Answer:
Inequality
Step-by-step explanation:
An inequality is mathematical sentence that compares expression that are not equal.
Instead of using an equal sign = , you use an inequality symbol (>, <, ≥, ≤, ≠) with an inequality.Use the method of Lagrange Multipliers to find any maximum or minimum values of the function f(x,y)=x2+y2 subject to the constraint xy=1.
Answer:
possible maximum and minimum values : f (1,1), f (-1,-1)
Step-by-step explanation:
Given function :
f(x,y) = x^2 + y^2
constraint = xy = 1
attached below is the detailed solution of the method of using Lagrange method of Multipliers to find the maximum and minimum values of the function
Calculate the mean deviation by median (by using the mid-point(x) of leaf weights. b) A fair die is rolled. Find the probability of getting an odd number or a prime number or both?
Answer:
hello attached below is the required table that is missing and the completed table as well
A) mean deviation = 0.1645
B) 2/3
Step-by-step explanation:
From the table we calculated the midpoint value (x) and c.f
N = 27
median class = 2.35 to 2.45
median = l + [ (N/2) - cf / F ] * H
= 2.35 + [ (13.5 - 13) / 6 ] *0.1 = 2.3583
hence mean deviation by median
= summation of fi |xi -M| / summation of fi
= 4.4417 / 27 = 0.1645
B ) probability of getting an odd number or prime number or both
the probability of an odd number = 1/2
also the probability of an even number = 1/2
while the probability of getting neither of them = 1/3
hence the probability of getting odd or prime or both
= 1/2 + 1/2 - 1/3 = 2/3
DUE AT 3:30 PLEASE HHHEEELLLLPPPPPP 100 POINTS IF CORRECT
Alyssa’s extended family is staying at the lake house this weekend for a family reunion. She is in charge of making homemade pancakes for the entire group. The pancake mix requires 2 cups of flour for every 10 pancakes. •Use the value of the ratio to fill in the following two multiplicative comparison statements. 1. The number of pancakes made is ________ times the amount of cups of flour needed. 2. The amount of cups of flour needed is ________ of the number of pancakes made. Question 1 options: Blank # 1 _____ Blank # 2_____
Answer:
1. 5 times
2. 1/5
Step-by-step explanation:
I can explain later if you want, but you seem like you're in a rush so I'll do it later :)
What decimal number does point A on the number line below represent? −0.75 0.75 −1.25 1.25
Answer:
-1.75
Step-by-step explanation:
Point A is in between - 1 and -2
This interval is split in 4 equal parts and has 3 marker points.
Point A is on the bottom marker point, which indicates:
-1 * 3/4 = - 3/4 = - 0.75Since it is below -1, we add up - 1 and - 0.75:
- 1 + (-0.75) = - 1.75Point A represents: -1.75 on the number line
Answer:
-0.75678obsf
Step-by-step explanation:
A pool measures 15 feet by 17 feet. A cement walkway is added around the pool,
to both the width and the length. The area of the pool and the cement walkway is
now 483 square feet. What is the width of the cement walkway?
Answer:
Width of the walkway = 3 feet
Step-by-step explanation:
Dimensions of a pool = 15 feet × 17 feet
After the addition of a cement walkway around the pool,
New dimensions of the pool (including walkway) = (l + 2x)(w + 2x)
Area of the pool and the cement walkway = 483 square feet
(15 + 2x)(17 + 2x) = 483 [Since, l = 15 feet and w = 17 feet]
255 + 30x + 34x + 4x² = 483
4x² + 64x = 483 - 255
4x² + 64x = 228
4x² + 64x - 228 = 0
x² + 16x - 57 = 0
By using quadratic formula,
[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
x = [tex]\frac{-16\pm \sqrt{(16)^2-4(1)(-57)}}{2\times 1}[/tex]
x = [tex]\frac{-16\pm 22}{2}[/tex]
x = 3.0 ft, -19 ft
Since, dimension can't be negative.
Therefore, width of the walkway = 3 ft
The width of the walkway is 3 ft
The pool measures 15 feet by 17 feet. This means the pool is rectangular.
