Una tabla estadística para resumir los resultados de la encuesta podría ser la siguiente:
Emoción/Sentimiento Porcentaje de Encuestados
Impaciente 43%
Preocupado por salud 34%
Solo 15%
Enojado 12%
Preocupado por vulnerables 55%
Feliz de pasar tiempo con familia 31%
Inspirado por adaptación 22%
Esta tabla muestra los diferentes sentimientos y emociones que los encuestados experimentaron durante la encuesta realizada por Global Advisor.
The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.
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(3+4x-2)4 2/7
please help or my mom said she was going to put me up for adoption which i don't care for i just want to get this work done
The value of x in expression is -1/8.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
(3+4x-2)4 2/7=0
(3+4x-2)16/7=0
48+64x-32=0
x=-1/8
Therefore, the answer of given algebra problem will be -1/8.
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please help me to find this!!!!!!
ASAP.............
9x _ 7i ≥ 3 ( 3x _7u )
Step-by-step explanation:
9x-7i > 3(3x-7u)
-9x-7i > 9x-21u
-7i > -21u
-i > -3u
i < 3u
Trapezoid PQRS with vertices P(-6, 2), Q(-2, -1), R(-2, -3), and S(-6, -6). Reflect in the line x=1
Graph the Trapezoid PQRS with vertices P(-6, 2), Q(-2, -1), R(-2, -3), and S(-6, -6). Reflect in the line x=1.
The preimage's point corresponds to the image's points in the following way:
P(-6, 2) → P'(6, 2)
Q(-2, -1) → Q' (2, -1)
R(-2, -3) → R'(2, -3)
S(-6, -6) → S'(6, -6)
(x,y)→(−x,y)
A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.
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please help ME EMERGENCY~
The amount that the salesperson will earn in commission from selling the couch is $ 27. 23.
The amount the sale of the couch by the store would get it is $ 467. 77.
How to find the commission ?The commission on the couch can be found by the formula :
= Selling price of couch x Commission to salesperson
= 495 x 5 . 5 %
= $ 27. 23
The money the store will get from the sale of the couch to Lin and her dad is:
= Selling price of couch - Commission to salesperson
= 495 - 27. 23
= $ 467 . 77
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The full question is:
Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5 1/2% of the selling price.
A.How much commission will the salesperson earn by selling a couch for $495?
B.How much money will the store get from the sale of the couch?
use point slope form to write the equation of a line that passes through the point (17,-7) with slope - 1/2
Answer:
y + 7 = -1/2 ( x - 17)
Step-by-step explanation:
y-y₁=m(x-x₁)
[tex]x_{1\\} = 17[/tex]
[tex]y_{1}[/tex] = -7
y - (-7) = -1/2(x - 17)
y + 7 = -1/2(x -17)
32. Solve the equation and check your solution: 3(x + 6) = 18 + 3x
Answer:
4
Step-by-step explanation:
18 = 3x + 6
18 - 6 = 3x
12=3x
12/3 = x
4 = x
Hope this helped, please mark the brainliest if it did! I put a lot of effort into my answers
g what is the root-mean-square speed (urms) of a co2 molecule that has an average ke of 5.44 x 10-21 j/molecule?
The root mean square speed of a carbon dioxide molecule at mentioned average kinetic energy is 1.57× [tex] {10}^{-11} [/tex].
The formula to find root mean square speed of carbon dioxide molecule using average kinetic energy is as follows -
c = ✓2KE/m, where c is root mean square speed, KE is kinetic energy and m is molecular mass
Keep the values in formula to find the root mean square speed.
