At least one patient will arrive in the following 15 minutes if the next patient arrives before 11:45 a.m.= ∗e −1.5 ≈0.777.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our question-
I If X indicates the number of patients who arrived in 1.5 hours at random, then X = Pois(6*1.5) = Pois (9)
P(X=7)=frac 9/7/7!e-9/approximately 0.17P(X=7)= 7! 9/7
\s ∗e \s−9 \s ≈0.117
(ii) If X indicates the number of patients who arrived in 15 minutes or less, then X = Pois(6*0.25) = Pois (1.5)
At least one patient will arrive in the following 15 minutes if the next patient arrives before 11:45 a.m.
P(X≥1)=1-P(X<1)
=1-P(X=0)
=1-frac 1.5 0 0!*e 1.5 Approximately 0.777P(X1)
=1−P(X<1)
=1−P(X=0)=1− \s0! \s1.5 \s0
\s ∗e \s−1.5 \s ≈0.777
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how to find the number of individuals in the sample with the specified characteristic x if n is 1200
The point estimate of the population is 0.415 round to the nearest thousandth as needed the margin error is 0.189.
In statistics, for point estimation, an unknown population parameter (e.g. population mean). More formally, it is applying a point estimator to data to obtain a point estimate.
Point estimation can be contrasted with interval estimation. Such interval estimates are usually confidence intervals for frequentist inference and confidence intervals for Bayesian inference. More generally, point estimators can be contrasted with set estimators. An example is the confidence rate or confidence rate. Point estimators can also be contrasted with distribution estimators. Examples include confidence distributions, randomized estimators, and Bayesian posterior distributions.
Based on the question,
The confidence interval of Lower bound is 0.226.
The confidence interval of Upper bound is 0.604.
X - E = 0.226. --------------------------- (1)
X + E = 0.604 ---------------------------(2)
Adding equation (1) and (2),
2X = 0.83
⇒ X = 0.83/2
⇒ X = 0.415
Putting X = 0.415 in equation (1),
0.415 + E = 0.604
⇒ E = 0.604 - 0.415
⇒ E = 0.189
Thus, the point estimate of the population is 0.415 round to the nearest thousandth as needed the margin error is 0.189.
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hw17b.6. find the residual consider solving the least squares problem given below where the svd is given for . what will be the 2-norm of the residual, i.e., for this linear least squares problem?
The least square solution using svd matrix that has minimal norm is calculated using factorization .
What is Least Square Method ?
The least squares method is used in finding best fit for a set of data points by minimizing sum of offsets from plotted curve.
The SVD (Singular value decomposition) is a factorization of a real/complex matrix.
This technique is widely used to decompose a matrix into several component matrices, which exposes many of useful and interesting properties of original matrix.
The system of equation is Ax=b, we calculate the SVD of A by A=UΣVT. The matrices U , VT have a special property that they are unitary matrices.
The main benefits of having unitary matrices like U and VT is , if we multiply one of these by its transpose, the result equals the identity matrix.
Therefore , factorization is used to find the least square solution .
The given question is incomplete , I answer the question in general according to my knowledge
Calculate least squares solution using svd a matrix has the singular value decomposition what is the solution to the least-squares problem that has minimal norm ?
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What is 1 1/9 as an improper fraction?
Answer:
the right answer is
1,2/9
Find the partial fraction decomposition of the rational expression with repeated factors.
The partial fraction decomposition of the expression with repeated factors is given as follows:
[tex]\frac{1}{x} - \frac{2}{x + 4} - \frac{1}{(x + 4)^2}[/tex]
How to obtain the partial fraction decomposition of the function?The function in this problem is defined as follows:
(-x² - x - 16)/(x³ + 8x² + 16x).
The decomposition is made considering the factors of the denominator, which are obtained as follows:
x³ + 8x² + 16x = 0.
x(x² + 8x + 16) = 9
x(x + 4)² = 0.
