(i) The average values for the variables andre, pri gpa, and act is sum of all the values divided by the total number of values.
(ii) The model atenderte 5 b0 1 b1 prigpa 1 b2act 1 u in equation form is atenderte = b₀ + b₁ x prigpa + b₂ x act + u
(iii) The slope coefficients is b₁ and b₂
(iv) The predicted atenderte if prigpa 5 3.65 and act 5 20 is atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u
(v) if student a has prigpa 5 3.1 and act 5 21 and student b has prigpa 5 2.1 and act 5 26, then the predicted difference in their attendance rates is 0.5
In this exercise, we will be exploring a regression model that predicts the attendance rate of students based on their academic performance variables. We will be using three variables to predict the attendance rate: "andre", "pri gpa", and "act". Here are the answers to the questions:
(i) To obtain the minimum, maximum, and average values for the variables "andre", "pri gpa", and "act", we need to first look at the data. The minimum value is the smallest value for each variable, the maximum value is the largest value for each variable, and the average value is the sum of all the values divided by the total number of values.
(ii) The regression model that predicts the attendance rate is written in equation form as
=> "atenderte = b₀ + b₁ x prigpa + b₂ x act + u".
This equation means that the predicted attendance rate (atenderte) is equal to the intercept (b₀) plus the product of the coefficient for "pri gpa" (b₁) and the value of "pri gpa" plus the product of the coefficient for "act" (b₂) and the value of "act".
(iii) The estimated slope coefficients (b₁ and b₂) tell us the expected change in the attendance rate for each one-unit increase in "pri gpa" or "act". If b₁ is positive, it means that as "pri gpa" increases, the attendance rate is expected to increase. Similarly, if b₂ is positive, it means that as "act" increases, the attendance rate is expected to increase.
(iv) To find the predicted attendance rate if "pri gpa" is 3.65 and "act" is 20, we can substitute these values into the regression equation:
atenderte = b₀ + b₁ x prigpa + b₂ x act + u
atenderte = b₀ + b₁ x 3.65 + b₂ x 20 + u
This will give us the predicted attendance rate for a student with "pri gpa" of 3.65 and "act" of 20. If there are any students in the sample with these values of the explanatory variables, then their actual attendance rate should be close to the predicted value.
(v) To find the predicted difference in attendance rates between student A (with "pri gpa" of 3.1 and "act" of 21) and student B (with "pri gpa" of 2.1 and "act" of 26), we can first use the regression equation to predict the attendance rates for each student:
Student A:
atenderteA = b0 + b1 x 3.1 + b2 x 21 + u
Student B:
atenderteB = b0 + b1 x 2.1 + b2 x 26 + u
Then, we can take the difference between the predicted attendance rates for each student:
=> atenderteA - atenderteB
=> 52.6 - 52.1 = 0.5
This will give us the predicted difference in attendance rates between the two students.
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Someone help me with this equation please!!
The given statement is transitive property.
What is transitive property?Transitive property is also called transitive property of equality when we have two equal values and either of this value is equal to third value.
DE≅XY AND [tex]\hat{DE}$$\approx\hat{XY} and \hat{XY}$$\approx$$\YZ, then\hat{DE}$$\approx$$\hat{YZ}[/tex]
This is a transitive property.
Here we have three values, initially first two values are equal and second & third values are equal.
Which gives any one of the value of first and second equals third value.
This is the transitive property.
Hence, the given statement is transitive property.
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Someone please explain how to solve this.
Just multiply each side by side
Step-by-step explanation:1.Times one side by another
2. Times your answer by the third side
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
The Pythagorean theorem describes the relationship between the lengths of legs a and b and the hypotenuse c of any
right triangle.
a² + b² = c²
Complete the equation below by writing an expression equivalent to the length of a, the leg of a right triangle.
Completing the equation below by writing an expression equivalent to the length of a, the leg of a right triangle is given below
a^2 + b^2 = c^2a^2 = c^2 - b^2a = square root of (c^2 - b^2)What is Pythagoras' Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Hence, the complete equation according to this theorem is given above.
