A small college has 10 professors in the Mathematics Department. The department teaches pure math, applied math, and
statistics. Professors are apportioned using Hamilton's apportionment method, according to the number of majors in each
field. There are 4 pure math majors, 12 applied math majors, and 12 statistics majors.
If the department receives a grant to hire 1 more professor, will the Alabama paradox occur? Why or why not?
Answers
Answer:
Yes, because while the total number of professors increases, the number of pure math professors decreases.
Step-by-step explanation:
Using Hamilton's method:
pure math 4/28 = 0.142857
applied math 12/28 = 0.42857
statistics = 12/28 = 0.42857
10 × 0.142857 = 1.42857
10 × 0.42857 = 4.2857
10 × 0.42857 = 4.2857
numbers of professors:
pure math 1
applied math 4
statistics 4
total 9
Add 1 to pure math
Final original numbers of professors using Hamilton's method
pure math 2
applied math 4
statistics 4
total 10
Add 1 professor to department.
11 × 0.142857 = 1.5714
11 × 0.42857 = 4.71428
11 × 0.42857 = 4.71428
numbers of professors:
pure math 1
applied math 4
statistics 4
total 9
Add 1 to applied math and 1 to statistics
Final new numbers of professors using Hamilton's method
pure math 1
applied math 5
statistics 5
total 11
Despite the addition of 1 professor to the department, the field of pure mathematics went from 2 professors to 1 professor. This is an example of the Alabama paradox.
Answer: Yes, because while the total number of professors increases, the number of pure math professors decreases.
Related Questions
Teresa bought 6 CDs that were each the same price. Including sales tax, she paid a total of 84.60 . Each CD had a tax of 0.80 . What was the price of each CD before tax?
Answers
Answer:0.70
Step-by-step explanation:
Evaluate pqr - s2t, if p = -2, q = 5, r = -7, s = 0, and t = 4.
I need help fast!!
Answers
The answer of the given expression is 70.
What is the meaning of Evaluation?Evaluation refers to the process of assessing, examining, or appraising something to determine its worth, effectiveness, or quality. It involves the systematic and objective assessment of various aspects or criteria to form an informed judgment or opinion.
What is known by expression?An expression refers to a combination of numbers, symbols, and mathematical operations that represents a mathematical computation or relationship. It can be as simple as a single number or variable, or it can be more complex involving multiple terms, operations, and functions.
we have to find pqr-s2t:
if p=-2, q=5, r=-7, s=0, t=4
putting values in the expression we get
-2×5×(-7)-0×2×4= 70
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answer this math question
Answers
The table in this problem is completed as follows:
8 pints for 1 gallon.40 pints for 5 gallons.64 pints for 8 gallons.What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
The constant for the relationship is:
k = 16/2
k = 8.
Hence the equation is:
y = 8x.
In which:
x is the number of gallons.y is the number of pints.Then the numeric values are:
x = 1, y = 8 x 1 = 8.x = 5, y = 8 x 5 = 40.x = 8, y = 8 x 8 = 64.More can be learned about proportional relationships at https://brainly.com/question/7723640
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Find the value that makes each equation true.
A. 110%n=11 n=
B.
(328 x 128) x k = 328 x (82 x 128)
K=
Answers
Answer:
A. [tex]n=100[/tex]
B. [tex]k=0[/tex]
Step-by-step explanation:
A. The equation "110% n = 11" can be solved as follows:
110% n = 11
To solve for n, we need to get rid of the percentage sign (%). We can do this by dividing both sides of the equation by 110%, or 0.110 (since 110% is equivalent to 1.1 in decimal form).
(110% n) / 110% = 11 / 110%
n = 11 / 0.110
n = 100
So, the solution for n in the equation "110% n = 11" is n = 100.
B. The given equation is:
(328 x 128) x k = 328 x (82 x 128) x k
To solve for k, we can simplify the equation using the properties of multiplication.
Step 1: Perform the multiplications inside the parentheses:
41984 x k = 328 x 10576 x k
Step 2: Rearrange the equation by applying the associative property of multiplication:
41984 x k = 328 x (10576 x k)
Step 3: Divide both sides of the equation by 328:
(41984 x k) / 328 = 10576 x k
Step 4: Cancel out the common factor of k on the left-hand side:
(41984 / 328) x k = 10576 x k
Step 5: Simplify the left-hand side:
128 x k = 10576 x k
Step 6: Subtract 10576 x k from both sides of the equation to isolate k:
128 x k - 10576 x k = 0
Step 7: Factor out k on the left-hand side:
k x (128 - 10576) = 0
Step 8: Simplify further:
k x (-10448) = 0
Step 9: Divide both sides of the equation by (-10448):
k = 0
So, the solution for k in the equation "(328 x 128) x k = 328 x (82 x 128) x k" is k = 0.
PLEASE HELP I JUST HELP i dont know how to answer this please asap
Answers
Answer:
see picture
Step-by-step explanation:
found an answer by someone else on brainly
link to explanation: https://brainly.com/question/15188850
18 students each collected the same number of Cans for a project. If the students collected a total of 306 cans, how many cans did each student Collect?
Answers
Using division operation, the number of cans collected by each of the 18 students is 17.
What is division operation?Division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
Division operation involves the dividend (the number being divided), the divisor (the number dividing the dividend), and the product called the quotient.
The total number of students engaged in the can collection project = 18
The total number of cans collected = 306
The number of cans collected by each, if each collected the same quantity = 17 (306 ÷ 18)
Thus, based on a division operation, the number of cans each student collected is 17.
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Eli decides to estimate the volume of a coffee cup by modeling it as a right cylinder.
Eli measures its circumference as 18.3 cm and its volume as 221 cubic centimeters.
Find the height of the cup in centimeters. Round your answer to the nearest tenth if
necessary.
Answers
the height of the cup is approximately 6.2 centimeters. Rounded to the nearest tenth, this is 6.2 centimeters.
what is Rounded to the nearest tenth ?
Rounded to the nearest tenth means to round a number to the nearest value that has one decimal place. To do this, we look at the digit in the second decimal place (the tenths place) and round up or down depending on whether that digit is greater than or less than 5.
In the given question,
We know that the volume (V) of a right cylinder is given by the formula:
V = πr²h
where r is the radius of the cylinder and h is its height.
We also know that the circumference (C) of a right cylinder is related to its radius (r) by the formula:
C = 2πr
From the given information, we can use the circumference to find the radius of the cylinder:
C = 2πr
18.3 = 2πr
r = 18.3 / (2π) ≈ 2.91
Now we can use the radius and the volume to find the height of the cylinder:
V = πr²h
221 = π(2.91)²h
h = 221 / (π(2.91)²) ≈ 6.2
Therefore, the height of the cup is approximately 6.2 centimeters. Rounded to the nearest tenth, this is 6.2 centimeters.
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34. The dimensions of Dawn's porch are shown.
Dawn's Porch
6 feet
A
B
6 feet
A. 32
2 feet
11 feet
What is the area, in square feet, of Dawn's porch?
B. 42
2 feet
C. 46
D. 50
Answers
Answer:
[tex]the \: answer \: for \: the \: question \: is \: 50[/tex]
Need help will give brainliest and 5 stars!
For this graph, for each vertical asymptote, write down the two limits that describe the graph of the function near the asymptote.
Answers
The limits on the vertical asymptotes of the function are given as follows:
[tex]\lim_{x \rightarrow -6^{-}} f(x) = \infty[/tex][tex]\lim_{x \rightarrow -6^{+}} f(x) = -\infty[/tex][tex]\lim_{x \rightarrow -2^{-}} f(x) = \infty[/tex][tex]\lim_{x \rightarrow -2^{+}} f(x) = -\infty[/tex][tex]\lim_{x \rightarrow 6^{-}} f(x) = -\infty[/tex][tex]\lim_{x \rightarrow 6^{+}} f(x) = \infty[/tex]What are the vertical asymptotes of a function?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
On a graph, at the vertical asymptotes, the graph just approaches the point, it does not cross the point.
Hence the vertical asymptotes are given as follows:
x = -6, x = -2 and x = 2.
We must observe the limits to the left(denoted by the - sign) and to the right (denoted by the + sign) of each asymptote.
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The probability of winning a profit of twice your wager is 1/6, the probability of winning a profit equal to your wager is 1/3, and all other probabilities of winning are zero. What is your expected value for this game? Assume the wager is $1.
Answers
The expected value for the game is 2/3.
What is expected value?The average value we would anticipate to find if we repeated an experiment several times is the anticipated value of a random variable. It is calculated by averaging the outcomes of multiplying each potential result of the random variable by the associated probability. In other words, it's the weighted average of all potential possibilities, with the weights being the likelihoods that each outcome would actually happen. In several disciplines, including finance, economics, and engineering, predictions and judgements are made using the expected value, a fundamental idea in probability theory.
Let us suppose the profit = X.
Thus,
Probability of winning twice our wager = 1/6 thus, the expected value is:
(2)(1/6) = 1/3
No, for profit equal to wager we have:
(1)(1/3) = 1/3
The total expected value is:
E(X) = (1/3) + (1/3) + 0 = 2/3
Hence, the expected value for the game is 2/3.
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For a confidence level of 99% with a sample size of 19, find the critical t value.
Answers
Using a t-distribution table with 18 degrees of freedom (19 - 1 = 18), we can find the critical t value for a two-tailed test at a 99% confidence level to be approximately 2.878.
Therefore, the critical t value for a confidence level of 99% with a sample size of 19 is 2.878 (rounded to three decimal places).
I hope this is right
PLEASE I NEED HELP ON THIS QUESTION
Answers
Answer:
A: -1 B: 2 C: -4 1/2
Step-by-step explanation:
Find the value of x. Assume that segments that appear to be tangent are tangent.
x =
(50 POINTs will give BRAINIEST FOR EFFORT)
Answers
Answer:
x = 28.27 units-------------------------
Tangent line is perpendicular to radius at the point of tangency.
It means the given is a right triangle.
Use Pythagorean theorem to find the missing side length.
One of legs is x, second leg is 15 units and the hypotenuse is the sum of 17 units and radius.
x² + 15² = (17 + 15)²x² + 225 = 1024x² = 1024 - 225x² = 799x = √799x = 28.27 units (rounded to the nearest hundredths)What integer is the square root of 115 closest to?
Answers
Answer:
10
Step-by-step explanation:
Some states now allow online gambling. As a marketing manager for a casino, you need to determine the percentage of adults in those states who gamble online. How many adults must you survey in order to be 99% confident that your estimate is in error by no more than three percentage points? Complete parts (a) and (b) below. a. Assume that nothing is known about the percentage of adults who gamble online. n= (Round up to the nearest integer.)
Answers
The sample size for part (a) is 2401, and the sample size for part (b) is 1417 if the margin of error is no more than two percentage points and use a confidence level of 95%
We have,
It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.
The formula for finding the MOE:
MOE =Z_{score} * s/√n
Where Z_{score} is the z score at the confidence interval
s is the standard deviation
n is the number of samples.
We have:
MOE = 2% = 0.02 and
α = 1-0.95 = 0.05
Let's assume the value of p = 0.5, and q = 0.5
From the table:
Z_(0.05/2)
= Z_(0.025)
= 1.96
n = 2401
For part (b):
p = 18% = 0.18, and q = 0.82
so, we get,
n = 1417.5 = 1417
Thus, the sample size for part (a) is 2401, and the sample size for part (b) is 1417 if the margin of error is no more than two percentage points and use a confidence level of 95%
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NEED HELP PLEASE NOW
Answers
Answer:
im pretty sure its the first one that you chose :)
Step-by-step explanation:
I just want the answers, I’ve been on the same lesson since Thursday and no teacher from my school will help ♀️
Answers
The standard form of the equation, based on the foci and co - vertices would x ² / 250 + y ² / 25 = 1 .
How to write the standard form ?The foci and co-vertices must be known to compose the equation of an ellipse, which requires determining a, b, and c values. The major axis, minor axis and distance between the center and foci are related to these variables.
Their connection can be symbolized as follows: a for major axis, b for minor axis, and c for the length of the distance between the center and foci:
a ² = b ² + c ²
a ² = 5 ² + 15 ²
a ² = 25 + 225
a ² = 250
a = √ 250
The standard equation would be:
x ² / a ² + y ² / b ² = 1
x ² / 250 + y ² / 25 = 1
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A new apartment complex with 90 one bedroom apartment units and 100 two bedrooms apartment units was built near a lake. Rental prices that will provide full occupancy are estimated as $1200 for one bedroom unit and $1800 for two bedrooms unit. A market survey suggests that for every $20 increase in price of one bedroom unit one less customer will sign a lease and for every $60 increase in price of two bedrooms unit two less customers will sign a lease. What rental price should the manager charge to maximize revenue?
Rental Price for One bedroom ____
Rental Price for Two bedroom ____
Answers
The manager should charge $1200 for one bedroom unit and $1800 for two bedroom unit to maximize revenue.
To maximize revenue, the manager should charge the prices that will provide full occupancy. According to the market survey, for every $20 increase in price of one bedroom unit, one less customer will sign a lease.
Therefore, the manager should charge $1200 for one bedroom unit to maximize occupancy. Similarly, for every $60 increase in price of two bedrooms unit, two less customers will sign a lease.
Therefore, the manager should charge $1800 for two bedroom unit to maximize occupancy.
Therefore, the optimal rental price to maximize revenue is $1200 for one bedroom unit and $1800 for two bedroom unit.
Therefore, the manager should charge $1200 for one bedroom unit and $1800 for two bedroom unit to maximize revenue.
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Hudson measure the volume of a sink basin by modeling it as a hemisphere. Hudson measures its circumference to be 91 3/4 inches. Find the sink's volume in cubic inches.
Round your answer to the nearest tenth if necessary.
Answers
Rounding to the nearest tenth, the sink's volume is approximately [tex]6328.2[/tex] cubic inches.
What is the Hudson measures?The circumference of a hemisphere is represented by the formula:
[tex]C = 2 \pi r[/tex]
here C is the circumference and r is the radius of the hemisphere.
it is given that the circumference C as [tex]91 3/4[/tex] inches. now convert into a decimal
[tex]91 3/4 inches = 91.75 inches[/tex]
we are having
[tex]91.75[/tex] inches [tex]= 2πr[/tex]
Solving for r, we get:
[tex]r = 91.75 / (2\pi) \approx 14.599[/tex] inches (rounded to three decimal places)
The volume of a hemisphere is represented by formula
[tex]V = (2/3)\pir^3[/tex]
Substituting our value of r, we get:
[tex]V = (2/3)\pi(14.599)^3 \approx 6328.2[/tex] cubic inches
Therefore, rounding to the nearest tenth, the sink's volume is approximately [tex]6328.2[/tex] cubic inches.
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A full waterbed mattress is 6 ft by 5 ft by 2 ft. The mattress is to be filled with water that weighs 62.4 lb/ft^3. Find the weight of the water in the mattress to the nearest pound.
The waterbed mattress contains approximately ___ lb of water
Answers
The waterbed mattress contains approximately 3,744 lb of water.
How to calculate the weight of the water in the mattress?To calculate the weight of the water in the mattress, the volume of the mattress is first calculated using the given formula below:
The measurement of the waterbed mattress = 6ft by 5 ft by 2 ft
The volume of the waterbed = Length× width × height
That is = 6×5×2 = 60ft³
If 62.4 lb = 1 ft³
X lb = 60 ft³
Make X the subject of formula;
X = 60× 62.4 = 3,744lb
Therefore, the weight of water that the mattress will contain would be= 3,744lb
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Which of the following rational functions is graphed below?
Answers
Answer:
The vertical asymptote is at x = -3, and the horizontal asymptote is at y = 1, so the correct answer is C.
Jenna threw a disc 18 yards to Karl, who threw it 11 yards in the same direction to Alice.
Start at 0 on the number line and move _____ to the right to represent Jenna throwing the disc to Karl.
Then move ______ to the right to represent Karl throwing the disc to Alice the result shows that.
Answers
In total the disc thrown 29 yards.
Start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl.
Then move 11 yards to the right to represent Karl throwing the disc to Alice.
The result shows that Jenna threw the disc 29 yards (18 + 11) in the same direction to Alice.
Therefore, in total the disc thrown 29 yards.
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NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #3
Answers
Answer:
The graph will be translated down 2 units.
The new horizontal asymptote is y=2 because the graph now crosses over the y axis at 2. This is at the point (0,2).
Given f(x)=3x^2−5 and g(x)=6x+1, what is the value of (g∘f)(2)?
Enter your answer, in simplest form, in the box.
Answers
If f(x)=3x²−5 and g(x)=6x+1, then the value of (g∘f)(2) = 43.
What is function?
A connection or statement involving one or more variables is called a function. A set of inputs and outputs are present.
First, we need to find f(2):
f(2) = 3(2)² - 5
f(2) = 3(4) - 5
f(2) = 7
Now we need to apply g to f(2):
g(f(2)) = g(7) = 6(7) + 1 = 43
Therefore, (g∘f)(2) = 43.
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write 0.08 as a percentage.
Answers
Answer:
8%
Step-by-step explanation:
help me solve this
Answers
Answer: ∠BEA
Step-by-step explanation:
Congruent: Same Angle Measure
Starting: ∠BHK
Congruent Angle: ∠BEA
draw a net for making a rectangular prism 5cm by 3cm by 1cm
Answers
Here is a net for making a rectangular prism with dimensions of 5 cm by 3 cm by 1 cm:
________
/ / |
/ / |
/_______ / |
| | |
| | |
| | |
| | /
| | /
|________|
The above net consists of six rectangles, where the first rectangle represents the base of the prism with dimensions of 5 cm by 3 cm, and the remaining five rectangles represent the sides of the prism.
What is a rectangular prism?A rectangular prism, also known as a rectangular cuboid, is a three-dimensional geometric shape that has six rectangular faces, where each face meets at right angles with its adjacent faces.
It is common in everyday objects such as boxes, books, and bricks, and they are used in various applications in mathematics, physics, engineering, etc.
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The cost in dollars to produce x shovels in a factory is given by the function C(x)=33x+430. The number of shovels that can be produced in h hours is given by the function N(h)=30h
7. Find the rule for C(N(h)).
8. Find the cost when h=12 hours
Answers
Okay, to find the maximum number of shovels that can be produced with $10,000, we need to do the following:
1) Set the cost function C(N(h)) = 10,000. So: 990h + 430 = 10,000
2) Subtract 430 from both sides: 990h = 9,570
3) Divide both sides by 990: h = 9.75 (round to 10 hours)
4) Substitute 10 hours into the function for number of shovels:
N(10) = 30(10) = 300 shovels
Therefore, the maximum number of shovels that can be produced with $10,000 is 300 shovels.
Let me know if you have any other questions!
QUICKLY HELP PLEASE ITS VERRY MUCH SO APPREICATED
Answers
The mean absolute deviation (MAD) of the data set include the following: A. 11.
How to calculate the mean absolute deviation?In Mathematics, MAD is an abbreviation for mean absolute deviation and the mean absolute deviation (MAD) of a data set can be calculated by using this formula;
MAD = 1/n ∑|x - μ|
Where:
n represents the number of data (observed values)μ represents the mean of the data set.x represents the individual data (values).By substituting the given parameters into the MAD formula, we have the following;
MAD = 1/10 [(325 - 290) + (310 -290) +(289-290)+(288-290)+(285-290)+(285-290)+(285-290) + (280-290) + (280-290) + (273-290)]
MAD = 1/10(35 + 20+1+2+5+5 +5 + 10 + 10 + 17).
MAD = 1/10(110)
MAD = 11
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4. You have been offered $3,000 in 4 years for providing $2,000 today into a business venture with a friend. If interest rates are 10%, is this a good investment for you?
Answers
Step-by-step explanation:
To determine if this is a good investment, we can use present value calculations to see what the $3,000 payment in 4 years is worth today:
Present value of $3,000 in 4 years at 10% interest rate = $3,000 / (1 + 0.10)^4 = $2,102.50.
If we invest $2,000 today and get a payment of $2,102.50 in 4 years, our net gain would be:
Net gain = $2,102.50 - $2,000 = $102.50
Therefore, investing $2,000 today with an interest rate of 10% and receiving $3,000 in 4 years would yield a net gain of $102.50.
While any gain is better than no gain, a return of $102.50 on an investment of $2,000 over a period of 4 years may not be considered a great investment. It's up to the individual to decide whether they feel that the potential gain is worth the initial investment and risk involved.