The interquartile range of the sample data represented on the stem and leaf diagram is 21.
What is the interquartile range?
IQR(interquartile range) is the difference between the third and first quartile.
The range of a set of data is the difference between the largest and smallest values. The difference is specific; the range of a set of data is the result of subtracting the sample maximum and minimum.
Range = Maximum value - Minimum value
Range = 23 - 02 = 21
We know that the range is the difference between the smallest and the largest value and in the interval we write it as:
From a to b where a is the smallest value and b is the maximum value.
Hence, The interquartile range of the sample data represented on the stem and leaf diagram is 21.
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you make $512.92 a week. if you work 36 hours find your hourly rate of pay
The hourly rate of pay is $14.25
To solve this, w
rewrite 2 5/8 into fraction
Answer:
i think 21/8
Step-by-step explanation:
because 2 times 8 plus 5 divided by 8 gives you 16 + 5 divided by 8 which is 21/8
Calculate Sample Variance for the following data collection: 10, 11,12, 13, 14, 18.
To calculate the variance follow these steps:
1. Work out the Mean
2. Then for each number: subtract the Mean and square the result .
3. Then work out the average of those squared differences.
The data are 10, 11, 12, 13, 14, 18
The first step find the mean
The mean = sum of data/number of data
The sum = 10 + 11 + 12+ 13 +14 + 18 = 78
The number =
Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32.
How can the triangles be proven similar by the SAS similarity theorem?
The triangles can be proven similar by the SAS similarity theorem based on this: B. Show that the ratios are equivalent, and ∠V ≅ ∠Y.
The properties of similar triangles.In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the side, angle, side (SAS) similarity theorem, in order to prove that theses two (2) triangles are similar, it needs to be shown that the ratio of the corresponding side lengths of these triangles are equal and that their corresponding angles are congruent as shown below:
Side UV = side XY
∠V ≅ ∠Y
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Complete Question:
Consider the two triangles.
How can the triangles be proven similar by the SAS similarity theorem?
Show that the ratios are equivalent, and ∠U ≅ ∠X.
Show that the ratios are equivalent, and ∠V ≅ ∠Y.
Show that the ratios are equivalent, and ∠W ≅ ∠X.
Show that the ratios are equivalent, and ∠U ≅ ∠Z.
Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 61 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 8.3 and a standard deviation of 2.4. What is the 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is 7.9067<m<8.6933.
What is a confidence interval?
In statistics, a confidence interval describes the likelihood that a sample size would fall between such a set range of values for a specific percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% likelihood that the true value comes inside that range if the following are examples of 10.00 produced using a statistical model with a 95% standard error of 9.50 - 10.50.In the study of chocolate chips,
sample size, n=61
mean, x=8.3
standard deviation, s=2.4
90% of the confidence interval
[tex]8.3-(\frac{1.28*2.4}{\sqrt{61} } ) < m < 8.3+(\frac{1.28*2.4}{\sqrt{61} } )[/tex]
7.9067<m<8.6933
The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is 7.9067<m<8.6933.
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Rewrite each explicit formula in the form of a function an = 19 - 7(n - 1)
Write the statement as a conditional statement, then tell which part is the hypothesis and which is the conclusion. Write the inverse, converse, and contrapositive of your conditional statement:
People who reduce their time in the shower will save money on water.
Conditional Statement: If people reduce their time in the shower then they will save money on water.
Hypothesis: "If people reduce their time in the shower"
Conclusion: "they will save money on water"
What is the conditional statement?A conditional statement is defined as the two fundamental components that make up a conditional statement are Hypothesis (if) and Conclusion (then).
Conditional Statement: If people reduce their time in the shower then they will save money on water.
Hypothesis: "If people reduce their time in the shower"
Conclusion: "they will save money on water"
Inverse Statement: If people did not reduce their time in the shower, then they will not save money on water.
Converse Statement: If they will save money on water then people reduce their time in the shower.
