Find the quartiles for these data values:
5,7,7,8,10,11,12,15,17
A. Q1=7, Q2=11, Q3=15
B. Q1=7, Q2=10, Q3=13.5
C. Q1=6, Q2=9, Q3=12
D. Q1=7.5, Q2=10.5, Q3=13.5
Answers
Q1 = 7, Q2 = 10, Q3 = 13.5
=============================================================
Explanation:
Start with {5,7,7,8,10,11,12,15,17}
Notice how this data set is already sorted for us from smallest to largest.
Cross off the first and last items to get {7,7,8,10,11,12,15}
Repeat the last step to get this smaller set {7,8,10,11,12}
Repeat again: {8,10,11}
Repeat one more time: {10}
The 10 is at the very center, so it is the median aka the value of Q2.
-------------
An alternative way to get the median is to follow these steps:
There are n = 9 numbers in the original set before we crossed off any items. The middle number is in slot 5 because n/2 = 9/2 = 4.5 rounds up to 5. The value in the fifth slot is 10, so 10 is the median.
There are 4 items below the median and 4 items above it, giving n = 4+1+4 = 9 items total.
-------------
Next, break the data set into two smaller groups
L = lower set = every value below the median
L = {5, 7, 7, 8}
U = upper set = every value above the median
U = {11, 12, 15, 17}
The median itself is in neither set L nor set U.
The median of set L is (7+7)/2 = 7, so this is the value of Q1
The median of set U is (12+15)/2 = 13.5 which is the value of Q3
-------------
Summary:
Q1 = 7
Q2 = 10 (aka the median of the original set)
Q3 = 13.5
Answer:
B. Q1=7, Q2=10, Q3=13.5
Step-by-step explanation:
First Solution:
The first quartile of the data set is 7.
The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.
5 7 7 8 10 11 12 15 17
So, the bottom half is
5 7 7 8
The median of these numbers is 7.
Second Solution:
The median of the data set is 10.
Quartile 2, also known as the median, is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
5 7 7 8 10 11 12 15 17
So, the median is 10 .
Third Solution:
The third quartile of the data set is 13.5.
The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.
5 7 7 8 10 11 12 15 17
So, the upper half is
11 12 15 17
The median of these numbers is 13.5.
Related Questions
Old MacDonals raises chickens and sheep on his farm. His livestock has a total of 55 heads and 142 legs among them (not counting the farmer). How many chickens and how many sheep does he have
Answers
The number of chickens and sheeps on the Old MacDonals farm is 39 and 16 respectively.
Simultaneous equationlet
x = number of chickeny = number of sheep'sx + y = 55
2x + 4y = 142
Multiply (1) by 2
2x + 2y = 110
2x + 4y = 142
subtract the equation4y - 2y = 142 - 110
2y = 32
y = 32/2
y = 16
substitute y = 16 into (1)
x + y = 55
x + 16 = 55
x = 55 - 16
x = 39
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The Yasuda family bought a toy that cost t dollars and a game that cost g dollars. Both were on sale. Which of these methods could the clerk use to calculate their total bill?
Answers
The equation that the clerk can use to calculate their total bill is t + g.
How to illustrate the equation?From the information given, Yasuda family bought a toy that cost t dollars and a game that cost g dollars.
The equation to calculate their total bills will be:
= t + g
where,
t = cost of toy
g = cost of game.
In this case, the equation that the clerk can use to calculate their total bill is t + g .
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area of sector................................
Answers
Answer:
A ≈ 25.1 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]
= π × 6² × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]
= 36π × [tex]\frac{\frac{4\pi }{9} }{2\pi }[/tex]
= 18 × [tex]\frac{4\pi }{9}[/tex]
= 2 × 4π
= 8π
≈ 25.1 cm² ( to the nearest tenth )
The weights of steers in a herd are distributed normally. The standard deviation is 200lbs and the mean steer weight is 900lbs. Find the probability that the weight of a randomly selected steer is between 1220 and 1320lbs. Round your answer to four decimal places.
