If sec x = -3, and x lies in quadrant II, find tan
x/2

A triangle is a shape used to represent the components of total health. True

As there are three players, the game will be played in cycles of 3 rounds. After each cycle is completed, the round after will be the round where every single player has 1 token less than they did at the beginning of the previous cycle.

After the first round of the game, player one will have 12 tokens, player two will have 15 and player three will have 14 left. Looking at this sequence, it is evident that player one will finish first.

Go a few rounds to establish the pattern:

Beginning chips: A B C

15 14 13

1st round:

12 15 14

2nd round: 13 12 15

3rd round: 14 13 12

So after 3 rounds and successive 3 rounds each player has one less than he started with at the beginning of the 3 round series.

So after 36 rounds each will be down 12 from the beginning:

                                            A B C

                                             3 2 1

On the 37 round A will give up his 3 to end at 0

37

For more clear understanding:

As player has one token less at the beginning of a new cycle than he/she had at the beginning of the previous cycle we go (12∗3)+1=37(12∗3)+1=37 to see how many turns it will take them to reach zero.

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A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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Let r be a partial order on set S, and let t be a subset of S. If a and a' are both elements of t, where a is the greatest element and a' is a maximal element, then it can be proven that a = a'.

To prove that a = a', we consider the definitions of greatest and maximal elements. The greatest element in a set is an element that is greater than or equal to all other elements in that set. A maximal element, on the other hand, is an element that is not smaller than any other element in the set, but there may exist other elements that are incomparable to it.

Given that a is the greatest element in t and a' is a maximal element in t, we can conclude that a' is not smaller than any other element in t. Since a is the greatest element, it is greater than or equal to all elements in t, including a'. Therefore, a is not smaller than a'.

Now, to prove that a' is not greater than a, suppose by contradiction that a' is greater than a. Since a' is not smaller than any other element in t, this would imply that a is smaller than a'. However, since a is the greatest element in t, it cannot be smaller than any other element, including a'. This contradicts our assumption that a' is greater than a.

Hence, we have shown that a is not smaller than a' and a' is not greater than a, which implies that a = a'. Therefore, if a is the greatest element and a' is a maximal element in t, then a = a'.

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Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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One-half of the dogs in each shelter are between the weights represented by the first and third quartiles, which are approximately 20-55 pounds for the first shelter and 25-65 pounds for the second shelter, respectively.

A box plot is a visual representation of a set of data that shows the median, quartiles, and outliers of the data. The box represents the middle 50% of the data, with the bottom and top edges of the box representing the first and third quartiles, respectively. The line inside the box represents the median, or the middle value of the data set. The "whiskers" extend from the edges of the box to the minimum and maximum values of the data set, but outliers beyond the whiskers are represented as individual points.

Now, let's look at the two box plots showing the weights of dogs in two different animal shelters. One-half of the dogs in each shelter are between the first and third quartiles, which are represented by the edges of the box in each plot.

If we take the first box plot, we can see that the first quartile is approximately 20 pounds and the third quartile is approximately 55 pounds. Therefore, one-half of the dogs in this shelter weigh between 20 and 55 pounds.

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The exact shape of a normal distribution is determined by its mean and standard deviation.

A normal distribution, also known as a Gaussian distribution or bell curve, is a symmetric probability distribution that follows a specific shape. The shape of a normal distribution is uniquely determined by its mean (μ) and standard deviation (σ).

Mean (μ): The mean represents the center of the distribution. It determines the location of the peak or highest point of the curve. Shifting the mean to the left or right will change the position of the peak accordingly.

Standard Deviation (σ): The standard deviation measures the spread or dispersion of the data. A smaller standard deviation indicates a narrower and taller curve, while a larger standard deviation results in a wider and flatter curve.

The combination of the mean and standard deviation determines the exact shape of the normal distribution. The curve is symmetric around the mean, and the standard deviation controls how quickly the probability density decreases as we move away from the mean.

The probability density function (PDF) of a normal distribution is given by the equation:

f(x) = (1 / (σ√(2π))) * e^(-((x-μ)^2) / (2σ^2))

where:

f(x) is the probability density at a given value of x

e is the base of the natural logarithm

π is a mathematical constant (approximately 3.14159)

The mean and standard deviation are the key parameters that determine the exact shape of a normal distribution. The mean determines the location of the peak, while the standard deviation controls the spread or dispersion of the data. By manipulating these parameters, we can alter the shape of the normal distribution to fit different datasets or statistical models.

