Answer: 3
Step-by-step explanation:
2/3 4/6
Kulijeet makes this bead string. She threads 3 white beads for every 1 black bead. When she finishes the bead string, it contains 20 beads altogether. How many of the beads are white?
The numbers for the first eight beads that are white are; 1, 5, 9, 13, 17, 21, 25, 29
How many of the beads are white?
step1
Arithmetic Sequence
We are told that she strings in this order;
3 white1 blackNow, after the first white bead, the next white bead is the 5th bead in total.
This means the difference in interval between white beads is; 5 - 1 = 4 beads
Thus, the numbers for the first eight beads that are white are
1, (1 + 4), (1 + 4 + 4), (1 + 4 + 4 + 4)…..
Thus, we have;
1, 5, 9, 13, 17, 21, 25, 29
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If an employee contributes $150 toward her retirement each month,
and her employer agrees to match 15% of that, then what is the
total monthly retirement contribution?
Two points should be noted: The 15% is first calculated using your annual gross wage rather than your take-home pay. Second, the business match is not included in your 15%.
Should I contribute more than 15% to retirement?You probably won't need to save more than 15-20 percent as you get older if you can save 15-20 percent of your salary when you're 30 for retirement. If you stay consistent throughout your professional life, starting early is a tremendous advantage.Your actual monthly contribution will increase when your salary increases if you consistently set aside 15% of your income, which will speed up the accumulation of your retirement savings.If you are under 72 years old and have income from a job or self-employment, you are eligible to make a contribution to your Individual Retirement Account (IRA) of up to $6,000. Up to $7,000 can be contributed if you are 50 years old or older.To learn more about business refer to:
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1. Find the net cost for the following:
List price $1236.92, less series discount 12/15/20
4 (2 points): consider the following linear transformation of a random variable: , where is the mean and is the standard deviation. find the expected value and standard deviation of .
The standard deviation of is equal to the standard deviation multiplied by, and the anticipated value of is equal to the mean.
The mean, which is the average of the random variable, is equal to the expected value of. It is determined by summing up all of the random variable's values and dividing the total number of values in the set. The result of multiplying the standard deviation by is the standard deviation of. By taking the square root of the variance, the standard deviation—a measurement of the range of data points from the mean—is created. By dividing the total of the squares of the deviations between each data point and the mean, the variance is computed.
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FOR WHICH INEQUALITY IS Z = 3 A SOLUTION??/
The inequality is z = 3 a solution. The correct answer would be an option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per option (A), the inequality is given as follows:
z+5 ≥ 9
z ≥ 9 - 5
z ≥ 4
As per option (B), the inequality is given as follows:
z+5 > 9
z > 9 - 5
Apply the subtraction operation,
z > 4
As per option (C), the inequality is given as follows:
z + 5 ≤ 8
z ≤ 8 - 5
z ≤ 3
Since the solution is less than or equal to three,
Then, this inequality is z = 3 a solution.
Hence, the correct answer would be option (C).
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This question seems incomplete, the complete question would be as:
For which inequality below is z = 3 a solution?
A. z+5 ≥ 9
B. z+5 > 9
C. z+5 ≤ 8
D. z+5 <8
help I don't get this
Answer:
me neither bro
Step-by-step explanation:
Solve the given proportion X/4 = 3/6 X=
Answer:
X/4=3/6
Start off by cross multiplying the tops and bottoms, so X/4=3/6 turns into 6X=12. Now divide by 6 on both sides.
6X=12 X=2
Answer:
2
Step-by-step explanation:
Cross Multiple and Divide
X. 3
----. = ----
4. 6
So what you want to do is multiply diagonally:
(6)(X) = 6X
(3)(4) = 12
Now that we have our two answers, we put an equal sign between them.
6X = 12
Now to get X alone. Since it's being multiplied by 6, you want to do the opposite and divide.
So remember to divide on both sides to get rid of the 6.
6X divided by 6 is just X.
12 divided by 6 is 2
We got our answers, put the equal sign in-between
X = 2
Paul needs 254 centimeters of red fabric and 321 centimeters of white fabric. The store has 3 meters of red fabric and 3 meters of white fabric. Will Paul be able to buy what he needs? If not, how much more will he need to buy elsewhere?
Paul will not be able to buy what he wants in terms of White Fabric and will need to buy 21 centimeters of white fabric elsewhere.
How to find the fabrics needed ?To find out if Paul will be able to buy all that he needs from the store, you need to convert the fabrics needed to a similar unit as the fabrics the shops have.
The stores have 3 meters of red fabric and 3 meters of white fabric. In centimeters this is:
1 meter = 100 centimeters
The centimeters are:
= 3 x 100
= 300 cm of each material
Paul needs 254 centimters of red fabric so will find what he needs.
He needs 321 centimeters of white fabric and so will need to buy elsewhere:
= 321 - 300
= 21 centimeters
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courtney has constructed a cricket out of paper and rubber bands. according to the instructions for making the cricket, when it jumps it will land on its feet half of the time and on its back the other half of the time. in the first 50 jumps, courtney's cricket landed on its feet 35 times. in the next 10 jumps, it landed on its feet only twice. based on this experience, courtney can conclude that
A confidence interval for estimating the cricket's true probability of landing on its feet is more narrow after the final 10 jumps than it was before the final 10 jumps. Thus, the correct answer is option D.
A confidence interval is a range of values that is likely to contain the true population parameter (in this case, the true probability of the cricket landing on its feet) with a certain level of confidence. The width of the interval depends on the sample size and the level of confidence.
In the first 50 jumps, the cricket landed on its feet 35 times out of 50, giving a proportion of 0.7. Based on this sample, a 95% confidence interval for the true probability of the cricket landing on its feet can be calculated. However, this interval will be relatively wide due to the small sample size.
In the final 10 jumps, the cricket landed on its feet only twice out of 10, giving a proportion of 0.2. Based on this sample, a 95% confidence interval for the true probability of the cricket landing on its feet can be calculated. However, this interval will be relatively narrow due to the large sample size.
When comparing the two intervals, it is clear that the interval based on the final 10 jumps is narrower than the interval based on the first 50 jumps. This means that after the final 10 jumps, Courtney has a more precise estimate of the true probability of the cricket landing on its feet than she did before the final 10 jumps.
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The complete question is -
Courtney has constructed a cricket out of paper and rubber bands. According to the instructions for making the cricket, when it jumps it will land on its feet half of the
time and on its back the other half of the time. In the first 50 jumps, Courtney's cricket landed on its feet 35 times. In the next 10 jumps, it landed on its feet only twice.
Based on this experience, Courtney can conclude that -
A. the cricket was due to land on its feet less than half the time during the final 10 jumps since it had landed too often on its feet during the first 50 jumps
B. a confidence interval for estimating the cricket's true probability of landing on its feet is wider after the final 10 jumps than it was before the final 10 jumps
C. a confidence interval for estimating the cricket's true probability of landing on its feet after the final 10 jumps is exactly the same as it was before the final 10 jumps
D. a confidence interval for estimating the cricket's true probability of landing on its feet is more narrow after the final 10 jumps than it was before the final 10 jumps
E. a confidence interval for estimating the cricket's true probability of landing on its feet based on the initial 50 jumps does not include 0.2, so there must be a defect in the cricket's construction account for the poor showing in the final 10 jumps
Evaluate 0.3 y+\dfrac yz0.3y+
z
y
0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.
The value of the expression when y = 10 and z = 5 is 5
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
0.3y + y/z
Also, from the question, we have the following values:
y = 10 and z = 5
substitute the known values in the above equation, so, we have the following representation
0.3y + y/z = 0.3 * 10 + 10/5
Evaluate the expression
0.3y + y/z = 5
Hence, the solution is 5
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you may want to review (page) . for help with math skills, you may want to review: quadratic equations for general problem-solving tips and strategies for this topic, you may want to view a video tutor solution of time in the air for a tossed ball. part a how long is the ball in the air before it hits the ground? (the student moves her hand out of the way.)
It takes 0.7143 seconds for the ball in the air to hit the ground.
Therefore the answer is 0.7143 s.
