If there is no line in the box to indicate the median, it is possible that the median has not been calculated or that the data set is too small to provide an accurate representation of the median.
A boxplot is a visual representation of the distribution of a set of data, and it typically consists of a box, two whiskers, and possibly some outliers. The box represents the interquartile range (IQR), which is the range between the first and third quartiles of the data. The median (or second quartile) is usually represented by a line within the box.
If there is no line in the box to indicate the median, it is possible that the median has not been calculated or that the data set is too small to provide an accurate representation of the median. With only 20 students, it is possible that the median may not be a meaningful representation of the central tendency of the data, especially if there are extreme outliers or skewed distributions. In such cases, it is best to consult other measures of central tendency, such as the mean or mode, to get a better understanding of the data.
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Write an indirect proof for the following statement:
A triangle can have at most 1 obtuse angle.
We can prove that the statement is false by contradiction, as if a triangle had two obtuse angles, the sum of the measures of the internal angles of the triangle would be greater than 180º.
What is proof by contradiction?To prove an statement by contradiction, we must simply take an statement that either accepts the statement (true) or rejects (false).
An angle is classified as obtuse if it has a measure that is greater than 90º.
The sum of the measures of the internal angles of a triangle is of 180º, hence if the triangle had two obtuse angles, then the sum of the measures of the internal angles of the triangle would be greater than 180º.
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need help with this question
The zeros of the equation x² - 4x + 4 = 0 is 2.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
A quadratic equation,
x² - 4x + 4 = 0.
To find the zeros:
Solving further,
x² - 4x + 4 = 0.
x² - 2x -2x + 4 = 0.
x(x - 2) -2(x - 2) = 0.
(x - 2)² = 0.
x = 2.
Hence, 2 is zeros.
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The complete question:
Solve the quadratic equation and find the zeros.
The equation,
x² - 4x + 4 = 0.
Use a sketch to find the exact value of the following expression.
sec[sin^-1(-4/7)]=
The exact value of the expression is 7√33/33
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given expression is sec[sin⁻¹(-4/7)]
We need to fine the exact value of the expression
sec[sin⁻¹(-4/7)]=√1-(-4/7)²/1-(-4/7)²
=√(1-16/49)/1-16/49
=√(1-16/49)/1-16/49
=√33/7/33/49
=√33/7×49/33
=7√33/33
Hence, the exact value of the expression is 7√33/33
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The table shows the number of goals made by two hockey players.
Player A Player B
2, 3, 1, 3, 2, 2, 1, 3, 6 1, 4, 5, 1, 2, 4, 5, 5, 11
Find the best measure of variability for the data and determine which player was more consistent.
Player B is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with a range of 10.
Player A is the most consistent, with an IQR of 1.5.
Player A is the most consistent, with a range of 5.
The best measure of variability is the standard deviation.
Player A is the most consistent, with an IQR of 1.5.
The correct option is C.
What is a standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
Given:
The table shows the number of goals made by two hockey players.
Player A:
2, 3, 1, 3, 2, 2, 1, 3, 6
Mean = 2.56
S.D. = 1.51
Player B:
1, 4, 5, 1, 2, 4, 5, 5, 11
S.D. = 3.03
The best measure of variability is the standard deviation.
Player A is the most consistent, with an IQR of 1.5.
Therefore, the best measure of variability is the standard deviation.
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Answer:1.5
Step-by-step explanation:
PLEASE HELP‼️‼️
Solve the problem.
As part of her retirement savings plan, Patricia deposited $200 in a bank account during her first year in the workforce. During each
subsequent year, she deposited $50 more than the previous year. Find how much she deposited during her twentieth year in the workforce.
Find the total amount deposited in the twenty years.
The amount deposited in the Patricia retirement savings plan are:
Amount deposited in the twentieth year is $1150.
Total amount deposited in time span of twenty years is $13,500.