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Answer:

C

Step-by-step explanation:

Hope this helps

Answer:

  D.  F(x) = (x +3)³ -2

Step-by-step explanation:

As with most multiple-choice math problems, you can try the different answers to see which is consistent with the information given in the problem. Here, that would mean you evaluate f(-3) to see if you get the value -2.

  A. (-3+2)³ -3 = -4 ≠ -2

  B. (-3 -3)³ -2 = -218 ≠ -2

  C. (-3 -2)³ -3 = -128 ≠ -2

 D. (-3 +3)³ -2 = -2 . . . . . . the correct choice

__

You are probably expected to understand that F(x) has been translated left 3 units and down 2 units from G(x). (The marked inflection point gives you the clue you need.) The transformation that translation does this is:

  F(x) = G(x -h) +k  . . . . .  G(x) translated by (h, k) units (right, up)

Translation left 3 and down 2 gives you (h, k) = (-3, -2), so ...

  F(x) = G(x -(-3)) -2 = G(x +3) -2

  F(x) = (x +3)³ -2

Answer:

AC = 16

KL = 5.625

Source(s):

Dude trust me

brainliest tho??

Step-by-step explanation:

5/KL = 12/13.5

12KL = 67.5

KL = 5.625

AC/18 = 12/13.5

13.5AC = 216

AC = 16

Answer:

yes

Step-by-step explanation:

:)

Answer:

  no

Step-by-step explanation:

The sides of the given lengths will form a right triangle if they satisfy the Pythagorean theorem.

  c² = a² + b²

  9² = 4² +6²

  81 = 16 +36 . . . . . not true

These side lengths do not form a right triangle. (They form an obtuse triangle.)

The equation of the tangent line at x=0 is y = x.

To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.

Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:

dy/dx = sin(2x^2+π/2)

Now we can evaluate this derivative at x=0:

dy/dx |x=0 = sin(2(0)^2+π/2)

        = sin(π/2)

        = 1

So, the slope of the tangent line at x=0 is 1.

To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).

Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:

y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt

      = 0

Therefore, the point on the tangent line is (0, 0).

Using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have:

y - 0 = 1(x - 0)

Simplifying, we get:

y = x

So, the equation of the tangent line at x=0 is y = x.

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Answer:

y = 320,000 ( 1.048 ) ^x

x = number of years

(the  ^  before the x symbolizes "to the power of," but I can't do that on my keyboard)

Step-by-step explanation:

formula i used:

A = amount that you start with

t = amount of years / time

%increase: you must convert your percent (4.8%) to a decimal (0.048)

A ( 1 + %increase ) ^t

Answer:

y = 320,000(1.048)^t  

Step-by-step explanation:

4.8% = 0.048.

The population grows by 1.048 per year.

The required equation is:

y = 320,000(1.048)^t

Answers:

(a)  9 cm

(b)  2 cm

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

Work shown for part (a)

A = s^2

s = sqrt(A)

s = sqrt(81)

s = 9

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

Work shown for part (b)

P = 4s

s = P/4

s = 8/4

s = 2

The side length of the square with area of 81 cm² is :

The side of the square with the perimeter of 8 m is :

Solution:

We're given the area of a square : 81 cm².

To find one of its sides, we need to take the square root of that.

So we have:

\(\sf{Side\:length{\square}=\sqrt{81}} \\ \\ \sf{Side\:length\square=9}\)

We know that if we take the square root of 81, we will get two solutions: 9 and -9; however we cannot use -9, because having a negative side length is impossible.

__________________________

To find the side length when given the perimeter, we divide it by 4, because the formula for a square's perimeter is P = 4a.

So if we rearrange that for a, we will get : a = P/4.

where a = side length

Solving,

The solutions of the equation 7x + 2x² + 8x² = 4x + 7x² will be 0 and -1.