Properties of a rectangle:Opposite sides are equal to each otherOpposite sides are parallel to each otherarea of the pool = lw
area = 15 × 17 = 255 ft²
A cement walkway is added around the pool, to both the width and the length.
area of the pool and the cement walkway = 483 ft²
Therefore,
area = lw
The width and length was added on both sides.
let
the side added to the width = x
the side added to the length = x
length = 2x + 17
width = 2x + 15
483 = (2x + 17)(2x + 15)
483 = 4x² + 30x + 34x + 255
4x² + 64x - 228 = 0
x² + 16x - 57
x² - 3x + 19x - 57
x(x - 3) + 19(x - 3)
(x + 19)(x - 3) = 0
x = -19 or 3
we can only use positive value of x. Therefore, x = 3
length = 2(3) + 17 = 23 ft
width = 2(3) + 15 = 21 ft
Therefore, the width of the walkway is 21 - 15 / 2 = 3 ft
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Angle Pairs Introduction
1. A shirt is priced $24.99. and is on sale for 20% off and subject to 5% sales tax.
final cost of the shirt?
I
Answer:
$20.99
Step-by-step explanation:
The sale causes the original price to be multiplied by 1 - 20% = 80%. The tax causes the sale price to be multiplied by 1 + 5% = 105%. The net effect is that the original price is multiplied by the product of these values:
final cost = $24.99(0.80)(1.05) = $20.99
What is the first step to solving this equation? -5c + 6 = -4
Answer:
subtract 6 from both sides.
-5c = -10
then divide both sides by -5 (negative divided by a negative is a positive)
c = 2
Step-by-step explanation:
Step-by-step explanation:
Hey, there!!
The given equation is : -5c + 6 = -4
The first step olis to take (+6) in right side,
[tex] - 5c = - 4 - 6[/tex]
now, another step is add ( -4 and -6)
[tex] - 5c = - 10[/tex]
Now, divide -10 by -5.
[tex]c = \frac{ - 10}{ - 5} [/tex]
Therefore, c= 2.
Hope it helps..
What is construction
Answer:
Consrution is the steps of building buildings or town.
Step-by-step explanation:
CONSTRUCTION IS THE ACT OF MAKING 《OR》BUILDING SOMETHING.......
HOPE IT HELP.......❣❣❣
A record weight for a red snapper was 46 pounds. A record weight for a sturgeon was 468 pounds. About how many times heavier than the red snapper was the sturgeon?
Answer:
10.17
Step-by-step explanation:
To find the answer the this question we must divide "468" by "46". We then get the answer 10.173913....... I rounded it to the hundredths place.
what is 3 feet, 3 feet, and 5 feet. What the total length?
Answer:
45 ft cubed
Step-by-step explanation:
3*3*5 is 9*5 which is 45 feet cubed.
There are 9 classes of 25 students each 4 teachers in two times as many chaperones as teachers each bus hold a total of 45 people what is the least number of busses needed for the field trip
Answer:
Least number of bus require for trip = 5 buses (Approx)
Step-by-step explanation:
Given:
Total number of classes = 9
Number of student in each class = 25
Number of teacher = 4
Number of chaperones = Double of teacher
Bus hold = 45 people
Find:
Least number of bus require for trip
Computation:
Total number of student = 9 × 25
Total number of student = 225
Number of chaperones = 4 × 2
Number of chaperones = 8
Total people = 225 + 8 + 4
Total people = 237
Least number of bus require for trip = Total people / Bus hold
Least number of bus require for trip = 237 / 45
Least number of bus require for trip = 5.266
Least number of bus require for trip = 5 buses (Approx)
Answer:
Least number of bus require for trip = 5 buses
Step-by-step explanation:
A Ferris wheel completes 4 revolutions in 10 minutes. The radius of the Ferris wheel is 40 feet.
What is the linear velocity of the Ferris wheel in inches per second?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
5.0in/secStep-by-step explanation:
[tex]Circumference = 2\pi r\\\\2 \pi \times 40 ft = 80\pi ft = 253.3274123 ft\\\\= 253.3274123 ft \times 12 \: \frac{inches }{feet} \\\\ = 3015.928947 in\\\\\\10 min = 10 min \times 60 \: sec / min = 600 sec\\\\4 \: revolutions / 10 min = 4 \times 3015.928947\: in / 600 sec \\\\ = 5.0 in/sec[/tex]
The linear velocity of the Ferris wheel is 20.1 inches per secnod.
What is the angular velocity of a rotating body?Suppose the body revolves θ angle in t time then the angular velocity of the body is
ω= θ/t
What is the linear velocity of a rotating body?Suppose the rotating body covers 's' distance in 't' which is actually 'rθ' distance in 't' time because, s=rθ.
