For the given distributions, we have that:
a) The traditional course has a range of 29.8, while the flipped course has a range of 28.2. Thus the traditional course is more dispersed using the range.
b) The traditional course has a standard deviation of 8.67, while the flipped course has a standard deviation of 7.63. Thus the traditional course is also more dispersed using the standard deviation.
What is the range of a distribution?
The range of a distribution is given by the difference between the greatest value and the smallest value.
Hence, for the Traditional classroom, the range is given by:
86.4 - 56.6 = 29.8.
For the Flipped classroom, the range is given by:
92.6 - 64.4 = 28.2.
Hence:
The traditional course has a range of 29.8, while the flipped course has a range of 28.2. Thus the traditional course is more dispersed using the range.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.Using a calculator, following the described procedure, the standard deviations are given as follows:
Traditional: 8.67.Flipped: 7.63.Hence:
The traditional course has a standard deviation of 8.67, while the flipped course has a standard deviation of 7.63. Thus the traditional course is also more dispersed using the standard deviation.
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You have 2 positive numbers. One number is one-fifth of the other number. The difference between the two numbers is 308, find the numbers. PLEASE HELP
Answer:
[tex]77, 385[/tex]
Step-by-step explanation:
Start by writing the equations in symbolic form. I will represent one number with an x and the other with a y.
One number is one-fifth of the other number:
[tex]x=\frac{1}{5}y[/tex]
The difference between the two numbers is 308:
[tex]y-x=308[/tex]
This difference is positive, therefore I am assuming that y is the larger number. In the first equation, I made x a part of y, so this should check out.
Now we have a system of equations:
[tex]\left \{ {{x=\frac{1}{5}y } \atop {y-x=308}} \right.[/tex]
I will rewrite the first equation for simplicity:
[tex]5x=y[/tex]
Now, I will substitute y from the first equation for y in the second equation:
[tex]5x-x=308[/tex]
Simplify:
[tex]4x=308\\x=77[/tex]
Now, use x to find y using the second equation:
[tex]y-77=308\\y=385[/tex]
Now, I can check the solutions by plugging them into the first equation!
[tex]x=\frac{1}{5}y\\ 77=\frac{1}{5}(385)\\77=77[/tex]
The solution is correct!
Graduation gift of $5,000 image that you are able to average 2.5% interest on the principal.
1. How much (simple) interest will you receive on your savings after one year?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (5000)(0.025)(1) \implies I = 125[/tex]
George mixes 1/4  cup of sugar with 1/8 cup of honey. Give the ratio of sugar to one cup of honey as a unit rate.
Find the slope of the lined graph
The slope of the lined graph is 5 / 3
How to determine the slope
The formula for determining the slope of a line is expressed as;
Slope = y2 - y1/ x2 - x1
From the graph shown;
y1 = -1y2 = 4x2 = 3x1 = 0Now, let's substitute the values
Slope, m = 4 - (-1) / 3 - 0
Find the differences
Slope, m = 4 + 1/ 3
Slope, m = 5 / 3
Thus, the slope of the lined graph is 5 / 3
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Evaluate the algebraic expression for the given value of the variable.
2x² - 5x; x = -6
The value is 102.
Here the expression is 2x² - 5x.
We have to find the value of the algebraic expression for x = -6.
Expression = 2x² - 5x
Now put the value of x = -6 in the expression, we get
2x² - 5x = 2(-6)² - 5(-6)
= 2×36 + 30
= 72 + 30
= 102
Therefore the value of an algebraic expression is 102.
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Which relation is a function?
Reason:
It is impossible to pass a single vertical line through more than one point on the graph. This relation passes the vertical line test.
The other graphs fail the vertical line test. For instance, in the upper right corner we have a vertical line through x = -1 which passes through more than one point. The input x = -1 leads to multiple outputs y = -1 and y = 3 at the same time.
A function is only possible when each input leads to exactly one output.
(9x+5) + (5x+9) in simplest term
Answer:
14x+14
Step-by-step explanation:
9x+5+5x+9
=9x+5+5x+9
=(9x+5x)+(5+9)
=14x+14
3 in
4 in
2 in What is the area of the shape?
