The lower quartile of the given data set is 63.
To find the lower quartile (Q1), we need to determine the value that divides the data set into the lower 25% of the values.
First, we need to sort the data set in ascending order: 61, 61, 62, 64, 66, 69, 69, 70, 72, 73, 74, 78.
Next, we calculate the position of the lower quartile using the formula: (n+1)/4, where n is the number of data points. In this case, we have 12 data points, so (12+1)/4 = 13/4 = 3.25.
Since 3.25 is not a whole number, we can find the lower quartile by taking the average of the data points at positions 3 and 4.
The data point at position 3 is 62, and the data point at position 4 is 64.
Therefore, the lower quartile (Q1) is the average of 62 and 64:
(Q1) = (62 + 64)/2 = 126/2 = 63.
Hence, the lower quartile of the given data set is 63.
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The next day you take Zeek to the Arizona State Fair. His mom gives him $30 to
spend. It costs $13 to get in and the $2 for every ride. How many rides can he ride?
● Define a variable, ex: x = ________.
● Write an equation to model this situation.
● Solve the equation for your variable.
● Write your answer in a complete sentence.
● Give the page a relevant title.
Answer:
Step-by-step explanation:
Let’s define the number of rides that Zeek can ride as “r”.
To determine how many rides Zeek can ride, we need to first subtract the cost of admission from his total budget:
$30 - $13 = $17
This means that Zeek has $17 left to spend on rides. Since each ride costs $2, we can set up the following equation:
$2r = $17
To solve for “r”, we divide both sides of the equation by $2:
r = $8.50
So Zeek can ride a maximum of 8 rides with the $17 he has left after paying for admission. However, since he cannot ride a fraction of a ride, he may be limited to only 8 rides or fewer.
A high school is building a new gym in the shape off a pyramid. Its base is a square with each side 500 feet long and has a slant height of 60 feet. What is the surface area of this pyramid?
The surface area of the pyramid is approximately 393,560 square feet.
To find the surface area of the pyramid, we need to find the area of each of the four triangular faces and the area of the square base.
The area of the square base is simply the area of a square with side length 500 feet:
Area of base =[tex](side length)^2 = (500 feet)^2[/tex]= 250,000 square feet.
To find the area of each triangular face, we need to know the length of one of the sides of the base and the slant height of the pyramid.
Since the base is a square, all sides have the same length of 500 feet.
Using the Pythagorean theorem, we can find the height of each triangular face:
height = √(slant heigh[tex]t^2[/tex] - base lengt[tex]h^2[/tex]/4)
height = √([tex]60^2 - (500/2)^2[/tex])
height = √(3600 - 62500/4)
height = √(3600 - 15625)
height = √20375
height ≈ 142.76 feet
Now we can find the area of one of the triangular faces:
Area of triangular face = (1/2) x (base length) x (height)
Area of triangular face = (1/2) x 500 feet x 142.76 feet
Area of triangular face ≈ 35,690 square feet
Since there are four triangular faces, the total surface area of the pyramid is:
Total surface area = 4 x (Area of triangular face) + (Area of base)
Total surface area = 4 x 35,690 square feet + 250,000 square feet
Total surface area ≈ 393,560 square feet
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PLEALSLE ANSWER FOR 70 POINTS
prove: the square of a number that is two more than a multiple of 3 is one more than a multiple of 3
Prove in below steps:
(3n + 2)² = 9n² + 12n + 4 = 9n² + 12n + 3 + 1 = 3(3n² + 4n + 1) + 1 = 1 more than a multiple of 3Proved
Is x-1
a factor of
x^5-3x^4-2x^3-5x^2+5x+12?
Correct The remainder when you divide is
The remainder theorem indicates that remainder when the polynomial x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) is 8
What is the remainder theorem?The remainder theorem specifies the relationship between the division of a polynomial by a linear factor to the value of the polynomial at a specified point
The remainder when the polynomial expression; x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by x - 1, can be found using the remainder theorem by plugging in x = 1 in the function as follows;
f(1) = 1⁵ - 3 × 1⁴ - 2 × 1³ - 5 × 1² + 5 × 1 + 12 = 8
The remainder when x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) therefore is 8
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What is the surface area of a sphere with diameter 8 cm?
Answer:
A≈201.06cm²
Step-by-step explanation:
A=4πr2
d=2r
Solving forA
A=πd2=π·82≈201.06193cm²
Is x-7
a factor of
x^5+5x^4-2x^3+4x^2+8x+3976
?
Correct The remainder when you divide is
x-7 is a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$[/tex], we can use the Factor theorem which states that if f(a) = 0, then x-a is a factor of f(x).the remainder when we divide [tex]x^5+5x^4-2x^3+4x^2+8x+3976$[/tex] by x-7 is 4054.
To check if x-7 is a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$,[/tex] we can use the factor theorem which states that if f(a) = 0, then x-a is a factor of f(x).
To check if x-7 is a factor, we evaluate the polynomial at x=7:
[tex]f(7) = 7^5+5\cdot7^4-2\cdot7^3+4\cdot7^2+8\cdot7+3976 = 384004$.[/tex]
Since [tex]$f(7)\neq 0$[/tex], we can conclude that x-7 is not a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$.[/tex]
To find the remainder when we divide [tex]$x^5+5x^4-2x^3+4x^2+8x+3976$[/tex]by x-7, we can use polynomial long division or synthetic division. Using polynomial long division, we get:
[tex]x^4 + 12x^3 + 82x^2 + 578x + 4046\\x-7 | x^5 + 5x^4 - 2x^3 + 4x^2 + 8x + 3976\\- x^5 + 7x^4[/tex]
------------
[tex]12x^4 - 2x^3 + 4x^2 + 8x\\ 12x^4 - 84x^3[/tex]
-------------
[tex]82x^3 + 4x^2 + 8x\\ 82x^3 - 574x^2[/tex]
--------------
[tex]578x^2 + 8x\\ 578x^2 - 4046[/tex]
------------
4054
Therefore, the remainder when we divide [tex]$x^5+5x^4-2x^3+4x^2+8x+3976$ by $x-7$ is $4054$.[/tex]
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What is the approximate perimeter of the triangle shown below?
Last question is 19.8…
The perimeter of the given triangle is: 19.2 units
What is the Perimeter of the Triangle?The formula for the distance between two coordinates is:
D = √[(y₂ - y₁)² + (x₂ - x₁)²]
Thus: (0, 3)(4, -2)
Slant distance on left side of triangle = √[(-2 - 3)² + (-3 - 0)²] = 5.8 units
Slant distance on right side of triangle = √[(-2 - 3)² + (4 - 0)²] = 6.40 units
Length of horizontal part of triangle = 7 units
Thus:
Perimeter of triangle = 5.83 + 6.40 + 7 = 19.2 units
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Write the number 0.08 in scientific notation
The scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex] where 10 raised to an exponent (-2).
In scientific notation, a number is expressed as the product of a coefficient and a power of 10.
To write the number 0.08 in scientific notation, it as a decimal number multiplied by a power of 10.
So, 0.08 can be written in scientific notation as 8 x [tex]10^{(-2)[/tex].
In scientific notation, the number is written as the product of a coefficient (8) and a power of 10 raised to an exponent (-2), indicating the decimal's position relative to the coefficient.
Therefore, the scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex].
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Which of the following statements are true?
Select all that apply.
A. 4 is a perfect cube.
B. 16 is a perfect square.
C. 2,197 is both a perfect square and a perfect cube.
D. 8 is a perfect cube.
E. 18 is neither a perfect square nor a perfect cube.
Answer:
B and D
Step-by-step explanation:
4²= 16
it's a perfect square
2³= 8
it's a perfect cube
I need help urgently on this problem, please and thank you
The inverse of function f is [tex]f^{-1}(x)=\frac{4}{x}-3[/tex].
The domain of f is (-∞, -3) U (-3, ∞).
The range of f = (-∞, 0) U (0, ∞)
The domain of f⁻¹ = (-∞, 0) U (0, ∞).
The range of f⁻¹ = (-∞, -3) U (-3, ∞).
How to determine an inverse function?In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value or domain) and dependent value (y-value or range) as follows;
f(x) = y = 4/(3 + x)
x = 4/(3 + y)
3 + y = 4/x
f⁻¹(x) = 4/x - 3
[tex]f^{-1}(x)=\frac{4}{x}-3[/tex]
By critically observing the graph of this rational expression (function) and its inverse shown in the image attached below, we can reasonably and logically deduce the following domain and range:
Domain of f = (-∞, -3) U (-3, ∞); {x|x ≠ -3}.
Range of f = (-∞, 0) U (0, ∞); {y|y ≠ 0}.
