The total distance travelled by Kyle is 210 m.
What is Pythagoras theorem?Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².
The given length of the field is 84 m.
And, the width is 35 m.
Now, the diagonal of the field can be calculated using Pythagoras theorem as below,
Diagonal = √((84)² +(35)²)
= 91
Then, the total length is found by summing the length, width and the diagonal as below,
= 84 + 35 + 91
= 210
Hence, Kyle run for the distance of 210 m.
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Given the table below, write a linear equation that defines the
dependent variable, c, in terms of the independent variable, a.
No need for steps only answer someone help please brainliest
Answer:
c = -(7/5)a + 15
Step-by-step explanation:
c= (8-15)/(4-0)×a+15
c= -(7/5)a + 15
The sum of two numbers is always greater than the larger of the two numbers?
False
Step-by-step explanation:The sum is the total of an addition problem.
Addition of Positive Numbers
Most commonly, people add together positive numbers. Positive numbers are numbers greater than 0. The sum of 2 positive numbers is always greater than the addends. For example:
2 + 3 = 5The sum of these positive numbers, 5, is greater than the larger number, 3. However, the addition of positive numbers is not the only way to add.
Addition of Negative Numbers
Negative numbers are numbers less than 0. If you add negative numbers, then the sum will be less than the addends. So, the statement above is not true. For example:
-2 + 3 = 1In this case, the sum, 1, is less than the larger number, 3. This disproves the statement given.
A taxi company charges $4 as soon as a passenger enters the cab, then $3/mile for the first 6 miles, and then $2/mile for the distances greater than 6 miles. What best models the taxi company’s charges?
The total charge /cost c of taxi company's for a trip of d miles will be
c = 0.6 d + 1.2
What is mile with example?
A mile (mi) is a customary unit of distance. It is generally used to express the distance between cities, roads, and the length of rivers.For example , one could say the distance of a marathon race is about 26.3 miles or 26.3 mi.Let c be the cost/charges and d be the miles.
Let $3/mile be the basic charge as well as the cost for the distance covered.
For 6 mile trip , the cost is $ 4.80 , then the cost of 3 miles is
$ 4.80 - $ 3.00 = $ 1.80
Therefore, the cost for 1 mile is $ 1.80 / 3 = $ 0.60
The basic fee for hiring the cab is $ 3.00 - $ 1.80 = $ 1.20.
Therefore the total charge /cost c of taxi company's for a trip of d miles will be
Total cost = cost for 1 mile + basic fee for hiring the cab
c = 0.6 d + 1.2
If the formula is correct we get the given cost :
For 3 miles , then the cost c = 0.6(3) + 1.2 = $ 3.00
For 6 miles , then the cost c = 0.6(6) + 1.2 = $ 4.80
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PLEASE ANSWER ASAP
Beverly is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Which TWO slope calculations can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
The slope calculations she can use to correctly show that △PQR is a right triangle are
(a) Slope of PQ = (y₂ - y₁)/(x₂ - x₁) = (1 - 5)/(-1 - (-2)) = -4(d) Slope of QR = (y₂ - y₁)/(x₂ - x₁) = (3 - 1)/(7 - (-1)) = 2/8 = 1/4How to determine the slope calculations she can use correctly?From the question, we have the following ordered pairs that can be used in our computation:
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
This means that
P = (-2,5),
Q = (-1,1)
R = (7,3).
The slope of the points are calculated using
slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
Slope of PQ = (y₂ - y₁)/(x₂ - x₁) = (1 - 5)/(-1 - (-2)) = -4
Also, we have
Slope of QR = (y₂ - y₁)/(x₂ - x₁) = (3 - 1)/(7 - (-1)) = 2/8 = 1/4
Hence, the equations are (a) and (d)
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x + 2 = - 19..............
