The median should be used to describe a normal or skewed distribution, as it is a better measure of the central tendency than the mean for these types of distributions.
The median is a better measure of the central tendency than the mean when describing a normal or skewed distribution. A normal distribution is a symmetrical distribution of data in which values are evenly spread around the mean. A skewed distribution is when one side of the distribution is longer than the other, with the mean being pulled away from the center. The median is the most appropriate measure of central tendency for both normal and skewed distributions because the mean can be distorted by outliers and extremes in the data. The median is the midpoint in the data and provides a better representation of the middle of the distribution, which can be useful in interpreting the data. Using the median to describe a large distribution or percentage is not as common as it is better to use the mean or mode for these types of distributions.
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Which of the following items has volume?
baseball diamond
floor rug
piece of paper
water bottle
The only option that represents an object with volume is; Option D: Water Bottle
How to find the volume of objects?An object that will have volume is a 3-D object which means that it has length, width and height. Thus, 2D objects cannot have a volume.
Let us access the given options;
A) Baseball diamond: This refers to the baseball field because of the shape of the infield. Thus, it has only length and width and is a 2D shape which doesn't have a volume.
B) Floor Rug: A floor rug, is a plane shape which means it s a 2D shape which doesn't have a volume.
C) A piece of paper: This is a plane shape which means it s a 2D shape which doesn't have a volume.
D) Water Bottle: This is a 3D shape that has length, width and height and as such it has volume.
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In AOPQ, m/O = (6x – 14)°, m/P = (2x + 16)°, and m/Q = (2x + 8)°.
Find m/Q.
The required measure of angle m∠Q is 42 degrees, as of the given condition.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°
Here,
In a triangle, the sum of the angles is always equal to 180 degrees. Therefore, for triangle OPQ,
m∠O + m∠P + m∠Q = 180°
Using the given information,
m∠O = (6x - 14)°
m∠P = (2x + 16)°
m∠Q = (2x + 8)°
(6x - 14)° + (2x + 16)° + (2x + 8)° = 180°
10x + 10 = 180°
10x = 170
x = 17
Substituting the value of x back into the expression for m∠Q,
m∠Q = (2x + 8)°
m∠Q = (2 * 17 + 8)°
m∠Q = 42°
So the value of m∠Q is 42 degrees.
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an actress has a probability of getting offered a job after a try-out of 0.15. she plans to keep trying out for new jobs until she gets offered. assume outcomes of try-outs are independent. hint: use a geometric random variable. find the probability she will need to attend more than 5 try-outs.
The probability that the actress will need to attend more than 5 try-outs is approximately 0.478.
Since the outcomes of each try-out are independent,
As per the given information,
Number of try-out is 0.15
probability means the possibilities.
We can model the number of try-outs needed to get an offer as a geometric random variable with the probability of success p = 0.15.
Let X be the number of tryouts needed to get an offer.
Then, X follows a geometric distribution with parameter p=0.15, and the probability of needing to attend more than 5 try-outs is:
[tex]P(X > 5) &= 1 - P(X \leq 5)[/tex]
=[tex]1 - \sum_{k=1}^{5} P(X=k)[/tex]
= 1 [tex]- \sum_{k=1}^{5} P(X=k)[/tex]
= [tex]1 - [(1-p)^0p + (1-p)^1p + (1-p)^2p + (1-p)^3p + (1-p)^4p][/tex]
=[tex]1 - [(1-p)^0p + (1-p)^1p + (1-p)^2p + (1-p)^3p + (1-p)^4p][/tex]
= 0.478
Hence the number of possibility required to attend more than 5 try-outs is approximately 0.478.
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Determine the better deal.
12 cans of soda for $4.79
24 cans of soda for $8.89
Answer:
24 cans of soda for $8.89 is the better deal.
Step-by-step explanation:
Divide 24 cans of soda for $8.89 by 2. That way, with the same amount of cans, you can determine which one is more expensive.
1) 12 cans of soda: $4.75
2) 12 cans of soda: $4.445
The second one is cheaper.
find all radicals expressions that are equivalent for 5 (2/3)
HOW DO I DO THIS??????????