Hence the denominators are as follows:
x.x + 4.(x + 4)².Then the decomposition is of:
A/x + B/(x + 4) + C/(x + 4)²
Then the expression will be given as follows:
[tex]\frac{A(x + 4)^2 + Bx(x + 4) + Cx}{x^3 + 8x^2 + 16x} = \frac{-x^2-x+16}{x^3 + 8x^2 + 16x}[/tex]
Then the system of equations, equaling the numerators, is given as follows:
A + B = -1. -> terms with x².8A + 4B + C = -1 -> terms with x.16A = 16 -> independent term.Hence:
16A = 16
A = 1.
B = -1 - A
B = -2.
C = -1 - 8A - 4B
C = -1.
Meaning that the third option is correct.
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The box for a computer game measures 19 cm by 14 cm by 1.5cm what is the total amount of plastic wrapping needed to cover the entire box if an extra 66cm² is needed to allow for the overlapping at the edges?
Applying the formula of the surface area of a box, the total amount of plastic wrapping needed to cover the box is: 697 cm².
How to Find the Surface Area of a Box?The total surface area of a box is the sum of all the areas of the six faces of the box.
The area of each face can be found by multiplying the length by the width of that face.
The area of each face is given as:
Area = length * width.
To find the amount of plastic wrapping needed to cover the entire box, you first need to find the surface area of the box.
The surface area of the box is given by:
Surface area = 2(19 cm * 14 cm) + 2(19 cm * 1.5 cm) + 2(14 cm * 1.5 cm)
= 2(266 cm²) + 2(28.5 cm²) + 2(21 cm²)
= 532 cm² + 57 cm² + 42 cm²
= 631 cm²
To find the total amount of plastic wrapping needed to cover the box, you need to add the extra 66 cm² needed to allow for the overlapping at the edges.
This gives a total of 631 cm² + 66 cm² = 697 cm² of plastic wrapping needed to cover the box.
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Solve: Show your work
0.321 x 50
Answer:
.321× 50
000
+ 1605X
therefore answer is 1.605
please help memeemeemee
Answer:
6
Step-by-step explanation:
it is a8=a1 +(n-1)x d
41=-1+ 7xd
42/7=d
d=6
Answer: 6
Step-by-step explanation:
[tex]a_1=-1\ \ \ \ \ \ \ \ a_8=41\ \ \ \ \ \ \ \ d=?\\\\\boxed{a_n=a_1+d(n-1)}\\\\Hence,\\\\a_8=-1+d(8-1)\\\\41=-1+7d\\\\41+1=-1+7d+1\\\\42=7d\\\\[/tex]
Divide both parts of the equation by 7:
6=d
Thus, d=6
Margaret rows 3 miles in 21 minutes. At that same rate, how many miles would she row in 60 minutes? If necessary, round your answer to the nearest tenth.
Group of answer choices
8.6
7
3.3
13
Answer: 8.6 miles
Step-by-step explanation:
Takes 21 divided by 3 = 1 mile in 7 minute
Then take 60 divided by 7 = 8.57
ground to nearest tenth = 8.6 miles
some other policies for fairness in congestion control are additive increase additive decrease (aiad), multiplicative increase additive decrease (miad), and multiplicative increase multiplicative decrease (mimd). discuss these three policies in terms of convergence and stability.
Congestion management allows for more efficient use of a shared network infrastructure by managing the flow of data packets into the network.
Additive increase and additive decrease (AIAD) This is the policy which follows the below rule
a(i)>0, b(i) =1, a(d)<0 b(d)=1
This policy doesn't converge to fairness which means that it is not stable.
Moreover, this doesn't converges to efficiency and if it is need to be stable then it must satisfy the condition a(d) = a(i)
Multiplicative increase and additive decrease (MIAD) This is the policy which follows the rule of a(i) =0, b(i) >1, a(d)<0, b(d)=1
This policy doesn't converge to fairness which means that it is not stable.