Answer: -21
Step-by-step explanation:
[tex]x+2=-19\\\\What\ value\ of\ x\ will\ make\ the\ left\ side\ equal\ to\ -19?\\\\Well,\ if\ we\ subtract\ 2\ from\ both\ sides,\ we\ get\ our\ answer...\\\\x+2-2=-19-2\\\\The\ 2\ and-2\ on\ the\ left\ cancel\ out\ leaving\ us\ with\\\\\boxed{x=-21}[/tex]
We can check our work by plugging back in -21 for x and getting -19 = -19
Jonathan Martinez has $85 deducted from his monthly pay for his group health insurance. His employer
pays 60% of the cost. What is the annual premium amount for Jonathan's group health insurance?
If his employer pays 60% of the cost. The annual premium amount for Jonathan's group health insurance is $2,550.
What is annual premium amount ?Annual premium can simply be defined as the premium a person is expected to pay per year or annually.
First step is to find the cost
Cost = $85/ (1-.60)
Cost = $85/.40
Cost = $212.5
Now let find the annual premium amount
Annual premium amount = Cost × 12 months
Annual premium amount = $212.5 × 12 months
Annual premium amount = $2,550
Therefore the annual premium amount is the amount of $2,550.
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Based on the graph of this normal distribution
a. The mean is ____
b. The standard deviation is ____
c. 68 % of the data values are between ____ and ____
d. 95 % of the data values are between ____ and ____
e. 99.7 % of the data values are between ____ and ____
The normal distribution based on the graph is:
a) The mean is 91.
b) The standard deviation is 1.
c) 68 % of the data values are between 90 and 92.
e) 99.7 % of the data values are between 87 and 94.
What is the normal distribution?
The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical plot of data around its mean value.
From the graph the mean is (x¯) = 91
a) The mean is 91
and Standard Deviation (σ)= (∑(x - x¯)²)
= (70-91)²+ (77-91)² +(84-91)²+(91-91)²+(98-91)²+(105-91)²+(112-91)²
= 1372 / 1371
= 1.0007293946
σ = 1
b) The standard deviation is 1.
if x¯ is the mean and σ is the standard deviation of the distribution, then 68% of the values fall in the range between (x¯−σ) and (x¯+σ).
= (91 -1) (91+1)
= 90 to 92
c) 68 % of the data values are between 90 and 92.
About 95% of the values lie within two standard deviations of the mean, that is, between (x¯−2σ) and (x¯+2σ).
(91-2) to (91+2)
89 to 93
d) 95 % of the data values are between 89 and 93.
About 99.7% of the values lie within three standard deviations of the mean, that is, between (x¯−3σ) and (x¯+3σ) .
(91-3) to (91+3)
87 to 94
e) 99.7 % of the data values are between 87 and 94.
Hence, the normal distribution based on the graph is:
a) The mean is 91.
b) The standard deviation is 1.
c) 68 % of the data values are between 90 and 92.
e) 99.7 % of the data values are between 87 and 94.
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can some help me understand this?
At a local gas station there are two different plans for car washes. Customers can either pay $12 per wash or pay $16 for a discount card that lowers the cost to $8 per wash. Write and solve an equation to find the number of car washes for which the cost of each plan is the same.
1. An equation that finds the number of car washes for which the costs of Plan A and Plan B are the same is 12n = 16 + 8n.
2. The solution of the equation shows that the number of car washes for which the cost of each plan is the same is 4.
What are equations?Equations are mathematical statements claiming that two or more mathematical expressions are equal or equivalent when solved.
Equations use numbers, constants, variables, and the equation symbol (=) to depict the equality of the mathematical expressions.
Plan A Plan B
Cost per cash wash $12 $8
Fixed cost $0 $16
Mathematical Expressions for the Carwash Plans:
Let Plan A = 0 + 12n
Let Plan B = 16 + 8n
The number of car washes when the two plans' costs are equal can be derived by equating the two mathematical expressions above:
12n = 16 + 8n
12n - 8n = 16
4n = 16
n = 4
= 4 car washes
Check:
Plan A = 0 + 12n
= 12(4)
= 48
= $48
Plan B = 16 + 8n
= 16 + 8(4)
= 16 + 32
= 48
= $48
Thus, solving the equation, we can conclude that choosing Plan B will take 4 car washes to equal the cost of Plan A.