Analyze the diagram below and complete the instructions that follow.
Applying the triangle proportionality theorem, the value of x and the value of y are:
C. y = 5, x = 10.
How to Apply the Triangle Proportionality Theorem?Since lines m and n are said to be parallel lines, therefore, according to the triangle proportionality theorem, the ratios below can be created.
4/12 = y/15 [proportional sides]
Cross multiply
(y)(12) = (4)(15)
12y = 60
Divide both sides by 12
12y/12 = 60/12
y = 5
x = 15 - y
Plug in the value of y
x = 15 - 5
x = 10
Thus, applying the triangle proportionality theorem, the value of x and the value of y are:
C. y = 5, x = 10.
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Round 40,313.04348 to the nearest hundredth.
Answer:
124.59
Step-by-step explanation:
Answer:
the answer would be 20,313,04
Step-by-step explanation:
last place = 8 rounds up makes the thousandth place 5 which rounds up and makes the hundreth place 0 which doesnt change tyhe 4 giving us our aanswer. PLEASE MARK BRAINLIEST.
The castle tower has a height of 14 m. Work out the height of the tree.
Because the height are in proportion, a possible value of the height of the tree is 70 m
How to determine the possible height of the tree?The complete question is added as an attachment
The given parameters from the question are given as:
Height of the castle tower = 14 metersHeight of the tree = unknownIn the above expression, we have the following observations:
The heights are not equalThe heights are in proportionFrom the figure, we can see that the height of the tree is about 5 times the height of the castle tower
This is represented as
Height of the tree = k * Height of the castle tower
Where
Scale factor, k = 5
Substitute the known values in the above equation
So, we have
Height of the tree = 5 * 14 m
Evaluate the products
So, we have
Height of the tree = 70 m
Hence, the possible height of the tree is 70 m
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Answer:
Step-by-step explanation:
Suppose that 23 of work is needed to stretch a spring from its natural length of 30 cm to a length of 44 cm.
(a) How much work is needed to stretch the spring from 34 cm to 36 cm? (Round your answer to two decimal places.)
(b) How far beyond its natural lehgth will a force of 45 N keep the spring stretched? (Round your answer one decimal place.)
cm
Need Help
a) The work done is 3.3 J
b) The new force would stretch it 1.9 cm beyond its natural length.
What is Hooke's law?Hooke's law states that, the force of elasticity that tends to stretch a spring is directly proportional to the extension that is caused by the force as long as we do not by any means exceed the elastic limit of the material. This implies that the Hooke's law can only be found to hold when the elastic limit of the material has not been exceeded and the material has not become plastic.
Now;
F = Ke
W =1/2 Fe
F = 2W/e
W = work done
F = force exerted
e = extension
F = 2 * 23 /(44 - 30) * 10^-2
F = 328.6 N
a) To stretch 34 cm to 36 cm;
W = 1/2 * 328.6 N * 2 * 10^-2
W = 3.3 J
The work done is 3.3 J
b) F = Ke
328.6 N/(44 - 30) * 10^-2 = K
K = 2347 N/m
Then;
45 N = 2347 N/m * e
e = 45 N/ 2347 N/m
e = 0.019 m or 1.9 cm
New length = 30 cm + 1.9 cm = 31.9 cm
The new force would stretch it to a distance of 31.9 cm or 1.9 cm beyond its natural length.
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Calculus 1 Question.
Answer: B
Step-by-step explanation:
f(2) = 2, and is defined/exists. Holes (and asymptotes) like the hole at (2, -2) ruins continuity. The limit exists, but is not equal to f(2) which is why continuity is ruined at x=2
Answer: B
Step-by-step explanation:
f(2) = 2 and exists/is defined Holes (and asymptotes) such as the one at (2, -2) destroy continuity. The limit exists, but it is not equal to f(2), hence continuity is broken at x=2.
Divide the polynomials.