Answers
Answer:
0.0369
Step-by-step explanation:
normalcdf (1220,1320,900,200) is 0.0369
Pls I do not know how to rotate without tracing paper
Answers
Answer:
Point A:
(1, 3) ------> (3, -1)
Point B:
(3, 3) ------> (3, -3)
Point C:
(3, 2) ------> (2, -3)
Step-by-step explanation:
To find the coordinates of a 90° clockwise rotation, use the following:
[tex](x, y)[/tex] -----> [tex](y, -x)[/tex]
This means you will switch the x and y coordinates of the point and then take the opposite of the x coordinate (if it is positive make it negative and if it is negative make it positive).
Point A:
(1, 3) ------> (3, -1)
Point B:
(3, 3) ------> (3, -3)
Point C:
(3, 2) ------> (2, -3)
evalute the expression (64)1\2
Answers
Answer:
32
Step-by-step explanation:
64×1÷2
64is divided by 2 =32
and 32×1=32
Solve Multi-Step Equations, Part 2 - Instruction
ceady
Solve the equation - 10(g - 6) = 65.
») What is the value of g?
g=
?
Answers
Answer:
g = -0.5
Step-by-step explanation:
Divide both sides by the numeric factor on the left side, then solve.
Answer:
g = -0.5 or -1/2
Step-by-step explanation:
-10(g – 6) = 65 : apply distributive property
(-10 • g) + (-10 • -6) = 65 : multiply
-10g + 60 = 65 : apply property of equal subtraction
-10g + 60 – 60 = 65 – 60 : subtract
-10g = 5 : apply property of equal division
-10g ÷ -10 = 5 ÷ -10 : divide
g = -0.5
Given the function f(x) = 2x, evaluate ƒ(3).
Answers
Answer:
f(3) = 6
Step-by-step explanation:
you substitute 3 for x.
So you have 2(3) which is 2 multiplied by 3 which is 6
Steve travels two times as fast as you. Traveling in opposite directions, they are 120 miles apart after 2.5 hours. Find the rate of travel
Answers
48 x 2= 96
The rate is 96.
PLEASE HELPP!!! I WILL MARK AS BRAINLIEST!!!
Which expression represents the area of the rectangle?
130x
130x + 3
130x2 + 30x
Answers
Answer:
130x+3
Step-by-step explanation:
The area is (10x)*(13x+3). 10x*13x=130x squared. So, it is 130x+3.
Answer: C: 130x2 + 30x
Step-by-step explanation:
the graph of the function f(x) = (x +2)(x + 6) is shown below. On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0). What is true about the domain and range of the function? The domain is all real numbers, and the range is all real numbers greater than or equal to –4. The domain is all real numbers greater than or equal to –4, and the range is all real numbers. The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4. The domain is all real numbers greater than or equal to –4, and the range is all real numbers such that –6 ≤ x ≤ –2.
Answers
Answer: Choice A
Domain = all real numbers
Range = real numbers greater than or equal to -4
=====================================================
Explanation:
The domain is the set of allowed x inputs of a function.
We can replace x with any number we want to get some output for y = f(x)
This tells us the domain is the set of all real numbers.
-----------
The range is the set of numbers y such that [tex]y \ge -4[/tex]
In other words, we can have y = -4 or y > -4
This is because y = -4 is the lowest output possible, as indicated by the vertex point.
Answer:
b
Step-by-step explanation:
Evaluate:
6-(2/3)^2
A. 17/3
B. 52/3
C. 49/9
D. 50/9
Answers
Answer:
The correct answer is: "Option [D]".
Step-by-step explanation:
Hi student, let me help you out!
....................................................................................................................................
Let's use the acronym PEMDAS. With the help of this little acronym, we will not make mistakes in the Order of Operations! :)
[tex]\dag\textsf{Acronym \: PEMDAS}[/tex]
P=Parentheses,
E=Exponents,
M=Multiplication,
D=Division,
A=Addition,
S=Subtraction.
Now let's start evaluating our expression, which is [tex]\mathsf{6-(\cfrac{2}{3})^2}[/tex]
According to PEMDAS, the operation that we should perform is "E-Exponents".
Notice that we have a fraction raised to a power. When this happens, we raise both the numerator (2 in this case) and the denominator (3 in this case) to that power, which is 2. After this we obtain [tex]\mathsf{6-\cfrac{4}{9}}[/tex].
See, we raised both the numerator and the denominator to the power of 2.
Now what we should do is subtract fractions.