Then the linear velocity of the rotating body is
v=s/t=r(θ/t)=r ω
i.e. v=r ω.
How to solve the problem?The speed of the Ferris wheel is given by 4 revs in 10 minutes. That means 4(2π) radians in 10 minutes.
Hence, the angular velocity of the Ferris Wheel is
ω= 8π/(10×60) rad/s= π/(75) rad/s
Hence, the linear velocity of the Ferris Wheel is
v=r ω= 40 Feet ( π/(75) rad/s)
= (12×40π)/(75) inch/s
= 20.1062 inch/s
≈20.1 inch/s (rounded to the nearest tenth)
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At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml.
(a) The normal distribution should be used for the sample mean because:________.
1. the sample population has a large mean.
2. the population distribution is known to be normal.
3. the population standard deviation is known.
4. the standard deviation is very small.
(b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance.
The hypothesis for a two-tailed decision is:_______.
1.. H0: μ ≠520, H1: μ = 520, reject if z < −1.96 or z > 1.96
2. H0: μ ≠520, H1: μ = 520, reject if z > 1.96 or z < −1.96
3. H0: μ = 520, H1: μ ≠ 520, reject if z > 1.96 or z < −1.96
4. H0: μ =520, H1: μ ≠ 520, reject if z > −1.96 or z < 1.96
Answer:
A) Population standard deviation is known.
B) Option 3
H0: μ =520,
H1: μ ≠ 520
z > 1.96 or z < -1.96
Step-by-step explanation:
A) The normal distribution should be used for the sample mean because the population standard deviation is known. Usually, when the standard deviation is unknown we don't use normal distribution except there is an underlying normal approximation.
B) Null Hypothesis:H0: μ =520,
Alternative hypothesis H1: μ ≠ 520
At 5% level of significance, from standard tables, we will reject H0 if;
The test statistic; z > 1.96 or z < -1.96
64. Determine whether the statement is true or false: The product of a rational and irrational number is
always irrational
Answer: TRUE
Step-by-step explanation:
you can't never change an irrational number into rational number
2 × √3 = 2√3 ⇔ still an irrational number
Answer:
False
Step-by-step explanation:
The product of two irrational number 2 is irrational. False. Counterexample: (√2) ∙ (−√2) = 2. (c) The sum of a rational number and an irrational number is irrational.
Help me please thank you
Answer:
x = 7
Step-by-step explanation:
To make L II M, the two angles ([2x - 3] & [x + 4]) have to be the same.
2x - 3 = x + 4 is the equation.
Simplify, and you will get x = 7
Hope this helps! Please tell me if I did anything wrong, thank you!
Answer please ! I’ll give 25 points !! Thank you
Answer:
a. 7%
b. 13%
c. 3%
d. I can conclude that poor nutrition affects academic performance because the chart shows that people with poor nutrition got the worst scores out of the people with better nutrition. The chart also shows that there are more kids below average than kids with excellent nutrition. Kids with poor nutrition also have less people above average then any other category.
Step-by-step explanation:
For the percentages, it is just a number out of the total, which is 1000.
Percentages are a number out of 100. Like, 35/100 is 35%. So the total is 1000 and if you divide it by 10, you'll get 100. That means you have to only divide the amount of kids in a category by 10, and you'll get the percentage.
Below average kids with poor nutrition has 70 kids.
70/1000. Divide 1000 by 10 to get 100. Since you divided the denominator, 1000, by 10, you need to do the same for the numerator, which is 70. 70 divided by 10 is 7, so it's 7%. It is sort of like a ratio!
Average kids with poor nutrition has 130 kids.
130/1000. Divide 1000 by 10 to get 100. Since you divided the denominator, 1000, by 10, you need to do the same for the numerator, which is 130. 130 divided by 10 is 13, so it's 13%.
Above average kids with poor nutrition has 30 kids.
30/1000. Divide 1000 by 10 to get 100. Since you divided the denominator, 1000, by 10, you need to do the same for the numerator, which is 30. 30 divided by 10 is 3, so it's 3%.
3(x-8) = -29.7 please solve for x
Answer:
The answer is x= -1.9.
Use the 3 to multiply the number and the letter in the bracket... which is...
3x-24=-29.7.
3x=-29.7+24.