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nonononononononnnono
Find a possible formula for the trigonometric function whose values are in the following table.
The formula possible formula for the trigonometric function whose values are in the following table is y = 6 x sin(π/2 * x) - 4.
What is a trigonometric function?Trigonometric functions are described as the periodic functions which denote the relationship between angle and sides of a right-angled triangle.
The formula for a trigonometric function is typically written as :
y = a sin (bx + c) + d
where a, b, c, and d are constants which tells us the amplitude, frequency, phase shift, and vertical shift of the function, respectively.
From the above table, the amplitude = 6,
the frequency is 2π/4 = π/2
the phase shift = 0, and
the vertical shift = -4.
Therefore, we can write the formula for the function as Y = 6 * sin(π/2 * x) - 4.
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help i will mark as brainliest i promise
The two-column table that can be used to prove the congruence relationships between the segments of the triangles are presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{KN}[/tex] ≅ [tex]\overline{MN}[/tex] [tex]{}[/tex] Given
[tex]\overline{NL}[/tex] bisects ∠KNM [tex]{}[/tex]
2. ∠KNL ≅ ∠MNL [tex]{}[/tex] Definition of bisected angle
3. [tex]\overline{NL}[/tex] ≅ [tex]\overline{NL}[/tex] [tex]{}[/tex] Reflexive property
4. ΔKNL ≅ ΔMNL [tex]{}[/tex] SAS congruence rule
5. [tex]\overline{KL}[/tex] ≅ [tex]\overline{ML}[/tex] [tex]{}[/tex] CPCTC
6. KL = ML [tex]{}[/tex] Definition of congruence
C.
[tex]{}[/tex] Statement [tex]{}[/tex] Reasons
1. [tex]\overline{BE}[/tex] ≅ [tex]\overline{CE}[/tex], [tex]\overline{AE}[/tex] ≅ [tex]\overline{DE}[/tex] Given
2. ∠AEB ≅ ∠CED [tex]{}[/tex] Vertical angles theorem
3. ΔABE ≅ ΔCED [tex]{}[/tex] SAS congruence rule
4. [tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex] [tex]{}[/tex] CPCTC
What are congruent segments?Congruent segments are segments that have the same lengths.
The details of the reasons used to prove the equivalence of sides KL and ML and the congruence of the segments [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are presented as follows;
Definition of bisected angles
Bisected angles are angles that are split in two angles of the same measure by a segment passing through their vertex.
Reflexive property
The reflexive property of congruence states that a segment is congruent to itself.
SAS congruence rule
The SAS, Side-Angle-Side congruence rule states that if two sides and an included angle of a triangle are congruent to two sides and an included angle in another triangle, then the two triangles are congruent.
CPCTC
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.
Definition of congruence
Geometric figures, such as segment, angles and shapes are congruent when their sizes and measurements are the same.
Vertical angles theorem
The vertical angles theorem states that vertical angles formed by the intersection of two lines are congruent
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a student committee has 6 membersâ€""4 undergraduate and 2 graduate students. a subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. what is the probability that there will be no graduate students on the subcommittee?
The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in
(4 choose 3) = 4 ways.
The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in
(6 choose 3) = 20 ways.
Therefore, the probability that there will be no graduate students on the subcommittee is:
Number of subcommittees with only undergraduate students / Total number of possible subcommittees
= 4 / 20
= 1/5
= 0.2
So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
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Select the correct point
One linear equation is defined by points (1,6) and (3, 7), while the other is defined by points (3,6) and (5,8). Which point represents the solution of
this system of equations?
Answer:
Step-by-step explanation:
o find the solution of a system of linear equations, we can find the point where the two lines intersect. The point of intersection represents the solution to the system of equations.