Note that 6 and -4/9 have unlike denominators. First, let's write 6 as a fraction: [tex]\mathrm{\cfrac{6}{1}-\cfrac{4}{9}}[/tex]. Now let's multiply the denominator and the numerator of the first fraction times 9: [tex]\mathrm{\cfrac{54}{9}-\cfrac{4}{9}}[/tex].
See, now the fractions have the same denominator. All we should do now is subtract the numerators: [tex]\mathrm{\cfrac{50}{9}}[/tex].
∴, the answer is Option D.
Hope this helped you out, ask in comments if any queries arise.
Best Wishes!
[tex]\star\bigstar\underline{\overline{\overline{\underline{\textsf{Reach \: far. Aim \: high. Dream \: big.}}}}}\bigstar\star[/tex]
[tex]\underline{\rule{300}{5}}[/tex]
Calculate 2/3, to the power of 3, therefore
[tex]\bf{\left(\dfrac{2}{3}\right)^{2}=\dfrac{2\times2}{3\times3}=\dfrac{4}{9} }[/tex]
[tex]\bf{6-\dfrac{4}{9} }[/tex]
Convert 6 to the fraction 54/9.
[tex]\bf{\dfrac{54}{9}-\dfrac{4}{9} }[/tex]
Since 54/9 and 4/9 have the same denominator, join their numerators to subtract them.
[tex]\bf{\dfrac{54-4}{9} \ \ \to \ \ \ Subtract }[/tex]
Subtract 4 from 54 to get 50.
[tex]\bf{\dfrac{50}{9} \ \ \to \ \ \ Answer }[/tex]
Therefore, the correct alternative is "D".
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Please solve with explanation (high points)
Answers
Real life scenarios of acute angles are:
Sighting a bird on a tree at an angle of 55 degrees.The angle between a ladder and the horizontal groundWhat are acute angles?Acute angles are angles that have a measure less than 90 degrees.
How to create the real life scenario?To create a real life scenario to illustrate acute angles, the following must be put in place:
The scenario must involve an angleThe angle must be less than 90 degrees.Real life scenarios that satisfy the above highlights are:
Sighting a bird on a tree at an angle of 55 degrees.The angle between a ladder and the horizontal groundRead more about acute angles at:
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In a certain board game, a 12-sided number cube
showing numbers 1 through 12 is rolled. In this game, a
number cube must be rolled until a number 9 or higher
appears.
What is the probability that the first such number is on
the 3rd roll?
Answers
Answer:
4/27 ezzzzzzzzzzzzzzzzzzzz
URGENT HELP A contest allows anyone to enter as many times as they would like and at the end of the contest, a winner is randomly chosen from all the entries. Suppose 450 people enter the contest. If Sabine entered 3 times and Joe entered 5 times, then what is the probability Joe or Sabine will win the contest?
Answers
Answer:
4/225
Step-by-step explanation:
Formula :
Probability (Event) = No. of times event has occurred / Total possibilities
==============================================================
Solving :
⇒ P (Joe or Sabine) = No. of times Joe or Sabine has entered / Total number of people
⇒ P (Joe or Sabine) = 3 + 5 / 450
⇒ P (Joe or Sabine) = 8/450
⇒ P (Joe or Sabine) = 4/225
Find the volume of the sphere. Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step expiation : 5575.3
Explanation:
The volume of a sphere is
V=4/3 x pi x r^2
And 22 is the diameter (d) but we need r (the radius)
r = d/2
r=22/2
r=11
Then plug in for r
V= 4/3 x pi x 11
V ≈ 5575.3
A toy rocket is shot vertically into the air from a launching pad 6 feet above the ground with an initial velocity of 88 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=−16t2+88t+6. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ? second(s) after launch.
(simplify your answer.)
Answers
a) The time taken by the rocket to reach the maximum height is 2.75 seconds.
b) The maximum height of the rocket will be 127 feet.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Given that:-
A toy rocket is shot vertically into the air from a launching pad 6 feet above the ground with an initial velocity of 88 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=−16t²+88t+6.a) The time taken by the rocket will be calculated as:-
We have a function h(t)=−16t²+88t+6. Now by taking the derivative of the function with respect to time and equating it to zero we will get the maximum time in which the rocket will reach the maximum height.
h(t) = -16t² + 88t + 6
h'(t) = 0
-32t + 88 = 0
32t = 88
t = 88 / 32 = 2.75 seconds
So the maximum time is 2.75 seconds.
b) Maximum height will be calculated as:-
Put the value of maximum time in the function h(t) = -16t² + 88t + 6 we will get the maximum height.
h(t) = -16t² + 88t + 6
h(2.75) = -16(2.75)² + ( 88 x 2.75 ) + 6
h(2.75) = 127 feet
Therefore the time taken by the rocket to reach the maximum height is 2.75 seconds and the maximum height of the rocket will be 127 feet.
