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?

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.

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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Answer:

-------------------------

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.

Answer:

[tex]the \: answer \: for \: the \: question \: is \: 50[/tex]

The limits on the vertical asymptotes of the function are given as follows:

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 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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The waterbed mattress contains approximately 3,744 lb of water.

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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Answer:

The vertical asymptote is at x = -3, and the horizontal asymptote is at y = 1, so the correct answer is C.

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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Answer:

im pretty sure its the first one that you chose :)

Step-by-step explanation:

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.

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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Answer:

see picture

Step-by-step explanation:

found an answer by someone else on brainly

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The standard form of the equation, based on the foci and co - vertices would x ² / 250 + y ² / 25 = 1 .

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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Rounding to the nearest tenth, the sink's volume is approximately  [tex]6328.2[/tex] cubic inches.

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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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.

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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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Answer: ∠BEA

Step-by-step explanation:

Congruent: Same Angle Measure

Starting: ∠BHK

Congruent Angle: ∠BEA

Answer:

8%

Step-by-step explanation:

The mean absolute deviation (MAD) of the data set include the following: A. 11.

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:

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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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).

The answer of the given expression is 70.

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.

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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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.

The expected value for the game is 2/3.

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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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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Answer:

A: -1 B: 2 C: -4 1/2

Step-by-step explanation:

Using division operation, the number of cans collected by each of the 18 students is 17.

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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The table in this problem is completed as follows:

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:

Then the numeric values are:

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Answer:

10

Step-by-step explanation:

Answer:0.70

Step-by-step explanation: