The Spirit Team will be selling popcorn as a fundraiser at the next basketball game to earn funds to go to Orlando for a competition. If they need the volume of the popcorn container to be under 220 cubic inches per serving, select all of the following dimensions of a cylinder they could use
3 inch radius and 4 inch height
4 inch radius and 4 inch height
9 inch radius and 9 inch height
4 inch diameter and 9 inch height
6 inch diameter and 9 inch height
9 inch diameter and 4 inch height\
(Please hurry)
Answers
Answer:1 and 2
Step-by-step explanation:
Given
Volume needed \(V=220\ in.^3\)
For first cylinder
\(r=3\ in.\)
\(h=4\ in.\)
\(V=\pi r^2h\)
\(V_1=\pi (3)^2(4)\)
\(V_1=113.11\ in^3\)
For second cylinder
\(r=4\ in.\)
\(h=4\ in.\)
\(V=\pi r^2h\)
\(V_2=\pi (4)^2(4)\)
\(V_2=201.08\ in^3\)
For Third cylinder
\(r=9\ in.\)
\(h=9\ in.\)
\(V=\pi r^2h\)
\(V_3=\pi (9)^2(9)\)
\(V_3=2290.51\ in^3\)
For fourth cylinder
\(r=4\ in.\)
\(h=9\ in.\)
\(V=\pi r^2h\)
\(V_4=\pi (4)^2(9)\)
\(V_4=452.448\ in^3\)
So, cylinder \(1\) and \(2\) are appropriate as it is under \(220\ in.^3\)
Answer:
1, 2, and 4.
Step-by-step explanation:
Don't forget for these 3 you had to cut the diamiter in half to get the radius.
Related Questions
What is the quotient of 2/3 and 5/6;
A.1 4/5
B.4/5
C.5/9
D.1 1/4
Answers
Help me pls ://////
Answers
Answer:
Sample size is 50. to Problem B= 40
Step-by-step explanation:
Which steps could be part of the process in algebraically solving the system of equations, y 5x = x2 10 and y = 4x – 10? select two options. y = x2 5x 10 y 5x = x2 10 4x – 10 0 = x2 – 9x 0 = x2 – 9x 20 one x-value of a solution to the system is 4.
Answers
Answer:
That would be :
4x – 10 = x2 – 5x + 10 ( y = 4x - 10 is substitute for y)
PROOF: y + 5x = x² + 10
(4x - 10) + 5x = x² + 10
4x - 10 = x² -5x + 10
0 = x2 – 9x + 20 (liked terms are grouped and simplified)
PROOF: 4x - 10 = x² -5x + 10
4x = x² -5x + 10 + 10
0 = x² -5x -4x + 20
0 = x² - 9x + 20
Solving:
x² - 9x + 20 = 0
x² - 5x - 4x + 20 = 0
(x - 5) (x - 4) = 0
⇒ x = 4 (as question says) OR x = 5
Step-by-step explanation:
hope this helps
Answer:
D,E
Step-by-step explanation:
PLEASE HELP!!!! DUE TOMORROW AND GRADED!!!! I WILL GIVE BRAINLIEST
Answers
Answer:
f(-3) = 6
Step-by-step explanation:
You want the value of f(-3) given a graph of f(x).
Reading a graphTo find the value of f(-3), locate -3 on the x-axis. Follow the vertical grid line to where it intersects the graph of f(x). Follow the horizontal grid line from there to the axis marked f(x), and read the value on the vertical scale.
The attachment shows this process, and that the value of f(-3) is 6.
__
Additional comment
Unless there is information to the contrary, the usual assumption is that each grid line represents one unit. Positive is to the right of the vertical axis, and up from the horizontal axis. Then x=-3 is 3 grid lines left of the vertical axis.
The notation f(x) means the value of function f depends on the value x. The expression f(-3) is the function value when x=-3. Here, it is found by reading the graph. In other situations, it might be found from a table or by evaluating an algebraic expression.
The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?