Moreover, this doesn't converges to efficiency and if it is need to be stable then it must satisfy the condition b(i)a(d)/ 1- b(i)
Multiplicative increase multiplicative decrease (MIMD) This is the policy which follows the below rule a(i) =0 , b(i) >1 , a(d)=0, 0<b(d)<1
This policy doesn't converge to fairness which means that it is not stable.
Moreover, this doesn't converges to efficiency and if it is need to be stable then it must satisfy the condition b(i)≥ 1 and 0≤ b(d)<1.
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find the percentage of the first quantity with
reference to the second quantity: 480 units, 560 units.
Answer:
85.7142857%
Step-by-step explanation:
To find the percentage, take the first quantity and divide by the second quantity
480/560 =.857142857
Then multiply by 100 %
857142857 * 100% = 85.7142857%
Triangle ABC is reflected over the x-axis. What are the coordinates of the image of the vertex A?
The image of vertex A will be at point (2,-5).
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The perimeter will be P = sum of all three side.
Point A is located at (2, 5), thus you look at the y-coordinate since you are reflecting it across the x-axis.
Given that it is five above the x-axis, you must travel five below it, or you can simply enter the opposite of five, which is -5.
So, A' is at (2, -5).
Hence, The image of vertex A will be at point (2,-5).
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Please help me! This assignment is due tomorrow.I have no clue how to do it.Im pretty sure it’s easy but BOT FOR ME HAHA.please help.
Answer:
it travels 25 nautical miles per hour
Step-by-step explanation:
150 nautical miles in 6 hours
150 / 6 = 25
25 nautical miles per hour
Answer: I think it is 25 nautical miles in one hour
Step-by-step explanation:
all you need to do is 150 divided by 6 to get one hour and that is 25 (this might be wrong)
4x+x=8+5x
with a correct solution :)
Answer:
no solution
Step-by-step explanation:
(3,3) and (1,-3) in linear equation
Answer:
3 x - y = 6
Step-by-step explanation:
the equation of a line is
ax + by = c
express the slope initially in the form of y=mx+b
b is the y- intercept (the point where it crosses the y axis)
m is basically the slope, to find m, you have to use a specific formula...
m = (y2 – y1) / (x2 – x1)
(x1, y1) (x2, y2) are 2 coordinate points...
(3,3) and (1, -3)
m = -3 -3 divided by 1 - 3 = -6/-2 = 3
so your formula for now is .. y = 3x + b (you dont know what b is yet)
Now, substitute the points into the equation.
3 = 9 + b. b = -6
final formula is,
Y=3x -6
u can also rearrange the formula in a standard form:
3x - y = 6
I REALLY HOPE THIS HELPS U!!
Which values are solutions to the inequality?
3r≤4r−6
Select each correct answer.
Responses
r = 4
r = , 4
r = 5
r, = 5
r = 6
r, = 6
r = 7
Answer:
3r < = 4r - 6
3r - 4r < = -6
-r < = -6
r > = 6........it is 6 and 7
Step-by-step explanation:
Answer:
your answer would be 6, and 7.
Step-by-step explanation:
Simplify
8(x + 3)^2 divided by 2(x + 3)
Answer:4(x+3)
Step-by-step explanation:
8(x + 3)^2 /2(x + 3)
4(x+3)
Answer:
4x³+36x²+108x+108
Step-by-step explanation:
Simplify
8(x + 3)^2 divided by 2(x + 3)
8·(x + 3)² : 2·(x + 3) =
8⋅(x²+6x+9):2⋅(x+3) =
(8x²+48x+72):2⋅(x+3) =
(4x²+24x+36)⋅(x+3) =
4x³+36x²+108x+108
Select all the values greater than -9
2.895
-10.56
-8.92
-15.782
0.504
-2.9
-18.376
The numbers that are greater than -9 are 2.895, -8.92, 0.504, -2.9
What is a positive number?