Keith and his friends are heading to the Thunder Beach water park. They plan to purchase the group package, which costs $78 for 6 people. That's $3 less per person than the normal cost for an individual. What is the normal cost for an individual?
describe to use or importance of points , lines , and planes in daily life
Points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.
What are points, lines, and planes?
Point: A point is a basic geometric object that represents a specific location in space.
Line: A line is a straight path that extends infinitely in both directions. It is made up of an infinite number of points that are all collinear, or lie on the same straight path.
Plane: A plane is a two-dimensional flat surface that extends infinitely in all directions.
Navigation: Points and lines are essential for navigation, both on land and in the air. For example, on a map, points represent specific locations, while lines represent roads, highways, and other paths that can be taken to get from one point to another.
Architecture and Design: Points, lines, and planes are critical for architecture and design. Architects use points to specify the locations of walls, columns, and other structural elements, while lines are used to create the edges of rooms and buildings. Planes are used to define the surfaces of walls, floors, and ceilings.
Art: Artists often use points, lines, and planes to create visual effects in their work. Points can be used to create texture, while lines can be used to create movement and depth. Planes can be used to create shapes and form.
Engineering: Points, lines, and planes are fundamental to engineering, which involves the design and construction of structures and machines. Engineers use points to specify the locations of components, while lines are used to create the edges of parts. Planes are used to define the surfaces of structures, such as the wings of an airplane.
Hence, points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.
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Find the center of the circle and the radius by completing the square. x2+y2−4y−8x+3=0
The radius of the circle is √17.
The center of the circle is (4, 2).
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
The equation of a circle with radius r and center (h, k) is
(x - h)² + (y - k)² = r²
Now,
x² + y² - 4 y - 8x + 3 = 0
x² - 8x + y² - 4y + 3 = 0
x² - 8x + 4² - 4² + y² - 4y + 2² - 2² + 3 = 0
(x - 4)² + (y - 2)² - 16 - 4 + 3 = 0
(x - 4)² + (y - 2)² = 16 + 4 - 3
(x - 4)² + (y - 2)² = √17
This means,
radius = √17 and center = (4, 2)
Thus,
The radius and center of the circle are √17 and (4, 2).
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Regis leans a 10-foot ladder against a wall. The base of the ladder makes a 65 angle with the ground.
A: What is the distance, In feet, from the base of the ladder to the base of the wall? Round to the nearest tenth of a foot.
B: Regis needs to move the ladder so that it reaches a window 9.6 feet above the ground.
How many feet closer to the building does he need to move the base of the ladder?
The distance from the base of the ladder to the wall is 4.23 feet. And the inclination angle will be 73.74°.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The length of the ladder is 10 feet. And the inclination angle is 65°. Then the distance from the bottom of ladder to the wall is given as,
cos 65° = x / 10
x = 4.23 feet
If the ladder reaches a window 9.6 feet above the ground, then the angle is given as,
sin θ = 9.6 / 10
sin θ = sin 73.74°
θ = 73.74°
The distance from the base of the ladder to the wall is 4.23 feet. And the inclination angle will be 73.74°.
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Arrange the digits 6, 0, 3, 2, and 4 to create the greatest possible five-digit number.
Answer:
The greatest possible five-digit number you can create with the numbers 6, 0, 3, 2, and 4 is 64,320.
Step-by-step explanation:
When it comes to creating the biggest number with a given set of digits, the one and only rule is to organize the digits from greatest to least, this way it ensures that you have the maximum possible values that aren't mitigated by having a small number before a larger one. Based on this, we can organize 6, 0, 3, 2, and 4 from greatest to least, which will be 64,320. Hence, the greatest possible five-digit number you can create with those given numbers is 64,320.
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5x+2y=-7 and 10x+4y= -14 no solution, solution, or infinite solution?
The system of equations 5x+2y=-7 and 10x+4y= -14 has unique solution which is (-7/5,0).
In general, a system of linear equations can have one of three possible outcomes:
One unique solution (as in this case)
No solution (if the equations are inconsistent)
Infinitely many solutions (if the equations are dependent)
To solve this system of equations, we can use the method of elimination or substitution. Let's use the method of elimination, which involves adding or subtracting the equations to eliminate one variable.