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A function's graph is shown below.
If you would like to enlarge the graph or marks numbers and letters easier to read, you may click on it to open it in a new window. You may then enlarge that window with your mouse. To further enlarge the image, use your browser's zoom capabilities. On a PC this is usually ctrl shift + fand zooming out is ctrl -). On an Apple computer this is usually apple shift + (and zooming out is apple - ).
Use interval notation or set notation to answer the following questions.
The domain of this function is _____
The range of this function is _____
The domain and the range of the function are given as follows:
Domain: [-3,3].Range: {-3}.How to obtain the domain and the range of the function?The domain of a function is the set containing all the values assumed by the input of a function, hence on the graph it is given by the values of x for which the function is defined.
The range of a function is the set containing all the values assumed by the output of a function, hence on the graph it is given by the values of y which the function assumes.
In this problem, the horizontal line is given as follows:
y = -3.
Hence the lone value assumed by output is of 3, meaning that the range is given as follows:
{3}.
In {} notation because it is a single element, not an interval.
The values of x, that is, the values of the horizontal axis assumed by the function are between -3 and 3, hence the domain is given by the following interval:
[-3, 3].
Which is a closed interval due to the closed circle.
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Find the interest rate for a $6000 deposit accumulating to $6957, compounded annually for 6 years.
The interest rate for a $6000 deposit accumulating to $6957, compounded annually for 6 years is r=2.49%.
What is meant by interest rate?The interest rate is the amount charged by the lender to the borrower over and above the principal amount. In terms of the receiver, a person who deposits money in any bank or financial institution obtains additional revenue due to the time value of money, which is referred to as interest received by the depositor.
Here's a simple interest formula: Interest = P x R x T, P = Principal Amount (the beginning balance).
Given, Amount=6957, P=6000, t=6 years
A=P[tex](1+(r/n)^{nt}[/tex]
6957=6000(1+(r/1))[tex](1+(r/1))^{6}[/tex]
[tex](1+(r/1))^{6}[/tex]=6957/6000
=1.1595
ln[tex](1+(r/1))^{6}[/tex]=ln(1.1595)
6(1+(r/1))=ln(1.1595)
(1+(r/1))=ln(1.1595)/6=0.0246
(1+(r/1))=[tex]e^{0.0246}[/tex]
1+r=1.02490508
r=0.02490508
r=2.49%
The interest rate for a $6000 deposit accumulating to $6957, compounded annually for 6 years is r=2.49%.
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A projectile of mass 0.213 kg is shot from a cannon. The end of the cannon’s barrel is at height 6.5 m, as shown in the figure. The initial velocity vi of the projectile has a horizontal component of 7.5 m/s.
The projectile rises to a maximum height of ∆y above the end of the cannon’s barrel and strikes the ground a horizontal distance ∆x past the end of the cannon’s barrelDetermine the time it takes for the pro- jectile to reach its maximum height. The acceleration of gravity is 9.8 m/s2 .
Answer in units of s.
part 2 How long does it take the projectile to hit the ground?
Answer in units of s.
part 3
What is the horizontal range ∆x of the shot? Answer in units of m.
this is physics
The time it takes for the projectile to reach its maximum height would be 0.77 s. The time it takes for the projectile to hit the ground is 2.67 s.
The horizontal range ∆x would be 20.3 m.
To determine the time it takes for the projectile to reach its maximum height, we can use the formula:
t = (vi sin(θ)) / g
where t is the time, vi is the initial velocity, θ is the angle of launch, and g is the acceleration of gravity.