A number can be zero, negative, or positive. Zero has no positive or bad aspects. The most frequent positive numbers in daily life include 34, 9.22, and other examples such as these. They are typically depicted on a number line to the right of zero, growing larger as you move to the right.
Given number is -9 which is a negative number.
All positive numbers are always greater a negative number
In the given number, the positive numbers are 2.895, 0.504.
Thus 2.895 and 0.504 are greater than -9.
The negative numbers whose absolute less than 9, they are also greater than -9.
The absolute value of -10.56, -8.92, -15.782, -2.9, -18.376 are
|-10.56| = 10.56 >9
|-8.92| = 8.92 <9
|-15.782| = 15.782 > 9
|-2.9| = 2.9 < 9
|-18.376| = 18.376 >9
Therefore -8.92 and -2.9 are also greater than -9.
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pollsters are concerned about declining levels of cooperation among persons contacted in surveys. a pollster contacts 77 people in the 18-21 age bracket and finds that 65 of them respond and 12 refuse to respond. when 294 people in the 22-29 age bracket are contacted, 259 respond and 35 refuse to respond. assume that 1 of the 371 people is randomly selected. find the probability of getting someone in the 22-29 age bracket or someone who agreed to respond.
The probability of getting someone in the 22-29 age group to respond or someone who agreed to respond is 259/371
Let X be the event of contacting the 18-21 age group
Let Y be the event of contacting 22-29 age group
Let A be th event that the pollster responded
Let B be the event that they did not respond
Here,
Probability no. of favorable outcomes/total no. of outcomes/
Hence,
n(A) = 65 + 259
= 324
P(A) = 324/371
Similarly, P(Y) = 294/371
Now,
P(A∩Y) = 259/371
We know that P(C ∪ D) = P(C) + P(D) - P(C∩D)
Therefore, P(A∪Y) = P(A) + P(Y) - P(A ∩ Y)
= 324/371 + 294/371 - 259/371
= 359/371
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Find x, given
AD = BC = 6m.
The value of x in the trapezium is 60 degrees.
How to find the angle of a trapezium?A trapezium is a quadrilateral . The sum of angles in the trapezium is 360 degrees. The legs of the trapezium ABCD are congruent.
The length AB and CD are parallel to each other.
Let's find the angle x as follows:
Therefore, using trigonometric ratios,
cos x = adjacent / hypotenuse
Where
adjacent side = 3 m
hypotenuse side = 6 m
Hence,
cos x = 3 / 6
cos x = 1 / 2
x = cos ⁻¹ 0.5
x = 60 degrees
Therefore,
x = 60 degrees.
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How do you simplify 3/4 + (1/4−16) ?
Answer:
To add fractions, find the LCD and then combine.
3/4 + (1/4−16)= −15
Step-by-step explanation:
1. Noah placed an empty bowl on a scale. He added different amounts of a liquid to the bowl, recording the amount of liquid added, in tablespoons, and the total weight of the bowl and liquid, in grams, each time on a scatter plot. He fit the line
y = 14.75x+861.82 to the data in his scatter plot, where x represents the amount
of the liquid, in tablespoons, and y represents the total weight of the bowl and the
liquid, in grams. Determine the weight, in grams, when 18 tablespoons on the liquid are placed in the bowl. determine the approximate number of tablespoons of the liquid noah needs to add so that the total weight is 1,200 grams
1. The weight for 18 tablespoons is 1127.32 grams.
2. The number of tablespoons of the liquid noah needs to add so that the total weight is 1,200 grams is 23 tablespoon.
What is the weight when 18 tablespoons on the liquid are placed in the bowl?It's vital to note that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the information, Noah placed an empty bowl on a scale and the equation is given as:.
y = 14.75x + 861.82
x = the amount of the liquid, in tablespoons
y = the total weight
The weight for 18 tablespoons will be:
y = 14.75x + 861.82
y = 14.75(18) + 861.82
y = 1127.32
The liquid that Noah needs to add so that the total weight is 1,200 gram will be:
y = 14.75x + 861.82
14.75x + 861.82 = 1200
Collect like terms
14.75x = 1200 - 861.82
14.75x = 338.18
Divide
x = 138.18 / 14.75
x = 23
The tablespoons is 23.
