Compare the three data sets on the right.
(a) Which data set has the greatest sample standard deviation?
Which data set has the least sample standard deviation?
(b) How are the data sets the same? How do they differ?
Answers
Answer:A just took the test and got a 100
a) The graph II will tell the greatest sample standard deviation.
and, the least sample standard deviation is given by Graph III.
b) The three data sets have same mean, median and mode but different
standard deviation.
what is Standard Deviation?The term "standard deviation" (or "[tex]\sigma[/tex]") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given:
From the Graph we can say the the dispersion of data from the mean tells about the Standard deviation.
Then, the graph II will tell the greatest sample standard deviation.
and, the least sample standard deviation is given by Graph III.
b) The data sets have same mean but different standard deviation.
So, The three data sets have same mean, median and mode but different
standard deviation.
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Related Questions
How do you do these questions? With step by step instructions please
Answers
Answer: n = 3 n = 4
Upper Sum ≈ 3.41 Upper Sum ≈ 3.25
Lower Sum ≈ 2.15 Lower Sum ≈ 2.25
Step-by-step explanation:
You are trying to find the area under the curve. Area = height x width.
Height is the y-value at the given coordinate --> f(x)
Width is the distance between the x-values --> dx
n = 3
First, let's figure out dx: the distance from -1 to +1 is 2 units. We need to divide that into 3 sections because n = 3 --> dx = 2/3
So the points we will evaluate is when x = {-1, -1/3, 1/3, 1}
For the upper sum, we find the max y-value for each interval
For the lower sum, we find the min y-value for each interval
Next, let's find the height for each of the x-values:
f(x) = 1 + x²
f(-1) = 1 + (-1)² = 2
f(-1/3) = 1 + (-1/3)² = 1 + 1/9 --> 10/9
f(1/3) = 1 + (1/3)² = 1 + 1/9 --> 10/9
f(1) = 1 + (1)² = 2
Interval Max Min
{-1, -1/3} f(-1) = 2 f(-1/3) = 10/9
{-1/3, 1/3} f(-1/3) = 10/9 f(0) = 1 (vertex lies in this interval)
{1/3, 1} f(1) = 2 f(1/3) = 10/9
Now, let's find the Area: A = f(x) dx:
[tex]\text{Upper Sum:}\quad A=\dfrac{2}{3}\bigg(2+\dfrac{10}{9}+2\bigg)\\\\.\qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{46}{9}\bigg)\\\\.\qquad \qquad \qquad =\dfrac{92}{27}\\\\.\qquad \qquad \qquad =\large\boxed{3.41}[/tex]
[tex]\text{Lower Sum:}\qquad A=\dfrac{2}{3}\bigg(\dfrac{10}{9}+1+\dfrac{10}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{29}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{58}{27}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.15}[/tex]
*****************************************************************************************
n = 4
First, let's figure out dx: the distance from -1 to +1 is 2 units. We need to divide that into 4 sections because n = 4 --> dx = 2/4 = 1/2 (simplified)
So the points we will evaluate is when x = {-1, -1/2, 0, 1/2, 1}
For the upper sum, we find the max y-value for each interval
For the lower sum, we find the min y-value for each interval
Next, let's find the height for each of the x-values:
f(x) = 1 + x²
f(-1) = 1 + (-1)² = 2
f(-1/2) = 1 + (-1/2)² = 1 + 1/4 --> 5/4
f(0) = 1 + (0)² = 1
f(1/2) = 1 + (1/2)² = 1 + 1/4 --> 5/4
f(1) = 1 + (1)² = 2
Interval Max Min
{-1, -1/2} f(-1) = 2 f(-1/2) = 5/4
{-1/2, 0} f(-1/2) = 5/4 f(0) = 1
{0, 1/2} f(1/2) = 5/4 f(0) = 1
{1/2, 1} f(1) = 2 f(1/3) = 5/4
Now, let's find the Area: A = f(x) dx:
[tex]\text{Upper Sum:}\qquad A=\dfrac{1}{2}\bigg(2+\dfrac{5}{4}+\dfrac{5}{4}+2\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{26}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{13}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{3.25}[/tex]
[tex]\text{Lower Sum:}\qquad A=\dfrac{1}{2}\bigg(\dfrac{5}{4}+1+1+\dfrac{5}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{18}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{9}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.25}[/tex]
Find g(-2) + h(4) if g(x)= 5-2x and h(x) = - x2 pls help
Answers
Answer:
-7
Step-by-step explanation:
g(x)= 5-2x and h(x) = - x^2
g(-2) + h(4)
First find g(-2)
g(-2) = 5 -2(-2) = 5 +4 = 9
Then find h(4) = - 4^2 = -16
g(-2) + h(4) = 9-16 = -7
Answer:
-7
Step-by-step explanation:
Substitute -2 into g(x) equation,
g(x) = 5 - 2x
g(-2) = [5 - 2(-2)] = 9
Substitute 4 into h(x) equation,
h(x) = -x^2
h(4) = [-(4)^2] = -16
Therefore,
g(-2) + h(4) = 9 + (-16) = -7
Your math teacher is only giving three tests this quarter. They count equally and your quarter grade will be the average of the tests. You scored a 79% on the first test and an 84% on the second test. If your quarter grade is below a 75% you will be grounded from your phone. What scores will get you into trouble on your report card?