First, we need to choose a variable to eliminate. Looking at the coefficients of x and y, we see that we can eliminate y by multiplying the first equation by -2 and adding it to the second equation:
-10x - 4y = 14
5x + 2y = -7
-5x = 7
Now we can solve for x:
-5x = 7
x = -7/5
We can substitute this value of x into one of the equations to solve for y. Let's use the first equation:
5x + 2y = -7
5(-7/5) + 2y = -7
-7 + 2y = -7
2y = 0
y = 0
Therefore, the solution to the system of equations is (x,y) = (-7/5,0).
This is called a unique solution, meaning there is only one possible solution for the system of equations.
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Complete Question:
Solve
5x + 2y = -7
10x + 4y = -14
And find the number of solutions for the equation
Please answer this with a step-by-step explanation or at least a vide attachment. Thanks! :)
The estimate for the number of the paintings that are over 70 years old is given as follows:
68 paintings.
How to obtain the estimate?The histogram shows the number of observations that appear in each range of the data-set.
24 of the paintings in the gallery are over 90 years old, hence the height of each small square is of:
24/(3 x 4) = 2 units.
Then the estimate of those over 70 years old is given as follows:
11 x 2 = 22 between 70 and 80.11 x 2 = 22 between 80 and 90.24 over 90.Then the total amount is of:
2 x 22 + 24 = 68.
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HELP I REALLY NEED IT!!
Answer:
Below
Step-by-step explanation:
Since the center (h,k) is (4,1) and the circle passes through (4,-4) the radius is 5 ( from y = 1 to -4 ...a distance of 5 )
the equation for a circle is of the form (x-h)^2 + (y-k)^2 = r^2
becomes (x-4)^2 + ( y-1)^2 = 5^2 < ==== graph this equation
radius = 5 then the diameter = 10 then circumference = pi * d = 10 pi
What is the standard function of f? F(x)=4(x+6)2+5
The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.
What is the definition of a function?
A function is defined as a connection between a set of inputs and a single output. A function is a link between inputs that corresponds to exactly one output. Every function has a domain, a co-domain, and a range. A function is often denoted as f(x), where x represents the input. The general representation of a function is y = f(x).
There are several types of functions in mathematics. Here are a few examples:
An injective function or a one to one function exists when there is a mapping for a range for each domain between two sets.
Surjective functions, also known as Onto functions, are employed for transferring more than one element from domain to range.
A polynomial function is a function composed of polynomials.
Functions that may be used to inverse another function are known as inverse functions.
Now,
Given function is F(x)=4(x+6)2+5
=(4x+24)2+5
=8x+48+5
=8x+53
hence,
The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.
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Area of this figure?
Answer:
213 ft^2
Step-by-step explanation:
In this problem, we can create a larger rectangle that engulfs this image with a few missing pieces on the corners. The area of that rectangle would be 18ft * 17 ft = 306 ft^2. The sum of the missing pieces is 2ft * 7ft + 5ft * 6 ft + 7ft * 7ft = (14 + 30 + 49)ft^2 = 93 ft^2. So, the area of this figure is 306 - 93 = 213 ft^2
ANSWER: S=173ft^2
_._._._._._._._._._._._.
What is the equation of the line that passes through the point (-3,1)(−3,1) and has a slope of \frac{2}{3}
3
2
?
Answer:
y = (2/3)x + 3
Step-by-step explanation:
first we need to find the y-intercept
we can do this by using what is given, the point (-3,1) and the slope (2/3)
using the slope-intercept formula: y = mx + b.
m = slope
b = y intercept
we can plug in the x and y values we were given
so,
1 = (2/3)(-3) + b
we can now easily solve for b
1 = (2/3)(-3) = b
first multiply
1 = -2 + b
then add 2 to both sides, this way we isolate b
3 = b
now that we have the y intercept we can write the equation of the line
y = (2/3)x + 3
if you really wanted to, you can check if this is correct by plugging in the point again and seeing if the equation is true.
1 = (2/3)(-3) + 3
multiply first
1 = -2 + 3
add the like terms
1 = 1
The sum of two numbers is 14. Four less than twice the smaller number is equal to the larger number x. Find the larger number.