The time it takes for the ball to hit the ground can be calculated using the formula for vertical motion with constant acceleration (g = 9.8 m/s²):
t = √(2 * h / g)
where h is the height the ball is thrown and t is the time it takes to hit the ground.
Plugging in the values to find time:
t = √(2 * 2.50 m / 9.8 m/s²)
t = √(0.51) s
t = 0.7143 s
So, the ball is in the air for approximately 0.7143 seconds before it hits the ground.
--The question is incomplete, answering to the question below--
"A student standing on the wall throws a ball straight up. The ball leaves the student's hands with a speed of 19.0 m/s when the hand is 2.50 m above the ground.
How long is the ball in the air before it hits the ground? (the student moves her hand out of the way.)"
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Find the inverse Laplace transforms of the following functions. First, perform partial-fraction expansion on G(s); then, use the Laplace transform table. (a). G(s)= 1 / s(s+2)(s+3) (b). G(s)= 10 / (s +1)^2(s+3) (c). G(s)= [100(s+2) / s(s^2 + 4)(s+1)] e^-x
(d). G(s)= 2(s+1) / s(s^2+s+2) (e). G(s)= 1 / (s+1)^3 (f). G(s)= 2(s^2+s+1) / s(s+1.5)(s^2 +5s+5)
(g). G(s)= [2+2se^(-x) + 4e^(-2x)] / [s^2 + 3s + 2] (h). G(s) = 2s+1 / (s^2 + 6s^2 +11s +6)
(i). G(s) = (3s^3 + 10s^2 + 8s + 5) / (s^4 + 5s^3 + 7s^2 + 5s +6)
The inverse Laplace transform of G(s) is 1 + 2e^(-2t) + 3e^(-3t).
(a). G(s)= 1 / s(s+2)(s+3)
Using partial fraction expansion, we can write G(s) as 1/s + 2/s+2 + 3/s+3. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 1/s is 1, the inverse Laplace transform of 2/s+2 is 2e^(-2t) and the inverse Laplace transform of 3/s+3 is 3e^(-3t). Therefore, the inverse Laplace transform of G(s) is 1 + 2e^(-2t) + 3e^(-3t).
(b). G(s)= 10 / (s +1)^2(s+3)
Using partial fraction expansion, we can write G(s) as 5/s+1 + 5/s+3. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 5/s+1 is 5e^(-t) and the inverse Laplace transform of 5/s+3 is 5e^(-3t). Therefore, the inverse Laplace transform of G(s) is 5e^(-t) + 5e^(-3t).
(c). G(s)= [100(s+2) / s(s^2 + 4)(s+1)] e^-x
Using partial fraction expansion, we can write G(s) as 50/s + 50/s+1 + 50/s+2 + 50/s+4. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 50/s is 50, the inverse Laplace transform of 50/s+1 is 50e^(-t), the inverse Laplace transform of 50/s+2 is 50e^(-2t) and the inverse Laplace transform of 50/s+4 is 50e^(-4t). Therefore, the inverse Laplace transform of G(s) is 50 + 50e^(-t) + 50e^(-2t) + 50e^(-4t)e^-x.
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A set of electric toothbrush prices are normally distributed with a mean of 87 dollars and a standard deviation of 8 dollars.
What proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars?
The proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars are 0.0099.
What is Normal Distribution?A normal distribution in statistics is defined as the type of continuous probability distribution where the datas are arranged in a symmetrical bell shaped graph.
Given that,
Mean, μ = 87
Standard deviation, σ = 8
We have to calculate P (104.60 < x < 108.20).
For that find z score.
z = (x - μ) / σ
At x = 104.60, z = (104.60 - 87) / 8 = 2.2
At x = 108.20, z = (108.20 - 87) / 8 = 2.65
From the z table,
P(z < 2.65) = 0.9960 and P(z < 2.2) = 0.9861
P (104.60 < x < 108.20) = 0.9960 - 0.9861 = 0.0099
Hence the proportion is 0.0099.
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find the volume v of the described solid s. the base of a solid s is the region enclosed by the parabola y
The volume of the solid that is in the parabola is 3.48[tex]\pi[/tex] after integration will carried out.