Amount deposited by Patricia in the first year ' a₁ ' = $200
Difference between the amount deposited in the subsequent year is
'd' = $50
Amount deposited during 20th year
Let 'n' be the 20th year
The above situation represents it is arithmetic progression problem
nth term of A.P. is :
aₙ = a₁ + ( n - 1 ) d
Substitute the value we get,
a₂₀ = 200 + ( 20 - 1 ) 50
⇒ a₂₀ = 200 + 19 × 50
⇒ a₂₀ = 200 + 950
⇒ a₂₀ = $1150
Total amount deposited in twenty years
S₂₀ = (n/2) [ 2 a₁+ ( n - 1 )d ]
Substitute the value we get,
⇒S₂₀ = ( 20 /2 ) [ 2(200 ) + 19 × 50 ]
⇒ S₂₀ = 10 [ 400 + 950 ]
⇒S₂₀ = $13,500
Therefore, the amount deposited in the twentieth year is $1150 and total amount deposited in twenty years is $13,500.
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Divide the following fractions!
Answer: a - a / (7a/3 - 21b)
Step-by-step explanation:
First, let's simplify the numerator:
(a^2 - 3ab) / 3b = a^2/3b - 3ab/3b = a^2/3b - a
Next, we'll simplify the denominator:
7a - 21b = 7a/3 - 7b
Now, we can simplify the entire expression:
(a^2/3b - a) / (7a/3 - 7b) = (3b * a^2/3b - 3b * a) / (7a - 21b * 3) = a - a / (7a/3 - 21b)
Eddie made a video. The video included 5-minute introduction followed by short segments. Each segment was 8 minutes long. Eddie's video was 149 minutes long. How many segments were in Eddie's video?
WILL GIVE BRAINLIEST!
You are deciding what carb you want to eat for dinner, and you decide to look at the ratio of cooking times between rice to pasta. Rice takes 20 minutes to cook, and pasta takes 12. What is the ratio of cooking times for the rice to pasta?
(Make sure your ratio is simplified for your final answer)
5 : 3 is the ratio of cooking times for the rice to pasta .
What does a math ratio mean?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A percentage is an equation in which two ratios are made equal to one another.
You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Rice takes 20 minutes to cook
pasta takes 12
the ratio of cooking times for the rice to pasta = 20 : 12
= 5 : 3
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Write an equation of the line that passes through (-4,-1) and is perpendicular to the line y=x+6
Answer:
y = -x + 5
Step-by-step explanation:
To find the equation of the line that is perpendicular to the line y = x + 6 and passes through the point (-4, -1), we'll use the slope-point form of the equation of a line. The slope of a line perpendicular to y = x + 6 is -1, which we can find using the negative reciprocal of the slope of y = x + 6. The slope of y = x + 6 is 1. The negative reciprocal of 1 is -1.
So the equation of the line perpendicular to y = x + 6 that passes through the point (-4, -1) is given by:
y - (-1) = -1(x - (-4))
Expanding and simplifying the right-hand side, we get:
y + 1 = -x + 4
y = -x + 5
suppose that 17 boys and 22 girls are randomly lined up. what is the probability that the 27th person is a boy?
Using probability we know that there is a 43% chance that the 27th person in the line would be a boy.
What is probability?Probability is simply the possibility that something will happen. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.
The study of events that fit into a probability distribution is known as statistics.
So, we know that:
The boys are 17.
The girls are 22.
Probability formula: P(E) = Favourable events/Total events
Then, the probability that the 27th person is a boy:
P(E) = Favourable events/Total events
P(E) = 17/39
P(E) = 0.43
P(E) = 43%
Therefore, using probability we know that there is a 43% chance that the 27th person in the line would be a boy.
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Amit drives a car daily to his office from his home. The distance is 24 km. On a particular day, he left
his home at 8:15 AM, drove for 5 km at a speed of 60 kmph. After that he was stuck in a traffic jam of 1
km during this stretch he could drive only at a speed of 15 kmph.
(Figure shown above is upto scale) Which of these is the closest to the MINIMUM speed at which he
should drive after the traffic jam to ensure that he reaches the office by 8:45 AM?
(Assuming that he can drive the way he wants to, without any traffic jams.