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15 ( y - 4 ) - 2 (y - 9 ) + 5 (y + 6) = 0
Answers
Answer:
y = 2/3
Step-by-step explanation:
Assuming you are looking for "y":
15 * ( y - 4 ) - 2 * (y - 9 ) + 5 * (y + 6) = 0
15y - 60 - 2y + 18 + 5y + 30 = 0
15y - 2y + 5y -60 + 18 + 30 = 0
18y = 60 - 18 - 30
18y = 12
y = 12/18
y = 2/3
To make 1 batch of green paint, Ethan mixes 2 3/8 (Fraction) just so you know
ounces of blue paint and the same amount of yellow paint. How many ounces of blue paint is needed to make 5 batches of green paint?
Select the correct values to give your answer as a mixed number:
Answers
Answer:
[tex]11\frac{7}{8}[/tex] ounces
Step-by-step explanation:
Since Ethan needs [tex]2 \frac{3}{8}[/tex] ounces of blue paint to make 1 batch of green paint, we can multiply the amount of blue paint needed by 5 to see how much blue paint he'll need for 5 batches of green paint.
[tex](2 \frac{3}{8})5 = 10 \frac{15}{8} \rightarrow \boxed{11\frac{7}{8}}[/tex]
This means he will need [tex]11\frac{7}{8}[/tex] ounces of blue paint to make 5 batches of green paint.
If line m and n are parallel and line p is the transversal, Find out the angles a, b and c from the
Answers
Answer:
∠A = 55°∠B = 55°∠C = 125°Wxndy~~
solve it step by step
Answers
The solution for this expression is:[tex]9\sqrt{6}-15\sqrt{15}+6\sqrt{10}-50[/tex].
Properties of MultiplicationThe properties of multiplication are:
Distributive: a(b±c)= ab±acComutative: a . b = b. aAssociative: a(b+c)= c(a+b)Identity: b.1=bHere, you should apply the distributive property for solving this expression.
[tex](3\sqrt{3}+2\sqrt{5} )*(3\sqrt{2}-5\sqrt{5})\\ \\[/tex]
Applying the distributive property, you have:
[tex]9\sqrt{6}-15\sqrt{15}+6\sqrt{10}-10*\sqrt{25} \\ \\ 9\sqrt{6}-15\sqrt{15}+6\sqrt{10}-10*5\\ \\ 9\sqrt{6}-15\sqrt{15}+6\sqrt{10}-50[/tex]
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help..and give the right reasons and statement
Answers
The triangles ΔAED and ΔCGF are similar to each other. Then angle ∠A is congruent to angle ∠C.
What is the SAS similarity theorem?ΔABC is similar to ΔDEF only if the ratio of two sides of ΔABC and the corresponding two sides of ΔDEF is equal and the angle included on both sides are congruent.
Suppose the two sides of ΔABC are AB and BC, and that of DEF is DE and EF, then for SAS similarity, we need
and
∠ABC = ∠DEF
In triangles ΔAED and ΔCGF,
AE = CF
AD = CG
∠E = ∠G = 90°
Then the triangles ΔAED and ΔCGF are similar to each other. Then angle ∠A is congruent to angle ∠C.
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√-11
please solve this perblom
Answers
Answer:
3.31662479
Step-by-step explanation:
3.31662479
Solve, using the substitution method.
3m − n = 2
2m + n = − 7
(−1, −5)
(–10, –1)
(–2, –5)
(−5, 1)
Answers
Step-by-step explanation:
Hello there!
Here is the solution to our problem:
To begin with, we give our equations labels as below;
3m − n = 2 ...................eq.1
2m + n = − 7 ..................eq.2
Then, Let's manipulate eq.2
2m + n = − 7
n = -7 - 2m ...............eq3
And finally substitute the manipulated eq.3 into eq.1
3m − n = 2
3m − (-7 - 2m) = 2
3m + 7 + 2m = 2
5m = -5
m = -1
Substitute the value of m into eq.3
n = -7 - 2(-1)
= -5
In terms of x and y;
(x,y) : (m, n) => (-1, -5)
Therefore (m, n) = (-1, -5)
I hope this helps.