The first linear equation can be determined by finding its slope and y-intercept using the given points:
m = (7 - 6) / (3 - 1) = 1
b = 6 - m * 1 = 6 - 1 * 1 = 5
y = mx + b
y = x + 5
The second linear equation can be found similarly:
m = (8 - 6) / (5 - 3) = 1
b = 6 - m * 3 = 6 - 1 * 3 = 3
y = mx + b
y = x + 3
Since the two lines have the same slope, they are coincident and represent the same line. The solution to the system of equations is therefore any point on this line, but since we were asked for a specific point, we can choose (3,6) as the solution.
During a sale, a store offered a 35% discount on a tablet computer that originally sold for $340. After the sale, the discounted price of the tablet computer was marked up by 35%. What was the price of the tablet computer after the markup? Round to the nearest cent.
The marked-up price of the discounted tablet computer is $298.35.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, During a sale, a store offered a 35% discount.
So, The discounted price of the computer tablet is,
= [(100 - 35)/100]×340.
= (65/100)×340.
= $221.
Now, The price is marked up by 35% which is,
= [(100 = 35)/100]×221.
= (135/100)×221.
= $298.35.
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Write a general formula to describe the following variation: F is directly proportional to the square of d, and F = 40 when d = 5.
Answers:
40 = 5k
F = 8d
F = 1.6*d^2
F = kd
A general formula to describe is F = 1.6×d² will be correct answer.
What in math is a proportional?A relationship is considered proportional if the ratio remains constant. For instance, the average number of apples produced per tree is a measure of proportionality, and the number of trees in an orchard is inversely related to the number of apples produced in a harvest. When two quantities are proportionate with one another, then expand and contract at the same pace, keeping the relationship constant.
Finding the general formula we obtain:
F=kd²
40=k×5²
k=1.6
so, F =1.6×d².
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Belle has a collection of trading cards. The table shows how many of each type of card she has. A card will be randomly drawn from her collection and replaced 60 times
Type: Number:
Baseball 13
Football. 8
Basketball. 5
Soccer. 9
What is a reasonable prediction for the number of times a basketball or soccer card will be drawn?
What is the approximate distance between point W (3, 6) and point Z (8, -2)?
Answer:
hope this helps!!! That’s the answer!
Step-by-step explanation:
Answer:
9.43 units.
Step-by-step explanation:
To find the distance between two points in a 2D plane, you can use the Pythagorean theorem. The formula for finding the distance between two points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values for W and Z:
d = √((8 - 3)^2 + (-2 - 6)^2)
d = √(5^2 + (-8)^2)
d = √(25 + 64)
d = √89
The distance between the points W and Z is approximately 9.43 units.
Terri wants to know the height of the big Christmas tree on the town square. She stands 20 feet from the base of the tree. Elliot places a mirror on the ground between Terri and the tree so that she can see the top of the tree in the mirror. The mirror is located 16 feet from the base of the tree. If Terri's eye level is 5.5 feet from the ground, how tall is the tree?
Answer:
22ft
Step-by-step explanation:
Always good to try and draw out the scenario, it can make it more easily understandable.
Have a look at the pic.
Hope its clear.
In the World of Numbers, there are many number-machines, which work in the following way: the machine adds the two beginning digits of the number and replaces them by their sum. For example, beginning with the number 87312 and using six machines we obtain:
87312-15312-6312-912-102-12-3
How many such machines should be used in order to get to the number 450 from the number 900?
The number of machines used in order to get to the number 450 from the number 900 is 9.
What is an expression?An expression contains more than one term with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
900 to 450
We need a number of machines such that 450 is the last output starting from 900.
Now,
If we subtract 50 from each consecutive number we get,
900, 850, 800, 750, 700, 650, 600, 550, 500, 450
So,
We use 9 machines to get 450 from 900.
Thus,
9 machines should be used in order to get to the number 450 from the number 900.
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FIND THE PERIMETER AND AREA OF THE EQUILATERAL TRIANGLE
Answer: look at the image for the solution and the answer
Step-by-step explanation:
find the gcf 24x^3+36^2
The greatest common factor of the 24x³ + 36x² is 12x².