The Larger number is 8
What is a linear equation in one variable?
The fundamental equation used to represent and solve for an unknown quantity is a linear equation in one variable. It is always a straight line, and it is simply shown graphically. A mathematical statement is simply represented by a linear equation.
Given that, the sum of two numbers is 14 and the larger number is four less than twice the smaller number
let the larger number be 'a' and the smaller be 'b'
from the question,
a + b = 14 .....eq 1
a = 2b - 4 .....eq 2
By substituting eq 2 in eq 1:
2b - 4 + b = 14
3b - 4 = 14
3b = 14 + 4 = 18
b = 6
a = 2b - 4 = 2*6 - 4 = 8
Therefore, The two numbers are 8, 4
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a motorist buys a 5litre can of gear oil.she uses 800ml.what percentage of oil has she used and what remains
Step-by-step explanation:
1000ml=1 litre
800 divided by(1000 multiplied by 5)=16%
The start of a quadratic sequence is shown
below.
What is the nth term rule for the sequence?
-5, -2, 3, 10, 19,
Answer:
nth term = n²-6
Step-by-step explanation:
we know our nth-term formula is going to be of the form an² + bn + c. We just have to find a, b, and c.
In this series,
-5, -2, 3, 10, 19....
a=1, b=0, c=-6
nth term = n²-6
if n=1 then,
nth term=1²-6
⇒nth term=-5
Two years ago, Rita was 3 times as old as Cheryl. In 3 years, Rita will be twice as old as Cheryl. How old are the girls now?
The current age of Rita is 17 years and Cheryl is 7 years respectively, according to mentioned data.
Let us assume Rita's present age be x and Cheryl's age be y.
Rita's age two years ago = 3 × Cheryl's age two years ago
x - 2 = 3 (y - 2) - equation 1
Rita's age after three years = 3 × Cheryl's age after three years
x + 3 = 2 (y + 3) - equation 2
Solving equation 1
x - 2 = 3y - 6
x = 3y - 6 + 2
x = 3y - 4
Solving equation 2
x + 3 = 2y + 6
x = 2y + 6 - 3
x = 2y + 3
Keep the value of x from equation 2 in equation 1
2y + 3 = 3y - 4
Rearranging the equation
3y - 2y = 3 + 4
y = 7
Keep the value of y in equation x = 2y + 3
x = 2×7 + 3
x = 14 + 3
x = 17
So, Cheryl's and Rita's age is 7 and 17 years respectively.
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help pls i’m stuck!!
Step-by-step explanation:
inscribed angles subtended by the same arc are equal.
the angle FGH is "based" on the same arc (FH) as the angle FJH.
so, FGH = FJH = 56°.
How is [tex]\frac{22}{7}[/tex] a rational number
Answer:
Step-by-step explanation: 22/7 is a rational number because it can be expressed as a ratio or fraction of two integers. The numerator (22) and denominator (7) are both integers, and the denominator is not equal to zero, so 22/7 is a well-defined fraction. Since every fraction represents a rational number, 22/7 is also a rational number
There were 230,600 jobs available in the field of radiology in the year 2014. Each year, that number is expected to grow by 0.9%.
Write a function that gives the expected number j(t) of jobs in radiology t years from the year 2014.
Answer:
J(t) = 230,600(1.009)^t
Step-by-step explanation:
J(t) = 230,600(1 + 0.009)^t, or
J(t) = 230,600(1.009)^t If this is Wrong ill do. it again!!
Someone help fast I need the answer (In a live class)
Answer:
216 in^3
Step-by-step explanation:
Volume = 6 in. * 4 in. * 9 in. = 216 in^3
Find an equation of the line of symmetry of triangle ABC.
Answer:
The equation of the line of symmetry of triangle ABC is:
3x + 2y = 86Step-by-step explanation:
The line of symmetry of an isosceles triangle bisects the vertex angle (the angle opposite the base) and is perpendicular to the base of the triangle.
As AB = AC, then angle A is the vertex angle of the isosceles triangle ABC.
If B and C lie on the line with equation 3y = 2x + 12, then the line of symmetry is the line that is perpendicular to this line and passes through A (4, 37).