Have a nice studies.
Urgent help……………………:::::::::::
Answers
Answer:
The percentage of people enjoy New years Eve only = 3%
Step-by-step explanation:
The data indicates, The percentage of people enjoy New years Eve = 28%
The percentage of people enjoy New years Eve and Memorial Day = 12%
The percentage of people enjoy New years Eve and Forth of July = 18%
The percentage of people enjoy Enjoy all the three = 5%
The percentage of people enjoy New years Eve only
= The percentage of people enjoy New years Eve
- The percentage of people enjoy New years Eve and Memorial Day
- The percentage of people enjoy New years Eve and Forth of July
+ The percentage of people enjoy Enjoy all the three
= 28% - 12% - 18% + 5%
= 3%
A distribution has the five-number summary shown below. What is the
interquartile range (IQ) of this distribution?
Answers
Answer:
tiookvgvc. jbjvth kivtcth jjvf h. bkbgv
Answer:
The IQR of the given distribution is
Step-by-step explanation:
The given distribution has the five-number
28, 34, 43, 59, 62
Divide these numbers in two equal parts.
(28, 34), 43,( 59, 62)
Now divide each parenthesis in two equal parts.
(28), (34), 43,( 59), (62)
It means first quartile is the average of 28 and 34. Third quartile is the average of 59 and 62.
The interquartile range (IQR) of this distribution is
Therefore the IQR of the given distribution is 29.5.
6 liters of a gas has a pressure of 4 atmospheres. The gas's original pressure was 6 atmospheres.
What was the original volume in liters?
Enter your answer as a decimal to the 10th place, like this: 4.2 l
Answers
The original volume of the gas would be 4.00 liters
What is Boyle's law?Boyle's law is a gas law that states that the pressure of a gas is inversely proportional to it's volume with temperature kept constant.
It is represented thus;
P1V1 = P2V2
Where P1 = Original pressure = 6 atmospheres
V1 = Original volume =?
P2 = Final pressure =4 atmospheres
V2 = Final volume= 6 liters
How to calculate the original volumeMake the original volume V1, subject of formula
V1 = P2× V2 ÷ P1
V1 = 4× 6 ÷ 6 = 24 ÷ 6 = 4. 00 liters
Hence, the original volume of the gas is 4.00 liters
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The average profit on each car sold was $2430, correct to the nearest $10. Calculate the lower bound for the total profit. Write down the exact answer.
Answers
The lower bound for the profit is $2425.
What is the lower bound?When a number of rounded off to the nearest $10, it means that the value of the number in the units place, if greater than 5 becomes zero and one is added to the $10 number. If the number is less than 5, there is no change in the $10 number and the units number becomes 0
The possible values of the average profit are 2425, 2426, 2427, 2428, 2429, 2430. 2431. 2432, 2433, 2434
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why does the equation 3x+7=-3x+2+6x has no solution?
Answers
Answer:
[tex]3x+7=-3x+2+6x[/tex]
Combine the like terms on the right side of the equation.
[tex]3x+7=3x+2[/tex]
Eliminate 3x from the equation.
[tex]7\neq 2[/tex]
Seven will never equal 2.
Step-by-step explanation:
[tex]3x+7=-3x+2+6x[/tex]
Combine the like terms on the right side of the equation.
[tex]3x+7=3x+2[/tex]
Eliminate 3x from the equation.
[tex]7\neq 2[/tex]
Seven will never equal 2.
A circle has a diameter that extends from (4.-6) to (-8,10). What are the coordinates the center of the circle?
Answers
============================================================
Reason:
For now we'll only focus on the x coordinates. They are 4 and -8. Plot them on a number line and find the midpoint. To do this, add those values up and divide by two
(4 + (-8))/2 = -4/2 = -2
The value -2 is right in the middle of 4 and -8; hence it's the midpoint.
Repeat those steps for the y coordinates
(-6+10)/2 = 4/2 = 2
These two midpoints help lead to (x,y) = (-2, 2) which is the midpoint the given endpoints. By extension, it is the center of the circle.
Visual confirmation is shown below. I used the midpoint command in GeoGebra. Desmos is another graphing tool you can use.