 1/3?
A. (-9, 18)
B. (-3, 6)
C. (-1,2)
D. (0,0)
Answer:
C
Step-by-step explanation:
since the dilatation is centred at the origin then multiply the coordinates of the point by scale factor of [tex]\frac{1}{3}[/tex]
(- 3, 6 ) → ([tex]\frac{1}{3}[/tex] (- 3), [tex]\frac{1}{3}[/tex] (6) ) → (- 1, 2 )
Find the volume and surface area of a square pyramid. Volume of a pyramid: v = 1/3(area of base) x (height) surface area of a pyramid: a = 1/2(perimeter of base) x (slant height) + (area of base) a pyramid has a height of 4. 7 in. And a slant height of 5. 2 in. Its base is a square with sides of 3. 5 in. Find the pyramid's volume and surface area. Volume (to the nearest tenth) = in3 surface area (to the nearest tenth) = in2.
The Volume of the Pyramid=19.19in³
Surface Area of the Pyramid=48.65in²
What is meant by volume?Volume is a unit of measurement for the area occupied in three dimensions. It is widely quantified and measured using SI-derived units, alternative imperial units, or US standard units (such as the gallon, quart, cubic inch). Volume and length (cubed) have a similar meaning.
First, volume was calculated using naturally occurring vessels with a similar shape, and then using standardized containers. Calculating the volume of numerous common three-dimensional forms is made simple by arithmetic formulas. The volumes of increasingly complicated shapes can be calculated using integral calculus.
Given that,
Height of the pyramid =4.7
Pyramid's slant height= 5.2
Base of pyramid is a square with side=3.5
Volume of the pyramid=(1/3)(3.5×3.5)×(4.7)
=19.19 in³
The surface area of a pyramid=((1/2)×(4×3.5)×5.2)+(3.5×3.5)
=18.65in²
Therefore, the volume of the pyramid=19.19 in³
And the surface area of the pyramid=18.65in²
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What are the 2 conditions for a system to be linear?
Homogeneity and additivity are the two conditions for a system to be linear.
A system is called Linear if it has two mathematical properties, homogeneity and additivity. If you can show that system has both properties, then you have proven that the system is linear.
Homogeneity means that a change in the input signal's amplitude results in a corresponding change in the output signal's amplitude.
Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same.
Additivity means signals added at the input produce signals that are added at the output.
The value of a magnitude corresponding to a whole object is equal to the sum of the values of the magnitudes corresponding to its parts for any division of the object into parts.
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If the 1st person save 1/4 of total , 2nd person saves 2/3 and 3rd person saves 1/10 , which fraction left to pay for the birthday party.
After solving the fractions, we can conclude that the fraction left for the pay birthday party is 17/3.
What are fractions?An element of a whole is a fraction.
The number is represented mathematically as a quotient, where the numerator and denominator are split.
Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
So, calculate as follows:
1 * 1/4 = 1/4 ...(1)
1/4 * 2/3 = 2/12 ...(2)
2/12 * 1/10 = 2/120 ...(3)
Fraction left to pay:
1 - (1/4 + 2/12 + 2/120)
1 - (30+20+2/120)
1 - (52/120)
1 - 13/30
30-13/30
17/30
Therefore, after solving the fractions, we can conclude that the fraction left for the pay birthday party is 17/3.
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Caysen and Kyle are selling T-shirts and sweatshirts with the school logo. Caysen sells 6 T-shirts and 4 sweatshirts for $212. Kyle sells 3 T-shirts and 5 sweatshirts for $202. Part A Write a system of equations to represent the situation. Using x for the price of t-shirts and y for the price of sweatshirts. Caysen: 6x+4y=212 Kyle: 3x+5y=202 Part B Solve the system of equations using elimination or substitution. Show your work. x = y = Part C What does the solution of the system mean in this situation?
Part A: The system of equations is
6x + 4y= 212
3x + 5y= 202
Part B: The solution of the system of equation is x= 14 and y= 32
Parte C: The solution means that the price of t-shirts and the price of swatshirts are $14 and $32 respectively.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
A solution to a system of two or more linear equations is a solution that simultaneously satisfies all the equations in the system.
