Using the variable x, write the interval [2,6] using set-builder notation.
Answers
Writing the interval [2,6] using set-builder notation, is:
{ x | x ∈ R, 2 ≤ x ≤ 6 }
How to write an interval in set builder notation?Real numbers (R) include all rational and irrational numbers.
Thus If we need to write the interval [2,6] using set-builder notation, we will write as:
{ x | x ∈ R, 2 ≤ x ≤ 6 }
This is interpreted as x belongs to a set of real numbers greater than or equal to 2 but less than or equal to 6
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Related Questions
Troy uses colored sand to make sand art. The storage container for his sand is shaped like a right square prism. He pours some of the sand into a display container shaped like a right triangular prism. When he is done, the height of the sand left in the storage container is 4 in. What is the height of the sand in the display container?
Answers
The height of the sand in the display container is 12 inches when the display container is right triangular prism.
What is right triangular prism ?
A right triangular prism is a three-dimensional geometric shape with two parallel triangular bases and three rectangular faces. The rectangular faces connect the corresponding vertices of the triangular bases.
To find the height of the sand in the display container, we need to use the fact that the volume of sand in the storage container is equal to the volume of sand in the display container.
The storage container has a length, width, and height of 6 inch, 6 inch, and 6inche, respectively. Then, the volume of the storage container is:
\(V_{storage} = L * W * H = 6 * 6 * 6 = 216 inch^3\)
Similarly, let's assume that the display container has a base of length 4 inch and height 9 inches and height of sand be H.
Then, the volume of the display container is:
\(V_{display} = (1/2) * b * h * H = (1/2) * 4 * 9 * H = 18H\)
where (1/2) is the area of the triangle base of the display container.
Since the volumes of sand in both containers are equal, we can set these expressions equal to each other and solve for h:
216 = 18H
H = 12 inches
Therefore, the height of the sand in the display container is 12 inches.
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a vendor had 200 balloons for sale .If he sold 125 of them,what percent remains unsold?
Answers
Answer: 37.5%
Step-by-step explanation:
200-125=75
75 divided by 200 is 0.357
since we need percent so were gonna move the decimal point 2 places so the final answer is 37.5% remain unsold
A recycling truck begins its weekly route at the recycling plant at point A, as pictured on the coordinate plane below. It travels from point A to point B, then points C, D, and E, respectively, before returning to the recycling plant at point A at the end of the day. The truck’s route is illustrated on the coordinate plane below. If each unit on the coordinate plane represents one mile, what is the total distance the truck travels on its route?
A. 41
B. 38
C. 13
D. 5
(The picture of the graph should be there, I apologize if it isn't clear enough. Also, please explain the answer in detail, I want to try to understand it so when I approach a problem like this, I will know what to do)
Answers
Answer:
41
Step-by-step explanation:
Answer:
B. 38Step-by-step explanation:
Use Pythagorean theorem to find line lengthsWe see the figure formed by the route is symmetric and
BC = EACD= DEThe total distance is the perimeter of the polygon
1. AB is horizontal line, 2 units long (from -1 to 1)
1 - (-1) = 2 miles2. BC = √((5-1)²+(2 -(-1))²) = √(16 + 9)= √25 = 5 miles
EA = BC = 5 miles3. CD = √(13-2)² + (5-1)²) = √121+16 = √137 = 11.7 miles
DE = CD = 11.7 milesTotal
2 + 5*2 + 11.7*2 = 35.4 milesClose option is option B
Suppose that the function g is defined, for all real numbers, as follows. Find g(-5) ,g (-2), and g(-1)
Answers
If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.
A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :
g(x) = {-(1/2)x + 1, for x<-2
= {-(x+1)², for -2≤x≤1
= {4 for x>1
We have to find the value of g(-5) ,g (-2), and g(-1),
For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,
⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,
For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function
"-(x+1)²" will be used,
⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,
For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,
⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,
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Last year there were 90 players in the So Cal Soccer League. This year, the enrollment decreased by 30%. How many players are now in the league?