In this case, the initial velocity has a horizontal component of 7.5 m/s, so we can assume that the initial velocity is 7.5 m/s and the angle of launch is 90 degrees (since the projectile is launched horizontally). Therefore, the time it takes for the projectile to reach its maximum height would be:
t = (7.5 m/s × sin(90)) / 9.8 m/s2 = 0.77 s
To determine the time it takes for the projectile to hit the ground, we can use the formula:
t = (2 ∆y) / (vi sin(θ))
where t is the time, ∆y is the maximum height, vi is the initial velocity, and θ is the angle of launch.
Since we know that the projectile rises to a maximum height of ∆y above the end of the cannon's barrel, the initial velocity has a horizontal component of 7.5 m/s and the angle of launch is 90 degrees, we can calculate the time it takes for the projectile to hit the ground as follows:
t = (2 ∆y) / (7.5 m/s x sin(90)) = (2 ∆y) / 7.5 m/s = 2.67 s
To determine the horizontal range ∆x of the shot, we can use the formula:
∆x = (vi × t) cos(θ)
where ∆x is the horizontal range, vi is the initial velocity, t is the time, and θ is the angle of launch.
In this case, we know that the initial velocity has a horizontal component of 7.5 m/s, the time it takes for the projectile to hit the ground is 2.67 s, and the angle of launch is 90 degrees.
Therefore, the horizontal range ∆x would be:
∆x = (7.5 m/s × 2.67 s) × cos(90) = 20.3 m.
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there were 7,000 raffle tickets sold at the school carnival. Each ticket cost $0.25. How much money did the school raise by selling raffle tickets
Answer: $1750
Step-by-step explanation:
7000x$0.25 = $1750
Please ANSWER ASAP
Dorothy is trying to prove that △PQR is a right triangle.
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Which TWO slope calculations can she use to correctly show that △PQR is a right triangle?
Select TWO of the answers below.
in the picture
The slope of C and D in the picture shows that ΔPQR is a Right Triangle.
What is slope of line?
Slope of line is defined as the angle of line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂).
If the product of slopes of any two sides is equal to -1, then those two sides are perpendicular
Given,
The vertices of △PQR are at P(-2,5), Q(-1,1), and R(7,3).
Slope of PQ = (y₂ - y₁)/(x₂ -x₁ )
= (1 - 5)/(- 1 - (-2)
= -4/1
= - 4
Slope of QR = (y₂ - y₁)/(x₂ -x₁ )
= 3 - 1/7 - ( -1)
= - 1 / 4
The product of Slope of PQ and QR is - 1. It means lines PQ and QR is perpendicular to each other consequently △PQR is a right triangle.
Therefore,The slope of C and D in the picture shows that ΔPQR is a Right Triangle.
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What is the completely factored form of 12xy – 9x – 8y + 6?
(3x – 2)(4y – 3)
3x(4y – 3) – 2(4y + 3)
–6x(4y – 3)(4y – 3)
(3x – 2)(4y – 3)(4y – 3)
Step-by-step explanation:
the answer
(3x-2)(4y-3)
Answer: (3x-2)(4y-3)
Step-by-step explanation:
Sebastian and zoey had 3068 buttons in all. Sebastian and Valeria had 2103 button in all. Valeria has half as many buttons as zoey.how many buttons do they have in all.
The total number of buttons they have is 4033.
What is a system of equations?A system having more than two equations is known as a system of equations.
Given that, Sebastian and Zoey had 3068 buttons, Sebastian and Valeria had 2103 buttons, and Valeria has half as many buttons as Zoey.
The equations corresponding to the statements are:
S + Z = 3068 (1)
S + V = 2103 (2)
V = Z/2 (3)
Subtract equation (2) from equation (1):
Z - V = 965
Substitute V = Z/2 into the above equation:
Z - Z/2 = 965
Z/2 = 965
Z = 1930
Substitute Z = 1930 into equation (3):
V = 1930/2
V = 965
Substitute V = 965 into equation (2):
S + 965 = 2103
S = 1138
The total number of buttons is:
S + V + Z
= 1138 + 965 + 1930
= 4033
Hence, the total number of buttons they have is 4033.