c = ✓2×5.44×[tex] {10}^{-21} [/tex]/44
Performing multiplication and division on Right Hand Side of the equation
c = ✓2.47×[tex] {10}^{-22} [/tex]
Taking square root on Right Hand Side of the equation
c = 1.57× [tex] {10}^{-11} [/tex]
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turn − 5/7 and 8 into a quadratic equation
Answer:
To turn -5/7 and 8 into a quadratic equation, we first need to convert 8 into an equation by adding 8 to both sides. The equation becomes: -5/7 = x^2 + 8. Then, we can expand the right side into a complete square, using the formula (b/2)^2. The equation becomes:
-5/7 = (x^2 + 8) + (4/2)^2
-5/7 = x^2 + 8 + 4
-5/7 = x^2 + 12
Finally, we can rearrange the equation to make the right side equal to 0, and then factor it. The final equation is:
x^2 + 12 + 5/7 = 0
x^2 + 12 + 5/7 = (x + 6/√7)(x + 6/√7) = 0
Step-by-step explanation:
In the first step, we added 8 to both sides to make the equation -5/7 = x^2 + 8. In the next step, we added 4 to the right side to complete the square. The purpose of completing the square is to get a perfect square on the right side, which will make it easier to factor the equation.
Next, we rearranged the equation to make the right side equal to 0, so that we can factor the equation. The equation x^2 + 12 + 5/7 = 0 can be factored as (x + 6/√7)(x + 6/√7) = 0, where (x + 6/√7) is a binomial that satisfies the equation.
The shape of Tina's kitchen is a rectangle 925 cm long by 485 cm wide.
a) Work out the area of Tina's kitchen in square meters.
Show how to use estimation to check your answers.
Flooring costs $56 per square meter.
It is only sold in whole numbers of square meters.
B) How much does Tina pay to buy flooring for her kitchen floor?
Show how to use inverse operations to check your answer
a) The area of Tina's kitchen is 44.8625 square meters. b) Tina cost $2520 to buy flooring for her kitchen floor.
a) To work out the area of Tina's kitchen in square meters, we need to divide the area in square centimeters by 10,000, which is the number of square centimeters in a square meter:
Area = length x width = 925 cm x 485 cm = [tex]448,625 cm^2[/tex]
Area in square meters =[tex]448,625 cm^2 / 10,000 cm^2/m^2 = 44.8625 m^2[/tex]
b) To find how many whole square meters of flooring Tina needs, we round the area of the kitchen up to the nearest whole number:
Area in square meters rounded up = ceil(44.8625) = [tex]45 m^2[/tex]
The cost of the flooring is $56 per square meter, so Tina pays:
Total cost = [tex]45 m^2 * $56/m^2 = $2520[/tex]
To use inverse operations to check this answer, we can divide the total cost by the cost per square meter to get the number of square meters, and then multiply by the cost per square meter to check that we get back to the total cost:
Number of square meters =[tex]$2520 / $56/m^2 = 45 m^2[/tex]
Total cost = [tex]45 m^2 x $56/m^2 = $2520[/tex] (same as the original answer)
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Are the domain and range of function F? F(x)=x-6\x^2-3x-18
Answer:
domain: all x except -3, 6range: all y except 0, 1/9Step-by-step explanation:
You want the domain and range of the function ...
F(x) = (x -6)/(x² -3x -18)
DomainWe can simplify the function to ...
[tex]F(x) = \dfrac{x-6}{x^2-3x-18}=\dfrac{x-6}{(x-6)(x+3)}\\\\F(x)=\dfrac{1}{x+3}\quad x\notin\{-3,6\}[/tex]
The domain is the set of x-values for which the function is defined. It is undefined where the denominator is zero. So, x=-3 and x=6 are excluded from the domain, which would otherwise be all real numbers.
RangeThe range is the set of values that the function may have. Here, the function can have any y-value except 0 (the value of the horizontal asymptote), and 1/9, the location of the "hole" at x=6.
The range is all real numbers except 0 and 1/9.
In a group, 40% of the items are red. Of all the red items in the group, 30% also have stripes. What percentage of the items in the group are red and have stripes?
Answer:
12% of the items in the group are red and have stripes.
Step-by-step explanation:
Aassume that there is 100 items, 40 items red.
In the 40 items, 30% are striped.