Answers
63 players
step-by-step explanation:
30% of 90 is 27
0.30 • 90
90-27
63
Drag steps in the given order to evaluate this expression,
-3(-3+2) - 6
Answers
Answer:-3
Step-by-step explanation:
find the missing angle
Answers
Answer:
? = 77°
Step-by-step explanation:
the 3 angles in a triangle sum to 180° , that is
? + 35° + 68° = 180°
? + 103° = 180° ( subtract 103° from both sides )
? = 77°
Answer:77
Step-by-step explanation:
180-103=77
value of tan(90 - cot^-1(1/3))
Answers
Answer:
0.36
Step-by-step explanation:
We need to solve the first bracket first and then the others,
Value of Cos^ - 1(1/3) =70.53°
Then, 90 - the value of cosine
=19.47°
Then, put the new in the calculator:
Tan (19.47°)
and the answer comes 0.3535294237
then I use the nearest formula and got the answer = 0.36
Help help math straightforward answer ASAP pelsss thanks
Answers
Answer:
55 degrees
Step-by-step explanation:
a line is 180 degrees. also, all angles in any triangle add up to 180 degrees. so, find the missing angle in the triangle by 180-30-25=125 degrees. Then to find angle 4, 180-125=55 degrees.
The ages of registered voters in Smith County are normally distributed with a population standard deviation of 3 years and an unknown population mean. A random sample of 18 voters is taken and results in a sample mean of 55 years. Find the margin of error for a 95% confidence interval for the population mean. 20.01 20.10 1.282 20.05 1.645 20.025 1.960 20.005 2.576 2.326 You may use a calculator or the common z values above. • Round the final answer to two decimal places.
Answers
Answer:
The margin of of error for a 95% confidence interval for the population mean is of 1.39 years.
Step-by-step explanation:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.95}{2} = 0.025\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.
The margin of error is:
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
Population standard deviation of 3 years
This means that \(\sigma = 3\)
Sample of 18 voters
This means that \(n = 18\)
Margin of error:
\(M = z\frac{\sigma}{\sqrt{n}}\)
\(M = 1.96\frac{3}{\sqrt{18}}\)
\(M = 1.39\)
The margin of of error for a 95% confidence interval for the population mean is of 1.39 years.
For her party can Nina fill fewer than 10 bags with treats between 10 and 20 bags between 20 and 30 bags or more than 30 bags explain
Answers
The correct option regarding the number of bags filled by Nina, using proportions, is given as follows:
Between 20 and 30 bags.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates of the problem and basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem.
In this problem, a proportion is applied to find the number of bags filled by Nina, which is given by the division presented as follows:
Number of bags = Number of treats / Treats per bag.
The values of these parameters are given as follows:
Number of treats: 78.Number of treats per bag: 3.Hence the numeric value of the expression is:
Number of bags = 78/3 = 26.
Which is a number between 20 and 30.
Missing InformationThe problem states that Nina had 78 treats, and each bag has 3 treats, then it asks the correct option regarding the number of bags.
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solve missing values for triangles
Answers
Answer:
32±b±90=180(being the three angle of a treangle)
32±90±b=180
122±b=180
B=180-122
b=58 answer
90±23±d=180(being three angle of the trangle)
113±d=180
d=180-113
d=78 answer
Answer
:.b=58
:.d=78
Thank you
The difference in the x-coordinates of two points is 3, and the difference in the y-coordinates of the two points is 6. What is the slope of the line that passes through the points?
Answers
Answer:
2
Step-by-step explanation:
Slope is the ratio (quotient) of vertical change (the change in y) and the horizontal change (the change in x).
You may have heard "rise over run" as a phrase to help remember.
\(\frac{6}{3}=2\)
You are buying a used car which costs $10,200. You plan to sell the car after keeping it for 5 years. Research shows that this car will lose value at a rate of 8% per year. How much will the car be worth after 5 years?