*
147 mm^2
68 mm^2
16 mm^2
216 mm^2
Answers
Answer:
147 mm^2
Step-by-step explanation: The surface area has to be more, but not double the smaller figures surface area therefore the answer is 147 mm^2
The requried surface area of the larger solid is approximately 147 mm². Option A is correct.
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
Let's call the larger solid's surface area S.
Since the two solids are similar, their volumes have a ratio of (side length)³. Let's call the ratio of the side lengths of the larger to the smaller solid as k. Then:
\((k^3)(540 mm^3) = 857.5 mm^3\)
Simplifying the above equation, we get:
\(k = (857.5/540)^{(1/3)}\) =7/6
So, the larger solid is about 7/6=1.183 times bigger than the smaller solid in terms of side length. Since the surface area has a ratio of \((side length)^2\), we can find the surface area of the larger solid by:
\(S = (1.183^2)(108 mm^2) \approx 147 mm^2\)
Therefore, the surface area of the larger solid is approximately 147 mm². Answer: A.
Learn more about the surface area here: https://brainly.com/question/2835293
#SPJ2
Erin just bought a bag of gumballs with eight different colors of gumballs. One of the colors is Erin’s favorite. The manufacturer claims that each color is equally likely in every bag. Erin opens the bag and pulls out one gumball. Since it is not her favorite color, she puts it back in the bag with the rest of the gumballs. She shakes the bag to remix the gumballs inside. Erin continues this process until she pulls out her favorite color.What is the expected number of gumballs that Erin will need to pull out of the bag until she gets her favorite color?0.12556810
Answers
The expected number of gumballs Erin needs to pull out of the bag until she gets her favorite color is 8, which is the total number of gumball colors. This is because each gumball has an equal probability of being chosen, regardless of the previous choices. Therefore, Erin has an equal chance of choosing her favorite color on each turn. The probability of not getting her favorite color on the first turn is 7/8. After putting the gumball back and shaking the bag, the probability of not getting her favorite color on the second turn is also 7/8. This pattern continues until Erin finally chooses her favorite color.
The probability of not getting Erin's favorite color on any given turn is 7/8. This is because there are 8 colors in the bag, and only one of them is her favorite. Therefore, the probability of getting her favorite color on any given turn is 1/8.
The expected number of gumballs that Erin needs to pull out of the bag until she gets her favorite color can be calculated using the formula:
E(X) = 1/p
Where X is the number of gumballs Erin needs to pull out, and p is the probability of getting her favorite color on any given turn.
In this case, p = 1/8.
Therefore,
E(X) = 1/(1/8) = 8
Erin is expected to pull out 8 gumballs from the bag before she gets her favorite color. This is because each gumball has an equal probability of being chosen, regardless of the previous choices. Therefore, the expected number of gumballs that Erin needs to pull out until she gets her favorite color is equal to the total number of gumball colors in the bag.
To know more about probability visit:
https://brainly.com/question/17089724
#SPJ11
The expected number of gumballs that Erin will need to pull out of the bag until she gets her favorite color is 8.
Since there are eight different colors of gumballs in the bag, the probability of pulling out Erin's favorite color on any given try is 1/8. Since Erin puts the gumball back in the bag after each try and shakes the bag to remix the gumballs, each try is independent of the others.
To calculate the expected number of tries until Erin gets her favorite color, we can use the formula E(X) = 1/p, where p is the probability of the event happening and X is the number of trials until the event happens. In this case, p = 1/8 since there is a 1/8 chance of pulling out Erin's favorite color on any given try.
To know more about expected number visit:
https://brainly.com/question/30887967
#SPJ11
Problem5: Given the State-space Eq's
dv(t)/dt = -3 i(t)+ 2 u(t)
di(t)/dt = 5 v(t) - 2 i(t)
And the output equation y(t) = 61(t) + 3 u(t)
a) (1 points) Determine the state matrix A =.
b) (1 points) Determine the input matrix B =.
c) (1 points) Determine the output matrix C =.
d) (1 points) Determine the output matrix D=, direct transmission matrix
e) Draw signal flow graph and determine G(s)
f) determine transfer function Y(s)/U(s)
Answers
a) The state-space equations are as follows:dv(t)/dt = -3 i(t) + 2 u(t)di(t)/dt = 5 v(t) - 2 i(t)The state matrix A can be determined by setting the coefficients of the state variables to be equal to one and zero for the input variable.