Given that:

Equation, 7x + 2x² + 8x² = 4x + 7x²

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Simplify the equation, then we have

7x + 2x² + 8x² = 4x + 7x²

10x² + 7x = 4x + 7x²

3x² + 3x = 0

3x(x + 1) = 0

x = 0, -1

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Hope it helps u!

Step-by-step explanation:

why did you square the more complicated factor, why not square the x

p = x^2(60-x)

= 60x^2 - x^3

dp/dx = 120x - 3x^2

= 0 for a max of p

3x(40 - x) = 0

x = 0 or x = 40

obviously x=0 will produce the minimum product

if x = 40

then 60-40 = 20

so the two numbers are 40 and 20 (with 40 as the number that was squared in the product)

Your way should have worked too, but I notice that you jumped from

.... (60-x)^2 to

.....(60-x^2) , that is an error.

my product is (40^2)(20) = 32 000

btw, your two numbers don't even add up to 60

Answer:

the total time spent on backstroke is 64minutes

Step-by-step explanation:

get the ratio of backstroke then divide it by the total ratio then multiply by 120

(8/8+7)×120

=8×8

=64

Step-by-step explanation:

Hi there!

According to the question;

The gradient of line is 1/2 and passes through the point (4,-2).

Since, It has one point and gradient we use one point formula to find the equation of the line.

Note:

One point formula: (y-y1) = m (x-x1)

(4,-2) = (x1,y1)

So, using this formula we get;

(y+2) = 1/2(x-4)

Multiply both sides by 2.

2(y+2) = (1/2)*2(x-4)

2y+4 = x-4

Take 2y+4 in right side

0 = x-4 - (2y+4)

Therefore, x-2y-8 = 0 is the required equation.

Hope it helps!

Hi there!

We're given the following information:

With this information, we can go ahead and plug the data into the point slope equation: y - y₁ = m(x - x₁).

Plug in 1/2 for m, and (4,2) for x1 and y1:

\(\sf{y-y_1=m(x-x_1)}\)

\(\sf{y-(-2)=\dfrac{1}{2}(x-4)}\)

\(\sf{y+2=\dfrac{1}{2}(x-4)}\)

\(\sf{y+2=\dfrac{1}{2}x-2}\\\sf{y=\dfrac{1}{2}x-2-2}\\\\\sf{y=\dfrac{1}{2}x-4}\)

Hence, y = 1/2x - 4.

I hope that helps! :)

Answer:

y = 1

if you need answer of x

x = 2

Step-by-step explanation:

Let's solve your system by substitution.

4x+2y=10;3x+5y=11

Step: Solve4x+2y=10for x:

4x+2y=10

4x+2y+−2y=10+−2y(Add -2y to both sides)

4x=−2y+10

4x/4 = −2y+10/4

(Divide both sides by 4)

x= −1/2y+5/2

Step: Substitute −1/2y+5\2 for x in3x+5y=11:

3x+5y=11

3(−1/2y+5/2)+5y=11

7/2y+15/2=11(Simplify both sides of the equation)

7/2y+15/2+−15/2=11+/−152

(Add (-15)/2 to both sides)

7/2y=7/2

7/2y/7/2 = 7/2/7/2

(Divide both sides by 7/2)

y=1

Step: Substitute1for y in x= −1/2y+5/2:

x=−1/2y+5/2

x=−1/2(1)+5/2

x=2(Simplify both sides of the equation)

Step-by-step explanation:

the answer is = 650/50 = 13

so, she got 13, 50 rupee note.

hope this helps.

Answer:

\(\alpha=54^o\)

Step-by-step explanation:

\(\alpha+36^o=90^o\\\mathrm{or,\ }\alpha=90^o-36^o=54^o\)

The sample space of the spinner after spinning it twice is given by { (A, A) , (A, B ) , (A, C ), (A, D ) , ( B, A ), ( B, B ) , ( B, C ) ,  ( B, D ) ,  ( C, A ),

(C, B ) , ( C, C ) , (C, D ) , ( D, A ) , ( D, B ) , ( D, C ) , ( D, D ) }

Game played by Savannah using a spinner.

She spin the spinner twice.

To create a sample space for two spins of a spinner,

List all the possible outcomes of the first spin in one column.

And then list all the possible outcomes of the second spin in another column.

Then combine each outcome from the first column with each outcome from the second column to create all possible pairs of outcomes.