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Can someone please explain this question. Please give a step by step explanation
Answer:
45
Step-by-step explanation:
8 numbers summed and divided by 8 = 41
8numberssummed / 8 = 41
8numberssummed = 41 * 8 = 328
now taking out two numbers whose mean is 29 is the same as taking out two 29's from the sum ....so now there are SIX numbers
6numberssummed = 8numberssummed - 29 -29
= 328 -29 -29 = 270
so to find the mean of the remaining six numbers:
6numberssummed / 6 is 270/6 = 45
Answer:
mean = 45
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
given the mean of 8 numbers is 41 , then
[tex]\frac{sum_{8} }{8}[/tex] = 41 ( multiply both sides by 8 )
sum₈ = 328
given the mean of 2 of the numbers is 29 , then
[tex]\frac{sum_{2} }{2}[/tex] = 29 ( multiply both sides by 2 )
sum₂ = 58
Then
sum₆ = sum₈ - sum₂ = 328 - 58 = 270
then the mean of the other six numbers is
mean = [tex]\frac{sum_{6} }{6}[/tex] = [tex]\frac{270}{6}[/tex] = 45
the function f is defined by f(x)={2x−1for x<3for x≥3. what is the value of ∫51f(x)dx?
The value of the given function f (x) is 10
What is the value of the given function ?[tex]f (x) = \left \{ {{2 \text{ for x} < 3} \atop {x- 1 \text { for x } \geq 3} \right. \\\\[/tex]
Integrating the given functions,
[tex]\int\limits^5_1 {f(x)dx = \int\limits^3_1 2dx + \int\limits^5_3 (x- 1)dx[/tex]
[tex]\int\limits^5_1 {f(x)dx =2x + [\frac{x^{2}} {2} - x][/tex]
Applying the limits,
[tex]\int\limits^5_1 {f(x)dx =[2(3)-2(1)]+ [\frac{5^{2}} {2} - 5-\frac{3^{2}} {2} + 3][/tex]
[tex]\int\limits^5_1 {f(x)dx =[6- 2]+ [\frac{25} {2} - 5-\frac{9} {2} + 3][/tex]
[tex]\int\limits^5_1 {f(x)dx = 4 + 6[/tex]
[tex]\int\limits^5_1 {f(x)dx = 10[/tex]
The value of the given function on integrating using the limits is 10
What is integration?Integration is a technique for combining slices to discover the total. Finding areas, volumes, central points, and many other important things may be done with integration. When infinitesimal data are combined, notions such as displacement, area, and volume can be created. An integral assigns numbers to functions in a way that describes these concepts. Integration is the action of locating integrals. The integrals listed here are those that fall under the category of definite integrals, which can be thought of as the signed area of the region in the plane that is enclosed by the graph of a particular function between two points on the real line.Integration is a fundamental, crucial operation of calculus, along with differentiation.To learn more about integration, refer:
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A car takes 5 hours to cover a distance if it is moving with a speed of 40 mph. Find the time taken by the car if it is moving with a speed of 50 mph.
The time required = 4 hours
The time required by the car to move at a speed of 50 mph to reach a distance of 200 miles is 4 hours
What is Speed?
Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the distance traveled by the car be = D
Now , the speed S of the car = 40 miles per hour
The time required by the car to travel D distance is T = 5 hours
So , the Distance D is calculated from the formula
Distance D = Speed S x Time T
So , substituting the values in the equation , we get
Distance D = 40 x 5
Distance D = 200 miles
Now , the distance traveled by the car remains the constant
The speed of the car is S = 50 miles per hour
And let the time taken by the car to cover 200 miles at 50 mph be = T
Now to calculate Time T ,
Time T = Distance D / Speed S
Substituting the values in the equation , we get
Time T = 200 / 50
Time T = 4 hours
Therefore , the value of T is 4 hours
Hence , The time required by the car to move at a speed of 50 mph to reach a distance of 200 miles is 4 hours
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How do you use De Moivre's theorem to express (1 + i)^8?
The value of (1 + i)^8 is 16. De Moivre's describes how the power of a complex number can be calculated using the properties of its modulus and argument.
De Moivre's theorem states that for any complex number z = r * (cos(θ) + i * sin(θ)) and any integer n, we have:
zⁿ = rⁿ * (cos(n * θ) + i * sin(n * θ))
To use this theorem, we need to first express the complex number (1 + i) in terms of its magnitude and angle. We can do this by using the Pythagorean theorem to find the magnitude of the complex number, which is the square root of the sum of the squares of the real and imaginary parts.
In this case, the magnitude is the square root of 1^2 + 1^2, or √2.
The angle of the complex number can be found using the inverse tangent function. In this case, the angle is 45 degrees, since the tangent of 45 degrees is 1. Now that we have the magnitude and angle of the complex number, we can use De Moivre's theorem to find the value of (1 + i)^8. Substituting the values we found into the formula above, we get:
(1 + i)^8 = √2^8 * (cos(8 * 45) + i * sin(8 * 45))
= 2^4 * (cos(360) + i * sin(360))
= 16 * (1 + i * 0)
= 16
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lara chooses a number less than 100 she devides it by 3 and subtracts 11 divides by 2 her answer is 10.5 what was the number she started with
Answer: 96
Step-by-step explanation:
The easy way to do this is to start backward. The last step she did before she got 10.5 as her answer was dividing her answer by 2.
So we can just multiply 10.5 by 2 to reverse the last step.
After doing that we get 21. The step Lara did before dividing by 2 was subtracting 11.
So we can just add 11 to 21 to reverse this step.
After doing that we get 32. The step Lara did before subtracting 11 was dividing by 3.
So we can just multiply 32 by 3 to reverse this step.
After doing that we get 96. So the number that Lara started with is 96.
Solve (x+2)(x-3) using the foil method
Answer:
Step-by-step explanation:
x^2 - 3x + 2x - 6
x^2 - x - 6
Which of the following is the vertex form of Y = X² - 2x + 5 *?
(x -1)2 = y - 4 is the vertex form of the equation Y = X² - 2x + 5.
What is the vertex form?A quadratic function has the vertex form f(x) = a(x - h)2 + k, where a, h, and k are constants.
Obtain the equation y = ax2 + bx + c.
Determine -b / 2A.
The vertex's x-coordinate is given here.
Simply enter the value of -b / 2a into the equation for x and solve for y to obtain the vertex's y-coordinate.
The vertex's y-coordinate is given here.
So, we have the equation:
Y = X² - 2x + 5
Now, calculate as follows:
⇒ y = (x2 - 2x + 1) + 5 -1
⇒ y - 4 = (x -1)2
⇒ (x -1)2 = y - 4
Therefore, (x -1)2 = y - 4 is the vertex form of the equation Y = X² - 2x + 5.
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What is the solution set of [xl x>-5}u [xl x<5}?
all numbers except-5 and 5
The numbers between-5 and 5
The empty set
All real numbers
The solution set express the numbers between -5 and 5.
What is set in mathematics?It is a mathematical model contains various elements such as numbers, variables, sign and so on arranged in a sequence order. Different set represents different expression.
what is solution set?The elements of a set that satisfy certain given conditions.
in the question, the set represent the numbers which are > -5 and < 5.
hence, the set indicate the numbers between -5 and 5
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the radius of a sphere is incerasing at a rate of 2 ft/min. how fast is the volume changing when the radius is 3 feet
