Suppose two sets of scores have the same mean, but different
standard deviations, o, and o₂, with 0₂ > 0₁ Which statement
1
2
best describes the variability of these data sets?
02
(1) Data set one has the greater variability.
(2) Data set two has the greater variability.
(3) The variability will be the same for each data set.
(4) No conclusion can be made regarding the variability of
either set.
Answers
Data set two has the greater variability option (2) Data set two has the greater variability is correct.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
Two sets of scores have the same mean, but different standard deviations.
σ₁ and σ₂ (σ₂ > σ₁)
Coefficient of variation = [SD/(mean)]×100
[tex]\rm CV = \dfrac{\sigma }{|x|}\times100[/tex]
σ₂ > σ₁
Divide by |x| on both sides
σ₂/|x| > σ₁/|x|
[tex]\rm \dfrac{\sigma }{|x_1|}\times100 > \dfrac{\sigma }{|x_2|}\times100[/tex]
(CV)₂ > (CV)₁
Thus, data set two has the greater variability option (2) Data set two has the greater variability is correct.
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Related Questions
190 divided by 2 over 3
Answers
Reason
When you divide by a fraction, you flip the fraction and multiply
So 190 divided by 2/3 becomes 190 x 3/2
Factor 190 x 3/2, multiply across
190 x 3 = 570 then
570 divided by 2 = 285
Explain why a graph that fails the vertical-line test does not represent a function. Be sure to use the definition of a function in your answer
Answers
Explanation:
A function is a relationship where any one x-value/input only has one corresponding y-value/output. (note: a y-value can have multiple x-values).
> This can be called "assigning one y-value to every x element".
The vertical line test places a line that would connect all y-values of an x-value (that is, if it were to have multiple y-values). If multiple points can be found along the vertical line, it is, therefore, by the definition of a function, not a function. (Because an x-value will have more than one y-value).
So, a graph that fails the vertical-line test does not represent a function because an x-value will correspond with more than one y-value.
hope this helps!!
Alex's recipe calls for 1/3 cup of chocolate chips for every 2 cups of flour. If he increases the
amount of flour to 3 cups, how many cups of chocolate chips will he need?
Answers
Answer:
1/2 cup of chocolate chips
Step-by-step explanation:
Given ratio:
chocolate chips : flour = 1/3 cups : 2 cupsLet x be the unknown amount of chocolate chips:
[tex]\implies \sf \dfrac{1}{3}:2=x:3[/tex]
[tex]\implies \sf \dfrac{\frac{1}{3}}{2}=\dfrac{x}{3}[/tex]
Cross multiply:
[tex]\implies \sf 3 \cdot \dfrac{1}{3}=2 \cdot x[/tex]
[tex]\implies \sf 1=2x[/tex]
[tex]\implies \sf x=\dfrac{1}{2}[/tex]
Therefore, 1/2 a cup of chocolate chips will be needed for 3 cups of flour.
Let that be x
1/3/2=x/31/6=x/3x=3/6x=1/2 cupQuestion 1 of 10
What is the midpoint of the segment shown below?
O A. (6,3)
O B. (6,5)
O C. (3,5)
OD. (3, 3)
Answers
Answer:
[tex]\textsf{C.} \quad \left(3,\dfrac{5}{2}\right)[/tex]
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints of the line segment:
[tex]\textsf{Let }(x_1,y_1)=(-1,2)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(7,3)[/tex]
Substitute the defined endpoints into the midpoint formula and solve:
[tex]\implies \textsf{Midpoint}=\left(\dfrac{7+(-1)}{2},\dfrac{3+2}{2}\right)[/tex]
[tex]\implies \textsf{Midpoint}=\left(3,\dfrac{5}{2}\right)[/tex]
Midpoint
(-1+7/2,2+3/2(6/2,5/2)3,5/2)
9. P(no more than 16 | prime
Answers
9 out of 10 students prefer maths class over lunch how many students do not prefer math if 200 students were asked?
