How do I write a two-column proof for this problem?
Given: Isosceles △ABC with legs AB and AC, BD ⊥DC and CE⊥BE
Prove: BD ≅ CE
Answers
BD ≅ CE is proved and is shown below.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given are two triangles as shown in the figure.
Triangles ΔMPN and ΔSTU are congruent. We can write -
2x - y = 13
2x - 50 = 24
Now -
2x - 50 = 24
2x = 74
x = 3The measurements of [x] and [y] are 37 and 61 respectively.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is isosceles △ABC with legs AB and AC, BD ⊥DC and CE ⊥ BE.
In △BDC and △CEB, we can write -
∠D = ∠E = 90°
BC = BC {Common}
∠B = ∠C {Angles opposite to equal sides are equal}
By SAS criteria △BDC ≅ △CEB.
So, we can write -
BD ≅ CE
Therefore, BD ≅ CE is proved and is shown above.
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Related Questions
2,239 ÷ 7
Division compatible numbers
Answers
Answer:the answer is 319.857 and round to 320
Step-by-step explanation:
helppppppppppppppp
Ginny and Bob are both locksmiths.
Ginny uses the function f(x)=60x+80 to determine the charge to her customers, where x represents the number of hours of labor.
The table shows what Bob charges a customer for x hours of labor.
x (hours) 0 1 2 3 4
cost ($) 60 140 220 300 380
Which locksmith charges less for an initial fee for a service call?
Drag a value or name to the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Ginny charges Response area for an initial fee, and Bob charges Response area for an initial fee. Response area charges less for an initial fee.
Answers
For the initial fee, Bob charges less than Ginny.
What is unit rate?A unit rate means a rate for one of something.
Given that Ginny charges by uses the function f(x)=60x+80 where x represents the number of hours of labour.
Ginny initial charge = $80
Bob initial charge =$60
Hence, For the initial fee, Bob charges less than Ginny.
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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.
Answers
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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can some help me understand this?
Answers
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
Answers
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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The product of 8 and b, taken from 10
Answers
Step-by-step explanation:
10-8b
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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
Answers
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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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?
Answers
Answer:
36.2/4=length of each sandwich piece
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.
Answers
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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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 |.
Answers
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)
Answers
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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Three out of nine students passed the SHSAT test. What is the decimal equivalent of students who passed the test?
Ans :
Answers
Hence, the decimal equivalent of students who passed the test is [tex]0.33[/tex].
What is the decimal values?
Decimals are a set of numbers lying between integers on a number line.
Here given that,
Three out of nine students passed the SHSAT test.
So,
[tex]\frac{3}{9}=0.33[/tex]
Hence, the decimal equivalent of students who passed the test is [tex]0.33[/tex].
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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
Answers
Answer: $1750
Step-by-step explanation:
7000x$0.25 = $1750
Find the interest rate for a $6000 deposit accumulating to $6957, compounded annually for 6 years.
Answers
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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√(2) rational or irrational
Answers
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.
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2x-5y=0 a direct variation function, if so identify the constant of variation
Answers
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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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?
Answers
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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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)
Answers
Step-by-step explanation:
the answer
(3x-2)(4y-3)
Answer: (3x-2)(4y-3)
Step-by-step explanation:
⭐️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
Answers
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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x + 2 = - 19..............
Answers
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
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 _____
Answers
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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What is 3x +(-1) = -10 + 2x PLS HELP!!!
Answers
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]
____________________
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Have a great day!
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?
Answers
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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HELP ME OUUTT THANKS
Answers
Answer:
3/4n = 5/8
Step-by-step explanation:
your…. welcome……
I don’t trust meself so I might be wrong
Find the area of the circle to the nearest hundredth if the diameter =15cm
Answers
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
"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?"
Answers
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
Dave borrowed $7400 from his uncle with simple interest of 6% and eventually repaid $8288 (principal and interest). What was the time period of the loan?
Answers
The time period of the loan was 1 year.
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 ____
Answers
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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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}
Answers
{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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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.
Answers
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.
Learn more about the system of equations:
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