Your answer should be a polynomial.
x²-16
/
x+4
Answer:
x - 4
Step-by-step explanation:
The quickest way to do this is to Factor and "cancel". (Cancelling is not a mathematical term--it really is dividing)
x^2 - 16 is the difference of two squares. Its super-beneficial to recognize a difference of two squares and its factored form:
(x - 4)(x + 4)
Now you have:
(x - 4 )(x + 4) / x+4
The x+4 term "cancels" and you end up with x-4 as your answer.
You could also do this division problem using long division or synthetic division. You will get the same answer.
Write 98 as the product of prime factors. Write the prime factors in ascending order.
Step-by-step explanation:
2 × 7 × 7.................
70 POINTS Find the slope of the line pictured in the graph
-2
2
-1/2
1/2
The slope of the line passing through the coordinates (0, 0) and (6, 3) is 1/2
Slope of a lineThe formula for calculating the slope of a line is expressed according to the equations:
Slope = y₂-y₁/x₂-x₁
Using the coordinate points (0, 0) and (6, 3) on the line. On substituting, we will have;
Slope = 3-0/6-0
Slope = 3/6
Simplify
Slope =1/2
Hence the slope of the line passing through the coordinates (0, 0) and (6, 3) is 1/2
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please help me to understand thid Q
Answer:
True statements are 4 and 5
Step-by-step explanation:
This s basically using set theory to evaluate line segments
The union of two(or more) sets is the set of elements that are in either or both sets.
Here is an example
If set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6} then
A ∪ B = (1, 2, 3, 4, 5, 6}
Note that there cannot be any duplicates in a set
We have to treat the line segments as sets to solve this problem.
For easier explanation, I am going to view each segment as having points which I am labeling 1, 2, 3 etc.
The individual independent line segments are JL, LM, MN, and NT, basically each is a set of the points that comprise each segment
You have to visualize each of these line segments as being comprised of these points.
Note that these are distinct sets ie there is no common point when we consider the above 4 sets
Let set
JL have the points {1, 2, 3} we say JL = {1, 2, 3}
LM = {4, 5}
MN = {6, 7}
NT = {8, 9}
We see that there are no common points between each of the four sets below
1. JL ∪ MN = set of points that lie in JL or MN or both. Since JL and MN are distinct sets, the union of these two sets is s
JL U MN = {1, 2, 3} U {5, 6} = {1, 2, 3, 5, 6} . However, JM contains all the points from J to M which is {1, 2, 3, 4, 5} which is not the same as JL U MN
So Statement 1 is false
2. JL U MN = {1, 2, 3} U {6, 7} = {1, 2, 3, 6, 7} so it contains more points than MN{6, 7} and therefore Statement 2 is false
3. LM U LN
We can see that LN contains all the points in LM and MN = {4, 5, 6, 7}. LM U LN = {4, 5} U { 4, 5, 6, 7} = {4, 5, 6, 7}. But LM is only a subset of LN and has fewer points {4, 5} so Statement 3 is false
4. LM U LN
LM = {4, 5}, LN = {4, 5, 6, 7} so LM U LN = {4, 5, 6, 7} = LN. Remember sets don't duplicate. So Statement 4 is True
5. NT U JT
NT = {8, 9} and JT = set of all points in the segment from J to T which is all the points. So JT = {1, 2, 3, 4, 5, 6, 7, 8, 9} and NT U JT = {1, 2, 3, 4, 5, 6, 7, 8, 9} which is the set of all points in JT. Therefore Statement 5 is True
The figure below shows a graphical representation of what I wrote above. If you look at LN for instance, it has 4 points {4, 5, 6, 7} and therefore represents all the points in LM and LN (without duplication of points). This is Statement 4, by the way
The data represent the number of ounces of water that 26 students drank before donating blood: 8 8, 8, 16,16, 16, 32, 32, 32, 32, 32, 32 64 64, 64, 64, 64, 64, 64, 80 80, 80, 80, 88, 88, 88.
a. Create a dot plot for the data.
b. Create a box plot for the data.
c. What information about the data is provided by the box plot that is not provided by the dot plot?
d. What information about the data is provided by the dot plot that is not provided by the box plot?
e. It was recommended that students drink 48 or more ounces of water. How could you use a histogram to easily display the number of students who drank the recommended amount?