Answers
Answer: 180
Step-by-step explanation: 200 % 2 = 100
9/10 = 90/100
90 * 2 = 180
Answer:
20 students
If 9 out of 10 student prefer math over lunch, then 1 out of ten DO NOT. With this information you can set up a simple proportion: [tex]\frac{1}{10} =\frac{x}{200}[/tex].
To solve for x, you cross multiply as follows:
1*200=10x
200=10x
20=x
Hence, x equals 20, and 20 students do not prefer math over lunch.
Hope I helped!!!!!!!!!!!!!:)
Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (11, 0) and an eccentricity of three fifths question mark
quantity x minus 6 end quantity squared over 100 plus y squared over 64 equals 1
quantity x plus 6 end quantity squared over 64 plus y squared over 100 equals 1
quantity x plus 6 end quantity squared over 16 plus y squared over 25 equals 1
quantity x minus 6 end quantity squared over 25 plus y squared over 16 equals 1
Answers
The equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have:
The vertices of the ellipse = (1, 0) and (11, 0)
Eccentricity of ellipse = 3/5
We have equations:
[tex]\rm \dfrac{\left(x-6\right)^{2}}{100}+\dfrac{y^{2}}{64}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{64}+\dfrac{y^{2}}{100}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{16}+\dfrac{y^{2}}{25}=1[/tex]
[tex]\rm \dfrac{\left(x-6\right)^{2}}{25}+\dfrac{y^{2}}{16}=1[/tex]
From the fourth equation:
The vertices of the ellipse:
(1, 0) and (11, 0)
The eccentricity:
c² = a² - b²
c² = 25-16
c = 3
e = c/a = 3/5
Thus, the equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.
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Which of the following are true statements?
Answers
An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. The graph of this model would be:
a curved line that increases but then decreases.
a straight line that decreases only.
a straight line that increases only.
None of these choices are correct.
Answers
The graph of this model would be a straight line that increases only option third is correct.
What is a line graph?A line graph is a graph made up of segments of straight lines that connect the depicted data points.
We have:
An auto mechanic charges (C) an initial fee of $50 and then $40 per hour.
Let T be the total fee and h is the number of hours
T = 50 + 40h
The above equation represents a graph of a straight line as the slope of the line is positive.
m = 50
Thus, the graph of this model would be a straight line that increases only option third is correct.
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What graph best represents the data
Answers
A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. The correct option is A.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
A histogram is a statistical information presentation that employs rectangles to illustrate the frequency of data items in equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most frequent kind of histogram.
The best graph that can represent the given situation is Histogram. Hence, the correct option is A.
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Rewrite each of the following expressions without using absolute value: |x-5|+|x+5| if x<-5
Answers
For [tex]x < -5[/tex]:
[tex]x-5 < 0 \Rightarrow |x-5|=-(x-5)=-x+5\\x+5 < 0\Rightarrow |x+5|=-(x+5)=-x-5[/tex]
So
[tex]|x-5|+|x+5|=-x+5-x-5=-2x[/tex]
Follow the steps to find the
area of the shaded region.
First, use the formula
below to find the area
of the whole sector.
=
angle of sector
360
¹) πr²
Sector Area = [?] cm²
Round to four decimal places.
Sector Area
14 cm
46°
14 cm
Enter
Answers
Based on the calculations, the area of the whole sector is equal to 4,508 cm².
Given the following data:
Angle of sector = 46°.Radius of circle = 14 cm.How to calculate the area of a sector?Mathematically, the area of a sector can be calculated by using this formula:
Area of sector = θr²/2
Where:
r is the radius.θ is the central angle.Substituting the given parameters into the formula, we have;
Area of sector = 46 × 14²/2
Area of sector = 46 × 196/2
Area of sector = 9016/2
Area of sector = 4,508 cm².
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which expression is equivalent to...
Answers
Answer:
B
Step-by-step explanation:
Based on local population projections for 2010, school district 31 will lose 5 teaching positions, district 222 will lose 5 teachers, and district 225 will lose 2. Write a
signed number that represents the total number of teachers that these three school districts are projected to lose.
What is the signed number that represents the total number of positions that these three districts are projected to lose?