Contrapositive Statement: If they will not save money on water then people do not reduce their time in the shower.
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The second part of the problem is where i need help. The answers i have there have been given by other tutors
SOLUTION
From the given value
Since
[tex]\sin u=\frac{7}{25}[/tex]Then using trigonometrical ratios it follows
[tex]\cos u=\frac{24}{25}[/tex]Using hal -ngle it folows
[tex]\begin{gathered} sin(\frac{u}{2})=\sqrt{\frac{1-\frac{24}{25}}{2}} \\ s\imaginaryI n(\frac{u}{2})=\sqrt{\frac{1}{50}} \end{gathered}[/tex]Also
[tex]\begin{gathered} cos(\frac{u}{2})=\pm\sqrt{\frac{1+\frac{24}{25}}{2}} \\ cos(\frac{u}{2})=\sqrt{\frac{49}{50}} \\ cos(\frac{u}{2})=7\sqrt{\frac{1}{50}} \end{gathered}[/tex]Finally?
[tex]\begin{gathered} \tan(\frac{u}{2})=\pm\sqrt{\frac{1-\frac{24}{25}}{1+\frac{24}{25}}} \\ \tan(\frac{u}{2})=\sqrt{\frac{1}{49}} \\ \tan(\frac{u}{2})=\frac{1}{7} \end{gathered}[/tex]I need help finding the vortex angle with these three sides. I don’t really know how to do this sort of thing with an isosceles triangle. Once I know the vortex angle I can figure out the base angles.
Answer:
[tex]\begin{gathered} \text{ Smalles angle in the triangle}\colon \\ D=14.36\degree \\ \text{ The measure of the two congruent angles:} \\ Step-by-step explanation:To find the angle D, use the law of cosines, which is represented as:
[tex]\begin{gathered} d^2=e^2+f^2-2(e)(f)\cos D \\ 3^2=12^2+12^2-2(12)(12)\cos D \\ 9=144+144-288\cos D \\ -279==-288\cos D \\ \frac{-279}{-288}=\cos D \\ D=\cos ^{-1}(\frac{-279}{-288}) \\ D=14.36\degree \end{gathered}[/tex]Then, since the base angles are equal in measure:
[tex]\begin{gathered}Use the list below to complete each sentence.
factor
product
1. -3- (-12)=-12-(-3)
positive
negative
a. This equation is written using the
of Multiplication.
additive inverses
Distributive Property
b. Both factors in this equation are Poritiv
c. The product will be Distributive property
3. (5 (-9))-6-5-((-9). 6)
b. One
2. -7 (-8+8)=[-7 (-8)] + [-7.8]
a. This equation is written using the
b. The product of this equation is 0. This is because the sum of the
,-8 and 8, is equal to 0.
a. This equation is written using the
of Multiplication.
are positive.
c. The
negative
Commutative Property
Associative Property
is negative, while the other two
will be negative.
1a) This equation is written using the Distributive Property of Multiplication.
b) Both factors in this equation are negative.
c) The product will be positive.
2a) This equation is written using the Additive inverses of Multiplication.
b) The product of this equation is 0.
c) This is because the sum of (-8+8) is equal to 0.
3a) This equation is written using the Commutative Property of Multiplication.
b) The products of the commutative multiplications do not change.
c) This is because changing the order of factors does not affect the solution.
What are the properties of multiplication?The properties of multiplication are:
Identity Property of Multiplication (product of 1 and another factor remains the factor.)Associative Property of Multiplication (grouping order of factors does not change the product.)Distributive Property of MultiplicationCommutative Property of Multiplication (the order of factors does not change the product.)For the distributive property, multiplying the sum of two numbers by another number gives the same result as distributing the first number to both other numbers and multiplying them separately and adding.