What is the greatest common factor?It is the greatest factor common to all the numbers given such that there are no greater factors common other than that.
Example:
4 is the gcd of 12, 8, 16.
We have,
24x³ + 36x²
Taking out the common factor.
= 12x² (2x + 3)
Thus,
GCF of the expression is 12x².
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Heidi contributes 11% of her monthly salary towards her 401(k) and her employer matches her contribution up to 6% of her salary. If the interest rate of her 401(k) is 6.25% compounded monthly and her monthly salary is $3,250, determine the amount in her account after 15 years. Round to the nearest cent.
Answer:
The amount that will be in Heidi’s account after 15 years is option A. $164,146.52.What is Future Value?It can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:FV = M (((1 + r)^n - 1) / r)Where;FV = Future value of the amount need to findM = total monthly contribution which is Heidi’s monthly contribution of 11% of her monthly salary + Employer monthly contribution of 6% of Heidi’s monthly salary can be calculated as;= (11% of Heidi’s monthly salary + 6.25% of Heidi’s monthly salary) = (11% of $3,250) + (6.25% x $3,250) = $552.50r = Monthly interest rate= Annual interest rate of 401(k) / 12 = 6.25% / 12 = 0.0625 / 12 r = 0.00520833333333333n = number of months = Number of years x 12 = 15 x 12 n= 180Substituting all the values into equation (1), we have;FV = $552.50 (((1 + 0.00520833333333333)^180 - 1) / 0.00520833333333333)FV = $552.50 x 297.097770863934FV = $164,146.518402324Rounding to the nearest cent, we get;FV = $164,146.52Therefore, the amount that will be in Heidi’s account after 15 years is option A. $164,146.52.
Step-by-step explanation:
.
How to write a congruence statement
Answer:
Step-by-step explanation: A congruence statement expresses that two figures have the same size and shape. Here's how you can write a congruence statement step by step:
Write the two figures you want to compare. For example, you could write "Triangle ABC" and "Triangle DEF".
Use the symbol "≅" to indicate congruence. Place the symbol between the two figures, like this: "Triangle ABC ≅ Triangle DEF".
Label the corresponding parts of the two figures to show that they are congruent. For example, you could write "AB = DE", "BC = EF", and "AC = DF".
The final congruence statement would look like this: "Triangle ABC ≅ Triangle DEF, with AB = DE, BC = EF, and AC = DF". This statement says that Triangle ABC is congruent to Triangle DEF, and that the lengths of their corresponding sides are equal.
How many solutions does the following system of equations have?
a. 1
b. Infinitely many
c. 0
d. Not enough information
The correct option is B, the system of equations has infinitely many solutions.
How many solutions does the system of equations has?When we graph a system of equations, the points where the graphs of the equations intercept are the solutions.
In this case we can see a single line graphed, which only can happen when both equations of the system represent the exact same line.
Then the graphs intercept at infinite points, thus, the system of equatios has infininitely many solutions.
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Write the scale factor of abcde to zyxwv
The scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:
k = zy/ab.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The figures for this problem are given as follows:
Original: abcde.Dilated: zyxwv.Hence the scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:
k = zy/ab.
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Sage and Tom started the month with the same number of talk minutes on their cell phones. Sage talked for 7 minutes with her dad. Tom talked for 4 minutes with a friend and 3 more minutes with his mom. Do Sage and Tom have the same number of talk minutes left on their cell phone plans?
Question 1
Yes, Sage and Tom have the same number of talk minutes left in their cell phones. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The term "arithmetic operations" refers to the four basic mathematical operations that can be used to express any real number. Multiplication, division, addition, and subtraction are the four operations.
We are given that Sage and Tom both started the month with the same number of talk minutes on their cell phones.
So, let 'x' be the number of talk minutes on their cell phones.
Sage talked for 7 minutes with her dad.
So, talk minutes left in Sage's phone = x-7
Tom talked for 4 minutes with a friend and 3 more minutes with his mom.
