The scaled versions of the given rectangle are A rectangle with a height of 18.75 units and a width of 12 units, A rectangle with a height of 50 units and a width of 32 units and A rectangle with a height of 1.25 units and a width of 0.8 unit
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given that, A rectangle has a height-to-width ratio of 6.25:4.
4/6.25 = 0.64
The ratio of width to height should be 0.64 for the scaled versions of this rectangle.
A) A rectangle with a height of 18.75 units and a width of 12 units = 12/18.75 = 0.64
B) A rectangle with a height of 50 units and a width of 32 units = 32/50 = 0.64
C) A rectangle with a height of 1.25 units and a width of 0.8 unit = 0.8/1.25 = 0.64
Hence, The scaled versions of the given rectangle are A rectangle with a height of 18.75 units and a width of 12 units, A rectangle with a height of 50 units and a width of 32 units and A rectangle with a height of 1.25 units and a width of 0.8 unit
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The diagram below is used to sort out numbers.
Type each number in the correct location on the diagram.
3
30
333
3001
two-digit
numbers
multiples
of 3
three-digit
numbers
The solution is given as,
Two-digit numbers Multiples of 3 Three-digit numbers
30 3,30, 333, 333
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Place the given number in the appropriate place.
Numbers are 3, 30, 333, 3001,
Two digit number among the numbers = 30
Multiples of 3 among numbers = 30, 333, 3
Three-digit numbers among the numbers = 333
Thus, It is shown that the numbers are placed in their appropriate positions.
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Question 4
The weights for 12-month-old baby boys are normally distributed with a mean of 22.5 pounds and a standard deviation of 2.2 pounds.
Find the percentage to the nearest tenth of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds.
ANSWER -
Answer:
70.5%
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\large\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
Mean μ = 22.5Standard deviation σ = 2.2Therefore, if the weights of the 12-month-old baby boys are normally distributed:
[tex]\boxed{X \sim\text{N} \left(22.5,2.2^2 \right)}[/tex]
where X is the weight of the baby boy.
To find the percentage to the nearest tenth of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds find P(19.7 ≤ X ≤ 24.4).
Calculator input for "normal cumulative distribution function (cdf)":
Upper bound: x = 19.7Lower bound: x = 24.4σ = 2.2μ = 22.5[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=0.704548741[/tex]
[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=70.5\%[/tex]
Therefore, the percentage of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds is 70.5% (nearest tenth).
In the diagram below, angle f is congruent to angle i. Enter segments in the blanks provided that would result in a true equation.
The segments in the blank provided is GH/FH=IH/JH so that the equation is true
What are the 4 characteristics of similar triangles?Similar triangles differ in size but have the same form. Corresponding angles are identical in comparable triangles. Similar triangles have corresponding sides that have the same ratio. The ratio of the square of any two of their corresponding sides to any identical triangle's area is the same.
What are the 3 types of triangle similarity?The triangle similarity criteria are:
AA (Angle-Angle)
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
In the given question
<GHP=<IHJ (vertically opposite angles)
<JIH=<HPG (alternate angles)
From AA similarity critera
triangles JHI ~ triangle GHP
Hence
GH/FH=IH/JH
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Identify the line(s) of symmetry for the quadratic function below.
Answer:
y=-3
Step-by-step explanation:
A line of symmetry is the line where a function can be folded in half evenly. Here it occurs at y=-3
line of symmetry, the line at which point the graph begins to mirror itself, Check the picture below.
Recreating the Original Triangle
You will be using the following original triangle in the following activity.
With a ruler, measure the sides of the original triangle to the nearest millimeter. Write down the length of each side in your math journal.
With a protractor, measure the angles of the original triangle to the nearest degree. Write down the measure of each angle in your math journal.
SSS: Cut three pieces of string. Make each piece of string the length of one of the sides of the original triangle. Put the string together to form a triangle and trace the triangle on a separate piece of paper. Measure the angles of the triangle with your protractor.
Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Rearrange the string to make a different triangle. Is there any way to create a triangle that has different angle measures?
SAS: Choose two sides of the original triangle. Cut two pieces of string and make each piece of string the length of one of those sides. Measure the angle between the sides that you chose and draw an angle of that measure on a separate sheet of paper. Put the string together to form the sides of that angle and trace them. Draw in the third side of the triangle. Measure the third side that you drew and the two angles adjacent to that side.
Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Draw the starting angle elsewhere on your paper and rearrange the string to make a different triangle. Is there any way to create a triangle whose third side has a different length?