Therefore,A = [0 -3/2; 5/2 0]b) The input matrix B can be determined by setting the coefficient of the input variable to be equal to one and zero for the state variables. Therefore,B = [2; 0]c) The output equation y(t) = 61(t) + 3 u(t) can be written in matrix form as y(t) = [61 3]x(t) + [0]u(t).
Therefore, the output matrix C is [61 3].d) The direct transmission matrix D is determined by setting the input variables to zero. Therefore, D = [0].e) The signal flow graph can be drawn using the following diagram: Signal flow graph for the given system.
The transfer function G(s) can be found by multiplying all the elements on the paths from U(s) to Y(s) and dividing by all the elements on the loops that do not contain Y(s) or U(s). The transfer function is given by G(s) = (3s + 61)/(s^2 + (3/2)s)f) The transfer function Y(s)/U(s) can be found by setting C(sI - A)^-1 B + D. Therefore,Y(s)/U(s) = [61 3] [(s^2 + (3/2)s)^-1 3/2; -5/2 (s^2 + (3/2)s)^-1] [2; 0] + [0] .
State matrix A = [0 -3/2; 5/2 0]Input matrix B = [2; 0]Output matrix C = [61 3]Direct transmission matrix D = [0]Signal flow graph and transfer function G(s) = (3s + 61)/(s^2 + (3/2)s)Transfer function Y(s)/U(s) = [61 3] [(s^2 + (3/2)s)^-1 3/2; -5/2 (s^2 + (3/2)s)^-1] [2; 0] + [0].
In this problem, we are given the state-space equations and we are asked to determine the state matrix A, the input matrix B, the output matrix C, the direct transmission matrix D, the signal flow graph and transfer function G(s), and the transfer function Y(s)/U(s). The state matrix A can be determined by setting the coefficients of the state variables to be equal to one and zero for the input variable.
The input matrix B can be determined by setting the coefficient of the input variable to be equal to one and zero for the state variables. The output equation can be written in matrix form and the output matrix C can be determined. The direct transmission matrix D is determined by setting the input variables to zero.
The signal flow graph can be drawn and the transfer function can be found by multiplying all the elements on the paths from U(s) to Y(s) and dividing by all the elements on the loops that do not contain Y(s) or U(s). The transfer function Y(s)/U(s) can be found by setting C(sI - A)^-1 B + D. Therefore, we can determine all the required quantities for the given system.
We have solved the problem by determining the state matrix A, the input matrix B, the output matrix C, the direct transmission matrix D, the signal flow graph and transfer function G(s), and the transfer function Y(s)/U(s) for the given state-space equations.
To know more about signal flow graph:
brainly.com/question/22686900
#SPJ11
A hypothesis test is to be performed for a population mean. Which of the following does the probability of a type II error not depend on?
options:
The significance level
The sample mean
The sample size
The true (population) mean
Answers
When a thesis test is being performed for a population mean, the probability of a type II error isn't dependent on the sample mean. Option B is the right answer.
A type II error occurs when a null thesis isn't rejected despite it being incorrect. It's worth noting that the threat of making a type II error is affected by several factors, including the sample size, the true population mean, the position of significance, and the variability of the data.
As a result, the larger the sample size, the lower the threat of making a type IIerror.The true population mean also has an impact on the liability of a type II error. As the difference between the true mean and the hypothecated mean grows, the threat of a type II error decreases.
The position of significance is also pivotal in determining the threat of a type II error. As the significance position increases, the threat of a type II error decreases.
So, the correct answer is B
Learn further about probability at
brainly.com/question/17960337
#SPJ11
abc is a right triangle with ab=ac. bisector of <a meets bc at d. prove that bc = 2ad.
Answers
Answer:
Let ac=ab=5
With this, bc= 5√2
Step-by-step explanation:
So to find ad, Let ad be x
5√2=(2)(x)
(5√2/2)= x
This proves that bc=2ad
Classify the number -3.12122122212222...