1) -3(-12) = -12(-3)
= 36 = 36
2) -7 (-8+8) = [-7 (-8)] + [-7 (8)]
= -7(0) = [56 + - 56
0 = 0
3. (5 (-9))-6 = -5 ((-9) +6)
(-45)-6 = -5(-54)
270 = 270
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Question Completion:2) -7 (-8+8) = [-7 (-8)] + [-7 (8)]
3. (5 (-9))-6 = -5 ((-9) +6)
(PLS HELP, FINAL QUESTION!!!)
which of the following lists the correct values of a, h, and k for the function: f(x)=n^2+6
A) a = 1, h = 1, k = 6
B) a = 1, h = –1, k = 6
C) a = 1, h = 0, k = 6
D) None of the choices are correct.
Answer:
N^2+6 is in standard form, which is in ax^2+bx+c,
in order to get it to vertex form, which y=a(x-h)^2+k, we need to find the vertex, through x=-b/2a, in this case:
x=-0/2(1)=0, so h=0, then plug 0 in for n,
0^2+6=6,
which makes k=6,
therefore, the answer is c.
as for a, the value of a is constant in all forms, whether standard, vertex or factored, making a=1
Brainliest pls
=O EXPONENTS AND POLYNOMIALSProduct rule with positive exponents: UnivariateMultiply.-W3(-2²)Simplify your answer as much as possible.X 5?
Answer
Explanation: To solve this question we will just need to consider some rules as represented below
[tex]\begin{gathered} -a(-b)=+ab \\ x^a*x^b=x^{a+b} \end{gathered}[/tex]Step 1: Once we understand both rules above we can use them to simplify our equation as follows
[tex]\begin{gathered} -w^3(-2w^3) \\ +2*w^3*w^3 \\ 2*w^{3+3} \\ 2w^6 \end{gathered}[/tex]Final answer: So the final answer is
[tex]2w^{6}[/tex].
CAN SOMEONE HELP WITH THIS QUESTION?✨
The value of P = $5000, r = 3.6%/4 = 0.9%, n = 4n and amount after 10 years is $5450.
Compound interest may be defined as the interest which can be applied by any institution on any individual in which the interest amount after a year becomes principle for the next year. The formula for compound interest is given as A = P(1 + r/n) ^ nt where A is the amount, P is the principle, r is the interest rate, n is compounding frequency and t is the time. If compounded quarterly the principle will be same as in the question that is $5000, the interest rate will be divided by 4 that is r = 0.9% and the compounding frequency will be 4 times that is 4n. Now, we need to find the amount after 10 years that is t = 10 years. The amount will be
A = P(1 + r/4n) ^ 4nt
A = 5000(1 + 0.9/100×4×12) ^4×12×10
A = 5000(1.09)
A = $5450 which will be amount after 10 years.
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Jayla plays on the Strikers soccer team. The team worked on 5 new drills at yesterday's
practice, spending the same amount of time on each drill. Jayla was 15 minutes late and only
practiced for 40 minutes.
) Which equation can you use to find how long, x, the team spent on each drill?
The equation that can be use to find how long, x the team spent on each drill is 55 = 5x
How to represent equation?Jayla plays on the Strikers soccer team.
The team worked on 5 new drills at yesterday's practice, spending the same amount of time on each drill.
Jayla was 15 minutes late and only practiced for 40 minutes.
The equation that can be used to represent the situation is as follows:
where
x = time the team spent on each training drill
Therefore, the equation is as follows:
15 + 40 = 5x
55 = 5x
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Ten bags of beans cost GH¢350.00.
a)Find the cost of 6 bags.
b)Find the cost of 11 bags.
c)How many bags can GH¢245.00
buy?
With solutions
The cost of 6 bags is GH¢ 210
The cost of 11 bags is GH¢ 385
GH¢245.00 can buy 7 bags
Tens bags cost GH¢350.00
one bags cost = 350/10
= 35
The cost of 6 bags can be calculated as follows
1 bag= 35
6= x
cross multiply both sides
x= 35×6
x= 210
The cost of 11 bags can be calculated as follows
1= 35
11= y
cross multiply
y= 35 × 11
= 385
The number of bags GH¢245.00 will buy can be calculated as follows
1 = 35
x= 245
cross multiply both sides.