Parabola is a U shape curve whose eccentricity is 1.
The equation of parabola is y = 2-3x² and the x axis.
The cross section is perpendicular to y axis and the square.
The parabola is passes through the x axis put y = 0 in the equation of parabola.
0 = 2-3x²
x = [tex]\sqrt{\frac{2}{3} }[/tex]
Volume of the solid = [tex]\pi r^{2}h[/tex]
here r = y and h = dx
[tex]\pi (2-3x^{2} )^{2} dx=dv\\dv = \pi (9x^{4}-12x^{2} +4)dx\\[/tex]
Now, integrate the given equation to get the volume of the solid.
∫dv = ∫π(9x⁴-12²+4)dx
Put limits [tex]\sqrt[2]{\frac{2}{3} }[/tex] to 0
After integration and putting the limit we got V = 3.48[tex]\pi[/tex].
Hence, the volume of the solid is 3.48π.
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The complete question is:
Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y = 2 − 3x2 and the x−axis. Cross-sections perpendicular to the y−axis are squares.
write an equation of the line that passes through (3,1) and (0,10)
An equation of the line that passes through two points (x1,y1) and (x2,y2) can be found using the slope-intercept form:
Slope intercept form: what is it?
Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.
y = mx + b
where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we use the following formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the points given, we get:
m = (10 - 1) / (0 - 3) = -9/3
To find the y-intercept, we can use either of the given points and the slope:
b = y - mx
Plugging in the coordinates of the point (3,1) and the slope, we get:
b = 1 + (9/3) * 3 = 4
So the equation of the line that passes through (3,1) and (0,10) is:
y = -3x + 4
It's also possible to use the point slope form of a linear equation, which is y-y1=m(x-x1)
y - 1 = -3(x-3)
y = -3x + 9
Both equations are valid and represent the same line.
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The question is in the image below
Answer:
y=4/3x-3
Step-by-step explanation:
By using rise/run, you can see the slope in the equation, as it goes 4 units up and 3 units to the right.
For the y-intercept, you can see that the line intercepts (0,-3), which makes it the y-intercept.
Answer: y=-3+4/3x
Step-by-step explanation:
You get -3 because that is the point on the y axis
You get 4/3x from rise every additional point after
-------
run
Multiply:
[-7]
3 11
2
=
b₁
b₂
b₂
The value of b1 = -21, b2 =33, and b3 = 6 in the given matrix.
What is matrix?A collection of integers lined up in rows and columns so to produce a rectangular array is called a matrix. The elements, or inputs, of the matrix are the integers.
What is multiplication of matrix?A single matrix is created through matrix multiplication, sometimes referred to as matrix product and the multiplication of two matrices. This kind of binary operation is used. A scalar multiplication occurs when an integer is multiplied by a matrix. Scalar multiplication is the process of multiplying a matrix by a scalar value.
For the given matrix multiply each term of the matrix with 3 to obtain the value of b1. b2, and b3.
[tex]3\left[\begin{array}{ccc}-7\\11\\2\end{array}\right] = \left[\begin{array}{ccc}-21\\33\\6\end{array}\right][/tex]
Hence, the value of b1 = -21, b2 =33, and b3 = 6.
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What is the value of x?
The value of x in the given polygon is 31 degrees.
What are exterior angles?An exterior angle is an angle created by the expansion of the neighboring side and one of the sides of a closed shape construction, such as a polygon. Regardless of the number of sides in the polygons, the sum of the measures of the outside angles is equal to 360 degrees.
The sum of the exterior angle of any polygon is 360 degrees.
So,
360 = 57 + 41 + 82 +x + 62 + 87
360 = x + 329
x = 31
Hence, the value of x in the given polygon is 31.
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Use the information given below to find tan (a-B).
3
4
4
5'
tan a =
sin ß
I
with a in quadrant III
an (a - B) =
with ß in quadrant I
Give the exact answer, not a decimal approximation.
That since exact value of sin(A-β) depends on the cos(-β) value, which we miss, we are not able to determine the value.