Rational
Irrational
Answers
Answer:
-3.12122122212222 is rational
Step-by-step explanation:
it is rational because when you put repeating numbers into fractional form, both the numerator and denominator become non-fractional whole numbers
help with this question? thx
Answers
1.25 + 0.8 + 2.75 = $4.8
ANSWER: $4.8
Complete the explanation for why 2−3 is the same as 1 23 . Look at the pattern below. As the exponent goes down by , the value is of what it was before. 23 = 8, 22 = 4, 21 = 2, 20 = 1, x−x = 1 2 , x−x = 1 4 , x−x = 1 8 = 1 23
Answers
\(2^{-3}\) is the same as \(\frac{1}{2^3}\) because of the rule \(x^{-k} = \frac{1}{x^k}\)
The negative exponent says to take the reciprocal of the base to make the exponent positive. The original base is 2, of which the reciprocal is 1/2.
An artist earns $250 for her products each week. However, this amount can vary by $25 depending on the time of year. Part A: Define a variable and write an absolute value equation to represent the scenario. (4 points) Part B: Solve the equation, showing all steps. (4 points) Part C: What are the minimum and maximum amounts that the artist received for her products? (2 points)
Answers
Part A: The absolute value equation that represents the scenario is |x| = 25.
Part B: The solutions are x = 25 and x = -25.
Part C: The minimum amount the artist received for her products is $225 (250 - 25) and the maximum amount is $275 (250 + 25).
Part A:
Let's define the variable x to represent the amount by which the artist's weekly earnings can vary.
We know that this amount can vary by $25 depending on the time of year.
Therefore, the absolute value equation that represents the scenario is:
| x | = 25
Part B:
To solve the absolute value equation, we need to consider two cases: when x is positive and when x is negative.
Case 1: x is positive
If x is positive, then the equation becomes:
x = 25
Case 2: x is negative
If x is negative, then the equation becomes:
x = 25
To find the value of x in both cases, we solve for x:
Case 1: x = 25
In this case, the artist's weekly earnings can vary by $25 above the base amount of $250.
Therefore, the maximum amount the artist received is:
$250 + $25 = $275
Case 2: - x = 25
To solve for x, we multiply both sides of the equation by -1:
x = -25
In this case, the artist's weekly earnings can vary by $25 below the base amount of $250.
Therefore, the minimum amount the artist received is:
$250 - $25 = $225
Part C:
The minimum amount that the artist received for her products is $225, and the maximum amount is $275.
For similar question on absolute value.
https://brainly.com/question/729268
#SPJ8
given c(4,3) d(-4,-3) and cd is the diameter of the circle, find the radius of the circle
Answers
Answer:
use the distance formula to find the diameter of the circle. From there, you can divide the diameter in half to find the radius of the circle
Step-by-step explanation:
so... the distance formula is...
d = \(\sqrt{(x_{2} - x_1)^{2}+(y_2 - y_1)^{2} }\)
so...you just substitute the values into the equation
d = \(\sqrt{(-4-4)^2 + (-3-3)^2}\)
d = \(\sqrt{64+36}\)
d = 10
so...that means the diameter is 10
to find the radius you do 10/2 because radius is half of the diameter
so the radius is 5
hope that helps...that took so long to write out
Select the expression that results in a rational number.
Answers
The correct answer is A.\(\((5 \frac{1}{\overline{9}}) \times (-0.\overline{3})\)\), as it involves the multiplication of two rational numbers, resulting in a rational number.
The expression that results in a rational number is A. \(\((5 \frac{1}{\overline{9}}) \times (-0.\overline{3})\)\). To determine if an expression yields a rational number, we need to check if it involves the multiplication of two rational numbers. In option A, \(\(5 \frac{1}{\overline{9}}\)\) represents a mixed fraction, which can be expressed as the sum of a whole number and a fraction, both of which are rational. Similarly, \(\(-0.\overline{3}\)\) is a repeating decimal, which can be expressed as a fraction, also a rational number.Therefore, the product of these two rational numbers in option A will yield a rational number.