Domain of f⁻¹(x) = (-∞, 0) U (0, ∞); {y|y ≠ 0}.
Range of f⁻¹(x) = (-∞, -3) U (-3, ∞); {x|x ≠ -3}.
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what is the addictive inverse of 36
Answer:
Step-by-step explanation: -36
4.1.2 Calculate the total number of deaths for all the countries.
Calculating the total number of deaths for all countries requires collecting data from various sources and summing up the individual death counts. Here is a step-by-step guide on how to approach this calculation:
Identify reliable sources: Look for reputable sources that provide updated and accurate information on global death counts.
Gather country-specific data: Access the data provided by these sources and collect the individual death counts for each country.
Validate and verify data: Cross-reference the data from multiple sources to ensure consistency and accuracy.
Sum up the death counts: Add up the individual death counts for each country to obtain the total number of deaths.
Regularly update the data: As the situation evolves, keep track of new data releases and updates.
Calculating the total number of deaths for all countries requires collecting data from various sources and summing up the individual death counts. Here is a step-by-step guide on how to approach this calculation:
Identify reliable sources: Look for reputable sources that provide updated and accurate information on global death counts. Examples include official government health agencies, international health organizations (e.g., WHO), and reputable databases (e.g., Worldometer, Johns Hopkins University).
Gather country-specific data: Access the data provided by these sources and collect the individual death counts for each country. Ensure the data is recent and covers a comprehensive list of countries.
Validate and verify data: Cross-reference the data from multiple sources to ensure consistency and accuracy. Different sources may have slight variations, so it's important to verify the data and use the most reliable figures.
Sum up the death counts: Add up the individual death counts for each country to obtain the total number of deaths. Use a spreadsheet or calculator to perform the calculations accurately.
Regularly update the data: As the situation evolves, keep track of new data releases and updates. Update the total number of deaths accordingly to maintain accuracy.
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The question probable may be:
How to calculate the total number of deaths for all the countries?
8x^5+3x^4-23x in standard form
Answer:
Step-by-step explanation:
[tex]8x^5 + 3x^4 - 23x\\= 8x^5+3x^4+0x^3+0x^2-23x+0[/tex]
please show work I don't understand how to do this
Answer:
19.......
Step-by-step explanation:
correct
Answer:
x = - 2---------------------------
Solve the equation for x:
- 3 = - 8x - 9 + 5x simplify right side- 3 = - 3x - 9 add 9 to both sides9 - 3 = - 3x 6 = - 3x divide both sides by - 3x = - 6/3x = - 2pls answer me fast rapidly:
What is the surface area of this cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth. 18 yd 9 yd
The surface area of the given cylinder is approximately 1758.4 square yards.
To find the surface area of a cylinder, we need to calculate the sum of the areas of its curved surface (lateral surface area) and its two circular bases.
Given:
Height (h) = 18 yards
Radius (r) = 10 yards
π (pi) ≈ 3.14
Lateral Surface Area:
The lateral surface area of a cylinder can be calculated using the formula 2πrh, where r is the radius and h is the height.
Lateral Surface Area = 2πrh
Substituting the given values, we have:
Lateral Surface Area = 2 × 3.14 × 10 × 18
Lateral Surface Area = 1130.4 square yards (rounded to the nearest hundredth)
Circular Bases:
The area of a circle can be calculated using the formula πr^2, where r is the radius.
Area of a Circular Base = π[tex]r^2[/tex]
Substituting the given radius, we have:
Area of a Circular Base = 3.14 × [tex]10^2[/tex]
Area of a Circular Base = 314 square yards
To find the total surface area, we need to add the lateral surface area and the areas of the two circular bases.
Total Surface Area = Lateral Surface Area + 2 × Area of a Circular Base
Substituting the values, we get:
Total Surface Area = 1130.4 + 2 × 314
Total Surface Area = 1758.4 square yards (rounded to the nearest hundredth)
Therefore, the surface area of the given cylinder is approximately 1758.4 square yards.
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Question
'What is the surface area of this cylinder? What is the surface area of this cylinder? Use I ~ 3.14 and round your answer to the nearest hundredth_ 18 yd 10 yd square yards'
Help, what is the value of x if the volume is 133 1/3
If the volume is 133 1/3 in³, the value of x is equal to 5 inches.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
133 1/3 = 10 × x × 2 2/3
400/3 = 10 × x × 8/3
400/3 = 80x/3
80x = 400
x = 400/80
x = 5 inches.
