To enlarge a figure by scale factor of 1 , multiple the coordinates of pre-image by 1 though scale factor 1 won't affect anything .
Scale factor is a number by which the size of any geometrical figure or shape can be changed with respect to its original size. It is the ratio of the sizes of the original figure with the dilated figure.
The scale factor can either increase the size of an object or decrease the size of an object.
The basic formula:
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
Enlarging a shape means to change its size. To enlarge a shape, multiply all lengths of the shape by the scale factor. The scale factor tells us how many times larger the shape will be.
When the scale factor is 1 , a copy of a pre-image form . No, change in the image will happen . You will produce you an original image.
To know more about Scale factor here
https://brainly.com/question/29464385
#SPJ4
Solve the inequality and graph the solution. Just say the points (x, y).
1/2x < 6
No links or I will report. Please help.
The solved inequality for 1/2x < 6 is x < 12, and the graph is attached below.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
The relationship between two values that are not equal is described by inequalities. Equal does not necessarily mean unequal. The "not equal symbol" is typically used to denote that two values are not equal.
Given:
1 / 2x < 6
x < 6 × 2
x < 12
Therefore, the solved inequality for 1/2x < 6 is x < 12, and the graph is attached below.
To know more about inequality:
https://brainly.com/question/2038369
#SPJ1
Find the area of a regular octagon with a side length of 17 meters and an apothem length of 21
meters. Round your answer to the nearest meter. Be sure to label the unit.
Answer:
Step-by-step explanation:
An octagon is a 2-dimensional shape with 8 sides and the area is the space within the 8 sides of the shape. To calculate the area of the octagon we can use the area of an isosceles triangle. We divide the area of the shape into eight equal isosceles triangles and calculate it accordingly. A regular octagon has the length of the sides equal and the angles between these sides are equal. The measure of each interior angle is 135° and the exterior angles measure 45° each.
Area of Octagon Formula
The formula used to calculate the area of an octagon is:
2s2(1+√2), where s is the length of the side of the octagon.
In how many years will $ 1600 amount to $ 1852.20 at 5% per annum when compounded annually?
Answer:
3 years
Step-by-step explanation:
1600*[tex]1.05^{x}[/tex]=1852.20
1852.20/1600= [tex]1.05^{x}[/tex]
1.157625 = [tex]1.05^{x}[/tex]
[tex]log_{1.05} 1.157625= x[/tex]
x= 3
thus 3 years
2. Latrina is planning to serve hors d'oeuvres at her wedding. She plans on offering
8 hors d'oeuvres for every 3 people. If she has 240 people RSVP to the wedding, how many hors
d'oeuvres will she serve? Set up a proportion to solve.
I KNOW:
PLAN AND WORK:
I NEED TO KNOW:
SOLUTION:
She will serve 640 hors d'oeuvres to 240 people.
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,
Total number of people = 240
Number of hors d'oeuvres per 3 people = 8
Number of hors d'oeuvres to serve 240 people.
= 8 x 240 ÷ 3
= 8 x 240/3
= 8 x 80
= 640
Thus,
The number of hors d'oeuvres to serve is 640
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
the p-value is less than the significance level. (a) we have a type i error (b) we have a type ii error (c) we may have a type i error (d) we may have a type ii error
If the p-value less than the significance level then we have a type i error.
We know that if your P-value is less than the chosen significance level then you reject the null hypothesis i,e. accept that your sample gives reasonable evidence to support the alternative hypothesis.
Im statistics, a type i error means rejecting the null hypothesis when it's actually true, while type ii error means failing to reject the null hypothesis when it's actually false.
The chance that you commit type i errors is known as the type i error rate or significance level (p-value). This number is conventionally and arbitrarily set to o.o5 or 5%. Type ii errors are like "false negatives", an incorrect rejection that a variation in a test has made no statistically significant difference.
The probability of making a type i error is represented by alpha level, which is the p-value below which you reject the null hypothesis.
To know more about type i error here
https://brainly.com/question/15106854
#SPJ4
A contractor bought 7.6 to the power of 2 ft of sheet metal. she has used 2.3 to the power of 2 ft so far and has $159 worth of sheet metal remaining. The equation 7.6x-2.3x=159 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
what does the sheet metal cost per foot?
