Here is the correct interpretation of the question with the help of the text editor tool.
Use a parameterization to find the flux [tex]\int\limits \int\limits_s \ F. \ n \ d \sigma[/tex] of F = z²i + xj - 2zk in the outward direction
(normal away from the x-axis) across the surface cut from the parabolic cylinder z = 16 -y² by the planes x = 0 , x = 1, and z = 0 .
The flux is .
Answer:
[tex]-\frac{512}{3}[/tex]
Step-by-step explanation:
F(x,y,z) = (z² ,x , - 2z)
To find the flux across a surface : [tex]\int\limits \int\limits_s \ F. \ n \ dS = \int\limits \int\limits_D \ F. (r_u * r_v) \ dA[/tex]
The sphere z is given as = 16 -y², above x = 0 , x= 1, and z = 0
When z = 0 ⇒ 16 - y² = 0
⇒ y = ± 4
The parameterization is y=v⇒z= 16 -v² and x= u
⇒ r = (x,y, z) = ( u,v,16 - v²)
with 0 ≤ u ≤ 1 and -4 ≤ v ≤ 4
However the normal vector can now be determined as :
[tex]r_u = (1,0,0) , \ \ \ r_v = (0,1, - 2v)[/tex]
[tex]n = r_u*r_v = \left[\begin{array}{ccc}i&j&k\\1&0&0\\0&1&-2v\end{array}\right] = (0,2v,1)[/tex]
[tex]\int\limits \int\limits_s \ F. \ n \ dS = \int\limits \int\limits_D \ F. (r(u,v)) .(r_u*r_v)dA[/tex]
[tex]=\int\limits^1_0 \int\limits^4_{-4} [(16-v^2)^2 , u , -2 (16-v^2)](0,2v,1)dvdu[/tex]
[tex]=\int\limits^1_0 \int\limits^4_{-4} [2uv-2(16-v^2))dvdu[/tex]
[tex]=\int\limits^1_0 (uv^2 -32v+ \frac{2v^3}{3})^ ^4}__{-4}} du[/tex]
[tex]=\int\limits^1_0 (u(16-16)-32(8)+\frac{2}{3}(128))du[/tex]
[tex]= \int\limits^1_0 (-\frac{512}{3})du[/tex]
[tex]= - \frac{512}{3}(u)^ ^1}__0[/tex]
= [tex]-\frac{512}{3}[/tex]
The flux of a vector field across a surface is calculated by computing the surface integral of the vector field in the direction normal to the surface. This involves parametrizing the surface and taking antiderivatives based on the defined area. The direction of the flux is crucial as it determines the sign of the flux.
Explanation:To find the flux of the vector field upper Case Bold F across a surface, we need to compute the surface integral of upper Case Bold F in the given direction. For the given problem, the surface is defined by the parabolic cylinder z = 1 - y^2 and the planes x = 0, x = 1, z = 0. We parametrize this surface using two parameters x and y, with x ranging from 0 to 1, and y ranging from -1 to 1.
We then compute the surface integral by taking the antiderivative of the defined area with the boundaries of surface as the integral's bounds. This process might involve computation of multiple integrals if the surface is composed of multiple parts.
Note that the direction of the flux, which is normal away from the x-axis, is important for the calculation, as it determines the sign of the flux. The flux is positive if the angle between the vector field and the outward normal to the surface is less than 90 degrees, and negative otherwise.
Learn more about Flux Calculation here:https://brainly.com/question/32232670
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What is the solution to the inequality -4x < 8?
x < -2
x > -2
x < -24
x > -24
Answer:
x > -2
Step-by-step explanation:
-4x < 8
-8 < 4x
-2 < x
x > -2
Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 17 feet by 17 feet by 2 inches for a patio if the concrete costs $64.00 per cubic yard?
Answer:
$114.17
Step-by-step explanation:
First we need to convert cubic yard to cubic feet.
One yard is equivalent to three feet, so one cubic yard is 3^3 = 27 cubic feet.
So the cost of one cubic feet is 64/27 = $2.3704
We also need to convert from inches to feet.
One inch is 1/12 feet, so 2 inches is 2/12 = 1/6 feet
Now we need to find the volume of the slab:
Volume = 17 * 17 * (1/6) = 48.1667 ft3
Now, to find the cost, we can use a rule of three:
1 cubic feet -> $2.3704
48.1667 cubic feet -> X
X = 48.1667 * 2.3704 = $114.1743
Can anybody find the measure of arc KL and arc JK?
click on image for full picture
Answer:
Arc KL = 30°
Arc JK = 90°
Step-by-step explanation:
Arc KL is a connected to a central angle with the measurement of 30°. Because it is a central angle, the arc's measurement will be the same as the central angle's measurement:
Arc KL = 30°
Arc JK is connected to a central angle that has a right angle measurement sign. A right angle = 90°. Because it is a central angle, the arc's measurement will be the same as the central angle's measurement:
Arc JK = 90°
~
Answer:
arc kl= 30
arc jk=90
Step-by-step explanation:
HELP 100 POINTS GIVEN 1. An inground non-diving swimming pool has the following dimensions. It is 33 feet long and 14 feet wide. On the
shallow end, it is 3 feet 6 inches deep and slopes gradually to a depth of 5 feet 4 inches. A picture is below. What
shape(s) can be used to estimate the volume of the pool.
2. What volume formula(s) will be used for the shape listed in
number 1
3. The pool has dimensions that are in both feet and inches. Perform unit conversions on this step
4. Apply the dimensions from number 3 to the formula(s) listed in number 1 and calculate the approximate volume of
the pool.
5. Write the answer from number 4 in scientific notation. It can be approximated.
Answer:
14inches farenheight
Step-by-step explanation:
Answer:
14 inches farenheit
Step-by-step explanation:
Please help for both of them
Answer:
18 is for the top
6 is for the bottom
Answer:
1. C
2. D
Step-by-step explanation:
On a game show, a contestant randomly chooses a chip from a bag that contains numbers and strikes. The theoretical probability of choosing a strike is 1/8. The bag contains 7 strikes. How many chips are in the bag?
Answer:
Let x be the number of chips.
\frac{8}{x}=\frac{1}{5}
x = 40
The answer is: There are 40 chips in
Quadratic formula what is the expression for discriminant
Answer:
b^2-4ac
Step-by-step explanation:
By looking at that part after substituting and calculating, you can tell these things about the solution
find the x and the area of the shape perimeter is 64.5
Answer:
x=8
A = 192
Step-by-step explanation:
The perimeter is the sum of the outer lengths
17.9 + 22.6 + 3x = 64.5
Combine like terms
40.5 +3x = 64.5
Subtract 40.5 from each side
40.5 +3x -40.5 = 64.5 - 40.5
3x =24
Divide each side by 3
3x/3 = 24/3
x = 8
The area of a triangle is given by
A = 1/2 bh
The base is 3x = 3(8) =24
and the height is 2x = 2(8) =16
A = 1/2 (24) * 16
A =192
Find the surface area of this triangular prism.
Your answer would be 900m².
We can find this by finding the area of each of the shapes that make up the surface of this prism.
First there is the bottom of the prism, which would be 11 × 24 = 264m².
Then you have the two triangles on the sides of the prism, which are both (10 × 24)/2 each, which equals 120m² for each triangle. This means that the area for both triangles is 120 × 2 = 240m².
Next we have the area of the back of the prism, which is 11 × 10 = 110m².
Finally we need to find the area of the rectangle on top of the prism, which is 11 × 26 = 286m²
This means your final answer would be the sum of all of these, which is 264 + 240 + 110 + 286 = 900m².
I hope this helps!
Sandy plays tennis once every 6 six days. Jim plays once every 8 eight days. If they both played tennis today, in how many days will they play on the same day again?
Answer: 24 days
Step-by-step explanation:
Sandy plays tennis once every 6 six days while Jim plays tennis once every 8 eight days.
To get the number of days they will play on the same day again, we find the lowest common multiple for the numbers.
The lowest common multiple is the smallest positive integer which is evenly divisible by both 6 and 8.
6 = 6, 12, 24, 30
8 = 8, 16, 24, 32
The lowest common multiple is 24.
In 24 days, they will play on the same day again
Two sides of a rectangular fence are 5 5/8 feet long.The other two sides are 6 1/4 feet long.What is the perimeter?
Answer:
im not sure
Step-by-step explanation:
so sorry i didnt know the answer.
Answer:
the perimeter of the rectangle is 23.75 feet.
Step-by-step explanation:
5 5/8 × 2 = 11 1/4.
6 1/4 × 2 = 12 1/2
11 1/4 + 12 1/2 = 23 3/4 or 23.75
An artist is creating a sculpture where a globe with a diameter of 48 inches sits in a cone like a scoop of ice cream. She wants the cone of her sculpture to be geometrically similar to an actual ice cream cone that has a diameter of 2 1/2 inches and a height of 6 inches. What should be the height of the cone in the artist’s sculpture?
We have been an artist is creating a sculpture where a globe with a diameter of 48 inches sits in a cone like a scoop of ice cream. She wants the cone of her sculpture to be geometrically similar to an actual ice cream cone that has a diameter of 2 1/2 inches and a height of 6 inches.
We will use proportions to solve our given problem.
[tex]2\frac{1}{2}=2.5[/tex]
[tex]\frac{\text{Height of sculpture}}{\text{Diameter of sculpture}}=\frac{\text{Height of cone}}{\text{Diameter of cone}}[/tex]
[tex]\frac{\text{Height of sculpture}}{48}=\frac{6}{2.5}[/tex]
[tex]\frac{\text{Height of sculpture}}{48}\cdot 48=\frac{6}{2.5}\cdot 48[/tex]
[tex]\text{Height of sculpture}=6\cdot 19.2[/tex]
[tex]\text{Height of sculpture}=115.2[/tex]
Therefore, the height of the sculpture should be 115.2 inches.
Answer:
115 1/5
Step-by-step explanation:
This is 100% the answer because I took a test with this question and that was the correct answer
Please mark as brainliest :)~
what is p if 7/p = 3/10
Answer:
23 1/3 or 70/3 =p
Step-by-step explanation:
7/p = 3/10
Using cross products
7*10 = 3p
70 = 3p
Divide each side by 3
70/3 = 3p/3
70/3 =p
or as a mixed number
23 1/3 =p
The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of the total surface area to the lateral (curved) surface area of the cylinder?
Let r represent the radius of cylinder.
We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be [tex]1.5r[/tex].
We will use lateral surface area of pyramid to solve our given problem.
[tex]LSA=2\pi r h[/tex], where,
LSA = Lateral surface area of pyramid,
r = Radius,
h = height.
Upon substituting our given values in above formula, we will get:
[tex]LSA=2\pi r\cdot (1.5)r[/tex]
Now we will find the total surface area of cylinder.
[tex]TSA=2\pi r(r+h)[/tex]
[tex]TSA=2\pi r(r+1.5r)[/tex]
[tex]TSA=2\pi r(2.5r)[/tex]
[tex]\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}[/tex]
[tex]\frac{TSA}{LSA}=\frac{2.5r}{1.5r}[/tex]
[tex]\frac{TSA}{LSA}=\frac{25}{15}[/tex]
[tex]\frac{TSA}{LSA}=\frac{5}{3}[/tex]
Therefore, the ratio of total surface area to lateral surface area is [tex]5:3[/tex].
The formula in cell B1 is =A$2. Autofill is used by dragging B1's autofill box across to C1, D1, and E1. What formulas will appear in C1, D1, and E1, respectively?
Answer:
=A$2, =A$2, =A$2
Step-by-step explanation:
Autofill is used in excel to fill a series of cells automatically. If the formula in cell B1 is =A$2. On using autofill by dragging B1's autofill box across to C1, D1, and E1, =A$2, =A$2, =A$2 appear in C1, D1, and E1, respectively. Excel tries to guess and insert next values on the basis of selected data.
Answer:
Step-by-step explanation:
A$2 A$3 A$4
Simplify the expression.