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The length of a sandwich is 36.2 inches. Skyler cut the sandwich into 4 equal-sized pieces for him and his friends to eat for lunch.
Which expression represents the length of each piece of the sandwiches?
Answer:
36.2/4=length of each sandwich piece
√(2) rational or irrational
Answer:
√2 is irrational.
Step-by-step explanation:
√2 = p/q, where 'p' and 'q' are integers, q ≠ 0 and p, q have no common factors (except 1). Thus, p and q have a common factor 2. This statement contradicts that 'p' and 'q' have no common factors (except 1). We can say that √2 is not a rational number.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 6 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
PLEASE HELP !!!!! David is standing 500 feet away from the base of a cell phone tower. the angle of elevation from his eyes to the top of the tower is 78°. if David’s eyes are 6 feet above the ground how tall is the tower (EXPLAIN PLEASE)
The height of the tower is 2358 feets.
How to find the height of the tower?David is standing 500 feet away from the base of a cell phone tower.
The angle of elevation from his eyes to the top of the tower is 78°. David eyes are 6 feet above the ground . The height of the tower can be found as follows:
This situation forms a right angle triangle. Therefore,
using trigonometric ratios,
tan 78° = opposite / adjacent
tan 78° = x / 500
cross multiply
x = 500 tan 78°
x = 500 × 4.70463010948
x = 2352.31505474
Therefore,
height of the tower = 2352 + 6
height of the tower = 2358 ft.
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Find the area of the circle to the nearest hundredth if the diameter =15cm
Step-by-step explanation:
divide 15 by 2 to get the radius which is 7.5
then 7.5² = 56.25 x3.15=177.1875 round and its A=177.188
if this is incorrect someone else correct me
11. Rezolvaţi în mulţimea Z ecuaţia:
a) 3⋅(x + 7) =12; b) − 2⋅(x + 9) = −28;
c) 5⋅(3− 2x) = −10; d) 2x :| −5 | = 8;
e) 32 :(−2x) = 1; f) 7 ⋅(2 − x) = | −42 |.
⭐️This is a unit over polynomial functions. You need to graph the function,and what’s the x and y intercepts of the graph.
Function is in picture too
FUNCTION: f(x)=x^3 + 2x^2 -3
The intercepts of x-axis for the given polynomial function is (1. 0)
The intercepts of y-axis for the given polynomial function is (0, -3) and the graph is attached below:
What is meant by a function?A function of a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain in a function is the set X, and the codomain of the function is the set Y.
The first known attempt to define function can be found in the writings of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. The concept of a function was codified in terms of set theory at the end of the nineteenth century, which substantially expanded its realms of applicability.
Given function is,
f(x)=x³+2x²-3
The graph of the polynomial function is plotted below:
The intercepts of x-axis for the given polynomial function is (1. 0)
The intercepts of y-axis for the given polynomial function is (0, -3)
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What is 3x +(-1) = -10 + 2x PLS HELP!!!
Answer:
x= -9
brainliest plssAnswer:
[tex]\boxed{\boxed{\tt x=-9}}[/tex]
Step-by-step explanation:
[tex]\tt 3x+\left(-1\right)=-10+2x[/tex]
[tex]\tt 3x-1=-10+2x[/tex]
Subtract 2x from both sides:-
[tex]\tt 3x-1-2x=-10[/tex]
Combine 3x and -2x to get x:-
[tex]\tt x-1=-10[/tex]
Add 1 to both sides:-
[tex]\tt x=-10+1[/tex]
Add -10 and 1 to get -9:-
[tex]\tt x=-9[/tex]
____________________
Hope this helps you!
Have a great day!