Answers
Answer:
$6,722.63
Step-by-step explanation:
Now: $10,200
In 1 year: 0.92 × $10,200 = $9,384
In 2 years: 0.92 × $9,384 = $8,633.28
In 3 years: 0.92 × $8,633.28 = $7,942.6176
In 4 years: 0.92 × $7,942.6176 = $7,307.208192
In 5 years: 0.92 × $7,307.208192 = $6,722.63
Answer: $6,722.63
Answer:
$6,722.63
Step-by-step explanation:
Using this formula A=P(1-d/100)^n where
A = Amount
P = Principal
d = percent
n = number of year
A=P(1-d/100)^n
A = 10,200(1-8/100)⁵
A = 10,200(1-0.08)⁵
A = 10,200(0.92)⁵
A = 10,200(0.6591)
A= $6,722.63
p(5)=
p(1 or 2)=
p(odd number)=
p(not 6)=
p(even number)=
p(1,2,3,or 4)=
Answers
The probabilities, we need to understand the context. Assuming we are working with a fair six-sided die, where each face has an equal chance of landing, here are the probabilities:
P(5): Since there is only one face with a value of 5 on the die, the probability of rolling a 5 is 1/6.P(1 or 2): There are two faces with the values 1 and 2 respectively. Since these are mutually exclusive events (you can only roll one of them at a time), the probability of rolling a 1 or a 2 is 2/6, which simplifies to 1/3.P(odd number): Out of the six faces, three are odd numbers (1, 3, and 5). So, the probability of rolling an odd number is 3/6, which simplifies to 1/2.P(not 6): Since there is only one face with a value of 6, the probability of not rolling a 6 is 5/6.P(even number): Out of the six faces, three are even numbers (2, 4, and 6). So, the probability of rolling an even number is 3/6, which simplifies to 1/2.P(1, 2, 3, or 4): There are four faces with the values 1, 2, 3, and 4. Therefore, the probability of rolling any of these numbers is 4/6, which simplifies to 2/3.For such more questions on probability
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The perimeter of a rectangular garden is 110 feet. Find its dimensions if the length is 5 feet less than twice the width.
Answers
For this you can start by making a drawing
Since the perimeter is the sum of all the sides of a geometric figure then you would have
\(\begin{gathered} x+y+x+y=110 \\ 2x+2y=110\rightarrow(1) \end{gathered}\)On the other hand, since the length of the rectangular garden is 5 feet less than twice the width, then
\(\begin{gathered} x=2y-5 \\ \text{ Substract 2y from both sides of the equation} \\ x-2y=-5\text{ }\rightarrow(2) \end{gathered}\)Now, with (1) and (2) you have a system of linear equations. To solve it you can use the elimination method, like this
\(\begin{gathered} \mleft\{\begin{aligned}2x+2y=110 \\ x-2y=-5\end{aligned}\mright. \\ \text{Add both equations} \\ 3x+0y=105 \\ 3x=105 \\ \text{ Divide both sides of the equation by 4} \\ \frac{3x}{3}=\frac{105}{3} \\ x=\frac{105}{3}=35 \end{gathered}\)Finally to find the value of y, you can replace the value of x in (1) or in (2). For example in (1)
\(\begin{gathered} 2x+2y=110 \\ 2(35)+2y=110 \\ 70+2y=110 \\ \text{ Subtract 70 from both sides of the equation} \\ 70+2y-70=110-70 \\ 2y=40 \\ \\ \text{ Divide both sides of the equation by 2} \\ \frac{2y}{2}=\frac{40}{2} \\ y=20 \\ y=20 \end{gathered}\)Therefore, the dimensions of the rectangular garden are 35 feet length and 20 feet width.
Cars enter a car wash at a mean rate of 2 cars per half an hour. What is the probability that, in any hour, no more than 4 cars will enter the car wash
Answers
Answer:
1.56499409
Step-by-step explanation:
We solve using Poisson Distribution
P = λ^k × e^-λ/k!
λ is the average of events = mean rate of 2 cars per half an hour = 2 × 2 = 4
e is the euler's number
k is the number of events you want to know the probability = no more than 4
= ≤ 4
Hence:
P(≤ 4) = 4^4 × e^-4/4! + 4^3 × e^-4/3! + 4^2 × e^-4/2! + 4^1× e^-4/1! + 4^0× e^-4/0!
P(≤ 4) = 0.1953668148 + 0.1953668148 + 1.0826822659 + 0.0732625556 + 0.0183156389.
P(≤ 4) = 1.56499409
What is x when x=2-4+5
Answers
2⋅(3^6⋅3^−5)
PLZ NO LINK PLZZZZ
Answers
A spherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute.
