Answers
Answer:
1) k = -3
2) B. The curve would be narrower, but the vertex would be in the same position.
Step-by-step explanation:
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Question 1
When a graph is shifted up or down we add or subtract the number of units it has shifted from the function.
From inspection of the graph, the vertex of function j(x) is (0, 2)
From inspection of the graph, the vertex of function j(x) + k is (0, -1)
Therefore, function j(x) has been translated 3 units down.
Therefore, the value of k is -3, since the function of the graph is j(x) -3
Question 2
When discussing the stretching of curves, it is usual to always refer to it as a "stretch" rather than a stretch or compression.
If the scale factor a is 0 < a < 1 then the graph gets wider.
If the scale factor a is a > 1 then the graph gets narrower (i.e. "compressed").
h(x) to h(2x) means that the function h(x) has been stretched horizontally by a factor of 1/2. The other way to say this is that is have been compressed horizontally by a factor of 2. In any case, as a > 1 the graph gets narrower.
Therefore, the vertex would stay in the same place but the curve would be narrower.
Related Questions
The Rainbow Motor Motel is a 50-room facility with a restaurant to accommodate its guests. The motel is open 365 days a year, even on leap years; as Lurena Boucha, the proprietor, closes down the facility every February 29, her birthday, for an all day celebration of four years of successful operations. On the average, 98% of the rooms are available for sale. For the year just ended, the actual number of rooms sold totaled 15,000 and the number of guests for the year totaled 20,000. The projected occupancy rate for the next year is 82% of the available rooms based on past experience. The food information is as follows:
Sales $150,000, Beg Inventory 8,000, Purchases $70,000, Ending Inventory, $ 13,000 Consumption by employees (free of charge) $3,000, Number of checks 64,139. Cost of sales ?
Answers
From the information given, the cost of sales is $65,000. See the explanation below.
What is the definition of cost of sales?Add your initial inventory to the purchases made over the time period, remove that amount from your ending inventory, and that is your cost of sales.
Cost of Sales = (Bi + P) - Ei
Where Bi is Beginning Inventory
P is Purchases; and
Ei is Ending Inventory.
So the derivation of the solution above is?Beginning Inventory = 8,000
(add) Purchase = 70,000
Bi + P = 78,000
Ending Inventory = 13,000
Cost of sales = 78,000 - 13,000
= $65,000
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Drag each tile to the correct box.
Using the order of operations, what are the steps for solving this expression?
Answers
Step-by-step explanation/Answer:
PE(MD)(AS) (a good way to remember how to solve order of operations)
Start:
P: Parenthesis
E: Exponent
M: Multiplication & D: Division
A: Addition & S: Subtraction
:End
*Multiplication and Division are grouped together because they are on the same level, you decide which to do first depending on which comes first in the equation. The same applies for addition and subtraction.
So:
first thing we can look is the parenthesis, but before we can solve the whole thing we must notice the exponent only on the four. Since it is inside the parenthesis we must solve it first.
1. 4^2 = 16
now we will solve the addition inside the parenthesis
2. 16-13 = 3
now lets continue with pemdas, no more parenthesis so we tackle exponents
3. 5^2 = 25
Lets rewrite our equation with the changes we have made
8 × 3 ÷ 3 + 25 + 4 × 3
Now we solve multiplication and division
Equations is worked left to right, like english is read, so we will start on the left side and continue to the right, only solving multiplication and division.
4. 8 x 3 = 24
5. 24 ÷ 3 = 8
6. 4 x 3 = 12
new equation: 8 + 25 + 12
now we can use addition and subtraction (no subtraction luckily!)
7. 8 + 25 = 33
8. 33 + 12 = 45
A company makes Citi bikes. 95% (i.e., 0.95) pass final inspection. Suppose that 5 bikes are randomly selected. ( use binomial distribution formula ) do I need to use a factorial symbol V! When showing steps by step
a) What is the probability that exactly 4 of these 5 sports bikes pass final inspection?
b) What is the probability that less than 3 of these 5 sports bikes pass final inspection?
I got disconnected with my tutor
Answers
Using the binomial distribution, it is found that the probabilities are given as follows:
a) 0.2036 = 20.36%.
b) 0.0011 = 0.11%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
p = 0.95, n = 5.
Item a:
The probability is P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.95)^{4}.(0.05)^{1} = 0.2036[/tex]
Item b:
The probability is P(X < 3), hence:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.95)^{0}.(0.05)^{5} \approx 0[/tex]
[tex]P(X = 1) = C_{5,1}.(0.95)^{1}.(0.05)^{4} \approx 0[/tex]
[tex]P(X = 2) = C_{5,2}.(0.95)^{2}.(0.05)^{3} = 0.0011[/tex]
Then:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0 + 0.0011 = 0.0011.
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Mrs. Martin brought 100 cookies to her class. She gave each student the same number of cookies, and had 5 cookies left over. there are more than 10 students and less than 50 students in Mrs. Martin's class. How many students are in her class?
Answers
Answer:
Mrs. Martin has 19 Students
Step-by-step explanation:
first step: 100-5=95
second step: 95/19=5
So, 95 divided by the possible number of students which is 19 it yields the answer of 5 which is the number of cookies each of her student recieved.
cos^2 x = (1 - cos 2x)/2 A. True B. False
Answers
We know that cos2x=cos²x-sin²x
=cos²x-(1-cos²x) [since, cos²x+sin²x=1]
=cos²x-1+cos²x
=2cos²x-1
So, cos2x=2cos²x-1
Hence, cos²x= (1+cos2x)/2
Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables occurring on both sides of an equation. Geometrically, these identities involve certain trigonometric functions (such as sine, cosine, tangent) of one or more angles.
Most common trigonometric identities are:
- cos²x + sin²x = 1
- sec²x - tan²x = 1
- cosec²x - cot²x = 1
- cos2x = cos²x - sin²x
Therefore we get that the statement cos² x = (1 - cos 2x)/2 is false.
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cho hàm số f(x) liên tục trên đoạn [a;b] và có nguyên hàm F(x) thỏa F(a)=10;F(b)=2022 Khi đó \int _a^b\: f(x) dx bằng
Answers
The result follows from the fundamental theorem of calculus.
[tex]\displaystyle \int_a^b f(x) \, dx = F(b) - F(a) = 2022 - 10 = \boxed{2012}[/tex]
Quadrilateral WXYZ has vertices W(2, 10), X(10, 10), (10,2), and Z(2, 2). Determine if quadrilateral WXYZ is a rhombus.
A. No, quadrilateral WXYZ is not a rhombus.
B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.
C. Yes, quadrilateral WXYZ is a rhombus because the slopes of the diagonals are perpendicular.
D. There is not enough information to determine.
Please select the best answer from the choices provided
Answers
Answer:
B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.
Step-by-step explanation:
1) according to the given coordinates the equations of the sides are:
YZ: y=2; WZ: x=2; WX: y=10; XY: x=10. It means
2) YZ⊥WZ; YZ⊥XY; WX⊥XY; WX⊥WZ. To the additional, WX=WZ=YZ=XY, then
3) the given quadrilateral is sqare (rhombus with angles m∠=90°).
4) finally, the correct answer is
B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.
A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which there
were 2039 class attendees. The data is summarized in the table below.
Class Type and Member Status of Class
Attendees
Class Type
Barre
Boot Camp
Boxing
Spinning
Yoga
Member
.240
204
288
191
177
Non-Member
185
155
234
271
94
What is the probability that a class attendee is a non-member of the gym and is attending a barre class or is a member of the gym and is attending a boot camp class?
Enter a fraction or round your answer to 4 decimal places, if necessary.
Answers
The probability that a class attendee is a non-member of the gym and is attending a barre class or is a member of the gym and is attending a boot camp class is 0.009.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The marketing team has gathered data from a random month, in which there were 2039 class attendees.
The probability that a class attendee is a non-member of the gym and is attending a barre class
= 185/2039
= 0.09
The probability that a class attendee is a member of the gym and is attending a boot camp class
= 204/2039
= 0.10004
The probability for both the event would be
= 0.09 x 0.10004
= 0.009
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15 points help! Select the correct answer from the drop-down menu.
Consider the equation (x^m)³ = (113)5 x(x−8)—5
The value of mis
Reset
Next
Answers
Answer:The value of m for the given equation is, 35
Step-by-step explanation:
Given an equation: https://tex.z-dn.net/?f=x%5E%7B3m%7D%3D(x%5E%7B65%7D)*(x%5E%7B40%7D)
Use the above property on RHS in equation [1];
Since the base are same i.e, x ; we can add the exponents.
or
Using: , then a=b.