ASA: Choose one side of the original triangle. Cut one piece of string and make the piece of string the length of that side. Trace the string on a separate sheet of paper. Measure the angles on either side of the side that you chose, and draw angle of those measures on either side of the line you traced on the paper. Extend the sides of the angles until they intersect and form a triangle. Measure the two sides that you drew and the angle between them.
Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Rearrange the string and re-draw the two starting angles to make a different triangle. Is there any way to create a triangle that has different side lengths?
The original triangle⬇️
The properties of the triangles created from the original triangle based on triangle congruency rules are as follows;
SSS: The triangle created using the lengths of the three sides of the original should have the same length and angles as the original
The triangle formed using SSS is a unique triangle and no other triangle has similar dimensions
SAS: The lengths of the sides and the measure of the angles should be the same
The triangle created using SAS is a unique triangle and there is not a way to have a third side that has a different length
ASA; The triangle formed using the ASA of the original triangle should have the same length as the same lengths and angles as the original triangle
The triangle formed using ASA is a unique triangle and there is not a way to create a triangle that has a different side length.
What are congruent triangles?Two triangles are congruent if the lengths of the three sides of one triangle are congruent to the three sides of the other triangle or if they meet the other conditions of triangle congruency.
Length of first measured side of the triangle = 52 units
Angle made by the first measured side with the horizontal = 41°
Length of the second measured side of the triangle = 87 units
Angle the second measured side makes with the horizontal = 33°
Length of the third measured side of the triangle = 113 units
Angle the third side makes with the horizontal ≈ 6.5°
Let the vertices of the first side be A and B, we get;
∠A = 180° - (41° + 33°) = 106°
∠C = 33° - 6.5° = 26.5°
∠B = 41° + 6.5° = 47.5°
SSS: The SSS (Side-Side-Side) congruency postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Therefore, the lengths of the sides and the measures of the angles of the triangle created using the lengths of the three sides of the original triangle will be the same as the original triangle.
The SSS congruency postulate indicates that the triangle created using the same lengths of the three sides of the original triangle is a unique triangle and there are no other triangles having the same side lengths but different angles
SAS: The Side-Angle-Side, SAS, congruency postulate states that if the adjacent sides and an included angle of a triangle are congruent to two adjacent sides and an included angle of another triangle, then the two triangles are congruent.
Therefore, the triangle formed using two sides of the original triangle and the included angle between them will have the same length as the sides of the original triangle, and the triangle formed using the SAS of the original triangle is unique
The length of the third side of the triangle created using the SAS measurement is always the same as the length on the original triangle
ASA: The Angle-Side-Angle, ASA, congruency postulate states that if two angles and the included side of one triangle are congruent to two angles and an included side of another triangle, then the two triangles are congruent.
The triangle formed using the ASA is a unique triangles and therefore and there is no way to create a triangle that has a different side length
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A water coller filll 150 glae in 30 minute how many glae of water can the coller filll in one minute
Five water glasses each minute, one minute to fill the cooler.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units
Let's say you go to the store to buy six apples.
You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.
Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.
We are aware of the quantity of apples and the amount of money in the aforesaid problem.
According to our question-
divide 150 by 30 equal 5
= 5
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And bottom says solve for X someone help me
Answer:
2(x+8)=126
Step-by-step explanation:
GD is the bisector of CGE and 126 and the angle CGE are equal
I need to know the question to a problem 10”=14,521
Answer:
The value of n in this equation is 5.
Step-by-step explanation:
This can be determined by using the property of exponents that states that x^n * x^m = x^(n+m). In this case, 10^n * 10^5 = 14,521, so 10^(n+5) = 14,521. Solving for n, we get n = 5.
PLS HELP WILL GIVE BRAINLIEST!
1) the slope of the line x=8 is ______
2) the domain and range of a linear function are _________
Answer:
I tried as I can to solve it
if there are 720 different classes in one quarter, each in its own room, how many different rooms will be required?
if there are 720 different classes in one quarter at time, each in its own room, different rooms will be required 720 rooms.
To answer this question, we need to understand that each class needs its own room. Therefore, the number of rooms required will be equal to the number of classes. In this case, there are 720 different classes in one quarter, so 720 different rooms will be required. Each room can accommodate one class at a time, so the total number of rooms needed is 720.
Number of Classes = 720
Number of Rooms Required = Number of Classes = 720
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the famous kate lynn horsefeed is building a box as part of her science project. it is to be built from a rectangular piece of cardboard measuring 25 cm by 40 cm bycutting out a square from each corner and then bending up the sides. find the size of the corner square which will produce a container that will hold the most.
The original cardboard measures 25 cm by 40 cm. By cutting out a 10 cm by 10 cm corner square, the new measurement of the cardboard will be 15 cm by 30 cm. The volume of the container will be 4500 cm^3.