Rearrange the given equation 3y = 2x + 12 to slope-intercept form by dividing both sides by 3:
[tex]\implies y=\dfrac{2}{3}x+4[/tex]
Perpendicular lines have slopes that are negative reciprocals of one another. Therefore, the slope of the perpendicular line is -³/₂.
Substitute the found slope and point A (4, 37) into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-37=-\dfrac{3}{2}(x-4)[/tex]
Rearrange the equation to standard form:
[tex]\implies 2y-74=-3(x-4)[/tex]
[tex]\implies 2y-74=-3x+12[/tex]
[tex]\implies 3x+2y-74=12[/tex]
[tex]\implies 3x+2y=86[/tex]
Therefore, the equation of the line of symmetry of triangle ABC is:
3x + 2y = 86Fill each square with a number to make the addition results correct
If the array includes just the positive integers [tex]{\displaystyle 1,2,...,n^{2}}{\displaystyle 1,2,...,n^{2}}[/tex], the magic square is said to be normal. Some authors take magic square to mean normal magic square.
A magic square is a square grid of numbers that has the same sum for every row, column, and diagonal. It is a mathematical puzzle that has been known and studied for thousands of years. Magic squares can be of different sizes, but the most common are those with odd numbers of rows and columns.
The concept of magic squares dates back to ancient China, where they were believed to have mystical properties. In India, they were used for divination and as part of religious rituals. In Europe, magic squares were popularized in the 16th century, where they were used as a form of mathematical entertainment. Magic squares are not only interesting mathematical puzzles but also have practical applications.
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Complete Question: -
Fill the given squre with numbers from 0 to 8 ( using each of them exactly once) in such a way that the sum of the numbers in the first second and third rows are third rows are in the ratio 1 : 2 : 3. At the same time the sum of the numbers in the first second and third columns also have to be in the same ratio.
barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. the sums of the two numbers on each of the three cards are equal. the three numbers on the hidden sides are prime numbers. what is the average of the hidden prime numbers?
The average of the three hidden prime numbers is 5, as the sum of any two of the numbers is equal to 10, and since all three numbers are prime, the only possible values are 3, 5, and 7.
3 + 5 + 7 = 15
15/3 = 5
The average of the three hidden prime numbers is 5. This means that the sum of any two of the numbers on the cards must be equal to 10. Since all three numbers are prime,as the sum of any two of the numbers is equal to 10 the only possible values are 3, 5, and 7. Therefore, the three numbers on the hidden sides of the cards are 3, 5, and 7. To calculate the average, we add the three values together and divide by three. 3 + 5 + 7 = 15, and 15 divided by 3 is 5. Therefore, the average of the hidden prime numbers is 5.
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Find the radius of the circle circumscribed around an equilateral trapezoid, if the bases of the trapezoid are 9 and 15, and the height is 5.
What is 3 5/12 - 8/12 equal to?
Answer:
Step-by-step explanation:
first, write down on paper 3 5/12 - 8/12 then convert the mixed fraction into a more straightforward form. so 3 5/12 equals 37/12. then you do 37 - 8 = 29 so then change it into a fraction and the answer is 29/12. if you what it as a mixed fraction then it would be 2 5/12
For lunch, Joan bought a glass of milk for $1. 20, a turkey sandwich for $4. 70, as well as some sherbet for $3. 30. The tax came out to $1. 80, and Joan paid with $19. 0. How much change should Joan receive?
Joan paid with $19.00, she should receive $19.00 - $12.00, which equals $11.30 in change.So Joan should receive 11.30 in change.
Joan should receive $11.30 in change. To calculate this, we must start with the total cost of her items, which comes to $10.20 ($1.20 for the milk, $4.70 for the sandwich, and $3.30 for the sherbet). To this we must add the tax, which was $1.80. This brings the total cost to $12.00. Joan should receive $11.30 in change. To get this answer, we can use the following formula: Change = Total Payment - (Cost of Items + Tax). In this case, the formula would look like this: Change = 19.00 - (1.20 + 4.70 + 3.30 + 1.80). After calculating, the answer is 11.30. So Joan should receive 11.30 in change.
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