35x= 245
x= 245/35
x= 7
Hence GH¢245.00 can buy 7 bags, 6 bags cost GH¢210 and 11 bags cost GH¢ 385
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use the recipe to find the ratio of bananas to tomatoes in simplest form. put the ratio data in the first row of the ratio table below. the fill in the ratio table to create two equivalent ratios
Answer:
Bananas Tomatoes
1 3
2 6
3 9
4 12
Explanation:
The ratio of bananas to tomatoes can be calculated as the division of the number of bananas in the recipe over the number of tomatoes in the recipe. So, the ratio is:
[tex]\frac{2\text{ bananas}}{6\text{ tomatoes}}[/tex]Therefore, to find the simplest form, we can divide the numerator and denominator by 2 as:
[tex]\frac{2\div2}{6\div2}=\frac{1\text{ bananas}}{3\text{ tomatoes}}[/tex]Then, we can fill the table as:
Bananas Tomatoes Ratio
1 3 1/3
2 6 2/6 = 1/3
3 9 3/9 = 1/3
4 12 4/12 = 1/3
Where every ratio is equivalent to 1/3
2. Calculate each surface area to the nearest tenth of a square centimetre ) r = 10 cm b) a) d=7 cm 30 cm 22 cm 3. bbelow 1
The formula to find the surface area of a cylinder is:
[tex]\begin{gathered} S.A.=2\pi r^2+2\pi rh \\ \text{ Where} \\ S.A\text{. is the surface area,} \\ r\text{ is the radius, and} \\ h\text{ is the height of the cylinder} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} r=10\operatorname{cm} \\ h=22\operatorname{cm} \\ S.A.=2\pi r^2+2\pi rh \\ S.A.=2\pi(10cm)^2+2\pi(10cm)(22cm) \\ S.A.=2\pi(10cm)(10cm)+2\pi(10cm)(22cm) \\ S.A.=628.3cm^2+1382.3cm^2 \\ S.A.=2010.6cm^2 \end{gathered}[/tex]Therefore, the surface area of the given cylinder rounded to the nearest square centimetre is 2010.6 cm².
Is the ordered pair a solution of the equation? 4x+5y=-1; (1,-1) And 2x-3y=7; (8,-3)
The given equations are:
4x + 5y = - 1
2x - 3y = 7
For the ordered pairs to be a solution of the equation, the equation must be true when the points are substituted into the equation. That is, the right hand side must equal the left hand side.
For 4x + 5y = -1
To test if (1, -1) is a solution, substitute x = 1, and y = -1 into the equation.
4(1) + 5(-1) = -1
4 - 5 = -1 (True)
Therefore, (1, -1) is a solution for the equation 4x + 5y = -1
For 2x - 3y = 7
To test if (8, -3) is a solution, substitute x = 8, and y = -3 into the equation
2(8) - 3(-3) = 7
16 + 9 = 7 ( False)
Therefore, (8, -3) is not a solution for 2x - 3y = 7
Which of the expressions below has a sum of 0? select all that apply A. 4+(-4) B. 6.3 +(-3.6) C. 13+(-11) D. -9+9
Answer:
A. 4+(-4),
D. -9+9
Step-by-step explanation:
A expression has a sum of 0 when we have two equal numbers with inverse signals.
A. 4+(-4)
We have the same number(4), and they have inverse signals. So this expression has a sum of 0.
B. 6.3 +(-3.6)
6.3 and 3.6 are different numbers, so this expression does not have a sum of 0.
C. 13+(-11)
13 and 11 are different numbers, so this expression does not have a sum of 0.
D. -9+9
We have the same number(9), with inverse signals. So yes, this expression has a sum of 0.