Answer:
Step-by-step explanation:
he bought 7.6 ft2 of sheet metal He used 2.3 ft2 7.6x−2.3x= $95.40 simplify 5.3x = $95.40 divide by 5.3 to get x by itself x = 18 so each sheet of metal costs $18.00 per square foot.
total cost of
Task 2:
P3 Solve a practical engineering problem involving a geometric progression..
2) Car production in the first week of a new model was 150 cars. If production continues with
an increase of 1.75% per week find:
a) How many complete cars are produced in the 25th week
b) How many complete cars are produced in the first 6 months of production.
c) How many complete cars are produced in the next 6 months.
Considering the car production in Geometric progression (a) about 25th term is 7.00*10¹⁹ cars can be produced in the first 25th week. (b) in the first 6 months, there will be 7.1*10¹⁸ cars. ( c) production in the next 6 months would be 7.1*10¹⁸ cars too
How to determine total production?Geometric progression is the type of sequnce in which consecutive terms are gotten by the multiplication of a constant term known as the constant ratio.
the given parameyers are
a=150 cars
r=1.75%
r=1.75/100*150
r= 6.6
Nth term of GP is given as
Nth = [tex]ar^{n-1}[/tex]
a. The 25th term is given as
25th= [tex]150*6.6^{24}[/tex]
25th term is 7.00*10¹⁹
b. In a month, there are 4 weeks
in 6 months there are 4*6 = 24 weeks
524th term is 150*6.6²³
7.1*10¹⁸
c. In a month, there are 4 weeks
in 6 months there are 4*6 = 24 weeks
524th term is 150*6.6²³
7.1*10¹⁸
In conclusion there will be 7.00*10¹⁹ cars , 7.1*10¹⁸ cars and 7.1*10¹⁸ cars for options a, b, and c respectively
Learn more about Geometric Progression on https://brainly.com/question/4853032
#SPJ1
suppose the exam instructions specify that at most one of questions 1 and 2 may be included among the nine. how many different choices of nine questions are there?
The number of different choices for nine questions is 384, when at most one of questions 1 and 2 may be included among the nine.
Given, the exam instructions specify that at most one of questions 1 and 2 may be included among the nine.
We have to find the number of different choices for nine questions.
Now, using the concept of Permutation and Combinations we get
There will be three cases,
Case 1 : we include question 1
Case 2 : we include question 2
Case 3 : we neither include question 1 nor question 2
Case 1 :
question 1 is included, so question 2 can not be included and remaining 7 questions have 2 choices.
Case 2 :
question 2 is included, so question 1 can not be included and remaining 7 questions have 2 choices.
Case 3 :
neither question 1 nor question 2 is included and also remaining 7 questions have 2 choices.
Total choices = 2^7 + 2^7 + 2^7
So, the number of different choices of nine questions are 384.
Hence, the number of different choices of nine questions are 384, when at most one of questions 1 and 2 may be included among the nine.
Learn more about Permutations and Combinations here https://brainly.com/question/1216161
#SPJ4
A right triangle has one side that measures 4 in. The angle opposite that side measures 80o. What is the length of the hypotenuse of the triangle? round to the nearest tenth. 3. 9 in. 4. 1 in. 22. 7 in. 23. 0 in.
The length of the hypotenuse of the triangle is 4.1.
Here we have to find the length of the hypotenuse of the triangle.
Data given:
A right triangle has one side that measures 4 in and the angle opposite that side measures 80°
To determine the length of the hypotenuse of the triangle, the trigonometry function can be used.
sinФ = perpendicular/ hypotenuse
sin80° = 4/ hypotenuse
0.98 = 4/ hypotenuse
hypotenuse = 4/ 0.98
Hypotenuse = 4.0617 inch.
Therefore the length of the hypotenuse of the triangle to the nearest tenth is 4.1
To know more about the triangle refer to the link given below:
https://brainly.com/question/17335144
#SPJ4
1. If you decide whether or not you want to see a new movie or television program on the basis of the "coming attractions" or television commercial previews, are you using a sampling technique? A scientific sampling technique?
2. Name some possible sampling frames for the following:
a. Electric contractors
b. Tennis players
c. Dog owners
d. Foreign-car owners
e. Wig and hair goods retailers
f. Minority-owned businesses
g. Men over six feet tall
Yes. The decision of watching a movie on television is a technique of sampling.