How to find Sinβ using trigonometric identities?To determine (A-β), we can use trigonometric identities.
Tan(A) = 3/4 and sin() = 4/5 in Quadrant III.
The identification can be used for:
tan(A) = cos/sin(A) (A)
Sin(A) in this instance equals 3/4. * cos(A) (A)
We can adopt a different guise.
(A-sin) = sin (A)
(cos) - (cos (A)
Sin(β), so sin(A-) = (3/4 * cos(A)) (sin()) - cos()) (cos(A))
sin(A-β) = (3/4) - (4/5) * (sin(A) * (cos(A) * cos())
We can now apply the double angle formula.
cos(2A) = sin2 + cos2(A) (A)
Therefore, cos(A) = (1 - sin(A)2), and sin(A-) = (3/4) * (± √(1 - (3/4)^2) * cos(β)) - (4/5) * (3/4)
sin(A-β) = (3/4) * (± √(1 - (9/16)) * cos(β)) - (3/5)
The formula for sin(A-) is (3/4) * ((7/16) * cos()) - (3/5)
That since exact value of sin(A-) depends on the cos(-) value, which we miss, we are not able to determine the value.
Therefore, using the equation given, it is impossible to figure out the precise value of (A-β).
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
The solution for the equation 2.3p - 10.1 = 6.5p - 4 - 0.01p is p = -4.19/6.1
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
2.3p - 10.1 = 6.5p - 4 - 0.01p
Solve for p.
2.3p - 10.1 = 6.5p - 4 - 0.01p
Combining the like terms.
2.3p - 10.1 = 6.49p - 4
4 - 10.1 = 6.49p - 2.3p
-6.1 = 4.19p
p = -4.19/6.1
Thus,
The solution is p = -4.19/6.1
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ANYONE GOOD AT MATH PLEASE HELP!
Answer:
Is it 0? sorry if this is wrong
Step-by-step explanation:
Answer:
f(g(0)) = -2
Step-by-step explanation:
We have our two equations, f(x) and g(x).
We work our way from the inside to the outside. Our inside equation is g(0). If we match g(x) to that, that would mean x = 0. So on that g(x) graph, when the x=0, the graph intercepts the y axis at y = 1.
Now that we know that g(0) = 1, we can plug that into the original equation, making it f(1) instead of f(g(0)). Now that we have f(1), we can go to our f(x) equation.
Matching the equations, it shows the x=1. On our f(x) graph, we'll find x=1 and trace down or up (down in this case) to the point where the graph intercepts at that point. Thats where we can then trace that point to the y axis and we see that our line hits the y axis at -2, making that the answer.
1 Charlotte uses two boards to build a tabletop. How
wide is the tabletop?
8/10m
1/2 + 3/10 =
5/10 + 3/10= 8/10
What are the coordinates of the midpoint of the segment whose endpoints are H (-2, 4) and K (2, –3)?
The coordinates of the midpoint of the segment whose endpoints are H (-2, 4) and K (2, –3) is (0,1/2)
What are the coordinates of midpoint of the line segment AB?Suppose we've two endpoints of a line segment as:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
x = [tex]\dfrac{p+m}{2}[/tex]
and y =[tex]\dfrac{q+n}{2}[/tex]
Given;
The endpoints= H (-2, 4), K (2, –3)
X coordinate of midpoint;
-2+2/2=0
Y coordinate of midpoint;
4-3/2=1/2
Therefore, the midpoint will be (0,1/2)
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Solve the following using roots 5x^2-45=0
The solutions to the equation 5x² - 45 = 0 are -3 and 3.
What are the solutions to the equation?Given the equation in the question;
5x² - 45 = 0
To solve using square root property, add 45 to both sides.
5x² - 45 + 45 = 0 + 45
5x² = 45
Divide both sides by 5
5x²/5 = 45/5
x² = 45/5
x² = 9
Take the square root of both sides.
√(x²) = √9
x = ±√9
x = -3, 3
Therefore, the value of x are -3 and 3.
