26. A mathematics department has ten faculty members but only nine offices, so one office must be shared by two individuals. In how many different ways can the offices be assigned?

Answers

Answer 1

The different ways can the offices be assigned will be 36.

What is the combination?

The arrangement of the different things or numbers in a number of ways is called the combination.

It is given that:-

A mathematics department has ten faculty members only nine offices, so one office must be shared by two individuals

The number of the different ways are:-

[tex]^9C_2=\dfrac{9!}{(9-2)! \times 2!}[/tex]

[tex]^9C_2=\dfrac{9!}{(7)! \times 2!}[/tex]

[tex]^9C_2=\dfrac{9\times 8 \times 7!}{(7)! \times 2!}[/tex]

[tex]^9C_2=\dfrac{9 \times 8} 2}\ =36[/tex]

Therefore the different ways can the offices be assigned will be 36.

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Related Questions

Point J (3, -7) is dilated from the origin by a scale factor of 2. What are the coordinates of J'?

Please please help I need to get my work done ASAP!!

Answers

To figure out the figure by a scale factor of 2, you multiply both the x and y value by 2.

3 x 2 = 6
-7 x 2 = -14

So, the coordinates of J are (6,-14)
Hope this helped! :)

According to the frequency table, what is the mean of the score?
Round your answer to the nearest tenth.

A) 6.0
B) 6.1
C) 6.2
D) 6.3

Answers

A) 6.0

I hope this is right

The mean of the scores is approximately 6.2. The correct answer is (C).

What is arithmetic mean?

The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.

To calculate the mean of the scores based on the given frequency table, we need to multiply each score by its corresponding frequency, sum up the results, and then divide by the total frequency.

Let's perform the calculations:

(1 x 1) + (2 x 1) + (3 x 3) + (4 x 1) + (5 x 4) + (6 x 5) + (7 x 6) + (8 x 5) + (9 x 3) + (10 x 1) = 167

1 + 2 + 9 + 4 + 20 + 30 + 42 + 40 + 27 + 10 = 185

The total frequency is 1 + 1 + 3 + 1 + 4 + 5 + 6 + 5 + 3 + 1 = 30

Now, we divide the sum (185) by the total frequency (30) to find the mean:

185 / 30 = 6.1667

Rounding this value to the nearest tenth, the mean of the scores is approximately 6.2.

Therefore, the answer is C) 6.2.

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Problem-solving: Comparing Strategies

Answers

Didn’t do 1. 2 is 12. 3 is 112.5. And 4 is 2.

calculate the volume of the following figure

Answers

Answer:

24 units³

Step-by-step explanation:

Formula:

Volume (V) = length (l) × width (w) × height (h)

V=3×4×2=24 units³

Answer:

the answer should be 24 units^3 because the formula for finding volume is V= lwh so we need to multiply 2 times 3 and 4 and when we do that we get an answer of 24 so a is the correct answer and have a great day.

Step-by-step explanation:

Pls help me I dont understand giving brainliest if correct

Answers

Answer:6

Step-by-step explanation:

Heron's Formula is: area = sqrt(s(s-a)(s-b)(s-c)) and s is the semiperimeter

Putting the side lengths in would be:

s = (a + b + c)/2

area = sqrt(6(6-5)(6-4)(6-3)) = sqrt(6*1*2*3) = 3*sqrt(2)

So the answer is 3*sqrt(2) which is equal to 6

Answer:

6 units²

Step-by-step explanation:

You want the area of the 3-4-5 right triangle.

Area

The area formula for a triangle is ...

A = 1/2bh

where b represents the "base" and h represents the "height". The height is always measured to the vertex opposite the base, in direction perpendicular to the base.

Right triangle

The perpendicular legs of a right triangle have the necessary relationship for either one to be considered the "base", and the other to be the "height."

Here, that means we can call the side of length 3 units the "base" and the side of length 4 units the "height", or vice versa.

This means the area is ...

A = 1/2(3 units)(4 units) = 6 units²

Additional comment

Heron's formula for the area of a triangle based on all three side lengths can be used for this, but is more work than necessary.

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If the rectangle below is enlarged using a scale factor of 1.5, what will be the area of the new rectangle?