For more questions on rational numbers:
https://brainly.com/question/19079438
#SPJ8
Find the missing side (to 2dp)
Answers
Answer:
x = 17.74 cm
Step-by-step explanation:
tan 29 = x/32
0.5543 = x/32
x = 17.74 cm
Answer:
17.74 to 2 dp.
Step-by-step explanation:
tan 29 = x/32
x = 32 tan 29
= 17.7379.
Exponential functions
Answers
Answer: -15^2
Step-by-step explanation: It goes down by -225 every time so the exponent form would be -15^2. Just keep on subtracting 225 every number. Add 225 for the 0x only.
if the world's population increased exponentially from 6.081 billion in 2000 to 7.504 billion in 2018 and continued to increase at the same percentage rate from 2018 to 2024, calculate to 2 decimal places what the world's population would have been in 2024.
Answers
Assuming the same percentage rate of population growth from 2018 to 2024 as from 2000 to 2018, the world's population in 2024 would be approximately 9.23 billion.
To calculate this, we first need to find the annual percentage rate of growth from 2000 to 2018. We can do this using the formula:
\(Annual growth rate = (final population / initial population)^{1 / number of years} - 1\)
Plugging in the values, we get:
\(Annual growth rate = (7.504 billion / 6.081 billion)^{1 / 18} - 1\)
Annual growth rate = 1.20%
Now we can use this growth rate to estimate the population in 2024. To do this, we can use the formula:
Population in 2024 = 7.504 billion * (1 + annual growth rate)^(number of years from 2018 to 2024)
Plugging in the values, we get:
Population in 2024 = 7.504 billion * (1 + 0.0120)^(6)
Population in 2024 ≈ 9.23 billion
Therefore, if the world's population continues to increase at the same percentage rate from 2018 to 2024 as it did from 2000 to 2018, the world's population would have been approximately 9.23 billion in 2024.
For more questions like Percentage visit the link below:
https://brainly.com/question/23921767
#SPJ11
How many distinct positive integer factors does 60 have?
Bonus (For Brainliest): how many perfect squares are between 1600 and 3600?
Answers
The number of distinct positive integer factors that 60 has will be 12.
The perfect squares that are between 1600 and 3600 will be 19.
How to calculate the value?It should be noted that the factors of 60 include 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. Therefore, the factors are 12.
It should be noted that the perfect squares that are between 1600 and 3600 will be 19.
They're the numbers from 41 to 59. They are 19.
Learn more about factor on:
brainly.com/question/25829061
#SPJ1
geometry quick question help
Answers
Answer:
Angle 1: 127
Angle 2: 153
Step-by-step explanation:
First, let's find angle 1 by finding the angle that's supplementary to it.
To solve for it, we can set up an equation where the unknown angle and the other angles in the triangle it's in add up to 180:
x+95+32=180
x=53
Since angle 1 is supplementary to 53, that means that angle 1 is equal to 180-53 = 127.
Then, to find angle 2, we can find the angle that's supplementary to it.
To solve for that, we can set up an equation where that unknown angle and the other angles in the triangle it's in add up to 180:
26+127+x = 180
x = 27
Since angle 2 is supplementary to 27, that means that angle 2 is equal to 180-27 = 153.
create a video explaning the solution of this problem.
help me create a script and the answer for the problem thank you!
Answers
The grounded ends of the guy wires are 15 meters apart.
How to calculate tie valueUsing the Pythagorean theorem, we can calculate the length of the base (distance between the grounded ends of the guy wires).
Let's denote the length of the base as 'x.'
According to the problem, the height of the tower is 20 meters, and the length of each guy wire is 25 meters. Thus, we have a right triangle where the vertical leg is 20 meters and the hypotenuse is 25 meters.
Applying the Pythagorean theorem:
x² + 20² = 25²
x² + 400 = 625
x² = 225
x = √225
x = 15
Therefore, the grounded ends of the guy wires are 15 meters apart.