40×(30/100)=12%
12% of the items in the group are red and have stripes. This is found by multiplying the proportion of red items (40%) by the proportion of these red items that also have stripes (30%).
Explanation:We are given that 40% of items in a group are red. This is represented as 40/100, or 0.40. The question mentions that out of these red items, 30% also have stripes. This can be represented as 30/100, or 0.30. The question requires us to find out what percentage of the total items in the group are red and have stripes. To find this, we multiply 0.30 (the proportion of red items that are striped) by 0.40 (the proportion of items that are red).
So, 0.30 x 0.40 = 0.12 or 12%.
Therefore, 12% of the items in the group are red and have stripes.
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Here are 2 polygons. Select all sequences of translations, rotations, and reflections below that would take polygon P to polygon Q
The sequences of translations, rotations, and reflections bthat would take polygon P to polygon Q will be:
C Translate so that Ais taken to J. Then reflect over line BA
E Reflect over line BAand then translate by directed line segment BA.
What is translation?A function is translated when it is moved from where it was before. In geometry, a function that moves an object a specific distance is referred to as translation. Nothing else is done to change the object.
It is not scaled, reflected, rotated, or refracted. Every point of the object must be translated by the same amount and in the same direction.
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PLEASE HELP WHAT TYPE OF FUNCTION
the given function y = 3(4)ˣ, is an exponential function.
What is a logarithmic function?The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.
Given a function y = 3(4)ˣ
An exponential function is defined by the formula f(x) = a, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The exponential function is an important mathematical function which is of the form
f(x) = aˣ
therefore, we can say that the given function is an exponential function.
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Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠A1 is smaller than ∠A2.)
b = 121, c = 162, ∠B = 48°
The values of triangle ABC are
< A = 47.8 < C = 84.2a = 120.6How to find the angels in triangle ABCThe angles in triangle ABC is calculated using the sine rule which sates that the ratio of a side and the opposite angles are equal to each other
This represented by the formula
Sine A / a = Sine B / b = Sine C / c
applying the formula for the problem
Sine B / b = Sine C / c
Sine 48 / 121 = Sine C / 162
cross multiplying
Sine C = 162 * Sine 48 / 121
Sine C = 0.99495
C = arc sine (0.99495)
C = 84.2
Applying sum of angles in a triangle
< A + < B + < C = 180
< A + 48 + 84.2 = 180
< A = 180 - 48 - 84.2
< A = 47.8 degrees
side a
Sine A / a = Sine B / b
Sine 47.8 / a = Sine 48 / 121
121 * sine 47.8 / Sine 48 = a
a = 120.6
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Use this for question 6 to 8:
Four machines A, B, C and D produce respectively 30%, 30%, 15% and 25% of the total number of
items from a factory. The percentage of defective output from these machines are 1%, 1.5%, 3% and
2% respectively. Given that an item is to be selected at random from the total output.
6: Find the probability that the item will be defective.
(a) 0.105
(2 marks)
(b) 0.017
(c) 0.007
(d) 0.170
7: If an item selected at random is found defective, what is the probability that it is produced by
machine A
(2 marks)
(2 marks)
(d) 0.007
(a) 0.018
(b) 0.015
(c) 0.111
8: Find the probability that the item is produce by machine D
(a) 0.294
(b) 0.034
(c) 0.118
(d) 0.253
The probability that the item will be defective is 0.017, the probability that an item selected at random is defective is 0.018 and the probability that an item is produced by machine D is 0.25
What is the probability that the item will be defectiveUsing the formula of probability distribution to solve the given problem;
6: The probability that the item will be defective is the sum of the probabilities of a defective item from each machine:
(1% * 30%) + (1.5% * 30%) + (3% * 15%) + (2% * 25%) = 0.017
So the answer is b
7: If an item is selected at random and found to be defective, the probability that it was produced by machine A is the probability of a defective item from machine A divided by the overall probability of a defective item:
(1% * 30%) / 0.017 = 0.018
The answer is option a
8: The probability that the item was produced by machine D is the probability of a non-defective item from machine D divided by the overall probability of a non-defective item:
(25% * 98%) / (100% - 0.017) = 0.25 * 0.98 / 0.895 = 0.25
So the answer is (d) 0.253
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The surface of the area of a cylinder is 372pi square centimeters the radius is 6 cm what is the height of the cylinder
If the surface of the area of a cylinder is 372π square centimeters. Then the height of the cylinder is 31 centimeters.