Therefore, 3m=105.
Divide 3 on both sides of an equation:
Simplify:
m=35
Therefore, the valur of m is, 35.
The average THC content of marijuana sold on the street is 10.9%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street
Answers
(a) X ≈ N (0.10 , 0.02²)
(b) The probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11% is 31%.
(c) The 60th percentile is 11%.
The complete question is:The average THC content of marijuana sold on the street is 10%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to two decimal places and give THC content in units of percent. For example, for a THC content of 11%, write "11" not 0.11.A. X ~ N( , )
B. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11%.
C. Find the 60th percentile for this distribution.
According to the question,
The random variable X is defined as the THC content for a bag of marijuana that is sold on the street.
(a)The random variable X is Normally distributed with mean, μ = 0.10 and standard deviation, σ = 0.02.
Therefore, X ≈ N (0.10 , 0.02²)
(b) The value of P (X > 0.11) as follows:
P (X > o.11_ = P(X -μ/a > [tex]\frac{0.11-0.10}{0.02} \\[/tex])
= P(Z > 0.50)
= 1 -P (Z <0.50)
= 1- 0.69146
= 0.30854 ≈ 0.31
Hence,
the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11% is 31%.
(c)Let x represent the 60th percentile value.
Then, P (X < x) = 0.60.
⇒ P (Z < z) = 0.60
The value of z is,
z = 0.26.
Now put the value of x as follows:
z = x - μσ
0.26 = x - 0.100.02
x = 0.10+ ( 0.26 x 0.02)
x = 0.1052
x ≈ 0.11
Therefore,
The 60th percentile is 11%
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write the following situation as a proportion, 10 sandwiches feed 8 kids, how many sandwices will feed 30 kids
Answers
If f(x) = 2x+6 and g(x)= x3 what is (g f)(0)?
Answers
Answer:
[tex]27[/tex]
Step-by-step explanation:
[tex]g(f(0))=g(2(0)+3)=g(3)=3^3=27[/tex]
can you help me to solve this
Answers
Answer:
Is the question even complete ?
Step-by-step explanation:
If f(x) = x², and
g(x) = x1, then
f(g(x)) = ?
will give brainliest answer !!
Answers
Answer: 1, -2, 1
Step-by-step explanation:
[tex]f(g(x))=f(x-1)=(x-1)^{2}=x^{2}-2x+1[/tex]
Algebra 2 help needed image below
Answers
Answer:
8x + 100
Step-by-step explanation:
Your answer is correct! But because the equation is already set to "y =", you do not need the "f(x)" in your equation.
Given log base 2 =1/6, what is log base 4
Answers
Answer:
log x to the base 2 +log x to the base 4 =2
or log x/ log 2+ log x /lig 4 =2
or log x /log2 + log x /2.log 2 = 2
or log x/log 2(1+1/2)= 2
or log x/log 2 = 4/3
or 3.log x =4.log2
or logx^3=log 2^4
or x^3= 2^4
or x =(2)^4/3 or 2.(2)^1/3 ,Answer.
hope this helps
Step-by-step explanation:
Which ordered pair is a solution of the equation?
y=4x−7
Answers
Answer:
Unknown
Step-by-step explanation:
Hi! so you didn't add the ordered pair options but I will do my best :) so if you see the ordered pair (0.7) that could definitely be a solution because using the slope intercept form equation you gave I know that's our y Intercept. the slope is 4/1 so moving up 4 and to the right 1 or down 4 and to the left 1 on a graph could show you more points! If you don't want to draw it you could use Desmos and just put this equation in or give me the ordered pairs and I will give you your answer!
hope this helps :)
What is the result of M x H?????
I have asked 4 tutors and none of them know how to answer this.
Answers
Answer: m x H = [ -9 36 - 9/2 ]
Step-by-step explanation:
HELP ME PLEASE !!!!!!!
Suppose g(x) = f(x-3) -4. Which statement best compares the graph of
g(x) with the graph of f(x)?
A. The graph of g(x) is shifted 3 units right and 4 units up.
B. The graph of g(x) is shifted 3 units left and 4 units down.
C. The graph of g(x) is shifted 3 units left and 4 units up.
D. The graph of g(x) is shifted 3 units right and 4 units down.
Answers
Answer:
D. The graph of g(x) is shifted 3 units right and 4 units down.
Step-by-step explanation:
The graph of g(x) is shifted 3 units right and 4 units down
What should you substitute for y in the second equation (bottom equation) in order to solve the system by the substitution method?