The goal of this project is to build a container out of a rectangular piece of cardboard measuring 25 cm by 40 cm. To do this, a square must be cut out of each corner of the cardboard and the sides must then be bent up. In order to produce a container with the most internal volume, the corner square should be 10 cm by 10 cm. This will result in four equal sides and a larger internal volume. The larger internal volume will allow the container to hold more material, thus making it more efficient for the project.
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find the value of x.
What is the relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc?
Answer: The circumference itself can be considered a full circle arc length. Arc Measure: In a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc. Arc Length: In a circle, the length of an arc is a portion of the circumference.
An arc length is a portion of the circumference of a circle. You can use the measure of the arc (in degrees) to find its length (in linear units). In a circle, the ratio of the length of a given arc of the circumference is equal to the ratio of the measure of the arc to 360°.
It will help you.
Step-by-step explanation:
The basketball team scored a total of 109 points last game. They made a total of 47 shots, including 2-point shots and 3-point shots. how many 2-point shots did they make? How many 3-points did they make?
[please include steps]
Based on the above, the number of 3-points that they make is 25.
What is the Simultaneous equation about?Simultaneous equation is a form of two equations that have to be solved at the same time. Thus, the number of 2 points made is 17, while that of 3 points is 25.
A set of equations that has to be solved simultaneously so as to determine the values of the unknown variables is termed simultaneous equation.
The given question would result to a simultaneous equation as follows;
let the number of 2 points made by represented by m, and that of 3 points by n.So that;
m + n = 42 ..................
i2m + 3n = 109 ...............
ii multiply equation 1 by 3 and equation 2 by 1 to have;3m + 3n = 126 ............
iii 2m + 3n = 109 .............
iv subtract eqaution iv from iii
m = 17
substitute the value of m in equation 1 to have:
m + n = 4217 + n = 42n = 42 - 17 = 25m = 17, n = 25
Thus the number of 2 points made was 17, while that of 3 points made was 25.
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If C is ¼ of the distance from A to D if A is (3,7) and D is (11,11) where is C?
Answer:
(8.25, 9.75)
Step-by-step explanation:
To find the point that is ¼ of the distance from A to D, we first need to find the coordinates of D. Since A is located at the point (3, 7) and D is located at the point (11, 11), we can use the distance formula to find the distance between these two points. The distance formula is given by:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we have x1 = 3, y1 = 7, x2 = 11, and y2 = 11, so the distance between A and D is:
distance = √((11 - 3)^2 + (11 - 7)^2) = √(8^2 + 4^2) = √(64 + 16) = √80 = 8.944
Now that we know the distance between A and D, we can use this information to find the point that is ¼ of the distance from A to D. Since C is ¼ of the distance from A to D, it is located ¼ of the way along the line between A and D. This means that we can find the coordinates of C by taking the average of the coordinates of A and D, weighted by ¼ and ¾, respectively. In other words, the coordinates of C are given by:
C = ¼ * A + ¾ * D
where A and D are the coordinates of points A and D, respectively. Plugging in the coordinates of A and D, we get:
C = ¼ * (3, 7) + ¾ * (11, 11) = (0.75 * 3 + 2.25 * 11, 0.75 * 7 + 2.25 * 11) = (8.25, 9.75)
Therefore, the point C is located at the coordinates (8.25, 9.75).
The expression (x + 3)(x + 2) is the product of two binomials. Which expression is also
a product of binomials?
The expression which has product of two binomials is (5-n)(n+7).
What is Expression?An expression is combination of variables, numbers and operators.
Binomials are expressions containing the sum (or difference) of two terms.
The expression (x + 3)(x + 2) is the product of two binomials.
(pq)(qp), (5-n)(n+7), 3x(2x+5), 6x-2y
(pq)(qp) is not the product of binomials because pq and qp are products.
3x(2x+5) is not the product of binomials because 3x is not a sum or difference.
6x-2y is also not because it is one binomial, not two multiplied together.
(5-n)(n+7) is the product of two binomials.
Hence, (5-n)(n+7) is the expression which has product of two binomials.
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SOMEONE PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
y=-2/3x+4
Step-by-step explanation:
Rise/run (from the y-intercept to the next point you go down 2 and then to the right 3)
Y-intercept (where the line touches the y-axis) 4
Line a passes through the points (0, 4)
and (4, 0). Line b passes through the
points (0, 7) and (7, 0). Are the lines
parallel? Explain.