(a) Find the rates of change of the radius when r = 50 centimeters and r = 85 centimeters.
r = 50 ? cm/min
r = 85 ? cm/min
(b) Explain why the rate of change of the radius of the sphere is not constant even though dv/dt is constant.
A.) dr/dt as a function runs parallel to the volume function, which is not linear
B.) The rate of change of the radius is a linear relationship whose slope is dV/dt
C.) The rate of change of the radius is a cubic relationship.
D.) The volume only appears constant; it is actually a rational relationship.
E.) dr/dt depends on r2, not simply r.
Answers
Answer this with explanation please
Answers
The measure of angle MTU m∠MTU is 114 degree.
What is the measure of angle MTU?From the figure in the diagram:
Measure of angle STU is 145 degrees and measure of angle STM is 31 degree.
m∠STU = 145°m∠STM = 31°m∠MTU = ?Since, angle STU composes or is the sum of angle STM and angle MTU.
To find angle MTU, simply subract angle STM from angle STU.
m∠STU = m∠STM + m∠MTU
Hence:
m∠MTU = m∠STU - m∠STM
Plug in the given values and simplify
m∠MTU = 145° - 31°
Subtract 31 from 145
m∠MTU = 114°
Therefore, angle MTU measure 114°.
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Students at polk midle school ate given a fitnrss test. The results of their tests are shown .in the table. Use the table to answer questions a-c
Answers
In linear equation ,the time taken by Evian, Toby and J are 10, 9 and 12 minutes respectively.
What is linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.Using the concept of proportional relationship, the time taken by Evian, Toby and J are 10, 9 and 12 minutes respectively.
Using the concept of proportional relationship :
For Evian :
1.5 miles = 15 minutes
1 mile = x
1.5x = 15
x = 15 / 1.5
x = 10 minutes
For Toby :
2/3 miles = 6 minutes
1 mile = x
2/3x = 6
x = 6 ÷ 2/3
x = 9 minutes
For J :
0.75 miles = 9 minutes
1 mile = x
0.75x = 9
x = 9 / 0.75
x = 12 minutes
Therefore, the time taken by Evian, Toby and J are 10, 9 and 12 minutes respectively.
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The complete question is -
Students at Polk Middle School are given a fitness test. The results of their tests are shown in the table. Use the table to answer questions d-c. a. Find the time it takes each student to run 1 mile. FITNESS TEST RESULT Evian 1 1/2 miles in 15 minutes Toby: 2/3 miles in 6 minutes Jillian 3/4 miles in 9 minutes.
-3x + 10y = 11
-8x + 2y = -20
Answers
Answer:
(3, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define systems
-3x + 10y = 11
-8x + 2y = -20
Step 2: Rewrite systems
-8x + 2y = -20
Add 8x to both sides: 2y = 8x - 20Divide 2 on both sides: y = 4x - 10Step 3: Redefine systems
-3x + 10y = 11
y = 4x - 10
Step 4: Solve for x
Substitution
Substitute in y: -3x + 10(4x - 10) = 11Distribute 10: -3x + 40x - 100 = 11Combine like terms: 37x - 100 = 11Add 100 to both sides: 37x = 111Divide 37 on both sides: x = 3Step 5: Solve for y
Define original equation: -3x + 10y = 11Substitute in x: -3(3) + 10y = 11Multiply: -9 + 10y = 11Add 9 to both sides: 10y = 20Divide 10 on both sides: y = 2Step 6: Graph system
Check the system.
The number of students, S, serviced by the school system in the town of Emor,
t years from 2000can be modeled by the function S(t)=10,000(1.1)^t
The number of classrooms, C, in the town of Emor, t years from 2000 can be modeled by the function C(t)=450+40t, Let
D be the average number of students per classroom in Emor's school system
t years from 2000
Write a formula for
D(t)D in terms of: S(t)S, C(t)
Also, Write a formula for
D(t)D, in terms of t
Answers
The required expression is 10000x\((1.1)^{t}\)/(45 + 4t).
The expression representing the number of students serviced by the school system in the town of Emor, t years from 2000 is:
s(t) = 10000x\((1.1)^{t}\)
And the expression representing the number of classrooms in the town of Emor, t years from 2000 is:
C(t) = 450 + 4t
The expression D (t) represents the average number of students per classroom in Emor's school system t years from 2000.
Then the average number of students per classroom can be computed by:
Average number of students/classroom = Number of students/Number of classrooms
D(t) = s(t)/c(t)
= 10000x\((1.1)^{t}\)/(45 + 4t)
Thus,
The formula = 10000x\((1.1)^{t}\)/(45 + 4t).
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Which expression has both eight and N factors
Answers
Answer:
8n
Step-by-step explanation:
8n is the factor of both 8 and n. in the following question. Factor ⇒ If a number, that use to divide another number and we get zero as a remainder, the number is called the factor of another number.
A man pulled a cart filled with stones that had a total mass of 60 kg.
He increased the amount of force used to pull the cart from 60 N to 90 N, what is the new
acceleration of the cart?
Answers
a1 = f/m
a1 = 60/60 = 1ms^-2
a2 = f2/m
a2 = 90/60
a2 = 1.5ms^-2
The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²
What is Force ?The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.
Formula of force,
F = ma
Given that,
A man pulled a cart filled with stones that had a total mass of 60 kg
He increased the amount of force used to pull the cart from 60 N to 90 N
New acceleration of cart = ?
F = ma
Old acceleration,
60 = 60a
a = 1 m/s²
New acceleration,
90 = 60a
a = 90/60
a = 3/2
a = 1.5 m/s²
Hence, the new acceleration is 1.5 m/s²
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Solve: 3 = 21
m
I NEED HELP ON THIS QUESTION ITS MY LAST ONE.....
Answers
What is an equation that represents the line that passes through the points (1, 1) and (-2, 7)?
Answers
Not sure if this is correct but I hope this helps :)
I’ve been trying to figure this out
Answers
As a result, it is discovered that the answer to the given function problem is slant sample points of y = x -4.
What does the term function mean?Mathematical studies cover the areas and prospective applications of geometry as well as numbers and their variants, equations, and related structures. A group of inputs that collectively produce a similar result is referred to as a "function." Each input contributes to a single, distinguishable consequence in an output-input connection known as a function. Each activity has a scope, which is also known as a region or city or municipality. Commonly, functions are denoted by the letter f. (x). The origin is X. Across operations, one-to-one action, many-to-one activity, on activity, and on
Here,
Every one of the three asymptotes can be used to construct a rational function because rational functions can take any form.
This is depicted in both the linked graph and the graph of the function f(x that serves as a representation. The function's asymptotes are as follows.
The asymptotes for the vertical slope are x = -4,
The horizontal asymptotes are Y = 0 and.
Slant has an asymptote of Y = x -4.
An exponential function is used in our example function. That isn't generally perceived of as a polynomial, but it may be expressed as an endless degree polynomial. A rational function is typically described in publications as the percentage of polynomials.
As a consequence, the solution to the given function problem is slant sampling points, which are y.
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2. The table includes results from polygraph experiments. In each case, it was known if the
subject lied or did not lie, so the table indicates when the polygraph test was correct. Find the
test statistic needed to test the claim that whether a subject lies or does not lie is independent of
the polygraph test indication.
Polygraph test indicated
that the subject lied.
Polygraph test indicated
that the subject did not lie.
025.571
Did the Subject Actually Lie?
No (did not lie) Yes (lied)
15
32
42
9
(1 poir
Answers
We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
How to explain the hypothesisThe test statistic needed to test the claim that whether a subject lies or does not lie is independent of the polygraph test indication is the chi-square statistic.
In this case, the grand total is 90. The row totals are 57 and 33, and the column totals are 42 and 48. The expected frequencies are as follows:
The chi-square statistic is calculated as 0.177. The p-value for the chi-square statistic is calculated using a chi-square table. The degrees of freedom for the chi-square table are the number of rows minus 1, multiplied by the number of columns minus 1.
Since the p-value is greater than 0.05, we fail to reject the null hypothesis. We cannot conclude that whether a subject lies or does not lie is independent of the polygraph test indication.
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