Learn more about Pythagorean theorem on
https://brainly.com/question/343682
#SPJ1
A five feet tall woman is walking towards a 20 feet tall street lamp at a rate of 3ft/s. The distance between her and the street lamp is labeled by x and the length of her shadow which the lamp casts is labeled by y. Answer the following questions about this situation.Which of the following equations represents a relationship between dy/dt and dx/dt ?A. dy/dt = 1/3 *dx/dt B. dy/dt = 3 *dx/dt C. dy/dt = 4*dx/dt D. dy/dt = 1/4 *dx/dt
Answers
The equation representing the relationship between dy/dt and dx/dt that is rate at which the length of the woman's shadow is changing is equal to option C. dy/dt =4× (dx/dt).
Woman is walking towards the street lamp.
Rate at which the length of her shadow is changing as she walks.
Let us consider the height of the street lamp as h = 20 feet.
Height of the woman be w = 5 feet.
And the distance between the woman and the street lamp be x.
Length of the woman's shadow be y.
Triangles formed by the woman, the street lamp, and their shadows are similar.
Sides of similar triangles are in proportion,
This implies,
h / y = (h + w) / (x + y)
Solving for y we get,
⇒h(x + y) = y(h + w)
⇒hx + hy = hy + wy
⇒y = hx / w
Rate at which the length of the woman's shadow is changing by differentiating both sides of this equation with respect to time,
⇒ dy/dt = h(dx/dt) / w
Substitute in the values for dx/dt = 3 ft/s, h and w we get,
⇒dy/dt = (20)(3) / 5
⇒dy/dt = 60 /5
⇒dy/dt =12
⇒dy/dt = 4(3)
⇒dy/dt =4× (dx/dt)
Therefore, the rate at which the length of the woman's shadow is changing is given by option C. dy/dt =4× (dx/dt) .
learn more about length here
brainly.com/question/29292459
#SPJ4
please help im not that good during this online
Answers
Answer:
The angle is 50 degrees.
Evaluate the iterated integral by changing to cylindrical coordinates. ∫ 0 −2 ∫ √4 − x2 −√4 − x2 ∫ 3 0 xy^2 dz dy dx
Answers
The value of the iterated integral in cylindrical coordinates ∫ 0 −2 ∫ √4 − x2 −√4 − x2 ∫ 3 0 xy^2 dz dy dx is 0.
To change the integral to cylindrical coordinates, we need to express the bounds and the integrand in terms of cylindrical coordinates.
In cylindrical coordinates, we have:
x = r cosθ
y = r sinθ
z = z
where r is the radius, θ is the angle in the xy-plane, and z is the height.
The region of integration is the cylinder with radius 2, centered at the origin, and height 3 to 0. So the bounds are:
0 ≤ r ≤ 2
0 ≤ θ ≤ 2π
0 ≤ z ≤ 3
The integrand is given by:
\(xy^2\)
Substituting x and y with their cylindrical coordinate expressions, we get:
\(xy^2\) = \(r^3\)cosθ \(sin^2\)θ
Therefore, the integral becomes:
∫₀² ∫₀²π ∫₀³ r³ cosθ sin²θ dz dθ dr
The innermost integral with respect to z is easy to compute:
∫₀³ r³ cosθ sin²θ dz = [r³ cosθ sin²θ z]₀³ = 3r³ cosθ sin²θ
The middle integral with respect to θ is also easy to compute:
∫₀²π 3r³ cosθ sin²θ dθ = 0 (by symmetry)
Therefore, the integral reduces to:
∫₀² 0 dr = 0
So the value of the iterated integral is 0.
For more such questions on Iterated integral.
https://brainly.com/question/30425550#
#SPJ11
Which of the following graphs represent functions Circle your answers. If it is a function, state the domain
and range. If the graph is not included, make a table and graph the function by hand.
Answers
Answer:
Step-by-step explanation:
A). y = |2x - 3| + 1
Domain of function is defined by the x-values (Input values) and Range by the y-values(Output values).