So, talk minutes left in Tom's phone = x - (4 +3) = x -7
Hence, Sage and Tom have the same number of talk minutes left in their cell phones.
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A circle has a diameter of 26 feet what is the circumference
Use 3.14 for pie and do not round your answer be sure to include the correct unit in it in your answer
The circumference of a circle with a diameter of 26 feet is approximately 81.64 feet.
What is the circumference?
The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center. A meridian is any great circle passing through a point designated as a pole.
The formula for the circumference of a circle is 2 * π * r, where r is the radius of the circle.
To find the circumference, we first need to find the radius of the circle.
The diameter of the circle is 26 feet, so the radius can be calculated by dividing the diameter by 2:
r = 26 feet / 2 = 13 feet
Now that we know the radius, we can find the circumference:
C = 2 * π * r = 2 * 3.14 * 13 = 81.64 feet
Therefore, the circumference of a circle with a diameter of 26 feet is approximately 81.64 feet.
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Ethanedioic acid is a solid at room temperature. Calculate the mass of ethanedioic acid (H₂C2O4) needed to make 250 cm³ of a solution with concentration 0.0480 mol/dm³ Relative formula mass (M): H₂C2O4 = 90
Answer: 1.08g
Step-by-step explanation:
Concentration = Moles/ Volume
Moles = Concentration x Volume
Moles = 0.048 x 250/1000
Moles= 0.012
Moles= Mass / Relative Formula Mass
Mass = Moles x Relative Formula Mass
Mass = 0.012 x 90
= 1.08g
The graph of function f is shown.
The graph of exponential function passes through (minus 0.5, minus 8) and (5, 1) also intercepts the x-axis at the point 1 unit and y-axis at point minus 3
Function g is represented by the table.
x -1 0 1 2 3
g(x) -24 -4 0
Which statement correctly compares the two functions?
A.
They have the same y-intercept and the same end behavior as x approaches ∞.
B.
They have the same end behavior as x approaches ∞, but they have different x- and y-intercepts.
C.
They have the same x-intercept and the same y-intercept.
D.
They have the same x-intercept and the same end behavior as x approaches ∞.
The statement that correctly compares the two functions is
They have the same x-intercept and the same end behavior as x approaches ∞.
What is the end behavior of a function?A function's final behaviour is represented by the value of f(x) as x approaches infinity. Both functions in this scenario have the same final behaviour because they both have unbounded growth, or they both go to positive infinity.
To find y-intercept of a function we have to put x= 0
So, The y-intercept of f(x) is y = -3.
and, The y-intercept of g(x) is y = -4.
To find x -intercept of a function put y = 0
So, The x-intercept of f(x) is x = 1.
and, The x-intercept of g(x) is x = 1.
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Use the graph of the number of gallons of lemonade in a container, y, after drinking x glasses of lemonade.
The graph states that there are 2 number of gallons of lemonade in a container, y, after drinking 12 glasses of lemonade.
How to interpret a graph?
The horizontal scale across the bottom and the vertical scale along the side tell us how much or how many. The points or dots on the graph show us the facts. The lines connecting the points give estimates of the values between the points.
since , it is a decreasing graph because it has a negative slope . Therefore , as no of glasses increases the gallons numbers decreases.
Hence , the graph states that there are 2 number of gallons of lemonade in a container, y, after drinking 12 glasses of lemonade.
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Answer:
no run hide
Step-by-step explanation:
hide run boo
if you were to graph a sine function from the data listed in the table above, what values would be represented by the dependent variable and what would be represented by the independent variable?
If you were to graph a sine function from the data listed in the table the days since Jan 8 is an independent variable and amount of moon visible is dependent variable
Given that, we have to graph a sine function from the data listed in the table
From the table we can see that there a two types of variables, The days since the Jan 8 and the amount of moon visible
The independent variable is defined as the variables that does not depends on any other variables
The dependent variable is defined as the variables that depends on other variables
Here the days since the Jan 8 does not depends on any other variables, so it is an independent variable. similarly the amount of moon visible depends on the days since Jan 8 value, so it is a dependent variable
Therefore, the days since Jan 8 is an independent variable and amount of moon light visible is dependent variable
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The given question is incomplete, the complete question is :
if you were to graph a sine function from the data listed in the table above, what values would be represented by the dependent variable and what would be represented by the independent variable?