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Which of the following statements about quadrilaterals are true? Select each correct answer. Responses All squares are rhombuses, but not all rhombuses are squares. All, , squares, , are, , rhombuses,, , but, , not, , all, , rhombuses, , are, , squares., EndFragment, Opposite angles in a parallelogram are congruent. Opposite, , angles, , in, , a, , parallelogram, , are, , congruent., EndFragment, The diagonals of a rectangle are perpendicular.
All of the statements about quadrilaterals that are true include the following:
A. all squares are rhombuses, but not all rhombuses are squares.
B. opposite angles in a parallelogram are congruent.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapeziumGenerally speaking, a typical characteristics of all squares are rhombuses is simply that all squares are classified as rhombuses, but it is not all rhombuses that are classified as squares.
Additionally, the opposite angles of any parallelogram are always congruent because they form parallel lines. However, the diagonals of a rectangle, parallelogram, and trapezium are not perpendicular.
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Solve the system of linear equations by substitution.
5x+2y=9
x+y=-3
For each part, compare distributions (1) and (2) based on their medians and IQRs. You do not need to calculate these statistics; simply state how the medians and IQRs compare. Make sure to explain your reasoning.
a. (1) 3, 5, 6, 7, 9 (2) 3, 5, 6, 7, 20
b. (1) 3, 5, 6, 7, 9 (2) 3, 5, 7, 8, 9
c. (1) 1, 2, 3, 4, 5 (2) 6, 7, 8, 9, 10
d. (1) 0, 10, 50, 60, 100 (2) 0, 100, 500, 600, 1000
The medians and IQRs of two distributions can be compared to determine how the distributions differ. If the medians and IQRs are the same, the distributions are similar. If the medians and IQRs are different, the distributions are not the same.
a. The medians and IQRs of distributions (1) and (2) are the same; both have a median of 6 and an IQR of 4.
b. The medians and IQRs of distributions (1) and (2) are the same; both have a median of 6 and an IQR of 2.c. The medians and IQRs of distributions (1) and (2) are different; distribution (1) has a median of 3 and an IQR of 2, while distribution (2) has a median of 8 and an IQR of 2.
d. The medians and IQRs of distributions (1) and (2) are different; distribution (1) has a median of 50 and an IQR of 50, while distribution (2) has a median of 500 and an IQR of 400.
The median IQRs of two distributions can be compared to determine how the distributions differ. If the medians and IQRs are the same, the distributions are similar. If the medians and IQRs are different, the distributions are not the same.
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a carnival game charges each contestant \$2$2dollar sign, 2 to spin a wheel with 555 equally likely spaces: 333 spaces result in the contestant winning nothing. 111 space results in the contestant winning a prize whose value is \$1$1dollar sign, 1. 111 space results in the contestant winning a prize whose value is \$4$4dollar sign, 4. let xxx represent a player's net gain on a spin. for example, if the spin lands on the space where the contestant wins nothing, then x
If the spin lands on the space where the contestant wins nothing, then x = 0.
If the spin lands on a space where the contestant wins $1, then x = -1 + 1 = 0. If the spin lands on a space where the contestant wins $4, then x = -2 + 4 = 2.
The expected value of x can be calculated as follows:
E(x) = (333/555) × 0 + (111/555) × (-2 + 1) + (111/555) × (-2 + 4) = (111/555) * 2 = 0.4.
So, on average, the player's net gain per spin is 40 cents.
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a laboratory technician had a bottle that was 5/8 full if the technician used 3/4 of the bottles content, what fractional amount is left in the bottle
find an equation for the surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane.
The surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane.
The equation for the surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane is given by -
x = 3y2 + 3z2
To explain this equation, let us consider a point P(x, y, z) on the surface. The distance from this point P to the x-axis is given by |x|, and the distance from P to the yz-plane is given by √y2 + z2.
Now, the given condition states that the distance from P to the x-axis is 3 times the distance from P to the yz-plane. This can be written as |x| = 3√y2 + z2. By squaring both sides, we get x2 = 9(y2 + z2), which can be rearranged to give the equation x = 3y2 + 3z2.
This equation thus gives the surface consisting of all points p for which the distance from p to the x-axis is 3 times the distance from p to the yz-plane.
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