Answer: All the answers you need are attached in the file.
Step-by-step explanation: Hope it helps!
Paula knit knot hats. The number of hats h she can knit varies directly with the amount of yarn y in yards she has. The constant of proportionality is 42. Interpret the meaning of the point (378,9)
The meaning of the point (378,9) is with 9 yards of yarn, Paula can knit 378 knot hats.
Given that:-
The number of hats h she can knit varies directly with the amount of yarn y in yards she has.
Also, the constant of proportionality is 42.
Hence, we can write,
h ∝ y
h = ky
where, k is the constant of proportionality, hence,
h = 42y
We have to interpret the meaning of (378, 9).
From, the equation, h = 42y
We can observe that,
When y = 9
h = 42*9 = 378.
Hence, we can write that, the meaning of the point (378,9) is with 9 yards of yarn, Paula can knit 378 knot hats.
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How Much Money Did The Movie Theater Get? PLS ANSWER FAST I GIVE BRAINLIEST
Movie a costs 4 dollars
Movie b costs 5 dollars
Movie theater got 200 dollars and sold 47 ticket
How many tickets did movie a sell
Solving a system of equations, we conclude that 35 tickets for movie a were sold
How many tickets did movie a sell?
Let's define the variables:
x = tickets of movie a sold.y = tickets of movie b sold.Here we know that a total of 47 tickets were sold, then:
x + y = 47
And they sold for a total of $200, then:
x*$4 + y*$5 = $200
So we have a system of equations:
x + y = 47
x*$4 + y*$5 = $200
We want to solve this for x, then we need to isolate the variable y in one of the equations, doing that in the first one we get:
y = 47 - x
Now we can replace that in the other equation to get:
x*$4 + (47 - x)*$5 = $200
x*$4 + $235 - x*$5 = $200
$235 - x*$1 = $200
$235 - $200 = x*$1
$35 = x*$1
$35/$1 = x = 35
This means that 35 tickets for the movie a were sold.
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The figure on the right is a scaled copy of the figure on the left.
Answer:
Yes si true
Step-by-step explanation:
If you analyze the figures you will realize that they are the same, the size differentiates it but they have the same angles.
Question 1 (1 point)
A triangle with the coordinates listed below is reflected across the x-axis. What are
the new coordinates?
A(5,-2) B(0, 3) C(-4,1)
A(5,-2) B(0, -3) C(-4,1)
A'(5, 2) B'(0, -3) C'(-4,-1)
A(-5, -2) B(0, 3) C(4, 1)
A(-5, 2) B(0, -3) C(4, -1).
The reflection of the triangle gives the co-ordinates A'(5, 2) B'(0, -3) C'(-4,-1) .
In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a set of fixed points known as the hyperplane; this set is also known as plane of reflection or the axis. The mirror image of a figure in the axis or plane of reflection is the image produced by a reflection.
When an object is reflected across the x -axis , the image will be at same distance from the x axis as the object or point is on the cartesian plane.
So if a point P has the co-ordinates (x , y) . When reflected across the x-axis the the reflection has the co-ordinates P'(x , -y ) .
The co-ordinates of the 3 points are A(5,-2) B(0, 3) C(-4,1).
When reflected across the x-axis the co-ordinates become :
A(5,-2) →A'(5,2)
B(0, 3)→B'(0,-3)
C(-4,1)→C'(-4,-1)
Hence the second option is correct, the reflected image of the triangle has the coordinates A'(5, 2) B'(0, -3) C'(-4,-1) .
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What integer would be added to 15 to result in a sum of zero
Answer:
0+15 =15
Step-by-step explanation:
it is said that the sum should have a 0
The point (-2,8) is on the graph of y=f (x), which point must be on the graph of y=-f(x)
The point on the graph y = -f(x) is (-2 , -8)
According to the question the coordinates we have been given is (-2 , 8) and it is on the graph y = f(x)
That is we have been given that
f(-2) = 8 (1)
Now we have to find the point on the graph y = -f(x)
So we will choose the value of x = -2 in f(x)
Thus, putting the required value we get
y = - f(-2)
As the value of f(-2) is 8 from equation (1). we will equate the value in the above equation we get
y = -(8)
y = -8
Hence the point on the graph is (-2 , -8)
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An article is marked at $30 but sold for $36.