Given,
If you decide whether or not you want to see a new movie or television program on the basis of the "coming attractions" or television commercial previews.
We have to find that whether it is using a sampling technique here;
Here,
Yes, this is a sampling technique. This kind of sampling, meanwhile, is typically not of a scientific nature. Instead of being representative of those movies, the parts that are shown are typically the most entertaining. Although a subset of all potential television shows or movie scenes have been observed, they are not chosen at random to make up the sample.
That is,
Yes. The choice to watch a movie on television is a sampling technique.
Learn more about sampling technique here;
https://brainly.com/question/4542698
#SPJ4
PLEEASE I NEED THIS RN
Cars lose value the farther they are driven. A random sample of 11 cars for sale was taken. All 11 cars were the same make and model. A line was fit to the data to model the relationship between how far each car had been driven and its selling price.
Based on this equation, estimate The price of a car that had been driven 56000 km.
Based on this equation, estimate the price of a car that had been driven 56 thousand kilometers.
Step-by-step explanation:
identify the statistical test in which the mean difference between two groups are compared to a distribution of differences between means.
The statistical test that compares the distribution of mean differences between two groups to the mean difference between two groups is independent-sample t test.
Given that,
We have to find the statistical test that compares the distribution of mean differences between two groups to the mean difference between two groups.
We know that,
The independent Samples t take a look at analyzes the manner of two separate organizations to see if there's statistical guide that the populace imply values are statistically extensively distinctive. A parametric take a look at is the unbiased Samples t take a look at.
since, the two agencies are independent and we're checking if difference is good sized is independent-samples t test.
consequently, the statistical test that compares the distribution of imply differences between two companies to the imply difference among corporations is unbiased-pattern t check.
To learn more about statistic visit: https://brainly.com/question/23091366
#SPJ4
What is true about the angles in the diagram shown below? Triangle E F G is shown. Segment H K goes from side E F to side E G and forms triangle E H K. Angle E K H and angle E G F have right angle labels. Angle E is labeled x degrees. Angle F is labeled two x degrees. Enter the correct answers in the boxes.
Correct option is C and the angle D and F are complementary angles.
∠D+∠E+∠F=180⁰
....Angle sum property
∵∠E=90⁰
⇒∠D+∠F=180⁰
−90 ⁰
⇒∠D+∠F=90⁰
What is complementary angles?Complementary angles are defined with respect to the addition of two angles. If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.When two line segments or lines meet at a common point (called a vertex), at the point of intersection an angle is formed. When a ray is rotated about its endpoint, then the measure of its rotation in an anti-clockwise direction is the angle formed between its initial and final position.To learn more about supplementary angles refer to:
https://brainly.com/question/12919120
#SPJ1
a rock dropped into a pond causes a circular wave of ripples whose radius increases at 3 inches per second. how fast is the area of the circle of ripples expanding at the instant that the radius of the circle is 21 inches?
The area of the circle is increasing at a rate of 126π sq. inches per second
What are Derivatives?
The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.
Solution:
Area of Circle = πr²
To find the rate of change we need to use Derivatives
dA/dt = 2πr * dr/dt
we know that the radius is increasing at a rate of 3 inches per second so,
dr/dt = 3 inches per second
Rate of Change = 2π*21*3 inches per second
The area of the circle is increasing at a rate of 126π sq. inches per second
To learn more about Derivatives rom the given link
https://brainly.com/question/28376218
#SPJ4
you have a deck of 52 cards, and you keep taking pairs of cards out of the deck. if a pair of cards are both red, then you win that pair; if a pair of cards are both black, then i win that pair; if a pair of cards has one red and one black, then it's discarded. if, after going through the whole deck, you have more pairs than i do, then you win $1, and if i have more pairs than you do, i win $1. what is the value of this game in the long run?
The required value of this game in the long run has no value, as game will discarded because both players identical pairs.
Explain deck of 52 cards.A standard 52-card deck contains 13 positions in every one of the four French suits: clubs (♣), precious stones (♦), hearts (♥) and spades (♠). Each suit incorporates three court cards (face cards), Lord, Sovereign and Jack, with reversible (twofold headed) pictures. Each suit additionally incorporates ten numeral cards or pip cards, from one to ten.
According o question:After the blended matches are disposed of, there are an equivalent number of dark red still in the deck, so the two players will have similar number of pairs.
