The median is 133.5, the first quartile is 128, the third quartile is 139, and the interquartile range is 11.
What is median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
To find the median, first we need to order the data set from least to greatest:
106, 127, 129, 132, 135, 138, 140, 158
There are 8 data points, so the median is the average of the 4th and 5th numbers:
Median = (132 + 135) / 2 = 133.5
To find the quartiles, we need to divide the data set into four equal parts. Since there are 8 data points, the first quartile (Q1) is the median of the first half of the data set, and the third quartile (Q3) is the median of the second half of the data set.
Q1 = median of {106, 127, 129, 132} = (127 + 129) / 2 = 128
Q3 = median of {135, 138, 140, 158} = (138 + 140) / 2 = 139
The interquartile range (IQR) is the difference between the third quartile and the first quartile:
IQR = Q3 - Q1 = 139 - 128 = 11
Therefore,
The median is 133.5, the first quartile is 128, the third quartile is 139, and the interquartile range is 11.
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Final answer:
The median of the given data set is 133.5, with the first quartile (Q1) at 128 and the third quartile (Q3) at 139. The interquartile range (IQR) is 11, and the range is 52.
Explanation:
To find the median, first quartile (Q1), third quartile (Q3), and interquartile range (IQR) of a set of data, we first need to list the data in ascending order. The given data is: 106, 127, 129, 132, 135, 138, 140, 158.
The median is the middle number when the data set is ordered. Since there are 8 numbers, the median will be the average of the 4th and 5th numbers: (132 + 135) / 2 = 133.5. So the median is 133.5
To find the first quartile, which is the median of the lower half of the data (excluding the median if the number of data points is odd), we look at the first four numbers: 106, 127, 129, 132. The median of this subset is (127 + 129) / 2 = 128. So Q1 is 128.
Similarly, Q3 is the median of the upper half of the data. For the numbers 135, 138, 140, 158, the median is (138 + 140) / 2 = 139. So Q3 is 139.
The IQR is the difference between Q3 and Q1, so IQR = 139 - 128 = 11.
The range of the data is the difference between the max and min values, which is 158 - 106 = 52.
Which ordered pair could be removed so that the set of
ordered pairs is a function?
(4, -2)
(-3,2)
(3, 4)
(1,1)
The answer is (-3,2) because when it’s present in the graph the graph would not pass the vertical line test.
Another way to think about it is that -3 (input) has more than one output.
Answer:
The answer is (-3, 2)
Step-by-step explanation:
Let's define the two sets
A = {4, -3, 3, 1} and B = {-2, 2, 4, 1 -3}, so that the set of ordered pairs is a function , we should have that to every element from the first set (in this case A) corresponds (or is associate to) an element (and only one element) from the second set (in this case B). But we have that the element -3 in the set A (the domain) is related to the elements 2 and -3 which belong to the set B (the codomain), this in not allowed by the definition of function. So in order to the set of ordered pairs is a function we should remove the pair (-3, 2).
What is the total surface area of a cylindrical tank having
diameter 70 cm and height 1 m?
a) 22900 cm?
b) 92800 cm?
c). 29700 cm?
d) None of these
Answer:
Could be C) or D) None of these, 29688.05cm^2
Step-by-step explanation:
Did the question to round off to any numbers?
Formula for cylinder's T.S.A: 2 π r h + 2 π r^2
Diameter= 2 x radius
Radius = 70cm / 2 = 35cm
Height -> need to convert m to cm -> 100cm
Substitute these values into the formula:
2 x π x 35 x 100 + 2 x π x (35)^2 = 29688.05cm^2
Which equation represents y = −x^2 −2x + 3 in vertex form
Final answer:
The equation y = -x² - 2x + 3 can be expressed in vertex form as y = -(x + 1)² + 4.