(a) Is this a discount or a sale mark-up?
(b) What percentage difference does someone pay?
Which function is positive for the entire interval [–3, –2]? On a coordinate plane, a curved line with a minimum value of (0, negative 3) crosses the x-axis at (negative 3, 0) and (3, 0), and crosses the y-axis at (0, negative 3). On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5). On a coordinate plane, a curved line with a minimum value of (2, 4) and a maximum value of (0.5, 6), crosses the x-axis at (negative 1.5, 0) and crosses the y-axis at (0, 5). On a coordinate plane, a curved line with a minimum value of (negative 1.75, negative 3.9) and a maximum value of (0, 2), crosses the x-axis at (negative 2.2, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).
The function that is positive for the entire interval [-3,-2] is given by:
On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).
When a function is positive and when it is negative?We have to look at the graph of the function relative to the x-axis, as follows:
A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.The graphs for this function are given at the end of the answer, and the only function for which it is positive, that is, above the x-axis, in the entire interval [-3,-2] is the second, hence the correct option is:
On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).
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If Zendaya travels $5 and 3/7 of a mile in 3 hours on her roller skates. How far will she
travel in 1 hour?
1 and 17/21 miles per hour
7/114 miles per hour
114/7 miles per hour
16 and 2/7 miles per hour
Zendaya will travel $ 1 and 17/21 of a mile per hour on her roller skates.
Zendaya travels $5 and 3/7 of a mile in 3 hours on her roller skates. We can simply write this statement in mathematical form as,
Total distance covered by Zendaya in 3 hours on her roller skates = $( 5 + ( 3/7 ) of a mile
Total distance covered by Zendaya in 3 hours on her roller skates = $ ( ( 35 + 3)/7 ) of a mile
Total distance covered by Zendaya in 3 hours on her roller skates = $ ( 38/7 )
Total distance covered by Zendaya in 1 hours on her roller skates = $ (( 38/7 )/3 ) = $ (38/21) of a mile
or we can write also write ( 38 /21 ) miles per hour as ( 1 and 17/21 ) miles per hour.
So, Zendaya will travel $ 1 and 17/21 of a mile per hour on her roller skates.
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Subtract using the number line.
−23−(−113)
A number line ranging from negative three to three with an arrow on both ends and tick marks every one third
−123
negative 1 and 2 over 3
−23
negative 2 over 3
−13
negative 1 third
23
The evaluation of the subtraction operation using the number line is 2/3. The correct option is the last option 2/3
Subtracting using the number lineFrom the question, we are to evaluate the subtraction operation using the number line
From the number line we can observe that the magnitude of the distance between two successive mark is 1/3
Now, we are subtract
-2/3 - (-1 1/3)
If we count from - 1 1/3 to -2/3, we will observe that there are two marks.
Thus,
1/3 + 1/3 = 2/3
Hence, the evaluation of the subtraction operation using the number line is 2/3. The correct option is the last option 2/3
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Learn more on
2.
Four of the 5 hot dogs that Janet bought at the fair in her
last 5 visits were delicious. What percent of the hot dogs
that she bought were just to her liking?
Answer:
80 percent
Step-by-step explanation:
4/5 = 80 percent (4/5 = .8, .8*100= 80)
Find the distance between points A = (2, 0) and
B= (0, 9). Round your answer to the nearest tenth.
Show your work
Answer:
9.2
Step-by-step explanation:
You want the distance between A(2, 0) and B(0, 9).
DistanceThe distance formula is based on the Pythagorean theorem. It tells you the distance between (x1, y1) and (x2, y2) is ...
d = √((x2 -x1)² +(y2 -y1)²)
For the given points, this becomes ...
d = √((0 -2)² +(9 -0)²) = √(4+81) = √85
d ≈ 9.2
The distance between A and B is about 9.2 units.