Answers

Answer:

31.5 square inches

Step-by-step explanation:

7 x 1.5 = 10.5

2 x 1.5 = 3

10.5 x 3 = 31.5

Integral Calculus Problem:
[tex]\int\limits^1_4 {\frac{cosx}{1+e^1/x} } \, dx[/tex] = _

- Do not spam
- Do not copy and paste
- Do not add any unnecessary information
- Any of these will result in a report
- Please help, thank you

Answers

Answer:

[tex]\displaystyle \int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx \approx \boxed{0.862854}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Methods: U-Substitution and U-Solve

Special Integrals:

Sine Integral:
[tex]\displaystyle \int {\frac{\sin x}{x}} \, dx = \text{Si} (u) + C[/tex]Cosine Integral:
[tex]\displaystyle \int {\frac{\cos x}{x}} \, dx = \text{Ci} (u) + C[/tex]

Step-by-step explanation:

*Note:
The problem is too big to fit all work. I will assume that you know how to do basic calculus.

Step 1: Define

Identify given.

[tex]\displaystyle \int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx[/tex]

Step 2: Integrate Pt. 1

[Integrand] Rewrite:
[tex]\displaystyle \begin{aligned}\int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx & = \int\limits^1_4 {\frac{x \cos x}{x + e} \, dx \leftarrow \\\end{aligned}[/tex]

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Set u:
[tex]\displaystyle u = x + e[/tex][u] Differentiate [Derivative Rules and Properties]:
[tex]\displaystyle du = dx[/tex]

Step 4: Integrate Pt. 3

[Integral] Apply Integration Method [U-Substitution]:
[tex]\displaystyle \begin{aligned}\int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx & = \int\limits^1_4 {\frac{x \cos x}{x + e} \, dx \\& = \int\limits^{x = 1}_{x = 4} {\frac{(u - e) \cos (u - e)}{u} \, du \leftarrow \\\end{aligned}[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]:
[tex]\displaystyle \begin{aligned}\int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx & = \int\limits^1_4 {\frac{x \cos x}{x + e} \, dx \\& = \int\limits^{x = 1}_{x = 4} {\frac{(u - e) \cos (u - e)}{u} \, du \\ & = \int\limits^{x = 1}_{x = 4} {\cos ( u - e)} \, du - \int\limits^{x = 1}_{x = 4} {\frac{e \cos (u - e)}{u}} \, du \leftarrow \\\end{aligned}[/tex][2nd Integral] Rewrite [Integration Property - Multiplied Constant]:
[tex]\displaystyle \begin{aligned}\int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx & = \int\limits^{x = 1}_{x = 4} {\cos ( u - e)} \, du - e \int\limits^{x = 1}_{x = 4} {\frac{\cos (u - e)}{u}} \, du \leftarrow \\\end{aligned}[/tex]

Step 5: Integrate Pt. 4

Identify variables for u-substitution for the 1st integral.

Use another variable besides u to avoid confusion with earlier substitutions.

Set v:
[tex]\displaystyle v = u - e[/tex][v] Differentiate:
[tex]\displaystyle dv = du[/tex]

Step 6: Integrate Pt. 5

Solve the 1st integral using basic integration techniques listed under "Calculus":
[tex]\displaystyle \begin{aligned}\int\limits^{x = 1}_{x = 4} {\cos (u - e)} \, du & = \int\limits^{x = 1}_{x = 4} {\cos v} \, dv \\& = \sin v \bigg| \limits^{x = 1}_{x = 4} \\& = \sin (u - e) \bigg| \limits^{x = 1}_{x = 4} \\& = \sin (x) \bigg| \limits^{x = 1}_{x = 4} \\& = \sin 1 - \sin 4\end{aligned}[/tex]

Step 7: Integrate Pt. 6

To solve the 2nd integral, we use the same methods as "Step 6":

[tex]\displaystyle\begin{aligned}\int\limits^{x = 1}_{x = 4} {\frac{\cos (u - e)}{u}} \, du & = \int\limits^{x = 1}_{x = 4} {\frac{\sin e \sin u + \cos e \cos u}{u}} \, du \\& = \sin e \int\limits^{x = 1}_{x = 4} {\frac{\sin u}{u}} \, du + \cos e \int\limits^{x = 1}_{x = 4} {\frac{\cos u}{u}} \, du \\& = \sin (e) \text{Si} (u) \bigg| \limits^{x = 1}_{x = 4} + \cos (e) \text{Ci} (u) \bigg| \limits^{x = 1}_{x = 4} \\\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}\int\limits^{x = 1}_{x = 4} {\frac{\cos (u - e)}{u}} \, du & = \sin (e) \text{Si} (x + e) \bigg| \limits^{x = 1}_{x = 4} + \cos (e) \text{Ci} (x + e) \bigg| \limits^{x = 1}_{x = 4} \\& = \bigg[ \sin (e) \text{Si} (1 + e) - \sin (e) \text{Si} (4 + e) \bigg] + \bigg[ \cos (e) \text{Ci} (1 + e) - \cos (e) \text{Ci} (4 + e) \bigg] \\\end{aligned}[/tex]

Step 8: Integrate Pt. 7

Combine our 2 integral values to obtain a final answer:

[tex]\displaystyle \int\limits^1_4 {\frac{\cos x}{1 + \frac{e}{x}}} \, dx & = \int\limits^{x = 1}_{x = 4} {\cos ( u - e)} \, du - e \int\limits^{x = 1}_{x = 4} {\frac{\cos (u - e)}{u}} \, du \\\begin{aligned}& = \sin 1 - \sin 4 - e \bigg[ \sin (e) \text{Si} (1 + e) - \sin (e) \text{Si} (4 + e) + \cos (e) \text{Ci} (1 + e) - \cos (e) \text{Ci} (4 + e) \bigg] \\& \approx \boxed{0862854} \\\end{aligned}[/tex]

∴ we have evaluated the given special definite integral.

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Topic: Calculus

answer: .862854 i believe

Please help me with this I would give you 50 points.

Answers

Answer:

#1, x=57
#2, r=223
#3, h=17
#4, g=48

Step-by-step explanation:

A researcher weighed pumpkins grown across a certain region. The data are rounded to the nearest pound and displayed in this histogram.

What does the second bin represent?

Select from the drop-down menu to correctly complete the statement.

Sixteen pumpkins weigh

more than 2.4 pounds but no more than 4.8 pounds
more than 2.4 pounds but no less than 4.8 pounds
at least 2.4 pounds but no more than 4.8 pounds
at least 2.4 pounds but less than 4.8 pounds

Answers

at least 2.4 pounds but no more than 4.8 pounds

At least 2.4 no more then 4.8 pounds hope this helps

Sort the cards with there identical matches.

Answers

Answer:

A, C, E, L and G, H, B, D

Step-by-step explanation:

5. Write an expression.

a. 2 less than s
c. 5 times the quantity y - 2
b. the quantity 7 + x, squared
d. the quotient of 4 and x²

Answers

a. s - 2

b. (7+x)^2

c. 5y - 2

d. 4/x^2

a. s-2
c. 5(y-2)
b. (7+x)^2
d. 4/x^2

CAN SOMEONE HELP ME ON THIS HOMEWORK

Answers

Answer: The answer to 2, 6, 12, 16 is 9 and the answer to 5, 6, 12, 13 is 9

Step-by-step explanation: The mean of a set of numbers is another term for average. You add all of the numbers up like for example in the second set of numbers, 16+12+6+2 is equal to 36 and you then divide that sum by the amount of numbers you added which in this case is 4 so you get 36/4 which is equal to 9.

Mean of 2, 6, 12, 16 = (2 + 6 + 12 + 16) ÷ 4 = 36 ÷ 4 = 9

Mean of 5, 6, 12, 13 = (5 + 6 + 12 + 13) ÷ 4 = 36 ÷ 4 = 9

One thing we know for certain, much like the outrageous monsters we conjure in our worst nightmares, the deep ocean is an equally imaginative source of shock, awe, and outright fright.

What is the purpose of this sentence in the paragraph?

a

To connect two supporting ideas

b

To compare two unrelated creatures

c

To introduce a new topic and point

d

To summarize the main point of the article

Answers

Answer:

I think the answer is A but it is hard to know because I don't know what the passage is about.

( Brainliest, 50 points. SERIOUS ANSWERS ONLY ) Help me with this question!

Answers

It’s simple. See how many units there are for the shapes and scale it up or down. ex. if you had 5, 10, 15: then you could double and draw a shape with 10, 20, 30.

Which of the following numbers is prime?

12
15
7
6

Answers

Answer:

Step-by-step explanation:

A prime number is a number which has no factors other than itself and 1. In other words, this number can only be divided by itself and 1 and result in a whole number answer. All of the other choices can be divided by some other numbers and result in a whole number answer.

Factors of 12:

1, 2, 3, 4, 6, 12

Facotrs of 15:

1, 3, 5, 15

Facotrs of 7:

1, 7

Factors of 6:

1, 2, 3, 6

Answer:

The number (7) is a prime number.

What are prime and composite numbers?Prime numbers are such numbers that should have two factors, one and the number itself. An example of a prime number could be "2".

Factors of 2: 1 and 2 (Verifies the above definition)

Composite numbers are such numbers that have more than two factors. An example of a composite number could be 4.

Factors of 4: 1, 2 and 4 (Verifies the above definition)

Option A

Given number: 12

Let's list the factors of this number.

⇒ Factors of 12: 1, 2, 3, 4, 6, 12

The number provided is not a prime number because the number has more than two factors. Therefore, Option A is not correct.

Option B

Given number: 15

Let's list the factors of this number.

⇒ Factors of 15: 1, 3, 5, 15

The number provided is not a prime number because the number has more than two factors. Therefore, Option B is not correct.

Option C

Given number: 7

Let's list the factors of this number.

⇒ Factors of 7: 1 and 7

The number provided is a prime number because the number has exactly two factors. Therefore, Option C is correct.

Option D

Given number: 6

Let's list the factors of this number.

⇒ Factors of 6: 1, 2, 3, and 6

The number provided is not a prime number because the number has more than two factors. Therefore, Option D is not correct.

[tex]\overline{================================================}[/tex]

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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the table to answer the following questions.
Time (hours) Distance (miles)
2 90
3 135
5 225
6 270
1. Find the constant of proportionality.

2. Use the constant of proportionality to write a unit rate for the data in the table.

3. Write an equation to represent the relationship between time, t, and distance, d.

Can you please do step by step showing us how you got the answers?

Answers

Answer:

1. Time (hours): 1 Distance (miles): 45

2. 1;45

2;90

3;135

4;180

5;225

6;270

3. (c= constant of proportionality)

c= [tex]\frac{distance}{time}[/tex]

c=[tex]\frac{90 miles}{2 hours}[/tex]

c= 45 miles per hour

Step-by-step explanation:

So you may see for each hour they are going 45 miles by dividing 2 by 2 and 90 by 2, so there constant of proportionality is 45 miles per hour. (answer 3 is the step by step)

The price of one share of Acme Company declined $2 per day for 4 days in a row. How much did the price of one share change in total after the 4 days?**Just write the negative or positive number (Example. -1 or 1)

Answers

its either -8 or 8 im not sure which good luck tho!

The height of a cylindrical can is 4 7/16 inches and the radius is 3 inches. Which measurement is closest to the total surface area of the can in square inches?

A)83.64 in²
B)55.96 in²
C)41.82 in²
D)140.19 in²

Answers

Answer:

D)140.19 in²

Step-by-step explanation:

Answer this RIGHHT and you'll get Brainliest

Answers

Answer:

Circle is closed and Graph shaded to the left

Step-by-step explanation:

look at an model of a number line.

Hope this helps :)))))

Graph shaded to the left of the circle

A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 5 millimeters long, and the height of the equilateral triangle is 4.3 millimeters. The pyramid slant height is 7 millimeters. What is its surface area?

_____ Square Millimeters

Help!

Answers

Answer: I think it should be about 150.5 square mm

Step-by-step explanation:

I just multiplied all the dimensions you wrote...

By the way if its wrong please tell me so I can learn.

Thanks!