Explanation:
The equation y = -x² - 2x + 3 can be expressed in vertex form as:
y = -(x + 1)² + 4
To convert the equation to vertex form, we need to complete the square. Here are the steps:
Factor out a common negative from the first two terms: y = -1(x² + 2x) + 3
Take half the coefficient of x (-2/2 = -1) and square it: (-1)² = 1
Add the squared value inside the parentheses and subtract it outside: y = -(x² + 2x + 1) + 3 - 1
Simplify: y = -(x + 1)² + 2
The vertex form of the equation is y = -(x + 1)² + 4.
|x−3| =4 help me, please
Answer:
x=-1 or x=7
Step-by-step explanation:
|x−3|=4
x-3=-4 or x-3=4
x=-1 or x=7
What is the answer to adding 5/16 1/2
Answer:
1 1/3
Step-by-step explanation:
(5/6 x 1/1) + (1/2 x 2/3) + ?
the answers to that are 5/6 and 3/6 so
5/6 + 3/6 = ???
5 + 3/ 6 = 8/6
8 divided by 2/ 6 divided by 2 = 4/3
so divide the numerator and denominator 4 divided by 3
then convert that to a mixed number
1 1/3
Answer:
13/16.
Step-by-step explanation:
1/2 = 8/16 so:
5/16 + 1/2
= 5/16 + 8/16
= 13/16 (answer).
Solve the system of equations:
y= 2x - 5
y=x^2-5
Apex
Answer:
A is the answer
Step-by-step explanation:
(0, -5):
-5 = 2(0) - 5 >>> -5 = -5
-5 = (0)^2 - 5 >>> -5 = -5
(2, -1):
-1 = 2(2) - 5 >>> -1 = 4 - 5 >>> -1 = -1
-1 = (2)^2 - 5 >>> -1 = 4 - 5 >>> -1 = -1
The solutions of the given set of equations are (0, -5) and (2, -1) so option (A) will be correct.
What is a system of equal equations?The equation is a combination of variable and constant. Which could be in addition multiplication or subtraction.
Given y = 2x -5 and y = x² - 5
By putting the y value into another equation
2x -5 = x² - 5
x² - 2x = 0
x(x - 2) = 0
x = 0 and x = 2.
Now y corresponding to x = 0 is y = -5 and corresponding to x= 2 is y = -1.
Hence the possible set of coordinates among the options are (0, -5) and (2, -1).
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What is the sum of the geometric series 243-162+108.....+64/3
Answer:
[tex]\frac{463}{3}[/tex]
Step-by-step explanation:
The given geometric series is:
243-162+108.....+64/3
The first term is [tex]a=243[/tex].
The common ratio is:
[tex]r=\frac{-162}{243}=-\frac{2}{3}[/tex]
The sequence is finite, so we can generate all the terms by repeatedly multiplying by the common ratio until we get to the last term.
The complete series is
243-162+108-72+48-32+64/3
The sum is:
[tex]243+108+48+64/3-162-72-32=\frac{463}{3}[/tex]
Three students used factoring to solve a quadratic equation.
Jordan's Solution Keith's Solution Randall's Solution
The equation was solved correctly by . The solutions of the equation are .
Answer:
The solution was solved correctly by Keith
The solutions of the equation are x=-5,x=-12
Step-by-step explanation:
we have
[tex]x^{2}+17x+72=12[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}+17x=12-72[/tex]
[tex]x^{2}+17x=-60[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]x^{2}+17x+8.5^{2} =-60+8.5^{2}[/tex]
[tex]x^{2}+17x+72.25 =12.25[/tex]
Rewrite as perfect squares
[tex](x+8.5)^{2}=12.25[/tex]
square root both sides
[tex](x+8.5)=(+/-)3.5[/tex]
[tex]x=-8.5(+/-)3.5[/tex]
[tex]x=-8.5(+)3.5=-5[/tex]
[tex]x=-8.5(-)3.5=-12[/tex]
The solution was solved correctly by Keith
The solutions of the equation are x=-5,x=-12
Answer:
The first box is Keith and the second box is -5,-12
Step-by-step explanation:
40 POINTS NEED HELP FAST(sqrt is a radical)
1.)simplify:
sqrt425
sqrt628
sqrt128
2.)add:
-2sqrt7+3sqrt7
3.)subtract:
-3sqrt12-3sqrt3-3sqrt20
4.)multiply:
3sqrt3(3sqrt8)
3sqrt3(4-3sqrt5)
1)5sqrt17,2sqrt157,8sqrt2
2)sqrt7
3)-3(3sqrt3+2sqrt5)
4)18sqrt6,12sqrt3-9sqrt15
PLEASE ANSWER ASAP! THANK YOU! SUPER EASY! Mrs. Davis is planning to put a circular rug in her living room. The circumference of the rug is 31.4 ft. Use this information to answer the following questions. Use 3.14 for π. C=πD. A = π r^2.
Answer:
Part A) The diameter of the rug is [tex]10\ ft[/tex]
Part B) The radius of the rug is [tex]r=5\ ft[/tex]
Part C) The area of the rug is [tex]78.5\ ft^{2}[/tex]
Step-by-step explanation:
Part A) Find the diameter of the rug
we know that
The circumference of a circle (circular rug) is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
we have
[tex]C=31.4\ ft[/tex]
[tex]\pi=3.14[/tex]
substitute the values and solve for D
[tex]31.4=(3.14)D[/tex]
[tex]D=31.4/(3.14)=10\ ft[/tex]
Part B) Find the radius of the rug
we know that
The radius of a circle (circular rug) is half the diameter
we have
[tex]D=10\ ft[/tex]
[tex]r=D/2[/tex]
substitute
[tex]r=10/2=5\ ft[/tex]
part C) What is the area the rug is covering?
The area of the circle (circular rug) is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=5\ ft[/tex]
[tex]\pi=3.14[/tex]
substitute
[tex]A=(3.14)(5)^{2}[/tex]
[tex]A=78.5\ ft^{2}[/tex]
I neeed help please?!!!!
Answer:
(3,-3)
Step-by-step explanation:
An ordered pair is written with X first, then Y (X,Y).
X is the left and right axis Y is the up and down axis.
The dot is at X = 3 and Y = -3
It would be written as (3,-3)
3 cups to 8 cups in fraction form
Answer:
3/11
Step-by-step explanation:
A ratio for 3 cups to 8 cups is written as 3:8.
To turn this into a fraction, you must put the first number over the sum of both numbers.
3/3+8
3/11
What is the measure of bac
50
80
100
130
Answer:
80
Step-by-step explanation:
The measure of a triangle is 180.
Answer: The answer to your question is 80
Step-by-step explanation: The first thing you do is set up your problem to find the side measure of bac, which is an angle they are looking for. The problem would look like this:
180-50+50
180-100
=80 degrees
I need to do this division problem AND SHOW THE WORK!!! PLEASE HELP I need help with the one that is circled
Hello There!
First, we are give the problem which is 2,624/4
0 6 5 6
4 2 6 2 4
− 0
2 6
− 2 4
2 2
− 2 0
2 4
− 2 4
0
ANSWER IS 656
A certain corporation listed their sales in 100s as 1,700. What was their actual volume in thousands?
Answer: 170
Step-by-step explanation:
Based on the problem, you know that this corporation listed their sales in 100s as 1,700. This means that, to calculate their actual volume in thousands, you need to multiply 1,700 by 100 and divide the product by 1,000.
Let be "x" their actual volume in thousands.
Therefore, applying the corresponding procedure, you get that the value of "x" is the following:
[tex]x=\frac{(1,700)(100)}{(1,000)}\\\\x=\frac{170,000}{1,000}\\\\x=170[/tex]
Final answer:
To find the corporation's sales volume in thousands from a base of '100s', one needs to multiply 1,700 by 100 and then divide by 1,000, resulting in a sales volume of 170 thousand shares.
Explanation:
The question asks us to convert a corporation's sales figure from 100s to thousands. The listed sales are 1,700 in 100s, which means the sales are 1,700 × 100 shares. To convert this number into thousands, we divide by 1,000 because there are 1,000 units in one thousand.