Answers
Answer:
2+3+4 = 9
Add the three numbers of the three school districts that project to lose.
18 / 48 hrs left
Divide and answer the question.
Answers
Answer: I don’t understand
Step-by-step explanation:
An electrician charges a $40 fee to make a house call plus an hourly rate for labor. If the total bill that takes 2 hours comes to $99 what is the electrician hourly labor rate?
Answers
Reason
You can use the formula y=mx+b for this
We know y is the total bill of $99
We know b is the $40 fee (y intercept or starting point)
We know x is 2 hours
We are looking for m or rate
Substitute numbers for letters in formula
99= m(2) +40
Subtract 40 from both sides to isolate m
59=2m
Divide both sides by 2 to solve for m
M=$29.50
We can prove our answer by inserting our answer for “m” in the formula
99=29.50x2+40
99=99
Answer is correct
which ordered pair is a solution to the following system of inequalities
Answers
Answer:
it's 1,1 is the correct ans
Step-by-step explanation:
Because my teacher told its absolutely correct answer I got the same question in exam
Answer:
the answer should be the 2 one
Step-by-step explanation:
I got it right just had it.
What is the vertex of the absolute value function defined by f(x) =3|x+7|-2
Answers
The vertex of the absolute value function is (-7,-2)
How to determine the vertex?The function is given as:
f(x) = 3|x + 7| - 2
The above function is an absolute value function.
An absolute value function is represented as:
f(x) = a|x - h| + k
Where:
Vertex = (h,k)
By comparison, we have:
(h,k) = (-7,-2)
Hence, the vertex of the absolute value function is (-7,-2)
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use interval notation to express the following: the set of all numbers greater than or equal to 5 and less than or equal to 7
Answers
[5, +∞) ∪ (-∞,7] is the notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7.
We need to use interval notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7.
What is a set?A set is a mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Let x belong to the set of real numbers (R)
Now, x≥5 and x≤7.
So, x≥5⇒[5, +∞) and x≤7⇒(-∞,7]
Therefore, the notation will be [5, +∞) ∪ (-∞,7].
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Each phrase in the table describes two variables whick are strongly correlated. Select all phases that imply correlation without causation.
Answers
The complete question is attached below.
The most correct phases that imply correlation without causation are 1, 5, and 6.
What is correlation?The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.
The most correct phases imply correlation without causation are;
The number of stuffed animals produced at a factory and the number of newborn babies.
The number of videos rented and the number of films in the theater.
The number of pets in the neighborhood and the amount of grass nearby.
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Hi supreme turtle this is the question
Answers
Answer:
< $0 --------------$35------ $50>
Step-by-step explanation:
wait that's not the full question but uh I assume that's 30% off $50?
it would be 0.3x50 which is 15 and 50-15 is 35.
the range is 0 - $50 if I'm not mistaken
< $0 -------------------------- $50> scuffed number line
but 35 is somewhere around here?
< $0 --------------$35------ $50>
Write the number below as a fraction in its simplest form
0.125 the 1 and 5 are recurring
Answers
If we write 0.125 in the fraction form then we will get 7/20.
Given Number which is 0.125
We are given a number 0.125 and we have to write this in fraction form.
0.125 can be written as 125/1000 it can be written as 7/20 by cutting on the numerator and denominator.
Fraction is a combination of numerator and denominator. If a fraction is solved then it comes in the decimal form. Recurring means the numbers which are coming again and again after the decimal.
In this fraction we have to ignore 1 and 5 because we have no idea how many times it is coming after decimal.
Hence the number 0.125 can be written as 7/20 in the fraction form.
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What is the product of (2x - 1) (x + 4)
Answers
Answer: 2[tex]x^{2}[/tex]+7x-4
Step-by-step explanation:
Product implies multiplication so just multiply it out.
(2x-1) (x+4)
2x^2+8x-1x-4 (Combine like terms)
2x^2+7x-4
Which number is irrational?
C
-4
C
2
g
O 11
O 8.26
Answers
The irrational number in the given options is √11
What is an irrational number?Irrational numbers are set of all real numbers in mathematics that are not rational numbers in nature. By the word rational, we mean that they cannot be expressed or represented in a fraction of a/b.
where;
a = numeratorb = denominatorIn other words, it is impossible to describe an irrational number as the ratio of two integers.
From the given options, the square root of 11 is the only number that cannot be expressed as a fraction, therefore, we can conclude that it is considered the only irrational number in the given options.
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curved surface area of a cone = Trl, where r is the
radius and I is the slant height.
surface area of a sphere = 42, where r is the
radius.
The shape below is made from a hemisphere and a
cone, each with a radius of 6 cm.
Work out the surface area of this shape in terms of .
16 cm
6 cm
Not drawn accurately
Answers
Answer:
168π cm²
Step-by-step explanation:
The total surface area is the sum of the areas of the parts: a hemisphere and a cone.
__
area formulaThe area of a hemisphere is half the area of a sphere, so the total area is ...
total area = hemisphere area + cone area
= 2πr² +πrl
total area = πr(2r +l)
__
applicationFor the given dimensions, r = 6 cm, l = 16 cm, the total surface area is ...
total area = π(6 cm)(2(6 cm) +16 cm) = π(6)(28) cm²
total area = 168π cm²
Need help with this geometry question
Answers
Answer: QN=19
Step-by-step explanation:
Diagonals of an isosceles trapezoid are congruent, so NQ=PM.
By the segment addition postulate, NQ=QR+RN=3x+7.
So,
[tex]6x-5=3x+7\\\\3x-5=7\\3x=12\\\\x=4[/tex]
So, [tex]QN=3(4)+7=\boxed{19}[/tex]
Multiply and remove all perfect squares from inside the square roots. Assume a is positive.
3[tex]3\sqrt{5a}*8\sqrt{35a^{2} }[/tex]
Answers
The multiplication is 120*[tex]a^{3/2}[/tex].
What is exponents and powers?
Power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.
Given:
3√(5a) * 8 √(35a²)
= 3√(5a)* 8* a *√7* √5
= 3*8*5*a *√(7a)
= 120 [tex]a^{1/2+1}[/tex]
=120*[tex]a^{3/2}[/tex]
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Answer:
[tex]120a\sqrt{7a}[/tex]
Step-by-step explanation:
It's right on khan academy
Which of the following is the solution to 7√22 + 3√7
Answers
The value of this irrational Expression is 40.77 .
What is an Expression ?An expression is a mathematical statement consisting of variables , constants and mathematical operators.
The expression given is
7√22 +3√7
√22 = 4.69
√7 = 2.65
32.83 + 7.94
40.77
The value of this irrational Expression is 40.77 .
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answer is equivalent to ?
√16
√49
SA
A.
OB.
O c.
D.
16
49
16
49
316
Answers
The solution of the given expression is 9. So the correct answer is option B.
The complete question is given below:-
(√16 - √49 )² The solution of the given equation will be
A. 16
B .9
C .49
D. 316
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given expression will be calculated as:-
(√16 -√49 )² = (√16)² -2 (√16)(√46) + (√49 )²
= ( 16 - 2(4)(7) + 49 )
= ( 16 - 56 + 49 )
= 9
Therefore the solution of the given expression is 9. So the correct answer is option B.
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Given the expression: 6x10 − 96x2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Answers
The expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, B expression can be simplified by applying identity.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an expression:
Part A)
= 6x¹⁰ - 96x²
= 6x²(x⁸ - 16)
Part B)
[tex]\rm =6x^2(\left(x^4\right)^2-4^2)[/tex]
[tex]\rm =6x^2(\left(x^4+4\right)\left(x^4-4\right))[/tex]
[tex]\rm =6x^2\left(x^2+2x+2\right)\left(x^2-2x+2\right)\left(x^2+2\right)\left(x^2-2\right)[/tex]
Thus, the expression 6x¹⁰ - 96x² can be written by factoring out the greatest common factor is 6x²(x⁸ - 16) and for a part, the B expression can be simplified by applying identity.
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