HEYAAAAAAAAAAAAA I NEED HELP

Answers

Data Set : {8, 2, 5, 0, 1, 9, 2, 5, 2}

Arrange in ascending order : {0, 1, 2, 2, 2, 5, 5, 8, 9}

Range = Last Term - First Term = 9 - 0 = 9 is the range

Mean = sum of terms/number of terms = 34/9 = 3.777... = 3.78 is mean

Mode = the most appearing integer in the set = 2 is the mode

Median = The integer at the middle of the set = 2 is the median

======================

Range = 9Mean = 3.78Mode = 2Median = 2

Range: Highest minus the lowest value. 8-0 = 8 therefore the range is 8.
Mean: Add up all the numbers and divide by the amount of numbers. 8+2+0+1+9+2+5+2= 29 then divide by 9 = 3.22 therefore the mean is 3.22.
Mode: Number that appears the most frequent. There can be multiple. In this case the mode is 2.
Median: The middle number. First order from lowest to highest: 0,1,2,2,2,5,8,9. In this case the median is 2 and 2. So we simply add 2+2 which equals 4 and divide it by 2. Therefore the median is 2. Hope this helped!!

I need help its due today lol

Answers

Answer:

7= 120 8= 175

Step-by-step explanation:

all you have to do is times the numbers

Answer: the answer to number 7 is 17 answer to number 8 is 24

Step-by-step explanation:

Use the pythagorean theorem

a^2 + b^2 = c^2

i need some help with this!! i want my grade to go up

Answers

The answer is 8
the square root of 61 is close to the square root of 64, which is 8
24 + 8 = 32
32/4 = 8
BRAINLIEST? thank you!! :DD

the correct answer is 8.
24+8=32
32/4=8
the square root of 64 is 8

A. Simplify: -12/2 =
2. -8/ -2 =
3. ( -3)(2)(-4) =
4. (4)(-3)(-6)(2)=
5. (1/2)(-6)(1/4)(-8) =
B. On your Own
a. Make 10 multiplication of integers with 3 terms each
b. Make 20 divisions of integers.
C. Use a calculator

Answers

#1- -6
#2- -4
#3- 24
#4- 144
#5- 6
Don’t know the rest sorry

-6
-4
24
144
6

I only have time for those ): I hope this helps you pass!

Find the slope of the following graph.
A.1/2
B.2
C.-2
D.-1/2

Answers

answer is c have a a great day

37. Three married couples have purchased tickets for a play. Spouses are to be seated next to each other, and the six seats are in a row. In how many ways can the six people be seated?

Answers

1st seat 6 possible for each 6 only 1 possible(spouse) for seat 2

3rd seat 4 possible for each 4 only 1 possible(spouse) for seat 4

5th seat 2 possible for each 2 only 1 possible(spouse) for seat 6

6 x 4 x 2 = 48

OR 3 couples possible arrangements 3 x 2 x1 = 6

each couple 2 possible 2 x 2 x 2 = 8

therefore 6 x 8 = 48

35. Five cards are drawn from a deck. Find the probability of the specified event.
Obtaining at least one ace

Answers

Answer:

0.3412

Step-by-step explanation:

Please look at the photo for an explanation.

Brainliest! Help please, thank you!!!

Answers

Answer: 24

Step-by-step explanation:

12x2= 24

8x3=24

Answer:

8 × 3 = 2412 × 2 = 24

Notice a pattern, the products are both 24. This means that 8 and 12 share an LCD of 24.

I need help with this question! (20 POINTS)

Answers

Answer:

A (1,5) (1,8) (4,8) (4,5) = Square

B (2,5) (2,8) (4,8) (4,5) = Rectangle

C (2,3) (4,6) (8,6) (10,3) = Trapezoid

D (2,1) (2,5) (6,5) (6,1) = Square

Step-by-step explanation:

Just enter the coordinates into Desmos graphing calculator.

Using a Graphing Utility to Find Polar CoordiNtes CoordiNtes In Exercises 61-70, use a graphing utility to find one set of polar coordiNtes of the point given in rectangular coordiNtes.
66. (5,-\sqrt{2})

Answers

Awnser is (r,0)=(2,8,0.49)

(5/2, 4/3)

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