Thus, the calculation would be:
Multiply 1,700 by 100 to get the total sales in shares.
Divide the result by 1,000 to convert it into thousands.
(1,700 × 100) / 1,000 = 170,000 / 1,000 = 170.
Therefore, the actual volume of sales in thousands is 170.
What is the exact volume of the cylinder?
A .54π in³
B. 108π in³
C 162π in³
D. 324π in³
help me plz
Answer:
D
Step-by-step explanation:
Use the formula for the volume of a cylinder.
[tex]V=\pi r^2h[/tex]
Plug in the values we know.
[tex]V=\pi6^2*9 \\ \\ V=36\pi*9 \\ \\ V=324\pi[/tex]
The volume of the cylinder given will be 324π.
The volume of a cylinder is calculated by using the formula:
Volume = πr²h
where,
r = radius = 6 inches.
h = height = 9 inches
Volume = πr²h
Volume = π × 6² × 9
Volume = π × 36 × 9.
Volume = 324π
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the ratio of teachers to student is 1 to 26. Find an equivalent ratio
To find an equivalent ratio, multiply both the numerator and denominator of the given ratio by the same number. In this case, multiplying both 1 and 26 by 2 gives us an equivalent ratio of 2:52.
Explanation:To find an equivalent ratio, we can multiply or divide both the numerator and denominator of the given ratio by the same number. In this case, we can multiply both the numerator and denominator of the ratio 1:26 by 2 to get an equivalent ratio. Therefore, the equivalent ratio is 2:52.
The length And width of a rectangle each less than 1 unit long. Which statement is true about the area of the rectangle?
Area is calculated by multiplication of dimensions:
length×width= Area
both are lesser than 1, let's say 0.5 and 0.9 as examples.
0.5×0.5=0.25
0.9×0.9=0.81
you see the area is less than one and area can never be negative so first answer is the right answer.
The correct statement is option a. The area is between 0 square units and 1 square units
What is a rectangle?Any 2-diamensional figure bounded by 4 sides in which opposite sides are equal and parallel and all the 4 angles are right angled.
How to find which statement is true about the area of the rectangle?The area of rectangle can be calculated by the formula = Length x breadth( or width)Here the length and width of a rectangle each less than 1 unit long.Now, 0 unit<length<1 unit
0 unit<width<1 unit
∴ Area of the rectangle = (length x width)
We know that if any quantity whose value lies between 0 and 1 is multiplied to another quantity whose value also lies between 0 and 1 ,then the answer will also lie between 0 and 1.If the values of both the quantities are 1, then the product will be 1⇒ 0 square units <Area of the rectangle <1 square units
∴ The area of the rectangle is between 0 square units and 1 square units
The first option matches with the answer.
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Find the radius of the circle whose equation is x^2 + y^2 = 4.
Answer:
Radius = 2.
Step-by-step explanation:
We have been given equation of the circle which is [tex]x^2 + y^2 = 4[/tex].
Now we need to find the radius of the given circle [tex]x^2 + y^2 = 4[/tex].
To find that let's compare with the formula of the circle with standard equation of the circle [tex]x^2 + y^2 = r^2[/tex], where r is the radius.
We get [tex]r^2 = 4[/tex]
take square root of both sides.
[tex]r=2[/tex]
Hence radius of the given circle is r = 2.
what is the range of 4,5,10,10,16
Range is the biggest number minus the smallest from the list.
R = 16 - 4
R = 12
The range is 12.
Question 29
Find the short leg
Plz help
Answer:
7
Step-by-step explanation:
Since the triangle is right we can use the cosine ratio to find IR
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{IR}{TR}[/tex] = [tex]\frac{IR}{14}[/tex]
Cross- multiply
IR = 14 × cos60° = 14 × 0.5 = 7
The value of n is a distance of 1.5 units from -2 on a number line.
Click on the number line to show the possible values of n.
Answer:
The possible values of n are -0.5 and -3.5
Step-by-step explanation:
Analyze two cases
1) n-(-2)=1.5
Solve for n
n+2=1.5
n=1.5-2
n=-0.5
2) -2-n=1.5
n=-2-1.5
n=-3.5
see the attached figure
Answer:-0.5,-3.5
Step-by-step explanation:i did this
is 3(2 + x) equivalent to 6 + 3x
pplz tell me how to solve the problem plz cuz i dont wanna just ask a question and not know how to do it in the future
[tex]3(2 + x) \\ = 6 + 3x \\ = 3x + 6[/tex]
Yes it is because three times two is six and three times x is three x hope this helps
Find Q, if cos(Q + 60) = 0.0872, where 0 degrees < Q < 90 degrees
Answer:
Q = 25°
Step-by-step explanation:
Given
cos(Q + 60) = 0.0872, then
Q + 60 = [tex]cos^{-1}[/tex] (0.0872 ) = 85° ( nearest degree )
Q = 85° - 60° = 25°
Which value is the best estimate of the correlation
coefficient for the variables in the scatter plot?
A. -0.85
B. -0.3
C. 0.19
D. 0.92
Answer: Option D
D. 0.92
Step-by-step explanation:
The correlation coefficient "r" is a number between -1 and 1 that indicates how related are two variables X and Y.
The stronger the nearest correlation is, the value of r a -1 or a 1.
A negative correlation indicates that when X increases Y decreases.
A positive correlation indicates that when X increases Y increases.
A correlation close to zero implies that there is very little correlation of the variables. When this happens, the points are scattered in the graph.
In this case you can see in the graph that the points are not scattered, but aligned. You can also observe that when X increases Y increases also.
This allows us to conclude that the correlation is strong and positive. Therefore the correct option is option D.
[tex]r = 0.92[/tex]
Please Help!!!
If is approximately 43.64, find the sum of the first 101 terms of this series.
Answer:
the answer is A.
Step-by-step explanation:
that is a good good question
Answer:
C. 43.72
Step-by-step explanation:
just took it on edge
Help with this question !
Answer:
see explanation
Step-by-step explanation:
Given
T= 2π[tex]\sqrt{\frac{L}{g} }[/tex]
Square both sides
T² = 4π² [tex]\frac{L}{g}[/tex] ( divide both sides by 4π²
[tex]\frac{T^2}{4\pi ^2}[/tex] = [tex]\frac{L}{g}[/tex]
Multiply both sides by g
L = [tex]\frac{gT^2}{4\pi^2 }[/tex]
HEL ASSAP
1. The rectangle shown is dilated by a scale factor of 2.
(a) Calculate the length of each side of the dilated image.
(b) Draw the new image and label it .
A scale factor of 2 means the dimensions are multiplied by 2.
15 x 2 = 30
8 x 2 = 16
Please can someone help me with this question I need help ASAP
Answer:
3²
Step-by-step explanation:
Add the indices together
3⁸ ₓ 3⁴ = 3¹²
3² ₓ 3⁸ = 3¹⁰
Now we minus the indices since we are dividing
3¹² - 3¹⁰ = 3²
Given the points (-3,2) and (1,2) are vertices of a square, what two sets of coordinates could form the other two vertices
To find the other two vertices of the square given two points, create a diagonal line between the two points. The y-coordinate for the other two vertices will be the same as the given points, and the x-coordinate can be found by adding or subtracting the distance between the two given points from the x-coordinate of one of the given points.
Explanation:The other two vertices of the square can be found by creating a diagonal line from one given vertex to the other. The slope of this diagonal line is zero, indicating that it is a horizontal line. Since the other two vertices should be equidistant from the given points, the y-coordinate for both vertices would be the same as the given points, which is 2. To find the x-coordinate of one of the vertices, we can add the distance between the two given points (4) to the x-coordinate of one of the given points (-3), resulting in the x-coordinate of one of the other vertices being 1. Likewise, to find the x-coordinate of the other vertex, we can subtract the distance between the two given points from the x-coordinate of one of the given points, resulting in the x-coordinate of the other vertex being -7.
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