According to the information, it can be inferred that Amit has to drive at a speed of at least 60 km/h to get to work on time.
How to calculate the speed that Amit must have after the traffic jam to get to work on time?To calculate the speed that Amit must have after the traffic jam to arrive at work on time we must perform the following mathematical operation:
speed = 60 * 5 / 18 m/s = 50 / 3 m/s
distance = 5000m
time = 300 seconds = 5 minutes
According to the above he traveled 5 km distance in 5 minutes. On the other hand to calculate the speed that the rest of the journey must have we must:
speed = 15 * 5 /18 = 25/6 m/s
distance = 1000m
time = 240 seconds = 4 minutes
Distance left = (24km -6km = 18km= 18000m
Time left = 21 minutes = 1260 seconds
Speed = 14.28m/s
Speed = 14.28 × 18/5 kmph
Speed = 51.42 kmph
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If F(X)=11x-7, express in terms of P find F(p)
Answer:
Step-by-step explanation:
99.5 x 54 add 10
Put the following linear equation in slope intercept form:
−7x+3y=21
You should have 2 or more steps shown.
The slope-intercept form of the linear equation is:
y = 7 + (7/3)*x
How to write the linear equation in the slope intercept form?A linear equation in the slope-intercept form is:
y = a*x + b
So, to write the given line in that form, we just need to isolate the variable x.
We have the equation:
-7x + 3y = 21
3y = 21 + 7x
y = (21 + 7x)/3
y = 7 + (7/3)*x
That is the equation in the slope-intercept form.
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A local Best Buy sells 8 times as many iPads as target. The difference between their sales is 490 iPads how many did each sell?
Answer:
Step-by-step explanation:
Let's assume the number of iPads sold by Target as "x".
Then, the number of iPads sold by Best Buy would be 8 times this value, which is 8x.
We are given that the difference in their sales is 490 iPads. So we can set up an equation:
8x - x = 490
Simplifying and solving for x:
7x = 490
x = 70
Therefore, Target sold 70 iPads, and Best Buy sold 8 times as many, or 560 iPads.
Use the Distributive Proper
10
9. 2(-3x + 5)
The distributive property is often used to simplify algebraic expressions.
What is algebra?Algebra refers to the involving of unknown quantities into the block relationship between variables.
In this example, the expression 2(-3x + 5) can be simplified using the distributive property. The distributive property states that for any two numbers a and b, and a third number c, a(b + c) = ab + ac. Applying this property to our expression, 2(-3x + 5) = 2(-3x) + 2(5).
By expanding the expression, we see that 2(-3x + 5) = -6x + 10. This simplified expression is much easier to work with than the original expression. The distributive property can be applied to any expression in order to simplify it, making it easier to solve.
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A tennis-playing golfer has $15 to
spend on golf balls x, costing $ 1 each
and tennis balls y, costing 60 cents
each. He must buy at least 16
altogether and he must buy more golf
balls then tennis balls.
a) What is the greatest number of
balls he can buy?
b) After using them, he can sell golf
balls for 10 cents and tennis balls for
20 cents each. What is his maximum
possible income from sales?
(This questions is about inequalities and linear programming)
Maximum possible income from sales is $2.6
What do you understand by Linear Programming?Linear Programming also called linear optimization, is a method to achieve the best outcome(such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear Programming is a special case of mathematical programming (also known as mathematical optimization).
Linear Programming is used in many industries such as energy, telecommunication, transportation and manufacturing.
This linear function or objective function consists of linear equality and inequality constraints.
Given:
$15 to spend on golf balls x costing $1 each and
tennis balls y, 60 cents each.
Buy at least 16 together.
x + y ≥ 16
x + 0.6 ≤ 15
x - y ≥ 1
x = 9 and y = 7
[tex]9 + 0.6 \times 7[/tex]
9 + 4.2
13.2 < 15
x = 10 and y = 8
10 + 0.6 × 8
10 + 4.8
14.8 < 15
Maximum number of golf balls x = 10
And tennis balls y = 8
Greatest number of balls he can buy = 10 + 8 = 18
Maximum possible income = 10×0.1 + 8 × 0.2 = 1 + 1.6 = $2.6
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Eight bands are to perform at a weekend festival. How many different ways are there to schedule their appearances?
By using the permutation formula, it can be concluded that there are 40320 ways to schedule the bands' appearances.
Permutations are different arrangements of elements formed from n elements, taken from n or some elements. In permutation, arrangement, or order matter.
P(n,r) = n! / (n-r)! where:
n = number of objects
r = number of objects selected
If we want to know the ways to schedule the bands' appearances, it means that the arrangement matter. Thus we have to use the permutation formula:
P(n,r) = n! / (n-r)!
P(8,8) = 8! / (8 - 8)!
= 8!
= 40320 ways
Thus, there are 40320 ways to schedule the bands' appearances.
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the radius of a circle is increasing at a rate of 7 centimeters per minute. find the rate of change of the area when the radius is 4 centimeters.
By applying rate of change concept it can be concluded that the area will change at a rate of 176 cm² / minute.
Rate of change is the change in values of a dependent variable concerning the independent variables.
The rate of change of a function shows how the function is changing from one x value to another. Whilst, differentiation is when you have an instantaneous rate of change at a single point.
We have the following information:
The rate of change of a circle = 7 cm/minute = dr/dt
We have to find the rate of change of the circle when r = 4 cm
To do so, we will use the derivative of the circle area:
A = πr²
dA/dr = 2πr
dA/dt = dA/dr × dr/dt
= 2πr × 7
= 14πr
Now we input r = 4 cm into this equation:
rate of change of the area = 14*22/7*4
= 176 cm² / minute
Thus, when r = 4 cm, the area will change at a rate of 176 cm² / minute.
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Find the inverse of the equation
The inverse of the equation is f-1(x) = 2/(x - 3)
How to determine the inverse of the equationFrom the question, we have the following parameters that can be used in our computation:
f(x) = (3x + 2)/x
Express as
y = (3x + 2)/x
Swap x and y
This gives
x = (3y + 2)/y
So, we have
xy = 3y + 2
This gives
y(x - 3) = 2
Make y the subject
y = 2/(x - 3)
Hence, the inverse is f-1(x) = 2/(x - 3)
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Determine if 0. 54227406110177. Is rational or irrational and give a reason for
your answer.
ASAP pls help
The number 0.54227406110177, is non- repeating and non- terminating, so, that is an irrational number.
We have to determine that the number 0.54227406110177, is rational or irrational.
There is infinite numbers of rationals or irrationals between two real numbers. Rational number is of form p/q where q≠0 and p and q are integers. For example 1/2 , 1/4 are rationals. To identify if a number is rational or not, check the following conditions :
It is expressed in the form of p/q, where q≠0.After simplification, the ratio p/q is represented in decimal form. the decimal expansion of an rational number is repeating and terminating.The numbers which are not rational numbers are called irrationals. Here, see the number 0.54227406110177, no repetition of numbers in decimal form and non- terminating. So, it not a rational number. Hence, it is an irrational.
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5.8 + (-8.45) Please answer!!!!
5.8 + (-8.45)
Remove the plus sign and parentheses:
5.8 - 8.45
-2.65
That's your answer. Hope this helped!
Answer:
-2.65
Step-by-step explanation:
Hope this will help
Find the slope of 5,-7 and 6,-4
The slope from points (5, -7) and (6, -4) is 3.
The slope of a line:The slope of a line represents the stiffness or direction of a line. It is also defined as the change in the y-coordinate with respect to the x-coordinate.
The slope of a line from the points (x₁, y₁) and (x₂, y₂) is given by
Slope of a line (m) = [y₂ - y₁]/[x₂ - x₁]Here we have
Points (5, -7) and (6, -4)
As we slope of the line is [y₂ - y₁]/[x₂ - x₁]
Take (5, -7) = (x₁, y₁) and (6, -4) = (x₂, y₂)
Slope from given points = [-4 - (-7) ]/[6 - 5]
= [-4 + 7) ]/[1] = 3
Therefore,
The slope from points (5, -7) and (6, -4) is 3.
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Two cars, an Audi and a Tesla, travel a 100 mile journey.
Which car is fastest and by how much?
Write Audi or Tesla in the first box and state your answers in mph in the second box
100-
80
60-
40
20
100
Distance from starting point tri
80-
60-
40
20-
N+
Audi
2
2
Distance from starting point (miles)
Time (hours)
Tesla
2.
Time (hours)
Two cars, an Audi and a Tesla, travel a 100 mile journey. The fastest car is Audi by 30mph.
What is distance?While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."
The formula of the speed is given as:
Speed = distance / time
For Audi:
Speed = 100 / 2 = 50 mph
For Tesla:
Speed = 100 / 5 = 20mph
The difference between their speeds is:
50 - 20 = 30mph
Hence, the fastest car is Audi by 30mph.
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What are the polygon
Step-by-step explanation:
in geometry it is a plane figure with at least three straight sides and angles, and typically five or more.
Which fraction of the whole circle is this sector?
The fraction of the whole circle denoting the sector is 23/72.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
The whole circle has an angle of = 360°.
The measure of the sector of the angle is = 115°.
The fractional value of the sector is -
Measure of Sector angle / Measure of whole circle angle
Substitute the value into the expression -
115/360
23/72
Therefore, the fraction is 23/72.
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Answer the attached imagine. Please and thank you.
The solution of the given equation is -4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equations is 3|5 - x| + 2 = 29
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
3|5 - x| =27
5-x=9
x=-4
Therefore, the solution of an equation is -4.
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"Your question is incomplete, probably the complete question/missing part is:"
Find the solution set for the equation below.
3|5 - x| + 2 = 29
Consider DEF in the figure below.
The perpendicular bisectors of its sides are XW, YW, and ZW. They meet at a single point W.
(In other words, W is the circumcenter of ADEF.)
Suppose YW=24, DZ=66, and FW=74.
Find EY, DW, and DE.
Note that the figure is not drawn to scale.
On solving the provided question, we can say that in the provide quadrilateral DE = 132, DW = 74, EY = 70.
Describe the quadrilateral.In terms of geometry, a quadrilateral is a four-sided polygon with four edges and four corners. Its origins are in the Latin terms quadri and latus (meaning "side"). A rectangle is a two-dimensional form with four sides, four vertices, and four corners.
Two main types of concave and convex exist. Convex quadrilaterals also have a number of subclasses, such as trapezoids, parallelograms, rectangles, rhombuses, and squares. A rectangle is a two dimensional shape with four straight sides. Quadrilaterals come in many various shapes, such as parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
here,in the provide quadrilateral
The perpendicular bisectors of Its sides are X W, Y W, and Z W. They meet at a single point W.
from the question. So EW = DW = FW
and DZ=EZ
SO DE = 2 (DZ) = 2 × 66 = 132
EW = FW = DW = 74.
at At right triangle, EWY.
EW= 74, YW=24
Using Pythagoras theorem,
So EX² = EW²- WY² = 74² - 24² = 4900
EY = √4900 = 70.
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What does 5² × 1201 equal to
Answer:
30025
Step-by-step explanation:
5² × 1201
5^2 = 25
25 x 1201 = 30025
Which statement describes the end behavior of a given function? g(x)=x^2 + 5x/3x
Answer:
as x approaches - infinity g(x) approaches - infinity and as x approaches infinity g(x) approaches infinity
Step-by-step explanation:
so the third answer
Find the angle, correct to two decimal places, that the lines joining the given points
make with the positive direction of the x-axis:
a (−4, −2), (6, 8)
b (2, 6), (−2, 4)
c (−3, 4), (6, 1)
d (−4, −3), (2, 4)
e (3b, a), (3a, b)
f (c, b), (b, c)
Answer: look at the image, and u better give me brainliest for this
Step-by-step explanation: