The mean is 11.25 and median is 8, and from the employees' perspective, the median would be a better measure of central tendency to use for determining the raise cut-off point.
The mean and medianTo find the mean and median, we can start by arranging the data in ascending order:{1, 4, 5, 6, 7, 9, 9, 11, 15, 18, 27, 32}
Mean:The mean is the average value of the dataset. We can find the mean by summing up all the values and dividing by the total number of values:
mean = (1 + 4 + 5 + 6 + 7 + 9 + 9 + 11 + 15 + 18 + 27 + 32) / 12
= 135 / 12
= 11.25
Therefore, the mean of the dataset is 11.25.
Median:The median is the middle value in the dataset. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.
In this case, the dataset has 12 values, so we need to find the average of the 6th and 7th values:
median = (7 + 9) / 2
= 8
Therefore, the median of the dataset is 8.
From the employees' perspective, the median would be a better measure of central tendency to use for determining the raise cutoff point. This is because the median is not affected by outliers as much as the mean.
In this dataset, the value of 32 is much larger than the other values and could skew the mean upward, which would result in a higher cutoff point for the raise. On the other hand, the median is not affected by the outlier and provides a better representation of the central value of the dataset.
A 5% raise for employees who have been employed for at least 8 years (the median) would be more fair and reasonable for all employees.
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1. What is the volume of the prism below?
7 cm
3 cm
5 cm
Of a rectangular prism
The volume of the prism is 105 cm³.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given is a rectangular prism.
Volume of a rectangular prism = l × w × h
Here, l is the length, w is the width and h is the height.
Given that,
l = 7 cm, w = 3 cm and h = 5 cm
Substituting,
V = 7 × 3 × 5
= 105 cm³
Hence the volume of the given rectangular prism is 105 cm³.
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Translate the following phrase into an algebraic expression: "9 times 5 less than twice x"
Three side lengths of 6,8 and 15 units will form a triangle
Answer:
The area would be 360 because 8 x 6 x 15 = 720 divided by 2 = 360
What is the area of the figure below?
10cm
I need help plssssssssssssss
Work Shown:
[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(26) = \frac{x}{5.7}\\\\x = 5.7*\tan(26)\\\\x \approx 2.78007575482541\\\\x \approx 2.8\\\\[/tex]
Make sure your calculator is in degree mode.
A great-uncle has decided to give you a gift of $1,000. Being a financially savvy uncle, before giving you the money, he offers you a choice of the following: You can take the $1,000 today. You can wait five years and be given $1,200 instead 1. How will you decide if the offer presented by your great uncle is to your advantage? 2. Research interest rates for a savings account, checking account, and money market account at different financial institutions. Note the compounding period for each. How much would $1,000 be worth in each account in five years? 3. What are some factors that cause the value of money today to be different from its value in the future?
1. To decide if the offer presented by your great uncle is to your advantage, you need to consider the time value of money. This means that money available today is worth more than the same amount of money available in the future, due to the potential for earning interest or returns on the money. In this case, you need to compare the value of $1,000 today with the value of $1,200 in five years. If you can earn a rate of return greater than 4% over the next five years, it would be better to take the $1,000 today and invest it to earn a higher return. However, if you cannot earn a return greater than 4%, it would be better to wait and take the $1,200 in five years.
2. Interest rates and compounding periods will vary depending on the financial institution and type of account. As an example, let's assume that you are considering a savings account, checking account, and money market account with the following interest rates and compounding periods:
Savings account: 2% interest rate compounded annuallyChecking account: 0.1% interest rate compounded monthlyMoney market account: 2.5% interest rate compounded quarterlyUsing a compound interest calculator, the future value of $1,000 in each account after five years would be:
Savings account: $1,104.08Checking account: $1,005.02Money market account: $1,130.473. The value of money today can be different from its value in the future due to inflation, changes in interest rates, economic growth, and changes in the supply and demand for goods and services. Inflation is one of the biggest factors that can affect the value of money over time. If the rate of inflation is high, the value of money will decrease over time, meaning that the same amount of money will buy fewer goods and services in the future. On the other hand, if the rate of inflation is low, the value of money will increase over time, meaning that the same amount of money will buy more goods and services in the future. Interest rates can also affect the value of money, as higher interest rates can make it more attractive to save money, while lower interest rates can make it more attractive to borrow money. Economic growth and changes in the supply and demand for goods and services can also affect the value of money, as these factors can affect the overall price level of goods and services in the economy.
Lance bought 15 sets of 3 tennis balls. Some of the tennis balls, t, were lost during each of the 4 matches he played. Now, the are 37 tennis balls left. Which equation represents this situation?
Triangle ABC is similar to triangle FGH. Given the following angle measures, find the missing angle measures.
The measures of angles in similar triangles are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
Given that, Triangle ABC is similar to triangle FGH, we need to find the measures of the angles,
The sum of interior angles of a triangle = 180°
Considering Δ ABC,
∠ A + ∠ B + ∠ C = 180°
∠ C = 180°-(22°+75°)
∠ C = 83°
Since, we know that the similar triangles have congruent corresponding angles,
Therefore,
∠ A = ∠ F, ∠ B = ∠ G and ∠ C = ∠ H
Therefore, the measures of angles in Δ FGH are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°
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The shape of a piece of land is a parallelogram whose adjacent sides are 12m and 17m and the corresponding diagonal is 25m. find the area of the land
Answer:
The area of the land can be found using the formula A = 1/2*D1*D2, where D1 and D2 are the diagonals of the parallelogram. In this case, the area is 1/2*25*12 = 150m^2.
Answer:
180m^2
Step-by-step explanation:
since you said that two sides measure 12 and 17 and the diagonal is 25 you can use herons formula to find the area of each individual triangle then multiply it by two
using heron's formula it gives us the answer of 90 m^2 for one triangle so we can multiply it by two to get the area of the whole shape and 90x2=180m^2
What is 60 kph into miles?
60 kilometers per hour (kph) is equal to roughly 37.28 long hauls (miles) per hour( mph).
To convert kilometers per hour to long hauls per hour, you can use the following conversion formula:
long hauls per hour = kilometers per hour x0.621371.
Plugging in 60 kilometers per hour, we get,
long hauls per hour = 60 x0.621371
long hauls per hour ≈37.28.
Thus, 60 kilometers per hour is roughly 37.28 long hauls per hour.
A kilometer (km) is a unit of length or distance used in the metric system. It is roughly original to 0.621 long hauls.
Mile is a unit of length or distance used in the customary system of dimension, primarily in the United States and United Kingdom. One afar is original to 280 bases or 760 yards, which is roughly 1.609 kilometers in the metric system.
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Find the weighted average of the numbers -3 and 5 with 3/5 lf the weight on the first number and 2/5 on the second number.
The weighted average of the numbers is 0.1.
What is the average?The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.
Given that, average of the numbers -3 and 5 with 3/5
The weight of first number and 2/5 of second number.
Here, -3(3/5)+5(2/5)/2
= (-1.8+2)/2
= 0.2/2
= 0.1
Therefore, the weighted average of the numbers is 0.1.
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What specific measure of a geometric figure is shown on the image?
A. A 110° angle
B. A 180 mm side length
C. A 70° angle
D. A 70 mm side length
Answer:
It is B: A180 mm side length
How many liters in 1 kg?
Watch help video
Use the distributive property to write an
Answer:
4(5s +9t - 6)
equivalent expression
Submit Answer
Answer:
20s + 36t - 24
Step-by-step explanation:
4(5s + 9t - 6)
20s + 36t - 24
We can go any further, so that is the answer.
A survey found that 80% of
travel agents posses valid
passports. There are 2,460
travel agents at the
convention. Predict how
many hold valid passports.
Answer:
Step-by-step explanation:
There would be 1,968 people who hold valid passports.
Can someone help me ASAP!! I will give brainliest if possible. Due today!! PLEASE help me on part a and part b
Part A: What type of figure is shown above
Part B: Find the surface area of the figure
Part C: Show your work to support your answer in part B
Part A) The figure shows the prism.
Part B) the surface area of the figure is,
⇒ S.A = 270 in²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
By figure,
The shape shows the rectangular prism.
We know that;
The surface area of prism is,
⇒ S.A = 2B + ph
Where, B is base area, p is perimeter and h is height of prism.
