Statements with nested quantifiers: English to logic, part 4. About A student club holds an election for officers. Before the voting, members can nominate each other. It is also possible for a member to nominate himself or herself. Some of the members are new members. Some of the members are currently officers. The domain is the set of members of the club. One of the members of the club is named Sam. Define the following predicates. N(x, y): person x nominated person y for a position. W(x): person x is a new member. O(x): person x is currently an officer. Give a quantified expression that is logically equivalent to each of the following statements.
(a) All the new members nominated all the officers.
(b) One of the current officers did not nominate anyone.
(c) Everyone nominated someone.
(d) Someone nominated everyone.
(e) Everyone nominated someone other than themselves.
(f) Exactly one person nominated Sam.

Looks like f(x, y) = cot⁻¹(xy), as in the inverse cotangent.

If you're like me and you don't remember the derivative of the inverse trig functions, we can derive it as follows. Let y = cot⁻¹(x), so that for appropriate x we can write cot(y) = x. By the chain rule, differentiating both sides gives

-csc²(y) y' = 1

y' = -sin²(y) = -sin²(cot⁻¹(x)) = - 1 / (x² + 1)

Next, recall that the derivative of a function f(x, y) at a point (a, b) in the direction of a vector v is given by

∇ f(a, b) • v

Compute the gradient ∇ f(x, y) :

∇ f(x, y) = - y / ((xy)² + 1) i - x / ((xy)² + 1) j

At the point P, we have

∇ f(x, y) = - 8/17 i - 8/17 j

So, the derivative of f at P along v = - 4 i + 5 j is

(- 8/17 i - 8/17 j) • (- 4 i + 5 j) = - 8/17

Given:

[tex]\dfrac{\sin (x)}{1-\cos ^2 (x)}\tan \left(\dfrac{x}{2}\right)[/tex].

To find:

The expression, which is equivalent to the given expression.

Solution:

We have,

[tex]\dfrac{\sin (x)}{1-\cos ^2 (x)}\tan \left(\dfrac{x}{2}\right)[/tex]

[tex]=\dfrac{\sin (x)}{1^2-\cos ^2 (x)}\times \dfrac{1-\cos (x)}{\sin (x)}[/tex]         [tex][\because \tan \left(\dfrac{x}{2}\right)=\dfrac{1-\cos (x)}{\sin (x)}][/tex]

[tex]=\dfrac{\sin (x)}{(1-\cos (x))(1+\cos (x))}\times \dfrac{1-\cos (x)}{\sin (x)}[/tex]         [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

Cancel out the common factors.

[tex]=\dfrac{1}{1+\cos (x)}[/tex]

Therefore, the correct option is C.

    Given question is incomplete; find the complete question in the attachment.

    Simplified form of the given trigonometric expression will be represented by Option C.

Given expression is,

[tex][\frac{\text{sin(x)}}{1-\text{cos}^2(x)}]\tan(\frac{x}{2} )=\frac{\text{sin(x)}}{1-\text{cos}^2(x)}\times \frac{1-\text{cos}x}{\text{sinx}}[/tex] [Since. [tex]\text{tan}\frac{x}{2} =\frac{1-\text{cosx}}{sinx}[/tex]]

                          [tex]=\frac{1-\text{cos}x}{(1-\text{cosx})(1+\text{cosx})}[/tex]

                          [tex]=\frac{1}{1+\text{cosx}}[/tex]

   Therefore, Option C will be the correct option.

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Answer:

f, x, 7, -2

Step-by-step explanation:

Answer:

54°

Step-by-step explanation:

Since m<2 + m<1 is equal to 180, we can set up the equation to find m<1.

plug in 126 as m<2, so we get

126 + m<1 = 180

-126              -126

m<1 = 54.

From this knowledge, we know that

7.) 54°

8.) 126°

9.) 54°

10.) 126°

11.) 54°

12.) 126°

13.) 54°

14.) 126°

Answer:

4%

Step-by-step explanation:

Step 1:

1/25 = 4/100      Convert Fraction

Step 2:

4/100 = 0.04     Divide by 100

Step 3:

0.04 = 4%        Convert

Answer:

4%

Hope This Helps :)

Answer:

D

Step-by-step explanation:

You can rewrite the equation into slope intercept form and you get Y=10-5x/2 (The whole problem is being divided by 2).

You can leave -5/2 as it is because it's a lot easier to plot the point using Rise over Run or Rise/Run.

Hope this helps! :)

Answer:

9d2nxdc

Step-by-step explanation:

??????????

Answer:

The answer is 1.5, 9

Step-by-step explanation:

If you can see the graph the speed increases

The ordered pair on the line (1.5, 9). The correct answer would be an option (D).

An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.

The graph below represents the distance Manuel walks over several hours.

The first and second options are not accurate since the distance is measured in miles up to 10 miles, hence the options can't be correct

The correct answer is option D since the value at t = 1.5 is equal to 9 miles

Thus, the ordered pair is on the line (1.5, 9).

Hence, the correct answer is an option (D)

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The question seems to be incomplete the missing figure has been attached below.

Answer: 7x^2 + 2x + 7

Step-by-step explanation:

Combine likes terms that have alike variables and alike exponents.

(3x^2 + 4x^2) + (2x) + (2 + 5)

7x^2 + 2x + 7

Answer:

If I had to guess... I think it would be Y

Step-by-step explanation:

The reason why I think its Y is because the line on the graph seems to go constant till it gets to the tip. As you can see the line is less slanted meaning that she is going slower. (If you know what I mean.. I tend to be bad at explaining things hehe..)

Answer:

The figure was not included in your question?

Answer:

80 machines

Step-by-step explanation:

If a machine makes 20 gadgets every fourth (1/4) of an hour, it makes 80 machines every hour (20*4).

80 machines gadgets are made every hour.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

A factory makes 20 gadgets every 1/4 hour.

So, in an hour made = 20÷1/4 machines

                                  =20×4

                                  =80

i.e. If a machine makes 20 gadgets every fourth (1/4) of an hour,

it makes 80 machines every hour (20*4).

Hence, 80 machines gadgets are made every hour.

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Answer:

They are 62 and 64.

Answer:

Option C. 23

Step-by-step explanation:

To know the correct answer to the question given above, let us determine the sequence of Raul and Ivan. This is illustrated below:

From the question given above,

Raul's pattern: start with 15, add 2

Ivan's pattern: start with 11, add 3

For Raul:

Raul's pattern: start with 15, add 2

1st term = 15

2nd term = 15 + 2 = 17

3rd term = 17 + 2 = 19

4th term = 19 + 2 = 21

5th term = 21 + 2 = 23

6th term = 23 + 2 = 25

For Ivan:

Ivan's pattern: start with 11, add 3

1st term = 11

2nd term = 11 + 3 = 14

3rd term = 14 + 3 = 17

4th term = 17 + 3 = 20

5th term = 20 + 3 = 23

6th term = 23 + 3 = 26

Summary

Term >>>>> Raul >>>>>> Ivan

1 >>>>>>>>> 15 >>>>>>>> 11

2 >>>>>>>>> 17 >>>>>>>> 14

3 >>>>>>>>> 19 >>>>>>>> 17

4 >>>>>>>>> 21 >>>>>>>> 20

5 >>>>>>>>> 23 >>>>>>>> 23

6 >>>>>>>>> 25 >>>>>>>> 26

From the calculations made above, we can see that in the 5th term, both Raul and Ivan has the same number as 23.

Answer: 27,846

Step-by-step explanation: 357 x 78 = 27,846

Answer:

$27846

Step-by-step explanation:

One book cost = $357

So, for 78 books, it  will be $357 * 78

=> $27846

If my answer helped, kindly mark me as the brainliest!!

Thanks!!

Answer:

Someone hurry and help me and this person answer this becuase this s on my test  and we need help

Step-by-step explanation:

Answer:

C. y<3

Step-by-step explanation

got it right on edge

Answer:

The answer is 9.

Step-by-step explanation:

I had the question on one of my quizzes.

Answer:

Hi There!

Your answer is:

Length = 116

Width = 56

Step-by-step explanation:

L= 4+ 2w

Width=w

perimeter formula

l+l+w+w= perimeter

Subsitute L for 4+2w

(4+2w)+(4+2w) + (w) + (w) = 344

8 +4w+w+w = 344

8+ 6w = 344

-8

6w = 336

/6

w= 56

PLUG BACK IN!