For example, suppose the spinner has 4 equally sized sections labeled A, B, C, and D.

The sample space for two spins would be,

{ (A, A) , (A, B ) , (A, C ), (A, D ) , ( B, A ), ( B, B ) , ( B, C ) ,  ( B, D ) , ( C, A ),

(C, B ) , ( C, C ) , (C, D ) , ( D, A ) , ( D, B ) , ( D, C ) , ( D, D ) }

Here, there are 16 possible outcomes for two spins of the spinner.

Therefore, the sample space of all possible outcomes of two spins is equal to  { (A, A) , (A, B ) , (A, C ), (A, D ) , ( B, A ), ( B, B ) , ( B, C ) ,  ( B, D ) ,  ( C, A ), (C, B ) , ( C, C ) , (C, D ) , ( D, A ) , ( D, B ) , ( D, C ) , ( D, D ) } .

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Answer:

Step-by-step explanation:

Therefore, the sample space of all possible outcomes of two spins is equal to  { (A, A) , (A, B ) , (A, C ), (A, D ) , ( B, A ), ( B, B ) , ( B, C ) ,  ( B, D ) ,  ( C, A ), (C, B ) , ( C, C ) , (C, D ) , ( D, A ) , ( D, B ) , ( D, C ) , ( D, D ) } .

Respuesta:

Significar

Explicación paso a paso:

Las medidas del centro incluyen la media, la mediana y la moda. La media se obtiene tomando la suma de los valores dividida por el número de valores individuales (frecuencia). La mediana es el percentil 50 de la distribución y la moda es el valor que ocurre con mayor frecuencia si se trata de una distribución. De todas las medidas, la media es la más afectada por la presencia.

Dados los datos:

2,4, 5, 2, 3, 3, 3, 5

La media = Σx / N = 2.3

Modo = 3

Mediana = 2, 2, 3, 3, 3, 4, 5, 5 = 1/2 * nth = 1/2 * 8 = 4to término = 3

Si se agrega un valor extremo: digamos 80

2, 2, 3, 3, 3, 4, 5, 5, 2, 80

Nueva media = Σx / N = 11,88

Mediana = 1/2 (n + 1) th término

Mediana = 1/2 (10) término = 3

Modo = 3

Podemos ver que la inclusión de 80, que es un valor extremo, cambia significativamente el valor medio.

The solution to the system is x = 2 and y = 6, represented as the ordered pair (2, 6). This corresponds to option (B) in the answer choices.

To solve the system using substitution, we'll substitute the value of one variable from one equation into the other equation and solve for the remaining variable.

Given the system:

x + y = 8

y = 3x

Substituting the value of y from the second equation into the first equation, we have:

x + (3x) = 8

4x = 8

x = 2

Now, substitute the value of x into the second equation to solve for y:

y = 3(2)

y = 6

Therefore, the solution to the system is (2, 6). Option (B) is the correct answer.

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Answer:

¡Hola! Lo siento, pero no hablo español. ¡qué tengas un lindo día! También necesito puntos porque soy nuevo.

Step-by-step explanation:

It is correct to say that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. What is a perpendicular bisector? A perpendicular bisector is a line that intersects a line segment and forms a 90-degree angle. It divides the line segment into two equal halves.Each point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment. This means that the distance from any point on the line to one endpoint of the segment is the same as the distance to the other endpoint of the segment.

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Answer:The second one is better

Step-by-step explanation:

The highest number of month’s mostrn for which the men participated in the job training is 24 months.

What is sample?

The selection of a group of people from a statistical population to estimate attributes of the entire population is known as sampling in statistics, quality control, and survey technique. To gather samples that are representative of the population under consideration, statisticians try to use random sampling.

Given: Take the job training trial with a group of males where individuals could enrol in the programme commencing in January 1976 through around mid-1977. In December 1977, the programme comes to an end. Take into account that the train is the training's indicator variable.

Following are some calculations to determine how many guys in the sample took part in the job training programme:

185 men are accepted into the employment training programme out of the 445 who were supplied. By filtering data, it is provided where

train = 1

24 months was the longest period of time during which the guys took part in job training.

Therefore, the highest number of month’s mostrn for which the men participated in the job training is 24 months.

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