Here, The base area of the prism is,
B = 10 × 5 = 50 in²
The perimeter of the base of prism is,
p = 2 (5 + 10)
= 100 in
Height of prism = 1.7 in
Hence, We get;
The surface area of prism is,
⇒ S.A = 2B + ph
⇒ S.A = 2 × 50 + 100 × 1.7
⇒ S.A = 100 + 170
⇒ S.A = 270 in²
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What is the missing value in the ratio
videos. weeks
? 1
18. 2
27. 3
54. 6
Answer:
9
Step-by-step explanation:
54÷6= 9
27÷3= 9
18÷2= 9
hence the answer is 9.
its in the screenshot.
Answer:
1. 12 inches
2. 36 inches
Step-by-step explanation: Solve for side b using the Pythagorean therom since this is a right triangle.
[tex]a^2+b^2=c^2[/tex] - Where c is the largest side aka hypotenuse(if you are unsure, look at the side opposite to the right angle)
Substitute the given values to solve for the unknown side
[tex]9^2+b^2=15^2[/tex]
Expand
[tex]81+b^2=225[/tex]
Subtract 81 from both sides
[tex]b^2=144[/tex]
Which means
[tex]b=+-12[/tex]
but since its a triangle in the first quadrant and can only contain positive values, we disregard the negative solution. So b=12.
Lastly, for perimeter, just add all the side lengths together.
[tex]P=9+12+15[/tex]
Which means that the perimeter is 36 inches!
Acellus
40°
Find the value of x.
X
190°
x= [ ? ]
Enter
Resources
Help
The value of x for the given circle is 115°.
What is Geometry?Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and properties of objects in space. It includes the study of points, lines, planes, angles, curves, surfaces, and solids.
Using the Angles of Intersecting Chords Theorem,
When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.
So, angle x = (190° + 40°)/2 = 115°
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Given the following segment lengths find a length of the segment
The length of the line segment AB is 11/2 mm.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.
Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know a line segment parallel to one side of a triangle divides the other two sides in the same ratio.
Therefore, AC/AB = EC/ED.
22/AB = 44/11.
2/AB = 4/11.
4AB = 22.
AB = 11/2.
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Can somebody help with number 8 find the value of each variable using the properties of a Parallelogram
Answer:
Step-by-step explanation:
your going to have to show anwser choices
Does an ice cube with a lower volume melt faster or slower? This is for a math project
An ice cube with a lower volume will melt faster than an ice cube with a higher volume. This is because there is the less mass and surface area for the heat to transfer through, causing the ice cube to melt at a quicker rate.
For example, imagine two ice cubes, one with a volume of 2 cubic centimeters and another with a volume of 4 cubic centimeters. The ice cube with the lower volume (2 cubic centimeters) will melt faster than the ice cube with the higher volume (4 cubic centimeters) because there is less mass for the heat to transfer through. In conclusion, an ice cube with a lower volume will melt faster than an ice cube with a higher volume. This is due to the fact that there is the less mass and surface area for the heat to transfer through, causing the ice cube to melt at a quicker rate.
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Black diamond ski resort charges $25 for ski rental and 10$ an hour to ski bunny hill ski resort charges $50 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same
skiing for 5 hours will make the cost of skiing at both ski resorts equal.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given, Bunny Hill Ski Resort charges $50 for ski rentals and $5 per hour of skiing, while Black Diamond Ski Resort charges $25 for rentals and $10 per hour of skiing.
Let's define:
x as the number of hours of skiing
C₁ as the total cost of skiing at Black Diamond ski resort
C₂ as the total cost of skiing at Bunny Hill ski resort
At Black Diamond ski resort, the total cost of skiing is the sum of the cost of rental and the cost of skiing per hour:
C1 = 25 + 10x
At Bunny Hill ski resort, the total cost of skiing is the sum of the cost of rental and the cost of skiing per hour:
C₂ = 50 + 5x
We want to find at what point C₁ = C₂, so we set the two equations equal to each other:
25 + 10x = 50 + 5x
Simplifying the equation, we get:
5x = 25
Dividing both sides by 5, we get:
x = 5
Therefore, skiing for 5 hours will make the cost of skiing at both ski resorts equal.