100^(1/2)-125^(1/3)
PLEASE HELP OFFERING 24 POINTS
you invest 3200 in an account that pays an interest rate of 7.25% compounded continuosly
Kayla hit 4 homeruns at batting practice
out of 12 pitches thrown. What is the
experimental probability that Kayla will hit a
homerun at batting practice?
Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given,
Total number of trial = 12
Total number of favorable event = 4
Experimental probability of hitting home run is
[tex]P(home\ run)=\dfrac{Favorable\ event}{Total\ trial}[/tex]
[tex]P(home\ run)=\dfrac{4}{12}[/tex]
[tex]P(home\ run)=\dfrac{1}{3}[/tex]
Answer:1/3
Step-by-step explanation:Answer:
Step-by-step explanation:
Given,
Total number of trial = 12
Total number of favorable event = 4
Experimental probability of hitting home run is
Helllllllppppp ....,.:,:::;;,:()$?;;:/&//&
Answer:
The answer is 41>6t+7
Step-by-step explanation:
It said that he wants to earn "more than" $41 so the inequality sign is more than. Then it says $6 per hour so 6t. Then you add $7
Easy Question means Easy points
Topic: Volume
Focus on Scenario 2
Answer:
20,000 cm³
Step-by-step explanation:
The shape is a triangular prism
Base area × height
½ × 20 × 25 × 80
20,000 cm³
Answer:
20,000 cm³
Reason Why I know is because I had to do this very same thing :P
my equation is f(x)= x^2-16x-100 and i am using the complete the box method im really stuck
Answer:
x2-16x+100=0
Two solutions were found :
x =(16-√-144)/2=8-6i= 8.0000-6.0000i
x =(16+√-144)/2=8+6i= 8.0000+6.0000i
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-16x+100
The first term is, x2 its coefficient is 1 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is +100
Step-1 : Multiply the coefficient of the first term by the constant 1 • 100 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is -16 .
-100 + -1 = -101
-50 + -2 = -52
-25 + -4 = -29
-20 + -5 = -25
-10 + -10 = -20
-5 + -20 = -25
For tidiness, printing of 12 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 16x + 100 = 0
Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2-16x+100
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 8.0000
Plugging into the parabola formula 8.0000 for x we can calculate the y -coordinate :
y = 1.0 * 8.00 * 8.00 - 16.0 * 8.00 + 100.0
or y = 36.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-16x+100
Axis of Symmetry (dashed) {x}={ 8.00}
Vertex at {x,y} = { 8.00,36.00}
Function has no real roots
Solve Quadratic Equation by Completing The Square
2.2 Solving x2-16x+100 = 0 by Completing The Square .
Subtract 100 from both side of the equation :
x2-16x = -100
Now the clever bit: Take the coefficient of x , which is 16 , divide by two, giving 8 , and finally square it giving 64
Add 64 to both sides of the equation :
On the right hand side we have :
-100 + 64 or, (-100/1)+(64/1)
The common denominator of the two fractions is 1 Adding (-100/1)+(64/1) gives -36/1
So adding to both sides we finally get :
x2-16x+64 = -36
Adding 64 has completed the left hand side into a perfect square :
x2-16x+64 =
(x-8) • (x-8) =
(x-8)2
Things which are equal to the same thing are also equal to one another. Since
x2-16x+64 = -36 and
x2-16x+64 = (x-8)2
then, according to the law of transitivity,
(x-8)2 = -36
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-8)2 is
(x-8)2/2 =
(x-8)1 =
x-8
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-8 = √ -36
Add 8 to both sides to obtain:
x = 8 + √ -36
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Since a square root has two values, one positive and the other negative
x2 - 16x + 100 = 0
has two solutions:
x = 8 + √ 36 • i
or
x = 8 - √ 36 • i
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-16x+100 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -16
C = 100
Accordingly, B2 - 4AC =
256 - 400 =
-144
Applying the quadratic formula :
16 ± √ -144
x = ——————
2
In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written (a+b*i)
Both i and -i are the square roots of minus 1
Accordingly,√ -144 =
√ 144 • (-1) =
√ 144 • √ -1 =
± √ 144 • i
Can √ 144 be simplified ?