This caseIn this case, a system of linear equations must be proposed taking into account that:
x is the price of t-shirts.y is the price of sweatshirts.You know:
Caysen sells 6 T-shirts and 4 sweatshirts for $212. Kyle sells 3 T-shirts and 5 sweatshirts for $202.The system of equations to be solved is
6x + 4y= 212
3x + 5y= 202
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "y" from the first equation:
4y= 212 - 6x
y= (212 - 6x)÷ 4
y= 212÷4 - 6÷4x
y= 53 - 3/2x
Substituting this expression in the second equation:
3x + 5×(53 - 3/2x)= 202
Solving:
3x + 5×53 - 5×3/2x= 202
3x + 265- 15/2x= 202
3x - 15/2x= 202 - 265
-9/2x=-63
x= (-63)÷ (-9/2)
x= 14
Remembering that y= 53 - 3/2x, you get:
y= 53 - 3/2×14
y= 32
The solution of the system of equation is x= 14 and y= 32. This means that the price of t-shirts is $14 and the price of swatshirts is $ 32.
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68 miles+10 fewer miles+85 miles equal what?
The value of the expression will be;
⇒ 211 miles
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.
Given that;
The expression is,
⇒ 68 miles + 10 fewer miles + 85 miles
Now,
Since, The expression is,
⇒ 68 miles + 10 fewer miles + 85 miles
Hence, We get;
⇒ 68 miles + 10 fewer miles + 85 miles
⇒ 68 + (68 - 10) + 85
⇒ 68 + 58 + 85
⇒ 211
Thus, The value of the expression = 211 miles
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Yousef typed a 36-word paragraph in 23 minute. what is his typing speed, in words per minute? enter your answer in the box.
Yousef will be type 54 words in a minute approximately.
How do we solve it?We can calculate Yousef typing in minute by use unitary method.In 23 minute Yousef can typed about 36 words, then we got, 36 words = [tex]\frac{2}{3}[/tex] minutes.Then we can calculate result of Yousef typed in a minute by, [tex]\frac{36 * 3}{2}[/tex] = 54 words.The unitary method is used to calculate the value of a single unit from the values of multiple units and then use this value to calculate the value of the required number of units.This unitary method method is mostly used in ratio and proportion concept. Unitary Method has two variations, direct variation and indirect variation.Learn more about unitary method at: brainly.com/question/23423168
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there were 425 guests at a hotel. 170 guests ordered food. what percentage of the guests ordered food?
170/425=0.4
as a percent = 40%
Norm has an income of $32,690.
He paid a total of 15% of his income in tax.
How much tax did Norm pay?
The amount of the money paid by the Norm as a tax will be $4903.5.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Norm has an income of $32,690. He paid a total of 15% of his income in tax.
The amount of tax paid will be calculated as,
Amount = ( 32690 x 15 ) / 100
Amount = 32690 x 0.15
Amount = $4903.5
The Norm will pay $4903.5 in taxes.
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Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.
a. True
b. False
Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data is a true statement.
Extrapolation is a mathematical technique which involves predicting the value outside the defined range of the given variable using the relationship between the two given variables. With some categorical data, it is a crucial idea not only in mathematics but in other academic fields as well, such as psychology, sociology, and statistics. Extrapolation represents the estimation of a value based on extending the known factors or components outside of the area that is known. To put it another way, extrapolation is a mathematical technique where all the data values are treated as points, such x₁, x₂,....., xₙ. If statistical data is written as periodically sampled and approximates the next data point, it frequently exists in that data.Therefore, it is true that extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that outside the x-range.
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Find The Missing Angles
The value of all the missing angles in the triangles are;
∠1 = 37°
∠6 = 30°
∠4 = 63°
∠3 = 133°
How to find the missing angles of the triangle?We know that the sum of angles in a triangle is equal to 180 degrees. Thus, with this knowledge, we can find the angles 1 and 6.
Therefore;
∠1 = 180 - (70 + 73)
∠1 = 180 - 143
∠1 = 37°
∠6 = 180° - (107° + 43°)
∠6 = 180° - 150°
∠6 = 30°
Now, we know that sum of angles on a straight line is 180 degrees. Thus, we can find angle 4 as follows;
∠4 = 180° - (65° + 42°)
∠4 = 180° - 117°
∠4 = 63°
∠3 = 90 + 43
∠3 = 133°
Thus, the conclusion is that the missing angles are ∠1 = 37°, ∠6 = 30°, ∠4 = 63°, ∠3 = 133°
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