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A quilter created the following shape to use in a block for a new quilt.
A six-sided figure with a large base of 13 inches. The side to the right of the base is 7 and one-half inches. The small side parallel to the base is 5.18 inches. There are two sides that form a point at a right angle. The smaller is 5 inches, and the larger is 6 inches.
What is the area of the shape for the quilt block?
sixty-three and three fourths in2
one hundred twelve and one half in2
one hundred twenty-seven and one half in2
225 in2
The area of the quilt block 112.5 square inches.
The correct option is B: one hundred twelve and one half in²
What is the area of the quilt block?The area of the quilt block = area of a rectangle + area of a triangle
Ares of rectangle = length * breadth
Area of rectangle = 7.5 inches * 13 inches
Area of rectangle = 97.5 square inches
Area of the triangle = base/2 * height
base = 5 inches
height = 6 inches
Area of triangle = 5/2 inches * 6 inches
Area of triangle = 15 square inches
The area of the quilt block = 15 square inches + 97.5 square inches
The area of the quilt block = 112.5 square inches
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What is the function graphed below?
y = | x - 1|
y = | x | - 1
y = | x + 1|
y = | x | + 1
The function represented by the graph is y = |x + 1|
How to determine the function of the graphThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The equation of the graph is an absolute value graph
An absolute value graph is represented as
y = |x|
The function is shifted left by 1 units
So, we have
y = |x + 1|
Hence, the function is y = |x + 1|
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What are the rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1
The rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1 can be found using the Rational Root Theorem.
The Rational Root Theorem states that if a polynomial has a rational root, it will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is -1 and the leading coefficient is 1. The factors of -1 are -1 and 1, and the factors of 1 are 1. Therefore, the possible rational roots of this polynomial are -1/1, 1/1, or -1 and 1.
We can test these possible roots by plugging them into the polynomial and seeing if the result is 0.
P(-1) = (-1)^3 + 3(-1)^2 + (-1) - 1 = -1 + 3 - 1 - 1 = 0
P(1) = (1)^3 + 3(1)^2 + (1) - 1 = 1 + 3 + 1 - 1 = 4
Therefore, the only rational root of this polynomial is -1.
So, the rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1 are -1.
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What’s this answer
Which equation represents a line that is per
The equation which is perpendicular to the equation of line passing through the points (-4, 7) (1, 3):
y = 5/4x + 8.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
To find the equation of a line that is perpendicular to another line, we need to know the slope of the original line.
The slope of the line passing through (-4,7) and (1,3) is:
m = (3 - 7) / (1 - (-4)) = -4/5
The slope of any line perpendicular to this line would be the negative reciprocal of -4/5, which is 5/4.
Therefore, the equation of a line that is perpendicular to the line passing through (-4,7) and (1,3) would be of the form:
y = 5/4 x + b
where b is the y-intercept.
Among the given options, the equation that matches this form is:
A. y = 5/4 x + 8
So the answer is (A) y = 5/4x + 8.
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Tony spent a total of 140 minutes studying for his algebra test this total was 5 more than 3 minutes the amount of minutes he spent studying for his biology test how many minutes did Tony spend studying for his biology test
Proportionately, if Tony spent a total of 140 minutes studying for his algebra test, and this total was 5 more than 3 minutes the amount of minutes he spent studying for his biology test, the time Tony spent studying for his biology test was 132 minutes.
What is proportion?Proportion refers to the equation of two or more ratios.
Ratios show the relative size of a value compared to another.
Proportions are fractional values like ratios.
The total minutes Tony spent studying for his algebra test = 140
5 more than 3minutes = 8 minutes
140 > 132 by 8 minutes (140 - 8)
The time spent studying biology = 132
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Please help quickly!!! The triangles are similar. AC=___ units
Answer:
Step-by-step explanation:
EB/BC=15/12=5/4
ED/AC=X+5/Y=5/4
5y=4x+20
y=0.8x+4
7 27. MODELING REAL LIFE Find the length of the slide.
(See Example 6.)
MTR
12 ft
53°
The length of the slide shown is 15 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let l represent the length of the slide, hence:
sin(53) = 12/l
l = 12/sin(53)
l = 15 feet
The length is 15 feet
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