At 7:00 A.M. Joe starts jogging at
6 mi/h. At 7:10 A.M. Ken starts off
after him. How fast must Ken run in
order to overtake him at 7:30 A.M.?
Provide steps please
The speed at which Ken should run to overtake Joe by 7.30 is 9mi/h.
What is meant by the speed of an object?
The size of a change in an object's position over time is measured by its speed. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. It is a scalar value.
Given,
Time at which Joe starts jogging = 7 am
Time at which Ken starts jogging = 7.10 am
Speed of Joe = 6mi/h
Let Speed of Ken required to overtake Joe = x mi/h
Since Ken has to overtake Joe by 7.30, both will have travelled the same distance by 7.30.
Time taken by Ken to cover the distance = 7.30 - 7.10 20 minutes = 20/60=1/3 h
Time taken by Joe to cover the distance = 7.30 - 7 = 30 minutes = 1/2 h
Distance = speed * time
Both cover the same distance.
6 * 1/2 = x * 1/3
x = 9 mi/h
Therefore the speed at which Ken should run to overtake Joe by 7.30 is 9mi/h.
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how to solve x-5(x - 1)=x- (2x-3)
The value for x-5(x - 1)=x- (2x-3) which gives x = 2/3.
What is Solution of Equation?An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Given:
x-5(x - 1)=x- (2x-3)
Now, solving the Equation for x we get
x -5x + 5 = x - 2x + 3
-4x + 5 = -x + 3
-4x + x = 3 -5
-3x = -2
x= 2/3
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A business owner wants to have the front window of her store painted and is considering two artists for the job. Suzie has quoted a flat rate of $250 for the job. Jane's quote is $40 per hour, plus $50 to cover the cost of materials. Depending on how long it takes Jane to paint the window, these two could end up charging the same amount. How long would Jane have to take? Write a system of equations, graph them, and type the solution.
Jane would take 5 hours painting the window so both of them could end up charging the same amount
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
Let y represent the total charge for working x hours.
Suzie has quoted a flat rate of $250 for the job. For Suzie:
y = 250
Jane's quote is $40 per hour, plus $50 to cover the cost of materials. For Jane:
y = 40x + 50
For the two to charge the same amount:
250 = 40x + 50
40x = 200
x = 5 hours
Jane would spend 5 hours painting the window.
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Subtract 7x²-x-1 from x²+3x+3
Answer: The answer is x²+2x-8
Step-by-step explanation:
On the following scale drawing, the scale is 2 centimeters-1 meter.
1. Make a new scale drawing of this rectangular figure using the scale 3 centimeters-1 meter. Make sure to label the
new dimensions.
2. What are the actual dimensions of the figure?
7.8 cm
4.2 cm
The actual dimensions of the figure is 3.9 x 2.1
What is the scale factor ?Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.
For example, Two spheres look similar but could have different radii.
For the first dimension of 7.8 cm, we can set up a proportion using the scale factor:
2 cm : 1 m = 7.8 cm : x
where x is the actual length we want to find.
Solving for x, we get:
x = (7.8 cm x 1 m) / 2 cm
x = 3.9 m
Therefore, the first actual dimension is 3.9 meters.
For the second dimension of 4.2 cm, we can use the same method:
2 cm : 1 m = 4.2 cm : y
where y is the actual width we want to find. Solving for y, we get:
y = (4.2 cm x 1 m) / 2 cm
y = 2.1 m
Therefore, the second actual dimension is 2.1 meters.
So the actual dimensions of the figure are 3.9 meters by 2.1 meters.
To know more about Scale factor check:
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