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Find the area of the composite figure ?
The area of the composite figure is 81 yd². Option D
How to determine the areaThe composite figure is made up of a rectangle, a triangle and a trapezoid
The formula for the area of a rectangle is expressed as;
Area = length × width
Substitute the values
Area = 7(6)
Multiply the values
Area = 42 yd²
Area of the triangle = 1/2 base ×height
Area of the triangle = 1/2 × 6 ×5 = 30/2 = 15yd²
Area of the trapezoid = a+b/2 h
Substitute the values
Area = 7 + 9/2 (3) = 16/2(3) = 8(3) = 24yd²
Total area = 24 + 15 + 42 = 81 yd²
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The area of the composite figure is 81 cm²
What is area of composite figure?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Any figure that we can break and form more than one basic shape from is called a composite figure.
The figure consist of two trapezoid
Area of trapezoid 1 = 1/2( a+b) h
= 1/2 ( 12 + 7) 6
= 1/2 × 19 × 6
= 19 × 3
= 57cm²
area of trapezoid 2
= 1/2(a+b) h
= 1/2 ( 7+9) 3
= 1/2 × 16 × 3
= 8 × 3
= 24 cm²
Therefore the area of the composite figure
= 57 +24 = 81 cm²
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I need assistance for 1b
The two numbers are 15 and 15. The product of the two numbers is 225.
Let x and y be the two numbers we are searching for. We know that x + y = 30, so we can settle for y to get y = 30-x. The result of x and y is then, at that point:
[tex]P(x, y) = x(30 - x) = 30x - x^2[/tex]
To find the greatest item, we can take the subsidiary of P(x, y) concerning x and set it equivalent to 0:
dP(x, y)/dx = 30 - 2x = 0
Settling for x, we get x = 15. Subbing x = 15 into y = 30-x, we get y = 15. Hence, the two numbers that have an amount of 30 and produce the biggest conceivable item are 15 and 15.
The result of the two numbers is:
P(15, 15) = 15 * 15 = 225
So the result of the two numbers is 225.
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Use substitution to solve the system of equations. How many solutions are there? 12 x − 13 y = 5 x = 23 y + 10 There are no solutions. There is one solution. There are infinitely many solutions.
Answer: there is one solution
Step-by-step explanation:
12x − 13y = 5
x = 23y + 10
lets substitute x into the first equation.
12(23y + 10) - 13y = 5
276y + 120 - 13y = 5
263y = -115
y = -115/263
substituting for x:
x = 23(-115/263) + 10
x = -2645/263 + 10
x = -15/263
As we can see, we get one value of x;
this means there is one solution
please help i cant fail this
Answer:20%
Step-by-step explanation:
what would The number of discharge days for a patient admitted January 23 to February 15 is _____.
Answer:
The number of discharge days for a patient admitted January 23 to February 15 is 31 - 23 + 15 = 23
Given WX is tangent to ⊙S at point V, select all the statements that must be true.
A. m∠TVX =m∠TVX
B. m∠TSV =m∠UVX
C. m∠TVW = m∠TSV
D. m∠TUV =m∠TVW
E. m∠UVX =m∠VTU
Given WX is tangent to OS at point V, the statements that must be true include:
A. m∠TVX =m∠TVX
C. m∠TVW = m∠TSV
D. m∠TUV =m∠TVW
How to explain the tangentIn mathematics, a tangent is a line that touches a curve at exactly one point, without intersecting it at that point. The tangent line at a point on a curve represents the slope of the curve at that point. The concept of tangent is important in calculus, where it is used to calculate derivatives of functions.
TUV = 1/2MTU = TVW
TUV = TVW
Also, MTV = TSV = 2TVW
TVW = TSV
The correct options are A, C and D.
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I need some help with this problem please
(a) The result of row 1 and row 2 interchange is [3 -2 3]
[2 3 1]
(b) The result of multiplying and adding the matrix is [-1 5 -2]
[3 -2 3]
What is the row operation of the matrix?
The row operation of the matrix is calculated as follows;
The given matrix;
[2 3 1]
[3 -2 3]
To interchange row 1 and row 2, we determine it as follows;
R₁ ↔ R₂ = [3 -2 3]
[2 3 1]
The product of row 2 and -1 is calculated as;
-1 (R₂) = [-3 2 -3]
The addition of -1(R₂) + R₁ is calculated as;
-1(R₂) + R₁ = [-3 2 -3] + [2 3 1]
-1(R₂) + R₁ = [-1 5 -2]
new matrix = [-1 5 -2]
[3 -2 3]
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Which is a whole number?
0.86
2/5
98
35%
Answer:
98 is a whole number
Step-by-step explanation:
0.86 is a decimal
2/5 is a fraction
35% is a percentage
what is .3433 rounded to the nearest hundredth
Answer:
0.34
Step-by-step explanation:
4 or below go down low
5 or above fly like a dove
so the 33 part is lower than 50 so round down
Please help I’ll mark you as brainliest if correct
Answer:
5, 3
Step-by-step explanation:
What is -4 ≥ k - 2 I can not find it so please help...
Use the number properties rule to solve the equations below. Remember that PEMDAS tells you what to do first.
1) 5 + 16 = 16 + __
2) 450 + ___ = 50 + 450
3) 2 + ( 3 + 5 ) = ( 2 + 3 ) + _____
4) ( 7 + 4 ) + 6 = ___+ ( 4+6 )
5) 7 + 0 = ________
6) 15 – 0 = _______
7) (12 – 8 ) – 2 = _______
8) 12 – ( 8 – 2 ) = _________
9) 20 – 5 = _____
10) 5 – 20 = _______
Mark as true or false.
11) 16 + 4 = 4 + 16 ______________
12) 15 – 5 = 5 – 15 ______________
13) (3 + 4) + 5 = 3 + (4 + 5) ______________
14) (12 – 4) – 2 = 12 – (4 – 2) ______________
15) (10 -5) + 5 = 10 – (5 +5) ______________
After considering the given data we conclude that the value of the sub question are
A) 16
B) 50
C) 5
D) 7
E) 7
F) 15
G) 2
H) 6
I) 15
J) -15
And the marking the true and false
a) true
b) false
c)true
d) true
e) false
The number properties rule is a set of rules that help you solve mathematical equations. The rule is also known as the order of operations. The acronym PEMDAS is used to remember the order of operations. It stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right) ¹².
Let's solve the equations using the number properties rule:
A) 5 + 16 = 16 + __
We can solve this equation by subtracting 16 from both sides of the equation.
5 + 16 - 16 = 16 + __ - 16
5 = 16
The equation is not true.
B) 450 + ___ = 50 + 450
We can solve this equation by subtracting 450 from both sides of the equation.
450 + ___ - 450 = 50 + 450 - 450
___ = 50
The answer is 50.
C) 2 + ( 3 + 5 ) = ( 2 + 3 ) + _____
We can solve this equation by simplifying the parentheses first.
2 + (3 + 5) = (2 + 3) + _____
2 + 8 = 5 + _____
10 = 5 + _____
We can solve this equation by subtracting 5 from both sides of the equation.
10 - 5 = 5 - 5
5 = _____
The answer is 5
D) (7 + 4) + 6 = ___+ (4+6)
We can solve this equation by simplifying the parentheses first.
(7 + 4) + 6 = ___+ (4+6)
11 + 6 = ___+ 10
17 = ___+ 10
We can solve this equation by subtracting 10 from both sides of the equation.
17 - 10 = ___+ 10 - 10
7 = ___
The answer is 7
E) 7 + 0 = ________
The answer is 7
F) 15 – 0 = _______
The answer is 15
G) (12 – 8 ) – 2 = _______
We can solve this equation by simplifying the parentheses first.
(12 – 8 ) – 2 = _______
4 - 2 = _______
2 = _______
The answer is 2
H) 12 – (8 – 2 ) = _________
We can solve this equation by simplifying the parentheses first.
12 – (8 – 2) = _________
12 - 6= _________
6= _________
The answer is 6.
I)20 – 5= _____
20 - 5= _____
15= _____
The answer is 15.
J)5 –20= _______
5 - 20= _______
-15= _______
The answer is -15.
Mark as true or false.
a)16+4=4+16 ______________
True
b)15–5=5–15 ______________
False
c)(3+4)+5=3+(4+5) ______________
True
d)(12–4)–2=12–(4–2) ______________
True
e)(10-5)+5=10–(5+5) ______________
False
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18.3% of the animals in the local shelter are neither cats nor dogs. 2% of those animals that are not cats or dogs are rabbits. If there are 267 animals in the shelter, approximately how many of them are rabbits? Do not round any numbers until you finish the problem