What is the surface area of a right circular cylinder?Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,
SA = 2πrh square units
The surface of the area of a cylinder is 372π square centimeters the radius is 6 cm. Then the height of the cylinder is given as,
SA = 2πrh
372π = 2π x 6 x h
h = 372 / 12
h = 31 centimeters
The height of the cylinder is 31 centimeters.
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Julia downloaded a 22 MB file in 5 seconds on her tablet. Later she downloaded a 30 MB file on her smart phone in 6 seconds. Are these rates equivalent? Explain your reasoning.
22 MB in 5 seconds
how many MB per second
divide the 5 out
22/5 = 4.4 MBPS
30 MB in 6 seconds
30/6 = 5 MBPS
5 MBPS > 4.4 MBPS
No, they aren't equivalent because one is greater than the other.
Hope this helps,
- Jeron :- )
Which situation can be represented by the equation x + 14 = 25?
The situation that can be represented using the equation x + 14 = 25 is
illustrated below.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
Given an equation x + 14 = 25.
A situation can be represented as,
Joy and John are two friends, Joy has 14 chocolates, and together they have a total of 25 chocolates, How many chocolates John has?
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can someone help me with this
The distances traveled by the car are given as follows:
3 minutes: 3.45 kilometers.5 minutes: 5.75 kilometers.What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The parameters for this problem are given as follows:
v = 1.15 km/min, t = 1 min.
Hence the equation for the distance in km after t minutes is given as follows:
d = 1.15t.
Then after 3 minutes, the distance is of:
d = 1.15 x 3 = 3.45 km.
After 5 minutes, the distance is of:
d = 1.15 x 5 = 5.75 km.
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• On Dec. 9, Rick worked from half past seven o'clock a.m. to half past four o'clock p.m. He took a half-hour lunch break.
On Dec. 10, Rick worked from seven o'clock a.m. to half past four o'clock p.m. He took a half-hour lunch break.
On Dec. 11, Rick worked from half past eleven o'clock a.m. to five o'clock p.m. He did not take a lunch break.
•
On Dec. 12, Rick worked from half past seven o'clock a.m. to half past five o'clock p.m. He took a one-hour lunch break.
• On Dec. 13, Rick worked from half past seven o'clock a.m. to seven o'clock p.m. He took a one and a half-hour lunch break.
On Dec. 14, Rick worked from eight o'clock a.m. to five o'clock p.m. He took a one and a half-hour lunch break.
On Dec. 15, Rick did not work.
The timesheet of Rick's working hours is given below.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
From the given data points of Rick's working hours:
Date Start Time End Time Time away Regular hours
Dec. 9, 7:30 am 4:30 pm 30 minutes 8.5
Dec. 10, 7:00 am 4:30 pm 30 minutes 8.5
Dec. 11, 11:30 am 5:00 pm - 5.5
Dec. 12, 7:30 am 5:30 pm 60 minutes 9
Dec. 13, 7:30 am 7:00 pm 90 minutes 10
Dec. 14, 8:00 am 5:00 pm 90 minutes 4.9
Dec. 15, - - - -
Therefore, the timesheet is given.
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The complete question:
Make a timesheet for the following dates and times: Dec. 9, Rick...
Make a timesheet for the following dates and times:
Dec. 9, Rick worked from 7:30am to 4:30 p.m. He took a 30 min lunch break
Dec. 10, Rick worked from 7 am to 4:30 p.m. He took a 30 min lunch break
Dec. 11, Rick worked from 11:30 am to 5:00 p.m. He didn't take a lunch break
Dec. 12, Rick worked from 7:30 am to 5:30 p.m. He took an hour lunch break
Dec. 13, Rick worked from 7:30 am to 7:00 p.m. He took an hour and a half lunch break
Dec. 14, Rick worked from 8 am to 5 p.m. He took an hour and a half lunch break
Dec. 15, Rick did not work.