The volume of this cylinder is approximately 12,468.94 cubic feet.The radius is ___ feet.Use π = 3.14.
we have that
the volume of the cylinder is
V=pi(r^2)h
the radius is given
r=57 cm
Remember that
1 ft=30.48 cm
so
57 cm=57/30.48=1.87 ft
the radius is 1.87 ftHey I need help I got stuck I am struggling
According to the trigonometric relations in a right triangle, the following relation is valid:
[tex]\begin{gathered} \sin x\degree=\frac{\text{opposite leg}}{hypotenuse}=\frac{4.9}{7.5} \\ \sin x\degree=0.6533\ldots \\ x\degree=\arcsin 0.6533\ldots \\ x\degree\approx40.8\degree \end{gathered}[/tex]Given a system of linear equations in three variables \Biggl \lbrace \begin{matrix} 4x+3y+2z=12 \\ x+y+z=9 \\ 2x+4y+3z=20 \end{matrix}
You are going to solve the system by performing the following steps.
(5pts) Eliminate y from \biggl \lbrace \begin{matrix} 4x+3y+2z=12 \\ 2x+4y+3z=20 \end{matrix}
(5pts) Eliminate y from \biggl \lbrace \begin{matrix} x+y+z=9 \\ 2x+4y+3z=20 \end{matrix}
(5pts) Eliminate x from the two equations you got from part (1) and part (2).
(2pts) Find the solution for the given system.
(3pts) Check your solution for the given system.
Answer:
Step-by-step explanation:
n
2. The slope of a line is -4. Find the value of x so that the line passes through the points
(-1,7) and (x,-9). A graph
is provided if needed.
The value of the variable 'x' is calculated by solving equation of the line by using slope value is: x = 3
What is slope of a line?
The slope of a line explain the steepness of the line segment. It is ration of the coordinates of the y-axis and the vertical coordinates of the x-axis. Depending upon the slope value, it is classified as whether lines are parallel or perpendicular.
According to the question, the given parameters for the line segment is as written below:
Slope of a line = (-4) and the coordinate points = (-1, 7)(x,-9): (x1 = -1; y1 = 7)
Now, by using standard equation for the line segment: y = mx + c
where, 'm' is the slope; c is the y-intercept; (x, y) are coordinates
Substituting given values that is slope and y-intercept in the standard equation, we get:
y = mx + c
⇒ 7 = (-4)(-1) + c
⇒ c = 7 - 4 = 3
Therefore, the value of the y-intercept is: c = (3)
Equation of the line by substituting the value of the y-intercept as well as slope value in another equation whose coordinates are (x, -9):
-9 = (-4)x + (3) ⇒ -12 = -4x ⇒ x =3
Hence, the value of the variable 'x' is calculated by solving equation of the line by using slope value is: x = 3
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A certain species of fish require 1.5 cubic feet of water per fish to maintain a healthy environment. Find the maximum number of fish you could put in a tank measuring 5 feet by 3 feet by 4 feet.
Answer:
40
Step-by-step explanation:
Given information:
1.5 ft³ = Volume of water required per fish.Dimensions of the tank = 5 ft × 3 ft × 4 ftModel the tank as a rectangular prism.
[tex]\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\\\\implies \textsf{Volume of tank}&=\sf 5 \; ft \times 3\; ft \times 4 \; ft\\& = \sf 15\;ft^2 \times 4\;ft\\& = \sf 60 \; ft^3\end{aligned}[/tex]
To find the maximum number of fish that can be put in the tank, divide the found volume of the tank by the given volume of water required per fish:
[tex]\begin{aligned}\textsf{Maximum number of fish}&=\textsf{Volume of tank} \div \textsf{Water per fish}\\& = \sf 60\;ft^3 \div 1.5 \; ft^3\\& = \sf 60 \div 1.5\\& = \sf 40\end{aligned}[/tex]
Therefore, the maximum number of fish that can be put in the tank is 40.