From the graph,
Domain : (-∞, ∞)
Range : [1, ∞)
B). Table of the input-output values of the function,
y = x² - 2x + 1
x -2 -1 0 1 2
y 9 4 1 0 1
By graphing the function as attached,
Domain of the function : (-∞, ∞)
Range of the function : [0, ∞)
C). x² + y² = 3²
Domain of the function : [-3, 3]
Range of the function : [-3, 3]
D). x = 5
Domain of the line : [5, 5]
Range of the line : (-∞, ∞)
a particle P moves in a straight line such that, t s after leaving a point O, its velocity v ms^-1 is given by v=36t - 3t^2 for t>_ 0
1) find the value of t when the velocity of P stops increasing
2)find the value of t when P comes to instaneous rest
3) find the distance of P from O when P is at instaneous rest
4) find the speed of P when P is again at O
Answers
Answer:
jajjskslslskjsjxjj k k
A rotating sprinkler that sprays water at a radius of 11 feet is used to water a lawn. Determine the area of the lawn that is watered. Round your answer to two decimal places.
Answers
Answer:
379.94 ft
Step-by-step explanation:
A=3.14x R^2
If the distribution of observations were perfectly symmetrical and unimodal,
A the mean would be greater than the mode
B the mean, median mode would be the same
C the mode would be lesser than the median
D the median would be greater than the mean
Answers
If the distribution of observations were perfectly symmetrical and unimodal, option B) The mean, median, and mode would be the same.
In a perfectly symmetrical and unimodal distribution, the mean, median, and mode would be equal. This is because in such a distribution, the data would be evenly spread around a central value. The mean is calculated by summing all the observations and dividing by the total number of observations. Since the distribution is symmetrical, the sum of the observations on one side of the central value would be equal to the sum on the other side, resulting in a balanced mean.
The median is the middle value when the observations are arranged in ascending or descending order. In a symmetrical distribution, the middle value would be the same as the central value, leading to the median being equal to the mean.
The mode represents the value that appears most frequently in the distribution. In a perfectly symmetrical and unimodal distribution, all values would occur with the same frequency, resulting in multiple modes. However, since the distribution is unimodal, meaning it has only one peak, all the modes would coincide, and the mode would also be equal to the mean and median. Therefore, in a perfectly symmetrical and unimodal distribution, the mean, median, and mode would all be the same value, leading to answer B) The mean, median, and mode would be the same.
Learn more about median here: brainly.com/question/30891252
#SPJ11
using this sample data set:
10, 10, 12, 14, 30, 31, 32, 51, 77, 78, 80,
compute the values of Q1, Q2, and Q3.
Answers
The values of Q1, Q2, and Q3 for the given sample data set are as follows: Q1 = 12, Q2 = 31, and Q3 = 77.
To compute the quartiles, first arrange the data in ascending order: 10, 10, 12, 14, 30, 31, 32, 51, 77, 78, and 80.
Q1 represents the median of the lower half of the data. In this case, the lower half is {10, 10, 12, 14, 30}. Taking the median of this set gives us Q1 = 12.
Q2 represents the median of the entire data set. In this case, the data set is {10, 10, 12, 14, 30, 31, 32, 51, 77, 78, 80}. Taking the median of this set gives us Q2 = 31.
Q3 represents the median of the upper half of the data. In this case, the upper half is {32, 51, 77, 78, 80}. Taking the median of this set gives us Q3 = 77.
To learn more about “median” refer to the https://brainly.com/question/26177250
#SPJ11
What equation represents 10 less than the product of 7 and a number is 18?
Answers
The equation which correctly represents the word phrase; 10 less than the product of 7 and a number is 18 is; 7n - 10 = 18.
What equation correctly represents 10 less than the product of 7 and a number is 18?It follows from the task content that the equation which correctly represents 10 less than the product of 7 and a number is 18 be determined.
By interpreting each segment of the statement;
The product of 7 and a number can be written algebraically as; 7 × n = 7n.
Since the product statement has been analysed and has been expressed algebraically as 7n; it follows that the compound statement;
10 less than the product of 7 and a number can be written algebraically as;
7n - 10.
Therefore, the equation which represents the statement; 10 less than the product of 7 and a number is 18 is; 7n - 10 = 18.
Ultimately, the required algebraic equation is; 7n - 10 = 18.
Read more on word phrases and algebraic expression;
https://brainly.com/question/25991924
#SPJ1