Answer:
Yes, the lines are parallel. This is because the lines have the same slope. The slope of a line is a measure of how steep the line is, and it is calculated by taking the difference of the y-coordinates of two points on the line and dividing it by the difference of the x-coordinates of the same two points. In this case, the slope of line a is -1, and the slope of line b is also -1. Because the lines have the same slope, they are parallel to each other.
The table shows the number of cases of foodborne botulism in the United States for the years 2001 to 2005. Let x represent the
number of years since 2000. Find a linear model for the data. List the correlation coefficient.
U.S. Foodborne Botulism Cases
Year
Cases 39 28 20 16
2001 2002 2003 2004 2005
18
Source: Centers for Disease Control
Linear model:
Correlation coefficient: r =
Predict the number of foodborne botulism cases in the United States in 2007.
We require a more accurate and objective measure to determine the association between the two variables because visual exams are primarily subjective. We employ the linear correlation coefficient to express the degree and direction of the association between two variables:
[tex]r=\frac{\sum \frac{\left(x_i-\bar{x}\right)}{s_x} \frac{\left(y_i-\bar{y}\right)}{s_y}}{n-1}[/tex]
where the sample means and standard deviations of the x's are x and sx, respectively, and the y's are y and sy, respectively. n is the sample size. .
A different method of calculating the correlation coefficient is:
[tex]r=\frac{S_{x y}}{\sqrt{S_{x x} S_{y y}}}[/tex]
[tex]\begin{aligned}& \text { where } S_{x x}=\sum x^2-\frac{\left(\sum x\right)^2}{n} \\& S_{x y}=\sum x y-\frac{\left(\sum x\right)\left(\sum y\right)}{n} \\& S_{y y}=\sum y^2-\frac{\left(\sum y\right)^2}{n}\end{aligned}[/tex]
In honor of Karl Pearson, who created the linear correlation coefficient in the first place, it is also known as Pearson's product moment correlation coefficient. This metric quantifies the strength of the linear, or straight-line, relationship between the two variables as well as its positive or negative direction.
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The domain of a certain exponential function is all real numbers. The range of the function is all real
numbers greater than -3. The graph of the function has a horizontal asymptote at y = -3.
Select a graph or graphs to fit the description of the function.
One exponential function with the given features is y = 2^x - 3, and is graphed at the end of the answer.
How to define the exponential function?An exponential function is defined as follows:
y = a(b)^x + c.
In which:
a is the initial value.b is the rate of change.c is the horizontal asymptote.The graph of the function has a horizontal asymptote at y = -3, hence:
c = -3.
For a and b, they can assume any non-negative values, hence we attribute these following values:
a = 1, b = 2.
The graph is given at the end of the answer.
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This week, a pack of tomato plants costs $25. Next week, the plants are on sale for 15% off.
Larissa wants to know the price of the tomato plants if she buys them next week.
How much is the discount?
Price This Week
%
$
$
Price Next Week
%
25
$
Discount
15
?
%
The discount is $3.75 and the amount next week will be $21.25
How to illustrate the percentage?This has to do with a percentage. A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the pack of tomato plants costs $25. Next week, the plants are on sale for 15% off. Larissa wants to know the price of the tomato plants if she buys them next week.
The discount will be:
= 15% × $25
= $3.75
The amount next week will be:
= $25 - $3.75
= $21.25
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The median of a boulevard i 8 feet wide and 300 feet long. What i the area of the median?
By using the formula for area of rectangle, it can be calculated that Area of the median is 2400 sq. feet
What is area of rectangle?
The area of a rectangle is calculated by multiplying the length by the width. For example, if a rectangle has a length of 10 feet and a width of 6 feet, the area would be 10 x 6 = 60 square feet. The area of a rectangle is a two-dimensional measurement and is typically expressed in units squared, such as square feet or meters squared. Other shapes, such as a triangle or a circle, also have areas and are calculated differently.
If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is calculated by the formula
Area = [tex]l \times b[/tex]
Length of the median = 300 feet
Width of the median = 8 feet
Area of the median = 300 [tex]\times[/tex] 8 = 2400 sq. feet
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Determine the period.
Enter
Answer:
Your answer should be [tex]\frac{\pi }{7}[/tex]
Step-by-step explanation:
Looking at the x-axis we can say that is our b.
Period Formula: 2π/b.
x-axis is from 0 to 20.
b = 14 because of the rise to rise.
2π/14 = π/7
the difference between the sample statistic and the population parameter when sampling is done correctly is referred to as what?
A sampling error is the difference between a population parameter and a sample statistic.
Parameters are numbers that describe the properties of entire populations. Statistics are numbers that describe the properties of samples. For example, the average income for the United States is a population parameter. Conversely, the average income for a sample drawn from the U.S. is a sample statistic. The difference between a parameter vs a statistic is that a parameter is a fixed measure describing the whole population, while a statistic is a characteristic of a sample, a portion of the target population.