2,239 ÷ 7
Division compatible numbers
Answer:the answer is 319.857 and round to 320
Step-by-step explanation:
You’re planning to visit with 7 clients today and you estimate that at most each client will require 3/4 hours of your time. At most, how long does your estimate say it will take you to visit with all of these clients?
Mathematically, it will take you 315 minutes (5 hours, 15 minutes) at most to visit with all 7 clients.
How is the time determined?We can employ mathematical operations, including addition, subtraction, division, and multiplication to determine the total time required to visit the seven clients.
Since we know that a client requires 3/4 hours or 45 minutes of your visiting time, we can multiply 45 minutes by 7.
The product of the multiplication operation gives 315 minutes, which we can convert into hours and minutes by a division operation.
The number of clients visiting today = 7
The time it a client requires of your visit time = 3/4 hours
3/4 hours = 45 minutes (0.75 x 60)
For the 7 clients, it will take you 315 minutes (45 x 7)
315 minutes equal 5 hours and 15 minutes.
Thus, using basic mathematical operations, we can conclude that, at most, you require 5 hours and 15 minutes to attend to all seven clients today.
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"3. Four relationships are given.
Relationship A: x 3 2 1 y 2 2/3 1 2 / 3 2/3 Relationship B: 2x=y
Relationship C: y=2+x
Relationship D: x 3 6 y 6 12 In which two relationships are the constant of proportionality 2?"
Answer:
B and D
Step-by-step explanation:
A - check to see IF the relationship is proportional by dividing each y by its associated x:
2 2/3 ÷ 3 = 8/9
1 2/3 ÷ 3 = 5/9
2/3 ÷ 3 = 2/9
none of these match, so not even proportional
B - CoP is the coefficient of x (2)
C - not proportional because of the +2
D - do the same as A
6/3 = 2
12/6 = 2
both are the same and equal to 2
HELP ME OUUTT THANKS
Answer:
3/4n = 5/8
Step-by-step explanation:
your…. welcome……
I don’t trust meself so I might be wrong
2x-5y=0 a direct variation function, if so identify the constant of variation
Constant of variation for the direct function is y = [tex]\frac{2 x}5}[/tex]
What is Direct Variation?Direct variation in mathematics is the general form of formula y = k x where x and y are variables (numbers that change) and k is a constant
Convert to slope intercept form
2x -5y =0
Add 5y to both sides
2x-5y +5y =5y
2x=5y
divide both sides by 5
[tex]\frac{2x}{5}[/tex] =[tex]\frac{5y}{5}[/tex]
Cross multiply to solve for y
5(2x) =5(5y)
y = [tex]\frac{2 x}5}[/tex]
Therefore, the constant of variation y = [tex]\frac{2 x}5}[/tex]
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Which data set could be represented by the boxplot shown? (1 point)
boxplot with the minimum of 2, lower quartile value of 3, median of 5, upper quartile of 9, and maximum of 10
Group of answer choices
{0, 2, 3, 5, 8, 9, 10, 10, 12}
{2, 3, 3, 4, 5, 5, 8, 10, 10}
{2, 3, 4, 5, 5, 7, 7, 9, 10}
{2, 3, 4, 5, 5, 5, 8, 9, 10}
{2, 3, 4, 5, 5, 7, 7, 9, 10} is the required dataset to represent the boxplot.
What is Statistics?Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
Given,
boxplot with the minimum of 2
lower quartile value of 3,
median of 5,
upper quartile of 9,
and maximum of 10
In the given data sets {2, 3, 4, 5, 5, 7, 7, 9, 10} represents boxplot with the minimum of 2, lower quartile value of 3, median of 5, upper quartile of 9, and maximum of 10
Hence, {2, 3, 4, 5, 5, 7, 7, 9, 10} is the required dataset to represent the boxplot.
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The product of 8 and b, taken from 10
Step-by-step explanation:
10-8b
hope it helps. please mark brainliest