Length = 4+ 2w

Length = 4+ 2(56)

Length = 116

Width = 56

CHECK YOUR WORK

116+116+56+56= 344???

344 = 344 YES

HOPE THIS HELPS

Answer:

h(3) = 18

Step-by-step explanation:

Step 1: Define

h(t) = -3t + 6 + 7t

h(3) is x = 3

Step 2: Simplify

h(t) = 4t + 6

Step 3: Substitute and Evaluate

h(3) = 4(3) + 6

h(3) = 12 + 6

h(3) = 18

Step-by-step explanation:

*Syntax Error*

just consult with your teacher

Answer:

Step-by-step explanation:

Find the variable in the expression and see what has been done to it. Here, 'a' has been multiplied by c, and b has been subtracted from the product. Undo those operations in reverse order.

Undo the subtraction of b by adding b to both sides.

  g +b = ca -b +b

  g +b = ca . . . . . note b is no longer subtracted from the product

Undo the multiplication by dividing both sides by c.

  (g +b)/c = (ca)/c

  (g +b)/c = a

  a = (g +b)/c

__

The second problem is worked exactly the same way.

  u = 2x -2

  u +2 = 2x . . . . . add 2 to both sides

  (u +2)/2 = x . . . . divide both sides by 2

  x = (u +2)/2

Answer:

40 miles in 260 minutes

Step-by-step explanation:

Answer:

28.8 miles

Step-by-step explanation:

Answer:

Please explain your question better.

Step-by-step explanation:

60 - 720 = 660

660 divided by 12 = 55

Answer:

60

Step-by-step explanation:

$720 divided by $12 is 60.

I don't think I did this right.

Nope prolly not

Answer:

y = 65 degrees

Step-by-step explanation:

(this is what i remember from geometry at least so let me know if i got anything wrong)

2x+25 and 3x-10 are opposites which means they are equal to each other.

2x+25 = 3x-20 get the x values on the same side by subtracting 2 from both sides

25 = x-20 to get the x value alone add 20 to both sides

45 = x

now you can plug in x to either equation to find out what their degree is

2(45)+25 = 115 degrees

and since this equation and y are on the same line you can subtract 115 from 180 (a line is equal to 180 degrees) to find y

180-115 = 65 degrees

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle. The value of the variables x and y are 35 and 85, respectively.

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle.

The angle measuring (2x+25)° and (3x-10)° are vertical angles. Therefore, we can write,

(2x + 25) = (3x - 10)

2x + 25 = 3x - 10

25 + 10 = 3x - 2x

x = 35

Also, in the given image the angle measuring (2x + 25)° and y° are supplementary angles, therefore, we can write,

(2x + 25)° + y° = 180°

2x + 25 + y = 180°

Substitute the value of x,

2(35) + 25 + y = 180

70 + 25 + y = 180

95 + y = 180

y = 85°

Hence, the value of the variables x and y are 35 and 85, respectively.

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Explanation:

There are n = 5 items in set T

This means there are 2^n = 2^5 = 32 subsets

Answer:

7

Step-by-step explanation:

You have to but the numbers in order than you cross each of the ends until you get the middle number/median

Answer: 9

Step-by-step explanation:

The median in math is basicly the middle of the list. First, put the list in order from least to greatest. Then, find the middle. If there is no middle, add the two numbers in the middle. Add them together, and divide the sum by two. The quotient is the median.

In this case, there is a middle. The middle is nine. Nine is the median.

Answer:

Since this is an isosceles triangle, the angles opposite to the equal sides will also be equal

Therefore,

angle ABC  = angle ACB

We are given that angle ACB  is 30 degrees

Hence, angle ABC = 30 degrees

We know that according to the angle sum property, the sum of all interior angles of a triangle is 180 degrees

So, angle ABC + angle ACB + angle CAB  = 180 degrees

replacing the variables with values we already know

30 + 30 + angle CAB = 180

angle CAB = 180 - 60

angle CAB = 120 degrees

Hence the measure of angle A is 120 degrees