The triangle ABC is a Dilation of triangle DEF.
A dilation is a transformation that produces an image that is the same shape as the original one but in a different size. Each point is stretched outwards from the center point D by multiplying distances by the scale factor. So, the shape of triangles ABC and DEF are the same.
Since they have similar shapes, their angles will be the same. The largest angle measured in triangle DEF = The largest angle measured in triangle ABC.
Dilation can reduce the shape of an object. The dilation can also enlarge a shape proportionally resulting in a giant monster version of itself.
To know more about Dilation,
brainly.com/question/3457976
brainly.com/question/10253650
#SPJ4
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.
To learn more about circular visit: https://brainly.com/question/29400684
#SPJ4
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).
To learn more about the exponential function from the given link
https://brainly.com/question/2456547
#SPJ4
5. Max wants to start his own lemonade stand. It cost him $3 to make each cup of lemonade plus he has
to pay a $35 renters fee for his stand. He sells the lemonade for $5 per cup.
a. Write a system of linear equations for his cost and his revenue.
The linear equations for cost price and selling price are c = 3x + 35 and y = 5x.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Let Max make x cups of lemonade cup.
According to given conditions,
Cost of 1 cup of lemonade = $3.
Also, Max pay for renters fee = $35.
The cost of x cups of lemonade = 3x
The total cost c = 3x + 35
Since, Max sells lemonade for $5 per cup.
Let the selling price is represented by y,
Then selling price y = 5x
Hence, linear equations for cost price and selling price are c = 3x + 35 and y = 5x.
To know more about Equation on:
https://brainly.com/question/187506
#SPJ1
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
What are the 3 examples of equation?
1. y = 2x + 3
2. y = x^2 + 5x - 3
3. y = -2x^2 + 7x – 4
are the 3 examples of equation with y intercept.
1. The first example is a linear equation, which has the form of y = mx + b, where m is the slope and b is the y-intercept.
2. The second example is a quadratic equation, with the form of y = ax^2 + bx + c, where a, b, and c are coefficients.
3. The third example is also a quadratic equation, with the form of y = ax^2 + bx + c, where a, b, and c are coefficients.
Learn more about y intercept here
https://brainly.com/question/14180189
#SPJ4
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.
Learn more about system of equations:
brainly.com/question/14323743
brainly.com/question/1365672
brainly.com/question/20533585
brainly.com/question/20379472
#SPJ1
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
To learn more about area of rectangle, visit:
https://brainly.com/question/22490536
#SPJ4
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.
Learn more about extrapolation here
brainly.com/question/14643498
#SPJ4
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
#SPJ4
Where is the vertex in ABC?
The vertex in triangle ABC is at point A, B, and C.
Step by Step explanation :
Given triangle is represented by ΔABC
Triangle is representation of three line segment , three vertices , and three angles enclosed in it.Two rays meet at one point forms a vertex.When side AB and AC intersect each other at point A , point 'A' is known as vertex.When side BA and BC intersect each other at point B , point 'B' is known as vertex.When side CA and CB intersect each other at point C , point 'C' is known as vertex.Therefore, the vertex of the given triangle ABC is given by point A, B , and C.
The complete question is:
Where is the vertex in triangle ABC?
Learn more about vertex here
brainly.com/question/29030495
#SPJ4
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.
To learn more about combination
https://brainly.com/question/28065038
#SPJ4
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.
To know more about linear system here
https://brainly.com/question/29200055
#SPJ4
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.
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
To know more about Binomial distribution here
https://brainly.com/question/13609688
#SPJ4
Diego charges $60 for the first hour of consulting and $30 for each additional hour or fraction of an hour.
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
a tar heel basketball player makes 80% of his free throw attempts. among 3 attempts he has, the probability that he at least misses one is equal to
The probability that he at least misses one is equal to 61/125.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given in the question
basketball player makes 80% of his free throw attempts i.e.
P(Success) = 4/5 or 0.8
P(Miss the attempt) = 1 - 0.8 = 0.2 or 1/5
Number of sample (n) = 3
We need to calculate probability that he at least misses one i.e.
P(X > = 1) = 1 - P(X < 1) = 1 - P(X = 0)
Here we will use binomial probability distribution which can be calculated as
P(X = n |N, p)= NCn x (p^n) x (1-p)^(N-n)
P(X > = 1) = 1 - P(X < 1) = 1 - P(X = 0) = 1 - 3C0 x (1/5)^0 x (1 - 1/5)^(3-0)
= 1 - (1 x 1 x 64/125) = 1 - 64/125 = 61/125
Hence, the probability that he at least misses one is equal to 61/125.
To know more about probability, click on the link
https://brainly.com/question/24756209
#SPJ4
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
write the coordinates of the vertices after a reflection over the line y= -2
k'(4, -7)
L'(9, -7)
M'(6, -5)
N'(5, -5) are the new coordinates of the vertices.
Coordinates of a point:
A point's coordinates are a pair of numbers that pinpoint where it is precisely on a two-dimensional plane.
Remember that the x and y axes are two axes that are at right angles to one another and make up the coordinate plane.
A particular point's coordinates show how far along each axis it is situated.
The coordinate's sign is crucial. A positive number indicates moving upward or to the right (x) (y).
Negative numbers indicate turning left (x) or falling (y).
To know more about Coordinates of a point:
https://brainly.com/question/17281079
#SPJ1
can you give me one more day?
Answer:
sure
Step-by-step explanation:
just ask
Answer:
Only if you get it done by 11:59 tomorrow
Step-by-step explanation:
Given h(x)=4x-5 find h(4)
Step-by-step explanation:
16-5= 11
hope it's helpful
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%
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
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
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
To know more about volume of a pyramid, visit:
https://brainly.com/question/17615619
#SPJ4
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.
Learn more about confidence interval -
https://brainly.com/question/17097944
#SPJ4
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.
To learn more about contestant checkout https://brainly.com/question/27896050
#SPJ4
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.
Know more about fractions here:
https://brainly.com/question/29680548
#SPJ1
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
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.
More about the arithmetic sequence link is given below.
https://brainly.com/question/12373434
#SPJ1
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.
To know more about percentages follow
https://brainly.com/question/24304697
#SPJ1