Yes! The prime factorization of 144 is
2•2•2•2•3•3
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 144 = √ 2•2•2•2•3•3 =2•2•3•√ 1 =
± 12 • √ 1 =
± 12
So now we are looking at:
x = ( 16 ± 12i ) / 2
Two imaginary solutions :
x =(16+√-144)/2=8+6i= 8.0000+6.0000i
or:
x =(16-√-144)/2=8-6i= 8.0000-6.0000i
Two solutions were found :
x =(16-√-144)/2=8-6i= 8.0000-6.0000i
x =(16+√-144)/2=8+6i= 8.0000+6.0000i
Step-by-step explanation:
which prism has a greater volume prism a has 17 more cubic units of volume than prism B prism B has 3 more cubic units of volume than prism a prism B has 8 more cubic units of volume than prism a
Answer:
B
Step-by-step explanation:
I also took a test
The correct answer is that neither prism has a greater volume they must have the same volume.
Let denote the volume of prism A as [tex]\( V_A \)[/tex] and the volume of prism B as [tex]\( V_B \).[/tex] According to the problem statement, we have the following relationships:
1. Prism A has 17 more cubic units of volume than prism B:
[tex]\[ V_A = V_B + 17 \][/tex]
2. Prism B has 3 more cubic units of volume than prism A:
[tex]\[ V_B = V_A + 3 \][/tex]
3. Prism B has 8 more cubic units of volume than prism A:
[tex]\[ V_B = V_A + 8 \][/tex]
However there is a contradiction in the last two statements. Prism B cannot have both 3 more cubic units and 8 more cubic units than prism A. This suggests there might be a typographical error in the problem statement.
Assuming there is a mistake and we only consider the first two statements, we can solve for the volumes by setting the two equations equal to each other since both right-hand sides are equal to [tex]\( V_B \):[/tex]
[tex]\[ V_B + 17 = V_A + 3 \][/tex]
Now, we can solve for [tex]\( V_A \)[/tex]in terms of[tex]\( V_B \)[/tex] using the first equation:
[tex]\[ V_A = V_B + 17 \][/tex]
Substitute \( V_A \) into the second equation:
[tex]\[ V_B = (V_B + 17) + 3 \][/tex]
Simplify the equation
[tex]\[ V_B = V_B + 20 \][/tex]
This simplifies to:
[tex]\[ 0 = 20 \][/tex]
This is not possible, which means our initial assumption that the two statements could be true simultaneously is incorrect. The only logical conclusion, given the contradictory information, is that neither prism has a greater volume; they must have the same volume. This is the only way to satisfy the condition that each prism has more volume than the other by different amounts.
Therefore, the volumes of prism A and prism B are equal:
[tex]\[ V_A = V_B \][/tex]
This resolves the contradiction in the problem statement. The volumes of the two prisms must be the same for the given conditions to hold true.
Which graph shows a quadratic function with a discriminant value of 0 ?
D. Graph D. A graph that shows a quadratic function with a discriminant value of 0 is graph D.
In Mathemeatics, the number of zeros for any quadratic function by using the discriminant formula as follows;
Discriminant, D = b² - 4ac
where:
a, b, and c are constants.
Note:
If D equals 0, the quadratic equation has only one real solution.
If D is greater than 0, the quadratic equation has two real solutions.
If D is less than 0, the quadratic equation has two complex solutions
In this context, we can logically deduce that only graph D shows a quadratic function with a discriminant value of 0 because it has only one real solution (x = 1).
please please please help
Answer:
The inverse of the function is ±sqrt( (x+4)/2
Step-by-step explanation:
Set the function equal to y
y = 2x^2 -4
Exchange x and y
x = 2y^2 -4
Solve for y
Add 4 to each side
x+4 = 2y^2 -4+4
x+4 = 2y^2
Divide each side by 2
(x+4)/2 = 2/2y^2
(x+4)/2 = y^2
Take the square root of each side
±sqrt( (x+4)/2 )= sqrt(y^2)
±sqrt( (x+4)/2 )= y
The inverse of the function is ±sqrt( (x+4)/2
When finding the volume of a soup can, Tommy needs to calculate the area of the base. Describe what type of base Tommy’s soup can has and what formula he should use to find its area.