Write an equation of the line passing through point P(3,8) that is parallel to the line y\ ={1}{5}(x+4) NEEP HELP ASAP
Answer:
y = (1/5)(x + 37)Step-by-step explanation:
Slope-intercept form:
y = mx + bGiven line has a slope of m = 1/5.
Parallel lines have equal slopes, so the line we are looking for is:
y = (1/5)x + b and passing through point P(3,8).Substitute the coordinates and slope and find b:
8 = (1/5)*3 + bb = 8 - 3/5b = 7 2/5The line is:
y = 1/5x + 7 2/5 ory = (1/5)(x + 37)What is the domain of the function shown in the graph below? y 10 OSCO 7 6 5 4 3 2 1 I 1 -10 -8 -9 -5 -4 -3 -2 1 2 3 4 8 ON 5 9 10 - 2 -3 -4 -5 -8 -9 10
The function is define for all values of x greater than or equal -3 and less than or equal 3
Hence the domain of the function is;
-3 ≤ x ≤ 3
samuel carries three sacks of gravel to his motorcycle which weigh 800 cm³ cube how many liters did he carry?Plss answer it now I need help
Explanation:
To be able to determine the number of liters Samuel carried, let's convert first the 800 cm³ to liters.
The conversion formula is 1 cm³ = 0.001 liters.
So, to convert 800 cm³ to liters, let's multiply 800 by 0.001.
[tex]800cm^3\times\frac{0.001L}{1cm^3}=0.8L[/tex]Answer:
Sam has a piece of rope that is 3 1/2 feet long. He cuts the rope so that one piece is 1 1/3 feet long what is the length of the other half?
The length of the other half is:
[tex]\frac{7}{2}-\frac{4}{3}=\frac{7\cdot3-4\cdot2}{2\cdot3}=\frac{21-8}{6}=\frac{13}{6}[/tex][tex]\frac{13}{6}=\frac{12+1}{6}=\frac{12}{6}+\frac{1}{6}=2+\frac{1}{6}=2\frac{1}{6}\text{ fe}et[/tex]If measure of angle 3 = (5x + 12)° and measure of angle 7 = (8x)° find the value of ‘x’.
The value of x is 21
The other angles are 63°, 117°, 63°, 117°
Given:
The angles of a parallelogram ABCD are
∠A = 3x°
∠B = (5x+12)°
To find:
The value of x
Parallelogram ABCD,
∠A and ∠B are two adjacent sides
Properties of a parallelograms
Two opposite sides are parallelogram are equal and parallel to each other.
So, the adjacent sides are supplementary angles i.e. sum is 180°.
The opposite angles are equal.
Now,
∠A + ∠B = 180°
⇒ 3x + (5x + 12) = 180
⇒ 3x + 5x + 12 = 180
⇒ 8x + 12 = 180
⇒ 8x = 180 - 12
⇒ 8x = 168
⇒ x = 168 ÷ 8
⇒ x = 21
Thus,
The value of x = 21
The angles are
∠A = 3x = 3 * 21 = 63°
∠B = (5x + 12) = (5 * 21 + 12) = 105 + 12 = 117°
As opposite angles are equal so
∠A = ∠C = 63°
∠B = ∠D = 117°
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Determine the interval(s) for which the function shown below is decreasing.
When x increases the value of f(x) decreases called decreasing function thus the interval on which the function is decreasing is (-∞, -5] ∪ [-2, 2].
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given graph of a random function,
The value of f(x) decreasing when x is increasing is the interval on which we can say that function is decreasing.
If we look at the extreme left of the graph and come towards the right then the curve is going downward till x = -5.
Therefore, in interval (-∞, -5] function is decreasing.
The function is again going down in intervals [-2,2].
Therefore in inteval (-∞, -5] ∪ [-2, 2] the function is decreasing.
Hence "When x increases the value of f(x) decreases called decreasing function thus the interval on which the function is decreasing is (-∞, -5] ∪ [-2, 2]".
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The given question is incomplete complete question is attached below ;