3x=-5.7.
x=-5.7/3.
x=-1.9.
x is -1.9
Solve 3(x-8) = -29.7
Remove the brackets by dividing both sides by 3:
3(x-8) / 3 = -29.7 / 3
You will be left with:
x - 8 = -9.9
Take -8 to the other side so that you can be left with x. When you do this, the sign will change from negative to positive:
x = -9.9 + 8
x = 1.9
x is therefore -1.9
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Let Ebe the set of all even positive integers in the universe Zof integers, and XE : Z R be the characteristic function of E.
Then
1. XE(2) =
2. XP(-2) =
3. {z 62: XE() = 1} =
Answer:
[tex]\mathbf{X_E (2) = 1}[/tex]
[tex]\mathbf{X_E (-2) = 0 }[/tex]
[tex]\mathbf{\{ x \in Z: X_E(x) = 1\} = E}[/tex]
Step-by-step explanation:
Let E be the set of all even positive integers in the universe Z of integers,
i.e
E = {2,4,6,8,10 ....∞}
[tex]X_E : Z \to R[/tex] be the characteristic function of E.
∴
[tex]X_E(x) = \left \{ {{1 \ if \ x \ \ is \ an \ element \ of \ E} \atop {0 \ if \ x \ \ is \ not \ an \ element \ of \ E}} \right.[/tex]
For XE(2)
[tex]\mathbf{X_E (2) = 1}[/tex] since x is an element of E (i.e the set of all even numbers)
For XE(-2)
[tex]\mathbf{X_E (-2) = 0 }[/tex] since - 2 is less than 0 , and -2 is not an element of E
For { x ∈ Z: XE(x) = 1}
This can be read as:
x which is and element of Z such that X is also an element of x which is equal to 1.
∴
[tex]\{ x \in Z: X_E(x) = 1\} = \{ x \in Z | x \in E\} \\ \\ \mathbf{\{ x \in Z: X_E(x) = 1\} = E}[/tex]
E = {2,4,6,8,10 ....∞}
4. A ship traveled a distance of 50 km from port O at a bearing of 120°, then another 100 km to port B at a bearing of 200 °. What is the distance between ports O and B?
Step-by-step explanation:
Jesu
How is the following decimal written using bar notation? 3.126666666666...
Answer:
[tex]3.126666666666...=3.12\overline{6}[/tex]
Step-by-step explanation:
If the decimal number is repeating, then bar notation is used. A symbol called "bar" is used to express that type of numbers. it is placed at the top of the number that is repeating.
We have a number i.e. 3.126666666666...
We need express it in bar notation.
In this problem, 6 is repeating. It means "bar" is placed over 6.
So,
[tex]3.126666666666...=3.12\overline{6}[/tex]
It is the bar notation of 3.126666666666...
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x, y) = 2x2y, 2x2 + 4y2 = 12
Answer:
f(-2,-1) = -8 is the minimum value of f(x,y)
f(2,1) = 8 is the maximum value of f(x,y)
Step-by-step explanation:
f(x,y) = 2x²y under the constraint 2x² + 4y² = 12
Let g(x,y) = 2x² + 4y² - 12
df/dx = 4xy, df/dy = 2x², dg/dx = 4x and dg/dy = 8y
Now, using the principle of Lagrange multipliers,
df/dx + λdg/dx = 0 and df/dy + λdg/dy = 0.
Substituting the values of the variables, we have
df/dx + λdg/dx = 0 and df/dy + λdg/dy = 0.
4xy + 4xλ = 0 (1) 2x² + 8λy = 0 (2)
xy + xλ = 0
x(y + λ) = 0
x = 0 or y + λ = 0
Since x ≠ 0, y = -λ
Substituting y = -λ into (2), we have
2x² + 8λy = 0
2x² + 8λ(-λ) = 0
2x² - 8λ² = 0
2x² = 8λ²
x² = 4λ²
x = ±2λ
Substituting the values of x and y into the constraint equation, we have
2x² + 4y² = 12
2(±2λ)² + 4(-λ)² = 12
2(4)λ² + 4λ² = 12
8λ² + 4λ² = 12
12λ² = 12
λ² = 1
λ = ±1
Substituting the value of λ into x and y, we have
x = ±2λ = ±2(±1) = ±2
y = -λ = -(±1) = ±1
The minimum values of x and y are -2 and -1 respectively. Substituting these int f(x,y), we have
f(-2,-1) = 2(-2)²(-1) = 2 × 4 × (-1) = -8
So f(-2,-1) = -8 is the minimum value of f(x,y)
The maximum values of x and y are 2 and 1 respectively. Substituting these int f(x,y), we have
f(2,1) = 2(2)²(1) = 2 × 4 × 1 = 8
So f(2,1) = 8 is the maximum value of f(x,y)
12/5x - 2x = 3/10
solve for x
And show steps plz
Answer:
x=3/4
Step-by-step explanation:
First, we must combine like terms and find the common denominator (which is 5):
12/5x-2x
12/5x-10/5x=2/5x
Then, we cross multiply
[tex]\frac{2x}{5} =\frac{3}{10}[/tex]= 2x(10)=(3)(5)=20x=15
Then, we divide by 20 to get x:
x=15/20
and finally, we simplify the fraction
x=3/4
What could be the rule ?
Answer:
Divide by 3
Step-by-step explanation:
Answer:
Sub. 10
Step-by-step explanation: input is 15 and output is 5, So i would say 15-10= 5 I would think the rule is Subtract 10, im Guessing not for sure tho! :Dplease help!!!!! thank uuuuuuu
Step-by-step explanation:
here's the answer
Hope it helps◉‿◉
simplify the expression. -6(-8 + 3s) =
Answer:
The correct answer is 48 - 18s.
Step-by-step explanation:
To simplify this problem, we have to use the distributive property. To do this, we must multiply each term inside the parentheses by -6 (what is outside of the parentheses). This is modeled below:
-6(-8 + 3s)
= (-8 * -6) + (-6 * 3s)
Now, we can simplify what is inside the parentheses.
= 48 - 18s
Therefore, the correct answer is 48 - 18s.
Hope this helps!
x^2+6x-6=10 what’s the solution?
Answer:
-8,2
Step-by-step explanation:
Factoring:
(x+8)(x-2)
x is -8 or 2
Answer:
-8 and 2
Step-by-step explanation:
option 2 or b
x2-8x-9-y2+10y solve this
Answer:
in descending order, your answer would be x^2-y^2+2y-9. Hope this helps!
Step-by-step explanation:
Answer:-6x-9+8y.
Step-by-step explanation: 2x-8x-9-2y+10y -6x-9-2y+10y -6x-9+8y
Marissa is writing a book. The ratio of the number of pages she has written so far to the
number of hours she has spent writing is 5:8. Which statement is true?
On average, Marissa wrote 1 page every 3 hours.
On average, Marissa wrote 3 pages each hour.
On average, Marissa wrote 5 pages every 8 hours.
On average, Marissa wrote 8 pages every 5 hours.
Answer:
On average, Marissa wrote 5 pages ever 8 hours.
Step-by-step explanation:
The ratio is the number of pages to the number of hours she has spent writing so 5:8 means 5 pages every 8 hours.
On average, Marissa wrote 5 pages every 8 hours. Therefore, option C is the correct answer.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the ratio of the number of pages she has written so far to the number of hours she has spent writing is 5:8.
In 8 hours Marissa is writing 5 pages
Therefore, option C is the correct answer.
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Quadrilateral $ABCD$ has right angles at $B$ and $D$, and $AC=3$. If $ABCD$ has two sides with distinct integer lengths, then what is the area of $ABCD$? Express your answer in the simplest radical form.
Answer:
[tex]\sqrt{2}+\sqrt{5}[/tex]
Step-by-step explanation:
Since there are 2 diagonal angles that are 90 degrees, we can figure out the shape is made of 2 right triangles, so we can use the Pythagorean theorem to find out the length of each side.
The problem said that there must be 2 distinct sides with integer lengths, but there are no 2 integers that satisfy [tex]x^2+y^2 = 3^2[/tex] so we can deduce that both right triangles contain 1 integer value side and 1 non-integer value side.
There are only 2 positive integer values that would fit in [tex]x^2+y^2 = 3^2[/tex] for x: 1 and 2. That means the 2 triangles' equation is:
[tex]1^2+\sqrt{8}^2 = 3^2[/tex] and [tex]2^2 + \sqrt{5}^2 = 3^2[/tex].
Now, since these are right triangles, their areas are just going to be their 2 legs multiplied by 1/2.
The first triangle's area is:
[tex]1\cdot\sqrt{8}\cdot1/2 = 1\cdot2\sqrt{2}\cdot1/2 = \sqrt{2}[/tex]
The second triangle's area is:
[tex]2\cdot\sqrt{5}\cdot1/2 = \sqrt{5}[/tex]
The total area of the quadrilateral would be the sum of the 2 triangles, which is just [tex]\sqrt{2}+\sqrt{5}[/tex].
I hope this helped you.
The total area of the quadrilateral ABCD is [tex](\sqrt{2}+ \sqrt{5} )[/tex] and this can be determined by using the formula of the area of the triangle.
Given :
Quadrilateral ABCD has right angles at B and D, and AC=3. ABCD has two sides with distinct integer lengths.The following steps can be used in order to determine the area of ABCD:
Step 1 - Let the length of the segment AD be 'x' and the length of the segment CD be 'y'.
Step 2 - Now, apply the Pythagorean theorem on the triangle ACD.
[tex]x^2+y^2= 3^2[/tex]
Step 3 - According to the given data, ABCD has two sides with distinct integer lengths. So, there are two possibilities:
[tex]1^2+(\sqrt{8} )^2= 3^2[/tex]
[tex](2)^2+(\sqrt{5} )^2=3^2[/tex]
So, the possible sides of the quadrilateral will be [tex]\rm 1, \;2,\; 2\sqrt{2},\;and \;\sqrt{5}[/tex].
Step 4 - So, the area of the triangle ABC is:
[tex]A=\dfrac{1}{2}\times \sqrt{8} \times 1\\A = \sqrt{2}[/tex]
Step 5 - Now, the area of the triangle ACD is:
[tex]A'=\dfrac{1}{2}\times \sqrt{5} \times 2\\A' = \sqrt{5}[/tex]
Step 6 - So, the total area of the quadrilateral ABCD is:
[tex]{\rm Area } = \sqrt{2} + \sqrt{5}[/tex]
The total area of the quadrilateral ABCD is [tex](\sqrt{2}+ \sqrt{5} )[/tex].
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The data show the number of hours of television watched per day by a sample of people. Use technology to answer parts (a) and (b) below. a. Find the data set's first, second, and third quartiles. nothing nothing nothing (Type integers or decimals. Do not round.) b. Draw a box-and-whisker plot that represents the data set. Choose the answer below. Note that different technologies will produce slightly different results. A. 0 3 6 9 A boxplot has a horizontal axis labeled from 0 to 10 in increments of 1. Vertical line segments are drawn at the following plotted points: 0, 1, 6, 7, 9. A box encloses the vertical line segments at 1, 6, and 7 and horizontal line segments extend outward from both sides of the box to vertical line segments at 0 and 9. All values are approximate. B. 0 3 6 9 A boxplot has a horizontal axis labeled from 0 to 10 in increments of 1. Vertical line segments are drawn at the following plotted points: 0, 3, 6, 7, 9. A box encloses the vertical line segments at 3, 6, and 7 and horizontal line segments extend outward from both sides of the box to vertical line segments at 0 and 9. All values are approximate. C. 0 3 6 9
*see attachment for the data set given
Answer:
[tex] Q_1 = 2.5 [/tex]
[tex] Q_2 = 5.5 [/tex]
[tex] Q_3 = 8 [/tex]
The box plot is shown in the attachment below.
Step-by-step Explanation:
a. To find Q1, Q2 (median), and Q3, first order the data from the least to the largest. We would have:
0, 1, 1,1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9
Q2 which is also the median, is the middle value that divides the data set into two equal parts. In the data set given, Q2 is the data value between the 14th and 15th data value. The average of the 14th and the 15th data value would give us Q2.
0, 1, 1,1, 2, 2, 2, 3, 4, 5, 5, 5, 5, [5,Q2, 6], 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9
They are 5 and 6. Average = [tex] \frac{5+6}{2} = 5.5 [/tex]
Q1 is the middle value of the lower part of the data set from Q2 down to your left.
0, 1, 1,1, 2, 2, [2, Q1, 3,] 4, 5, 5, 5, 5, 5, Q2, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9
Q1 = average of the 7th and 8th value = [tex] \frac{2+3}{2} = 2.5 [/tex]
Q3 = [tex] \frac{8+8}{2} = 8 [/tex]
0, 1, 1,1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 5,Q2, 6, 6, 7, 7, 7, 8, [8, Q3, 8], 8, 9, 9, 9, 9, 9.