Y=x+3
3x-3y=9
Solved in substitution
The requried, given system of equations y=x+3 and 3x-3y=9 has no common solution.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
From the first equation, we can solve for y:
y = x + 3
Substitute y = x + 3 into the second equation:
3x - 3(x + 3) = 9
Simplify the right side:
3x - 3x - 9 = 9
-9 = 9 (inconsistent)
Since the equation -9 = 9 is inconsistent, the system of equations has no solution, which means that there are no values of x and y that make both equations true at the same time. It implies the system of equations has no solution.
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Charlie has a utility function U(A, B) = AB, the price of apples is $1, and the price of bananas is $2. If Charlie’s income were $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint? * 1 point a. 30 b. 15 c. 60 d. 6 e. 90
Charlie's utility function is given by U(A, B) = AB, where A is the number of apples he consumes and B is the number of bananas he consumes. The price of apples is $1, and the price of bananas is $2.
If Charlie's income is $120, he has a budget constraint given by:
1A + 2B = 120
To maximize his utility subject to this budget constraint, Charlie must use his income to purchase the combination of apples and bananas that gives him the greatest value of U(A, B).
The solution to this problem can be found by using the method of Lagrange multipliers. From the budget constraint, we can solve for A in terms of B:
A = 120 - 2B
Substituting this into the utility function, we have:
U(B) = (120 - 2B)B = 120B - 2B^2
To maximize U(B), we must find the value of B that maximizes this expression. Taking the derivative of U(B) with respect to B and setting it equal to zero, we find that:
dU/dB = 120 - 4B = 0
Solving for B, we find that:
B = 30
Thus, if Charlie chose the bundle that maximizes his utility subject to his budget constraint, he would consume 30 units of bananas. The answer is therefore a. 30.
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The line with equation a + 2b = 0 coincides with the terminal side of an angle θ in standard position and cos θ<0. What is the value of sinθ?
The value of sin( tetha) is -2/√5
What is intersection value?Point of intersection is the point where two lines meet.
a+2b = 0 can be related to x+2y = 0
Line x + 2y = 0 is end side of angle θ and cos θ < 0 means x < 0. Line is y = -x/2, slope -1/2 and the Line intersects unit circle when :
b = -1/2 a
therefore the slope is -1/2
Line intersect unit circle when:
x²+y² = 1
a²+b² = 1
a² +( - 1/2a)² = 1
a²+ a²/4 = 1
5a²/4 = 1
a² = 4/5
a = √ 4/5
the value of sin(tetha) at the point of intersection is y
y = -1/2a
y = -1/2√4/5
y = -2/√ 5
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For a moving object, the force acting on the object varies directly with the objects acceleration. When a force of 40 N acts on a certain object, the acceleration of the object is 4 m/s^2. If the acceleration of the object becomes 9 m/s^2, what is the score?
Answer:
Step-by-step explanation:
We can use the proportionality relationship between force and acceleration, which is given as:
force = constant × acceleration
Let's call the constant of proportionality k. Then we can write:
40 N = k × 4 m/s^2
Solving for k, we get:
k = 40 N / 4 m/s^2 = 10 Ns^2/m
Now we can use this value of k to find the force required for an acceleration of 9 m/s^2:
force = k × acceleration = 10 Ns^2/m × 9 m/s^2 = 90 N
Therefore, the force required for an acceleration of 9 m/s^2 is 90 N.
myra can type 70 words in 2 min. how many words can she type in 5 min
Answer:
first convert 2mins to seconds
60sec=1 min
which is 2×60=120sec
then70/120sec=0.583
convert 50mis to sec
5×60=300sec
so therefore 300sec×0.583=174.9words
HOPE IT HELPS
Answer: 175 words
Step-by-step explanation:
First start out by dividing how many amount (5 min) you are looking for by the amount (2 min) that we already know.
5 / 2 = 2.5
This gives us the key to finding our final answer.
Use this new number (2.5) and multiply it by 70 to get our answer.
70 x 2.5 = 175
I need help on question six, pls help me
Answer:
The surface area of the label is 28 squared inches.
Step-by-step explanation:
The dimensions of juice box are length=2 inches, breadth=1.5 inches and height= 4 inches.
The lateral surface area of a cuboid is given by 2(length+breadth)×height.
Now, lateral surface area of juice box = 2(2+1.5)×4
= 2×3.5×4
= 28 squared inches
Answer:
28 square inches
Step-by-step explanation:
Lateral surface of Cuboid:The label covers the lateral surface area of the box.
l = 2 in ; w = 1.5 in ; h = 4 in
[tex]\boxed{\text{\bf lateral surface area of cuboidal box = 2h*(l +w)}}[/tex]
[tex]\sf = 2*4 *( 2 +1.5)\\\\= 2 * 4 * 3.5\\\\ = 28 \ in^2[/tex]
Find the volume of a cone with a base diameter of 8 cm and a height of 6 cm .
Use the value 3.14 for π, and do not do any rounding.
Be sure to include the correct unit in your answer.
The volume of a cone with a diameter of 8 cm and a height of 6 cm is
100.48 cm³.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, The height of the cone is 6 cm.
Also given the diameter of the base 2r = 8 cm hence r = 4 cm.
Therefore, The volume of this cone is,
= (1/3)π(4)²×6 cm³.
= 32π cm³.
= 100.48 cm³
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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed.
Answer: C. The most accurate measure of center to represent the data in this case is the median of 20.
Step-by-step explanation: The median is the middle value in a dataset when the data is arranged in ascending or descending order. In this case, the donations are: 10, 10, 10, 10, 15, 15, 15, 19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55.
When we arrange these values in ascending order, we get: 10, 10, 10, 10, 15, 15, 15, 19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55.
The median is the value that separates the dataset into two equal halves. In this case, there are 18 values, so the middle value is the 9th value, which is 20.
The reason the median is the most accurate measure of center to use in this case is because the data is skewed. Skewness refers to the asymmetry in the distribution of data. In this case, the data is skewed to the right because there are a few large values (55) that pull the mean higher than the majority of the values.
Using the mean, which is calculated by summing all the values and dividing by the total number of values, would be influenced by these large values and may not accurately represent the typical donations received by the charity.
a company starts to track the number of phone calls received
Answer:
pls give more detail
Step-by-step explanation:
prove that if a sequence converges it has exactly one limit point. is the converse true? prove it or give a counterexample.
The counterexample proves that the converse of the theorem is not always true, and we have to be careful when making statements about limit points and convergence of sequences.
A sequence is a set of numbers that are generated one after the other in a specific pattern.
The theorem states that if a sequence converges, it will have exactly one limit point. In other words, if a sequence is getting closer and closer to a certain number, there will be only one number that it approaches. This is a fundamental idea in mathematics, and it is important to understand why it is true.
To prove this theorem, let's consider a sequence (a_n) that converges to a limit L. If there were two different limit points, say L1 and L2, then there would be a contradiction. This is because by definition, the sequence (a_n) would be getting closer and closer to L1 and L2 at the same time, which is not possible. Hence, it must be true that the sequence (a_n) has exactly one limit point, L.
The converse of this theorem is not always true. In other words, just because a sequence has exactly one limit point, it doesn't necessarily mean that it converges to that limit. To see why this is the case, let's consider the following sequence:
(2, 3, 4, 5, 6, ...)
In this sequence, the limit point is 6. However, the sequence does not converge to 6 because it is not getting closer and closer to 6 as it goes on. Instead, it is increasing by 1 with each term, and therefore it does not converge.
To know more about limit here.
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