Answers
Answer:
C. 3x - 9
Step-by-step explanation:
3x – y = 9 ___(1)
8x – 4y = 0 ___(2)
From (1) eq.
3x – y = 9
– y = 9 – 3x
y = - (-3x + 9)
y = 3x – 9
Hence, 3x - 9 should be substituted in the second equation to get the required answer.
Answer:
c
Step-by-step explanation:
solve for y in the first equation
y = 3x - 9
when you substitute, you will get a value of 9 for x and 18 for y
Triangle X Y Z is shown. The length of X Z is 12, the length of Y Z is 11, and the length of Y X is 6.
A scalene triangle has the lengths 6, 11, and 12. Keyla uses the law of cosines to find the measure of the largest angle. Complete her work and find the measure of angle Y to the nearest degree.
1. 122 = 112 + 62 − 2(11)(6)cos(Y)
2. 144 = 121 + 36 − (132)cos(Y)
3. 144 = 157 − (132)cos(Y)
4. −13 = −(132)cos(Y)
Answers
According to law of cosines if the lengths of triangle are 12,11,6 then the angle will be 114=157-132cos(Y)
Given the length of XZ is 12, length of YZ is 11 and the length of YX=6.
According to law of cosines the angle of a triangle when the length of sides are given can be written as:
[tex]c^{2} =a^{2} +b^{2} -2abcosd[/tex]
where c is the side opposite to the angle which we have to find and a and b are the rest sides.
We have to put the values of sides in the above law:
[tex]12^{2} =6^{2} +11^{2} -2*6*11cosY[/tex]
144=36+121-132 cos Y.
Hence the angle can be written as 144=36+121-132 cos Y.
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Using the Empirical Rule, it is found that:
Scores between 80% and 96% are within 2 standard deviations of the mean.
68 scores are within one standard deviation of the mean.
It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Considering the mean of 88% and the standard deviation of 4%, the scores that are within 2 standard deviations of the mean are:
88 - 2 x 4 = 80%.
88 + 2 x 4 = 96%.
68% are within 1 standard deviation of the mean, hence, out of 100:
0.68 x 100% = 68 scores.
What is the median of the above answer? Pls help fast.
Answers
Considering that the mean of the normal distribution is the same as the median, the median is of 88%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For the normal distribution, the median is the same of the mean, that is, the median is of 88%.
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Assume that 900 births are randomly selected and 4 at the births are girls. Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither
Answers
The number of girls are significantly low.
What is Probability ?Probability is the study of likeliness of an event to happen.
It is given that
900 births are randomly selected
The probability of birth of a boy or a girl is 1/2 = 0.5
Total chances of a girl is 900 * 0.5 = 450
The birth of girl observed is 4
Therefore the number of girls are significantly low.
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Help please I will give you a lot of points
Answers
Answer:
2 5/7 5/7 -1/7, -5/7, 1 2/7, -2 2/7, -1 5/7
How many units were started into production in a period if there were zero units of beginning work in process inventory, 4,714 units in ending work in process inventory, and 20,661 completed and transferred out units?
Answers
The number of the units were started into production in a period will be 25,375.
What is inventory?A industry's fully prepared kinds of goods, as well as the primary materials needed to make them, are considered to as inventory.
If there were zero units of beginning work in process inventory, 4,714 units of ending work in process inventory, and 20,661 completed and transferred out units.
Completed and transferred out = 20,661
Ending Inventory = 4,714
Units accounted for = 25,375
Beginning Inventory = 0
Units started into production = [Units accounted for – Beginning work in progress Inventory] = 25,375
Units accounted for = 25,375
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Angle RSU is complementary to angle UST. Angle QSR is congruent to angle RSU.
Lines Q, R, U, and T extend from point S from left to right. Angle R S T is a right angle.
Which statement is true about angles UST and QSR?
They are complementary.
They are supplementary.
They are congruent.
They are obtuse.
Answers
Answer:
Statement 1 is correct
Angles UST and QSR are complementary.
Step-by-step explanation:
Complementary angles are those angles whose addition gives result of 90°
Congruent angles are those angles which are equal to each other.we can say that there values are same.
Here angle RSU is complementary to angle UST.
Therefore there addition is equal to 90°
∠RSU + ∠UST = 90° - (i)
Here angle QSR is congruent to angle RSU.
It means ∠QSR =∠RSU -(ii)
From equation (i) and (ii)
∠QSR + ∠UST = 90°
So angles UST and QSR are complimentary angles.
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Answer: A. They are complementary.
Step-by-step explanation: RIGHT ON EDGE 2023
any solutions will each system of linear equations have? Match the systems with the correct number of
Solutions
Answers
Based on the information given, the correct options will be
y = x + 6 and 3x - 3y = -18 .... Infinitely many solutions.
y = -2x + 5 and 2x + y = -7 .... No solution.
y = -4x + 11 and -6x + y = 11 ... One solution.
Solving equations
y = -4x + 11 ....... equation i
-6x + y = 11 ...... equation ii
Put equation i into ii.
-6x + y = 11
-6x + (-4x + 11) = 11
-6x - 4x + 11 = 11
-6x - 4x = 11 - 11
-10x = 0
x = 0
Therefore, x = 0 and y = 11. This gives a solution for each variable.
y = -2x + 5 ..... i
2x + y = -7 ..... ii
Put equation I into ii
2x + y = -7
2x + (-2x + 5) = -7
2x - 2x = -7 - 5
0 = -12
This indicates no solution.
y = x + 6 ..... i
3x - 3y = -18 ..... ii
Put equation I into ii
3x - 3y = -18
3x - 3(x + 6) = -18
3x - 3x - 18 = -18
3x - 3x = - 18 + 18
0 = 0
This implies that there are infinitely many solutions.
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If REX ~ ROB, find the value of a.
Answers
Answer: 8
Step-by-step explanation:
As corresponding sides of similar triangles are proportional,
[tex]\frac{RX}{RB}=\frac{XE}{BO}\\\\\frac{6}{15}=\frac{a}{20}\\\\a=20\left(\frac{6}{15} \right)=\boxed{8}[/tex]
What is the solution of the following system?
Use the substitution method.
{3x+2y=11x−2=−4y
A.) The only solution is (12, - 5/2)
B.) The only solution is (4, - 1/2)
C.) There is no solution
D.) There are an infinite number of solutions
Answers
Answer:
B.) The only solution is (4, - 1/2)
Step-by-step explanation:
To solve this system of equations using the substitution method, we need to use one equation to find an expression for one of the terms or variables that can be substituted for that term or variable in the other equation.
__
expression for xHere, it is convenient to use the second equation to write an expression for x:
x -2 = -4y
x = 2 -4y . . . . add 2 to both sides
substituteUsing this expression for x, we can write the second equation as ...
3x +2y = 11
3(2 -4y) +2y = 11 . . . . . substitute for x
6 -10y = 11 . . . . . . . . eliminate parenthses
solveThis 2-step equation can be solved in the usual way:
-10y = 5 . . . . . . . subtract the constant to isolate the variable term
y = -5/10 = -1/2 . . . . . divide by the coefficient of the variable
x = 2 -4(-1/2) = 2 +2 = 4 . . . . . find the corresponding x-value
The only solution is (x, y) = (4, -1/2).
The only solution is (x, y) = (4, -1/2). so, the correct option is B.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
we have the system of equations;
3x+2y=11
x−2=−4y
By the substitution method;
use the second equation to write an expression for x:
x -2 = -4y
x = 2 -4y
substitute
3x +2y = 11
3(2 -4y) +2y = 11
6 -10y = 11
solve
-10y = 5
y = -5/10 = -1/2
x = 2 -4(-1/2)
x = 2 +2 = 4
Thus, The only solution is (x, y) = (4, -1/2). so, the correct option is B.
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Choose True or False, (T or F). Grouped data is a data that has not been organized into intervals.
Answers
The statement "Grouped data is a data that has not been organized into intervals" is false.
Data presented in class intervals, such as 0-20, 20-40, and so on, is referred to as "grouped data."
Ungrouped data is information presented as individual values or integers, such as 15, 63, 34, 20, 25, and so on.
Assume we have a set of data with values between 0 and 50, such as 2, 17, 0, 1, 8, 19, 43, 2, 1, 32, and so on. In this situation, we may divide the data into categories like 0-10, 10-20,...,40-50. The data in this case are simply grouped.
Hence, the statement "Grouped data is a data that has not been organized into intervals" is false.
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