Answers
3 tests at 75% each = 3 x 75 = 225 total points
First two tests = 79 + 84 = 163
Third test needs to be at least: 225 - 163 = 62%
So any score less than 62 would get you into trouble.
Skip count by twos.
30,_ _ _ _ _ _ _ _ _,50.
Answers
y varies inversely with x. If y = 5 when x = 60, find y when x = 150
pre cal
Answers
Answer:
y = 2 when x = 150
Step-by-step explanation:
Inverse variation is
xy = k
5*60 = k
300 = k
xy = 300
150y = 300
Divide by 150
150y/150 = 300/150
y = 2
Point R is on line segment QS. Given RS = 13 and QS = 20, determine the length of QR
Answers
Answer:
Length of QR = 7
Step-by-step explanation:
20 - 13 = 7
An open top box is to be made by a 24 in by 24 in. by 36 in. piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume?
Answers
Answer:
X= -12 +6√10
X= 6.973
Step-by-step explanation:
Volume of the box= (36-2x)(24-2x)x
Volume of the box
=( 864 -96x -4x²)x
But 864 -96x -4x²
=216 - 24x-x²
Solving for x quadratically
X= (24+12√10)/-2
X= -12 -6√10
X= -30.97
Or
X= (24-12√10)/-2
X= -12 +6√10
X= 6.973
X will definitely be a positive number
So X= -12 +6√10
X= 6.973
Increasing or decreasing the side length of the square that gives the
maximum volume, gives a volume that is less than the maximum.
The side length of the cut out square to get a box with the maximum volume is approximately 4.71 in.Reasons:
The given dimensions of the box = 24 in. by 36 in.
Let x represent the dimensions of the square removed from the corners, we have;
Width of box = 24 - 2·x
Length of box = 36 - 2·x
Height of the box = x
Volume of a box = Width × Length × Height
Therefore;
Volume of the box, V = (24 - 2·x)·(36 - 2·x)·x = 4·x³ - 120·x² + 864·x
At the maximum or minimum point of the volume, we have;
[tex]\displaystyle \frac{dV}{dx} = \mathbf{ \frac{d}{dx} \left(4 \cdot x^3 - 120 \cdot x^2 + 864 \cdot x \right )} = 0[/tex]Which gives;
12·x² - 240·x + 864 = 0
x² - 20·x + 72 = 0
Which gives;
[tex]\displaystyle x = \dfrac{20\pm \sqrt{(-20)^{2}-4\times 1\times 72}}{2\times 1} = \mathbf{10 \pm 2\cdot \sqrt{7}}[/tex]
At x = 10 + 2·√7, we have;
[tex]\displaystyle 10 + 2 \cdot \sqrt{7} > \frac{24}{2}[/tex]
2 × (10 + 2·√7) in. > 24 in. which is the width of the cardboard
Therefore, (10 + 2·√7) is too long to be cut from the cardboard
At x = 10 - 2·√7, we have;
V = 4·(10 - 2·√7)³ - 120·(10 - 2·√7)² + 864·(10 - 2·√7) ≈ 1,828.3
Therefore;
The maximum volume corresponds with a cut out square of side length x = 10 - 2·√7 inches ≈ 4.71 inches
The size of the square to be cut out each corner is x ≈ 4.71 inchesLearn more here:
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Find the value of x.
X=8
X=10
X=16
X=20
Answers
Answer:
D. 20Step-by-step explanation:
Find the required diagram to the question in the attachment.
From the diagram it can be seen that the distance of the lines projecting from the centre of the circle to the line segment is equal i,e they are both 8. This means that the length of both chords given will be equal. For the known chord length, it can be seen that the line perpendicular to the chord cuts them at the centre. and since both sides of the chord are parallel, the other sides too will be 10 making the total length to be 10+10 = 20.
Since the length of the known chord is equal to the length of the unknown chord x, hence, the value of x will also be 20
Answer:
D. x=20
Step-by-step explanation:
correct on EDGE2021
Express each rational number in decimal form.
[tex] \frac{3}{4} [/tex]
Answers
Answer:
.75
Step-by-step explanation:
there is only 1 number
0.75
The decimal forms of rational numbers either end or repeat a pattern. To convert fractions to decimals you just divide the top by the bottom — divide the numerator by the denominator — and if the division doesn't come out evenly, you can stop after a certain number of decimal places and round off.
fatima bought an xbox game that is 38.00 plus 9% sales tax what is the sales tax on the xbox game that fatima purchased answer
Answers
I used proportions to find the answer.
Part Percent
——— = —————.
Whole 100
Then, cross multiply.
Part • 100
—————
Percent • Whole
Finally, divide the numerator by the denominator. If you apply these steps to your problem, you will get $3.42.
is is 6 2/7 rational or irrational
is -19 rational or irrational
is -√100 rational or irrational
Answers
Step-by-step explanation:
6 2/7is rational
-19is rational but next I dont know
Brayden is working two summer jobs, making $18 per hour lifeguarding and making $9 per hour clearing tables. In a given week, he can work no more than 19 total hours and must earn a minimum of $270. If Brayden worked 14 hours lifeguarding, determine the minimum number of whole hours clearing tables that he must work to meet his requirements. If there are no possible solutions, submit an empty answer.
Answers
Answer: The amount he earns from lifeguarding = $252 ($18×14). The total amount he needs to make a week is $270.
$270-$252=$18, he needs to earn $18 more from clearing tables.
$18÷9=2, so the minimum number of whole hours clearing tables is 2
do all sets have subsets?
Answers
Answer:
yes
Step-by-step explanation:
Solve for x.
16 = -2x - 1
x = -8
x = -7
x = 7
x = 8
Answers
Step-by-step explanation:
16=-2x-1
17=-2x
x=-17/2
x=-8.5
(this one isn't in the correct order but it's one of the answers ¯\_(ツ)_/¯
16 = -2x - 1
-8=x-1
-7=x
x=-7
Find a unit vector that is orthogonal to both i + j and i + k.
Answers
Answer: i - j - k
Step-by-step explanation:
Taking the cross product between two vectors will give you a third vector that is orthogonal(perpendicular) to both vectors.
<1,1,0> x <1,0,1>
[tex]det(\left[\begin{array}{ccc}i&j&k\\1&1&0\\1&0&1\end{array}\right] )[/tex]
the determinate of the matrix: <1,-(1),-1>
or: i - j - k
Answer as a fraction (please help)
Answers
Alternative form: 12/47
what is -3.5+(-4.9)=?What is the answer please?
Answers
Answer:
The answer is -8.4
Students in a large statistics class were randomly divided into two groups. The first group had a midterm exam that was printed on canary paper while the second group had the exam printed on pale green paper. The exam scores of the two groups were then then compared.This experiment was not blind because:_______a. Students were allowed to keep their eyes open while taking the exam.b. The exam was too long.c. The students knew whether or not music was playing while they were taking the exam.d. Some of the students did not study for the exam.e. Students were randomized into the two groups.
Answers
Answer:
e. Students were randomized into the two groups.
Step-by-step explanation:
a vegetable farmer fills 2/3 of a crate with 5/7 of a pound of tomatoes. how many lbs can fit in one crate
Answers
Answer:
1 1/14 lbs
Step-by-step explanation:
We can use ratios to solve
2/3 crate 1 crate
----------------- = -----------------
5/7 lb x lbs
Using cross products
2/3x = 5/7 *1
Multiply each side by 3/2
3/2 * 2/3 x = 3/2 * 5/7
x = 15/14
x = 1 1/14
Answer:
[tex]\huge\boxed{\sf 1 \ crate = \frac{15}{14} \ lbs}[/tex]
Step-by-step explanation:
[tex]\sf \frac{2}{3}\ of \ a\ crate = \frac{5}{7} \ of \ a\ pound \\\\We \ need \ to \ find\ the \ weight \ of \ one \ crate\\\\So, Multiplying \ both \ sides \ by \ the\ reciprocal \ of \ \frac{2}{3} \ i.e. \frac{3}{2} \\\\1 \ crate = \frac{5}{7} * \frac{3}{2} \ lbs\\\\1 \ crate = \frac{5*3}{7*2} \ lbs\\\\1 \ crate = \frac{15}{14} \ lbs[/tex]
There was 1 liter of water in the water bottle. Tom drank 200 milliliters of water. How many liters of water are left?
Answers
Answer:
.8L
Explanation:
Logic
The liters of water left are 0.8 liters.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
The equations are useful in the determination of unknown parameters.
The quantity of water in a water bottle is 1 liter.
The amount of water Tom drank is 200 milliliters.
Let x be the amount of water left in the bottle.
The liter has to be converted into milliliters.
1 liters = 1000 milliliters
The equation formed is,
1000 - 200 = x
x = 1000 - 200
x = 800 milliliters.
The water left in the water bottle is 800 milliliters.
1000 milliliters = 1 liters
800 milliliters = 0.8 liters
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A bag contains 6 RED beads, 3 BLUE beads, and 11 GREEN beads. If a single bead is picked at random, what is the probability that the bead is RED or GREEN?
Answers
Answer:
17/20
Step-by-step explanation:
Total no. of beads = 6 + 3 + 11 = 20
We need RED or GREEN bead .
So no. of beads needed = 6 + 11 = 17
So probability of getting GREEN or RED beads = 17/20
I'm trying to find sin of (7pi/12) exactly using an angle of addition or subtraction formula could anyone help me
Answers
Answer:
(√2 + √6)/4.
Step-by-step explanation:
Use the addition formula
sin (A+ B) = sinAcosB + cosAsinB
sin (7pi/12) = sin( 3pi/12 + 4pi/12)
= sin(pi/4 + pi/3) = sin pi/4 cos pi/3 + cos pi/4 sin pi/3
= 1/√2 * 1/2 + 1/√2 * √3/2 (using the 45-45-90 and 30-60-90 triangles)
= 1 / 2√2 + √3/2√2
= √2/4 + √6/4
= (√2 + √6)/4
Write the equation of the line PERPENDICULAR to y = 3/2x + 6 that passes through the point (-3, 4).
Answers
Answer:
Step-by-step explanation:
perp. -2/3 slope
y - 4 = -2/3(x + 3)
y - 4 = -2/3x - 2
y = -2/3x + 2
What is 30/35 in simplest form?
Answers
Answer: 6/7
Step-by-step explanation:
A plane is a _____ figure
Answers
Answer:
bold
Step-by-step explanation:
hshsjjsududidididiidododododokdodkdjdndndnjdudududuididjdjdjd
A plane is a two dimensional figure.
What is the measure of r
Answers
360-100=260
260/2=103
Answer:
The two marks on the right and left side of the triangle means that it's an isosles triangle which means that the base angles are equal and any triangle in the world the sum of its angles is 180° and you have an angle with 100° so you should subtract 100 from 180 that gives 80° and dived 80 by 2 that gives you 40°
The grades in period 3 Algebra 2 have an average of 82% and vary by 12 percentage points. Formulate an absolute value equation that could be used to solve for the maximum and minimum grade.
|x______ | = _______
x = __________ (smaller number here)
x = _______ (larger nember here)
Blank 1:
Blank 2:
Blank 3:
Blank 4:
Answers
Answer:
[tex]|x - 85| = 12[/tex]
[tex]x = 73 \ (smaller\ number )[/tex]
[tex]x = 97 \ (larger \ number )[/tex]
Step-by-step explanation:
From the question we are told that
The grade is [tex]k = 85\%[/tex]
The variation is [tex]v = 12 \%[/tex]
Generally the absolute value equation is mathematically represented as
[tex]|x - 85| = 12[/tex]
=> [tex]x -85 = \pm 12[/tex]
So
[tex]x = 85 + 12[/tex]
[tex]x = 97 \ (larger \ number )[/tex]
And
[tex]x = -12 + 85[/tex]
=> [tex]x = 73 \ (smaller\ number )[/tex]
Angles, angles everywhere! Big ones, little ones, right
ones too! But this angle is something new. It has two
rays that meet at a vertex, and it measures 180
degrees. How complex! What angle am I? Draw me.
Answers
Answer:
Straight angle
<----------------------------->
You can determine if an angle is a straight angle only if it is 180 degrees. You can also draw it by drawing a straight line and drawing an arrow facing outward at each end.
Emma and Clair are planning to sell lemonade on their street. They have two recipes to choose from. Emma’s recipe calls for the juice of 5 lemons and 2 cups of water. Clair’s recipe calls for the juice of 2 lemons and 1 cup of water. Why will the first recipe taste more “lemony”?
Answers
Answer:
Emma's recipe will be more lemony because
5/2=2.5
2/1=2
Step-by-step explanation:
Answer:
The ratio of lemon juice to water in Emma’s recipe is 5 to 2; the ratio in Clair’s recipe is 4 to 2. Emma’s recipe will taste more lemony because it has a greater ratio of lemon juice to water.
Step-by-step explanation:
Sample Answer
The probability of a student passing
an examination is 2/3
If the student
takes three examination, what is the
Probability that he will not
pass
any of them.
Answers
===============================================
Explanation:
2/3 is the probability of passing a test, so 1/3 is the probability of failing
Note how 2/3 and 1/3 add to 3/3 = 1 to represent 100%
The probability of failing 3 tests in a row is (1/3)^3 = (1/3)*(1/3)*(1/3) = 1/27 assuming each test event is independent from one another.
-------
Side note: the probability of passing at least one test is 1-1/27 = 26/27 and the probability of passing all three tests in a row is (2/3)^3 = 8/27