So, No one will win the game.
Thus, the game will discarded.
To know more about deck of card visit:
brainly.com/question/19202591
#SPJ4
HELP PLEASE
3. Julia makes apple juice for 3 people by adding 5 cans of water to 1 cans of frozen
concentrate. If Julia needs to make apple juice for 8 people, how many cans of frozen apple
juice concentrate does she need?
0 3
0 3 1/
04
041/
For making apple juice for 8 people she needs 2.67 cans of frozen concentration
What is Proportion?
A proportion is a component, share, or quantity compared to the total. A proportion is a comparison of two integers, each representing a piece of a larger whole.
Solution:
Since, Julia needs 1 can of frozen concentration for making apple juice for 3 people
We can say for 6 people she needs 2 cans
Similarly for 8 people she needs 8/3 cans = 2.67 cans
To learn more about Proportion from the given link
https://brainly.com/question/19994681
#SPJ1
help please i need help
3m-8n/13
show work !
The verbal description of the algebraic expression 3m-8n/13 is; Three m minus eight n divided by thirteen
How to write algebra word problems?Algebraic word problems are defined as questions that need translation of sentences to equations and thereafter solving those equations usually having a single variable. Now, the single variable usually denotes an unknown quantity in a real-life scenario.
To solve an algebraic word problem, the following steps are taken;:
Define a variable.Write an equation using the variable.Solve the equation.If the variable is not the answer to the word problem, then use the variable to calculate the answer.Now, we want to write the verbal description of the algebraic expression given as 3m-8n/13.
This is expressed as Three m minus eight n divided by thirteen
Read more about algebra word problems at; https://brainly.com/question/21405634
#SPJ1
Complete question is;
Write a verbal expression for 3m-8n/13
What is the length of DE?
The value of the length of side DE is 6.3 units
How to determine the length of DE?From the question, we have the following parameters that can be used in our computation:
The triangles ABC and DBE
From the question, we can see that the following corresponding sides on the triangles:
Sides AD and DB
Sides CE and EB
This implies that these sides are congruent sides
This is evident by the marks on these sides
Also from the figure, we have that:
The endpoints of the line DE is at the midpoint of lines AB and BC
This means that we have the following equation
DE = 1/2 * AB
Substitute the known values in the above equation, so, we have the following representation
DE = 1/2 * 12.6
Evaluate the products
DE = 6.3
Hence, the length DE is 6.3 units
Read more about congruent triangles at
brainly.com/question/1675117
#SPJ1
A cylinder has height of 17 centimeters it volume 1921.68 cubic centimeters what is the radius cylinder
The radius of the cylinder is found to be 6 cm.
What is a right circular cylinder?A right circular cylinder is a three dimensional figure having its base and top as a circle and the height is perpendicular to circular base. The volume is given as V = πr²h.
Given that,
The height of the cylinder is 17 cm.
And, the volume is 1921.68 cm³.
Suppose the radius be r cm.
Substitute the corresponding values in the expression of volume V = πr²h as follows,
V = πr²h
=> 1921.68 = π × r² × 17
=> π × r² = 1921.68/17
=> r² = 1921.68/17π
=> r = 6
Hence, the radius of the cylinder is obtained as 6 cm.
To know more about cylinder click on,
https://brainly.com/question/16134180
#SPJ1
Find the equation of all horizontal asymptotes of the following function.
x → -∝ , f(x) → -∝ and x → ∝ , f(x) → ∝
What is a Function ?The exact same number of elements from Y are assigned to each element of X via a mathematical function from a set X to a set Y. The function's domain and codomain are respectively referred to as the sets X and Y as a whole.
What is the limit of a function ?The limit of a function in mathematics is a key idea in calculus and analysis regarding the behaviour of that function close to a specific input. Below are formal definitions that were initially developed in the early 19th century. Informally, a function f gives each input x an output f(x).
According to the given information
We are given with the function
[tex]f(x)=x^{6}+12x^{5} +26x^{4}-116x^{3}-363x^{2} +104x[/tex]
When
limit( x → ∝ ) = f(x) = ∝
limit( x → -∝ ) = f(x) = -∝
So
as x → -∝ , f(x) → -∝ and as x → ∝ , f(x) → ∝
To know more about Function
https://brainly.com/question/28971475
#SPJ1
() = 2^4 + 5^3 − 6^2 + 15 − 36
With All steps and work.