Thus, the difference is defined as sampling error.
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Solve the equation by subtracting the appropriate number from both sides and enter the value of x below. x + 2551 = 3105
Answer:
554
Step-by-step explanation:
x + 2551 - 2551 = 3105 - 2551
x = 554
Answer:
[tex]x + 2551 = 3105 \\ x + 2551 - 2551 = 3105 - 2551 \\ x = 554[/tex]
Will give brainliestttt PLEASE I NEED HELP :((((
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 4)(2, 8)(3, 16)(4, 32)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer.
Part B: Write a function to represent the data. Show your work. (4 points)Part C: Determine the average rate of change between station 2 and station 4. Show your work. (4 points)
Step-by-step explanation:
A
for a linear function the slope ratio has to be the same between every pair of data points.
between (1, 4) and (2, 8) we have
x changes by +1 (from 1 to 2).
y changes by +4 (from 4 to 8).
the slope is
+4/+1 = 4
between e.g. (2, 8) and (3, 16) we have
x changes by +1 (from 2 to 3).
y changes by +8 (from 8 to 16).
the slope here is +8/+1 = 8.
which is not the same as 4.
so, it is not a linear function.
it is an exponential function.
B.
the function is actually
f(x) = y = 2^(x+1)
an exponential function is of the form
y = a^x
in our case we have
4 = a¹ = 2²
8 = a² = a¹×2 = 2² × 2 = 2^(2+1)
16 = a³ = a²×2 = a¹×2×2 = 2²×2×2
we see
f(n) = a1×2^(n-1) = 2²×2^(n-1) = 2^(n+1)
C.
the average rate of change is
(the difference of the function results at the interval ends) / (the difference of the interval ends).
so, in our case
(f(4) - f(2))/(4 - 2) = (32 - 8)/2 = 24/2 = 12
the average rate of change between stations 2 and 4 is 12 (or 12/1).
Answer:
Um in an old question of mine you said "its been forever". That was my elijahmiraclechild account. I don't really remember you but I would like to
Step-by-step explanation:
Addilyn mow two lawn. The firt lawn i 6 meter long and 4 meter wide. The area of the econd lawn i 6 time big but ha the ame width a the firt. What i the length of the econd lawn?
The length of second lawn is found as the 36 sq. m.
Explain the term area of the 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.For the stated question-
First lawn:
Length = 6 mWidth = 4 mArea = length x width
A = 6 x 4 = 24 sq. m.
Second lawn:
Length = LWidth = 4 mArea A2 = 6 x Area of first lawnA2 = length x width
6 x A = L x 4
6 x 24 = L x 4
L = 6 x 6
L = 36 sq. m
Thus, the length of the second lawn is found as the 36 sq. m.
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Answer:
Step-by-step explanation:
36 is the answer
You need to determine where to place the beams so that the chains are fastened to the rollercoaster at a height of 25 feet. Write the equation you would need to solve to find the horizontal distance each beam is from the origin. (10 points).
Using the roller coaster as an example, draw a right triangle.
The equation used to find the horizontal distance: h² = 30² - 25².16.58 feet is the horizontal distance.What are ways to arrive at the equation?25 feet is listed as the height.The answer to the whole question is that the roller coaster measures 30 feet long.Use h to symbolize the horizontal distance.
The following expression can be used to get h given that roller coaster serves as a representation of the hypotenuse side length.
30² = h² + 25².
Assemble similar phrases.
h² = 30² - 25².
horizontal separation
In (a), there is:
h² = 30² - 25².
This results:
h² = 275
Take both sides' roots.
h = 16.58
Consequently, 16.58 feet are the horizontal distance.
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Seth is comparing scenarios to determine which starting point he should get dropped off at to get him to school faster. Seth's house is 17 miles from school. In which scenario does seth start closer to school? in which scenario does seth travel at a greater speed, and what was the rate?.
In linear equation, He travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Using linear function concepts, it is found that:
Seth starts closer to the school in the bus.
He travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.
From the graph of the bus, when he takes the bus, he is 13 miles from the school, as he starts at position 4 and ends at 17.
At his friend house, he is 13 miles from the school only after 3 minutes, which means that the bus will be closer.
The scenario with the greater speed is the one with the higher slope, that is, higher rate of change, which is the change in distance divided by the change in time.
In the bus, change of 13 miles in 24 minutes, thus
mᵇ = 13/24 = 0.5417
From the friend's house, change of 2 miles in 3 minutes, thus
mf = 2/3 = 0.6667
Thus, he travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.
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