Answer: The base is a circle and you can use the formula (pi)r^2 the find the area of the base
Step-by-step explanation:
a soup can is a cylinder and the base of a cylinder is a circle. you can google "area of a circle calculator" on google to show you the formula
Answer:
Sample response: The soup can has a circular base. The radius measure is needed. If the diameter is given, find the radius, which is half the diameter. Square the radius and multiply that answer by pi for the base area.
Step-by-step explanation:
I just did it on edge
Enrico buys 3/8 of cheddar cheese and 4/8 pounds of Swiss cheese .How much cheese did Enrico buy in all?
Answer: 7/8 pounds of cheese
Step-by-step explanation:
Add the two numbers.
4/8 + 3/8 = 7/8.
That is your answer.
can you actually help me with this so i can finish the math work if so thank you so much
Answer:
adbbcbaca
Step-by-step explanation:
Analyzing Student Work
Analyze Marika's steps. Which statement is true about
her work?
Marika solved the equation (6x +15)2 + 24 = 0. Her work
is below.
1. (6x + 15)2 = -24
2. V6x +15)2 = -24
In step 2, Marika should have simplified / -24 to be
4-6
3. 6x + 15 = -25
4. 6x = -2.5 - 15
-256-15
5. X=
There are no real solutions to this equation because
the square root of a negative number is not a real
number
There should be two real solutions to this equation
because -24 = +25.
Marika correctly solved this equation.
Answer:B
Step-by-step explanation:
Edge2021
Examine the number line and select all the statements that are true.
The sum of B and C is negative.
the product of A and B > the product of A and D
|A| < |D|
A - B = -2 2/3
A + D = B
The quotient of C and B is equivalent to -2/3
Answer:
the sum of B and C is negative
A + D = B
The quotient of C and B is equivelent to -2/3
Step-by-step explanation:
The quotient of C and B is equivalent to -2/3. Therefore, the correct option is option D among all the given options.
What is number line?A picture of numbers along a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, a whole number is a collection of numbers that contains all counting numbers.
Comparing numbers is made simpler by writing them on a number line. As seen in the aforementioned graphic, the integers to the left are smaller compared to the integers for the right. As an illustration, the numbers 0 and 1 are less than each other, as are the numbers -1 and -2. The sum of B and C is negative.
Therefore, the correct option is option D.
To know more about number line, here:
https://brainly.com/question/16191404
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1. According to the box and whisker plot below, what was the lower quartile weight of Frank's
classmates?
Weights of Frank's Classmates (in lbs.)
50 75 100 125 150
HHHHHHHHH
a) 65
b) 75
c)
95
d) 125
B
Step-by-step explanation:
I hoped this helped
Based on the provided box and whisker plot, the lower quartile (Q1) represents the 25th percentile of the data, which means 25% of the data points are below this value. To find the lower quartile weight of Frank's classmates, we need to identify the middle value of the lower half of the data.
The box and whisker plot separates the data into four quartiles: the lower whisker, the box (which contains Q1), the median (Q2), and the upper whisker. The box covers the interquartile range (IQR), which contains the middle 50% of the data.
Let's find the lower quartile (Q1) based on the provided data:
Weights of Frank's Classmates (in lbs.): 50, 75, 100, 125, 150
Step 1: Arrange the data in ascending order: 50, 75, 100, 125, 150
Step 2: Find the position of Q1:
Position of Q1 = (25/100) * (Total number of data points + 1)
Position of Q1 = (25/100) * (5 + 1)
Position of Q1 = (25/100) * 6
Position of Q1 = 1.5
Since the position is not a whole number, we need to take the average of the data points at positions 1 and 2.
Step 3: Calculate Q1:
Q1 = (Data at position 1) + [(Position of Q1 - Integer part of Position of Q1) * (Data at position 2 - Data at position 1)]
Q1 = 50 + [(1.5 - 1) * (75 - 50)]
Q1 = 50 + [0.5 * 25]
Q1 = 50 + 12.5
Q1 = 62.5
So, the lower quartile weight of Frank's classmates is 62.5 lbs.
To know more about Weights here
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