Please help me. I been working on this for 5 hours, and My brain can't even help me on one thing, and constant comments of WRONG WRONG WRONG just makes me feel so horrible doing this work.. Please help. any help will be appreciated. These two problems have me down to tears because I have no Idea what to do anymore. Please help.
Answer:
1. (2x-3)(x^2+3)(x+4)
2. (3x-1)(x+5)(4x^2+1)
Step-by-step explanation:
2x^4+5x^3-6x^2+15x-36
2x^4-3x^3+8x^3-12x^2+6x^2-6x+24-36
x^3(2x-3)+4x^2(2x-3)+3x(2x-3)+12(2x-3)
(2x-3)(x^3+4x^2+3x+12)
(2x-3)[x^2(x+4)+3(x+4)]
(2x-3)(x^2+3)(x+4)
12x^4+56x^3-17x^2+14-5
12x^4-4x^3+60x^3-20x^2+3x^2-x+15x-5
4x^3(3x-1)+20x^2(3x-1)+x(3x-1)+5(3x-1)
(3x-1)(4x^2+20x^2+x+5)
(3x-1)[4x^2(x+5)+x+5]
(3x-1)(x+5)(4x^2+1)
Describe the relationship between and when the two lines are perpendicular to . Also describe the relationship between and when is not perpendicular to ?
Perpendicular lines have slopes that are negative reciprocal of each other.
Parallel line have same slope.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
When two lines are perpendicular their slopes are negative reciprocal of each other and they also intersect at a point.
When two lines are parallel they have the same slope and they do not intersect.
learn more about lines and slopes here :
https://brainly.com/question/3605446
#SPJ1
How do you calculate modus?
Modus is a statistical measure that is used to identify the most frequently occurring number in a set of numbers.
To calculate modus, first arrange the numbers in numerical order. Then count the number of times each number occurs in the set. The number that occurs most often is the modus. To calculate modus, first list all the numbers in the set in numerical order. The number that appears most frequently is the modus. For example, if the set of numbers is [1, 2, 3, 3, 3, 4], the modus is 3 because it appears three times, which is more than any other number in the set.
Learn more about modus here
https://brainly.com/question/27990635
#SPJ4
calculate the volume of the pyramid below. V=blank cm3. 6,4,5,6
A nickle has a mass of 5 grams while a penny has a mass of 2. 5 grams. What is the mass in kilograms of a bag of coins containing 186 nickles and 72 pennies?.
Answer: 1.11 kg
Step-by-step explanation:
1 kg = 1000 grams
Nickle has a mass of 5 grams = 0.005 kg
Penny has a mass of 2.5 grams = 0.0025 kg
Now take 0.005 times 186 = 0.93 kg for 186 nickles
Next, take 0.0025 times 72 = 0.18 kg for 72 pennies
0.93 kg + 0.18 kg = 1.11 kg
So the bag is 1.11 kg
please help!!!!!!!!!!!!!
Answer:-3
Step-by-step explanation: -3 because when you do it I really don't know how to explain it srry
Which One Doesn't Belong? Identify the linear expression that does not belong with the other three. Multiple choice question. A) (−5x+3)−(−7x−1) B) (−3x+3)−(−5x−2) C) (x−6)−(−x−10) D) (−7x+2)−(−9x−2)
Answer:
Step-by-step explanation:
a d c
What does splitting a verb mean?
Splitting a verb represents the meaning to divide lengthwise basically by layers or along a grain.
Explanation:
Splitting a verb represents the meaning as follow :
Word split defines to divide any group into small groups or subgroups.Splitting a verb explains to divide lengthwise basically in layer form or along a grain.Splitting a large group into small groups as per the category defined .For example : Students participates in discussion divided into different groups.It makes the work easy .It represent any number or group apart forcibly.Therefore, splitting a verb represents to divide lengthwise basically layer wise or along a grain.
Learn more about splitting here
brainly.com/question/13188770
#SPJ4
Simplify (−7b)(−16b).
112b
−112b
112b^2
−112b^2
Answer:
112b^2
Step-by-step explanation:
When you multiply two negative numbers, the outcome will always become positive.
7bx16b= 112b^2
Answer:
112b^2
Step-by-step explanation: