What are the period and amplitude of the function?


period: π; amplitude: 1.5

period: π; amplitude: 3

period: π2; amplitude: 1.5

period: π2; amplitude: 3

Answer: The number of handshakes made by each participant can be calculated using the combination formula.

In this case, there are 35 participants, and each participant shakes hands with every other participant. When participant A shakes hands with participant B, it is the same handshake as when participant B shakes hands with participant A.

To find the number of handshakes made by each participant, we can use the formula:

where n represents the number of participants.

Plugging in the value for n = 35:

Simplifying the expression:

Therefore, the first participant will make 595 handshakes.

An approximate solution for the system of equations in this problem is given as follows:

C. x ≈ 5.81.

When we want to solve a system of equations graphically, we must obtain the point of intersection of the equations that compose the system.

The equations for this problem are given as follows:

From the graph, the x-coordinate of the point of intersection is given as follows:

x = 5.805.

Which is rounded as follows:

C. x ≈ 5.81.

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1. Alternate interior angle.

2. Alternate Exterior Angle.

3. Vertical Angles.

4. 13x + 2= 15x - 2

5. x= 2

Since AB || CD

and, <BGF = 13x + 2, <EHC = 15x - 2

1. <BGF and <EHC are Alternate interior angle.

2. <FHD and <EGA are Alternate Exterior Angle.

3. <FHC and <EHD are Vertical Angles.

4. <BGF = <EHC

13x + 2= 15x - 2

5. Solving for x we get

-2x = -4

x= 2

6. <BGF = 26 +2 = 28

<EHC = 28

<FHD = 28

<EGB = 180 - 28 = 152

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Answer:

To eliminate a variable, you need to choose a strategy that allows you to add or subtract the equations in such a way that one variable will be eliminated. Let's go through the given options to determine the correct strategy:

A. Multiply the first equation by 2. Then add the equations.

If you multiply the first equation by 2, you get 10x + 6y = 8. If you add this equation to the second equation, you will not be able to eliminate either variable, as the coefficients of x and y do not match.

B. Multiply the first equation by 5 and the second equation by 2. Then add the equations.

If you multiply the first equation by 5, you get 25x + 15y = 20. If you multiply the second equation by 2, you get -4x - 16y = 12. Adding these equations gives you 21x - y = 32. This strategy allows you to eliminate y.

C. Multiply the second equation by 5. Then add the equations.

If you multiply the second equation by 5, you get -10x - 40y = 30. If you add this equation to the first equation, you will not be able to eliminate either variable, as the coefficients of x and y do not match.

D. Multiply the first equation by 2 and the second equation by 5. Then add the equations.

If you multiply the first equation by 2, you get 10x + 6y = 8. If you multiply the second equation by 5, you get -10x - 40y = 30. Adding these equations gives you -34y = 38. This strategy allows you to eliminate x.

Based on the options given, the correct strategy to eliminate a variable in this system of equations is: B.) Multiply the first equation by 5 and the second equation by 2. Then add the equations.

The relative frequencies for this problem are given as follows:

A relative frequency is calculated as the number of desired outcomes divided by the number of total outcomes.

The total number of people is given as follows:

32 + 68 = 100.

Of those, 25 + 45 = 70 wear a watch, hence the relative frequency is given as follows:

70/100 = 0.7.

30 do not wear a watch, hence the relative frequency is given as follows:

30/100 = 0.3.

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the answer is (D) 11

Answer: It is a reflection of Reflections of You (second location) in the x-axis.

Step-by-step explanation: Based on the given information, the relationship between the new location (The Gridiron) and the previous locations can be determined.

The correct answer is:

   It is a reflection of Reflections of You (second location) in the x-axis.

The coordinates of the first three checkpoints of The Gridiron (A''(0,−5), B''(9,−5), and C''(4,−5)) indicate that they have the same y-coordinate (-5) as the corresponding checkpoints in the second location, Reflections of You. However, there is no indication of a reflection in the y-axis or any transformation related to the first location, Transformation Fitness Studios. Therefore, the correct answer is that The Gridiron is a reflection of Reflections of You in the x-axis.

The function g( x ) is translated to the left by 9 units and down by 5 units.

Given data ,

Let the first function be represented as f ( x )

where the value of f ( x ) = | x |

Let the translated function be g ( x )

where the value of g ( x ) = | x + 9 | - 5

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

On translating to the left , f ( x + a )

So , the function f ( x ) is translated 9 units to the left by f ( x + 9 ) = | x + 9 |

Now , when the function is translated 5 units down , f ( x ) - 5

So , the translated function is g ( x ) = | x + 9 | - 5

Hence , the function is translated to the left by 9 and up by 5 units.

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The maximum value of the inequality is P = 72

Given data ,

8x + 6y ≤ 48 can be rewritten as y <= (-4/3)x + 8. Graphing this inequality, we have a line with a slope of -4/3 passing through the point (0, 8). Shade the region below this line.

7x + 7y ≤ 49 can be rewritten as y <= (-1)x + 7. Graphing this inequality, we have a line with a slope of -1 passing through the point (0, 7). Shade the region below this line.

x ≥ 0 represents the x-axis or the region to the right of the y-axis.

y ≥ 0 represents the y-axis or the region above the x-axis.

Now, we evaluate P = 9x + 8y at the corner points of the feasible region to find the maximum value.

The corner points of the feasible region are the intersections of the lines. In this case, the corner points are:

A: (0, 0)

B: (0, 7)

C: (8, 0)

D: (6, 2)

Now, substitute these points into P = 9x + 8y:

P(A) = 9(0) + 8(0) = 0

P(B) = 9(0) + 8(7) = 56

P(C) = 9(8) + 8(0) = 72

P(D) = 9(6) + 8(2) = 66

Hence , the maximum value of P = 9x + 8y is 72, which occurs at the corner point C: (8, 0)

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The rate at which the depth of the liquid is increasing when it reaches one-third of the height of the bowl is (7/3)π cm³/s.

To ascertain the rate at which the liquid's depth rises, let's find the derivative of the depth function with respect to time.

Let;

The rate of change of the volume of the liquid with respect to time is constant and equal to 7π cm³/s.

To determine the height of the bowl, we can evaluate the curve y = [-4 / (8 - x)] - 1 when x = 4 and y = 7.6 and then find the absolute difference between the values.

h = |[-4 / (8 - 4)] - 1 - [-4 / (8 - 7.6)] - 1|

Let's calculate the rate at which the depth rises when it reaches one-third of the bowl's height.

D = depth of bowl

Using this relationship from the question given;

D = (1/3) * h

In order to determine the rate at which D will change with respect to time, let's differentiate both sides of the equation.

dD/dt = (1/3) * dh/dt

Since dh/dt is the rate at which the depth of the liquid is changing, which is constant and equal to 7π cm³/s, we can substitute it into the equation:

dD/dt = (1/3) * (7π)

Simplifying, we have:

dD/dt = (7/3)π cm³/s

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Answer:

6

Step-by-step explanation:

We can begin by finding EA, which is 1 unit.

Using similar triangles AEB and ADC, we can set up a ratio.

1:6=2:x+6.

if a:b=c:d, then ad=bc

x+6=12

x=6

Feel free to tell me if I did anything wrong! :)

Answer:

C

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{AB}{AC}[/tex] = [tex]\frac{AE}{AD}[/tex] ( substitute values )

[tex]\frac{2}{2+x+4}[/tex] = [tex]\frac{6-5}{6}[/tex]

[tex]\frac{2}{x+6}[/tex] = [tex]\frac{1}{6}[/tex] ( cross- multiply )

x + 6 = 12 ( subtract 6 from both sides )

x = 6

The amplitude and the period of the function are 3 and π

The Phase shift is 90 and the vertical shift is 2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3sin[2(θ - 90)] + 2

A sinusoidal function is represented as

f(x) = Asin(B(x + C)) + D

Where

Using the above as a guide, we have the following:

Amplitude = 3

Period = 2π/2 = π

Next, we have

Phase shift = 90

vertical shift = 2

Hence, the amplitude is 3 and the period is π

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Based on an exponential growth function, P = 6,000 (1.15)ⁿ, the population of the town with an initial population of 6,000 growing at 15% annually after n years is 15,960.

An exponential growth function is one of the two exponential functions, including an exponential decay function.

An exponential growth function is written in the form of y = abˣ, where y is the ending value after time x (the exponent), a is the initial value, and b is the growth factor based on a constant rate of growth.

The current population of the town = 6,000

The growth rate per year = 15% = 0.15

Growth factor = 1.15 (1 +1.15)

The number of years of growth, n = 7 years

P = 6,000(1.15)ⁿ

P = 6,000(1.15)⁷

P = 15,960

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The sample mean x¯ is 70.4.

The sample mean, denoted as x¯, can be obtained directly from the midpoint of the confidence interval.

In this case, the confidence interval given is (66.2, 74.6).

To find the sample mean, we take the average of the lower and upper bounds of the confidence interval:

x¯ = (lower bound + upper bound) / 2

Substituting the given values, we have:

x¯ = (66.2 + 74.6) / 2

Calculating the expression, we find:

x¯ = 140.8 / 2

Simplifying, we get:

x¯ = 70.4

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From the given list, we can choose the numbers 80 and 65 as potential values for the variable representing the height (in inches) of a bookcase.

Let's go through each number and reason why it could represent the height of a bookcase:

-80: It is highly unlikely for a bookcase to have a negative height as it implies being below ground or submerged. Negative heights do not make sense in this context, so we can eliminate -80 as a viable option.

10208: This number seems unreasonably high for the height of a bookcase. Most bookcases are not taller than a few feet or a couple of meters. A height of 10208 inches would be more than 850 feet, which is much larger than any standard bookcase. Therefore, we can eliminate 10208 as a realistic option.

80: This is a plausible height for a bookcase. Many bookcases range in height from a few feet to around six or seven feet, and 80 inches falls within this typical range.

65: Similarly, a height of 65 inches is also plausible for a bookcase. Smaller bookcases or shelves designed for specific purposes, such as children's bookcases or shorter units, often have heights around this range.

Based on these considerations, we can conclude that the numbers 80 and 65 are reasonable options for representing the height of a bookcase.

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Answer:

$20

Step-by-step explanation:

Gym city fees are:

Sign up = 30

6 monthly sub = 6 x 25 = 150

Total fees = 30 + 150

FitnessExpress fees are:

Sign up = 20

6 monthly sub = 6 x 30 = 180

Total fees = 20 + 180 = 200

Therefore, the difference between the two is $20

Answer:

b. 24 yd

Step-by-step explanation:

since we have a  right triangle we have to apply the Pythagorean Theorem:, to find the missing side

c^2 = a^2 + b^2

Where c is the hypotenuse of the triangle (10 yd) and a and b are the other sides.

Replacing with the values given:

10^2 = 6^2 + b^2

100 = 36+b^2

100-36 = b^2

64 = b^2

√64 = b

b= 8

Now, we can calculate the area:

A =1/2x base x height = 1/2 x 8 x 6 = 24 yd

Feel free to ask for more if needed or if you did not understand something.

Based on the information, the critical value of F to 3 decimal places is 2.17.

Here are the steps on how to calculate the critical value of F:

Identify the significance level. In this case, the significance level is 10%, or 0.10.

Identify the degrees of freedom. The degrees of freedom for the numerator is 1, and the degrees of freedom for the denominator is 23.

Look up the critical value of F in the F-table. The F-table is a table that lists the critical values of F for different significance levels and degrees of freedom.

The F-table shows that the critical value of F for a significance level of 0.10 and degrees of freedom of 1 and 23 is 2.17.

Therefore, the critical value of F to 3 decimal places is 2.17.

Here is the solution in mathematical form:

F = (60.0 - 54)/(14.9 / ✓(24)) = 2.17

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Since the equation is true, we can conclude that the following can be proven using a Pythagorean identity:

(15/8)² + 1 = (17/8)²

To determine which of the following can be proven using a Pythagorean identity, we need to use the given trigonometric values of tan Ø and sec Ø.

Given:

tan Ø = 15/8

sec Ø = 17/8

Using the Pythagorean identity for tangent and secant:

tan² Ø + 1 = sec² Ø

Substituting the given values:

(15/8)² + 1 = (17/8)²

Simplifying:

(225/64) + 1 = (289/64)

Combining fractions:

(225 + 64) / 64 = 289 / 64

Both sides have the same denominator, so we can compare the numerators:

289 = 289

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Answer:

1. positive integers
2. negative integers.
Explanation:
The two types of integers are positive integers and negative integers.

Positive integers are whole numbers greater than zero, such as 1, 2, 3, 4, and so on.

Negative integers are whole numbers less than zero, denoted by a negative sign (-) before the number. Examples of negative integers are -1, -2, -3, -4, and so on.

Together, positive and negative integers make up the set of integers, which includes all whole numbers both greater than and less than zero, including zero itself.

It should be noted that 78.03% of the lake's volume flows through the river in April and June.

First, we need to convert the volume of the lake from cubic miles to cubic feet. There are 5280 feet in a mile, so 0.67 mi³ is equal to 35,616,000 cubic feet.

Next, we need to divide the volume of water that flows through the river in April and June by the volume of the lake. This gives us a percentage.

(39,498.97 + 37,458.14) million cubic feet / 35,616,000 cubic feet

= 0.7803

Therefore, 78.03% of the lake's volume flows through the river in April and June.

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Answer:

x=61°

Step-by-step explanation:

angles in triangle add up to 180°

180°-80°-39°=x

61°=x

Answer:

Step-by-step explanation:

We know that,

Sum of three side of triangle is 180 °

So,

80°+ 39° + x = 180°

119°+ x = 180°

x = 180°-119°

x = 61°

Thus,

[tex] \underline{\rule{190pt}{4pt}}[/tex]

The rate of change for each linear function would be = increase 8 pt/gal. That is option B.

To determine the rate of each linear function, the relationship between the ratio X and y should be calculated as follows. That is;

When X( gallons) is 1 : Y( pints) is 8

Also X( gallons) is 2 : Y( pints) is 16

When reduced;

X = 1 when Y = 8

Therefore, the rate of change for each linear function would be when there is increase in 8 pints is 1 gallon.

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The other vertices of the square must be located at (1.5, -3.5), (-2.5, 6.5), and (3.5, -8.5) because these points make up the diagonals of the square with the given endpoints.

The vertices of one of the diagonals of a square are located at (-3,4) and (2,-1). To find the other vertices of the square, we can use the fact that the diagonals of a square intersect at their midpoints.

The midpoint of the diagonal with endpoints (-3,4) and (2,-1) can be found by averaging the x-coordinates and the y-coordinates separately. The x-coordinate of the midpoint is (-3 + 2)/2 = -0.5, and the y-coordinate is (4 + (-1))/2 = 1.5.

Now, we have the coordinates of the midpoint of the diagonal as (-0.5, 1.5). To find the other vertices of the square, we can reflect this midpoint across the given diagonal.

Reflecting the midpoint across the diagonal, we get the coordinates for the other vertices of the square as follows:

Vertex 1: (-0.5, 1.5) (the midpoint)

Vertex 2: (-0.5 + 2, 1.5 - 5) = (1.5, -3.5)

Vertex 3: (-0.5 - 2, 1.5 + 5) = (-2.5, 6.5)

Vertex 4: (-0.5 + 4, 1.5 - 10) = (3.5, -8.5).

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Answer: The probability that both events A and B will occur is 5/18 or 0.28.

Step-by-step explanation:

To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.

Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.

Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.

To find the probability that both events A and B occur, we multiply the probabilities:

Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.

The ratio of the original length of the longer candle to the shorter candle was 27/23.

Let us assume that,

the original lengths of the longer and shorter candles L and S, respectively.

Hence, We can set up two equations based on the information given:

L - 7x = S - 11x

where x is the length remaining after 3 hours

L = S + 4x

We can solve for x by substituting equation 2 into equation 1:

S + 4x - 7x = S - 11x

-3x = -6x

x = 2

Now we can use equation 2 to solve for L in terms of S:

L = S + 4x = S + 8

We know that after 3 hours, both candles had the same length remaining, so we can set up an equation based on this:

L - 3(7) = S - 3(11)

S + 8 - 21 = S - 33

S = 46

Therefore, the original length of the shorter candle was 46, and the original length of the longer candle was

L = S + 8 = 54.

The ratio of the original length of the longer candle to the shorter candle is:

L/S = 54/46 = 27/23

So, the ratio of the original length of the longer candle to the shorter candle was 27/23.

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The correct statement is :-c) Martin is less likely to win because getting two heads in a row is less likely than getting tails and heads.

To understand why this statement is correct, let's analyze the probabilities of the two patterns occurring.

The probability of getting two heads in a row (HH) in a single coin toss is (1/2) * (1/2) = 1/4, as each coin toss has a 1/2 probability of landing on heads.

The probability of getting tails and heads (TH) in a single coin toss is (1/2) * (1/2) = 1/4, as each coin toss has a 1/2 probability of landing on tails and a 1/2 probability of landing on heads.

However, in order for Martin to win the game, the first appearance of the pattern HH must occur before the first appearance of the pattern TH. This means that Martin needs to get two heads in a row (HH) before getting tails and heads (TH).

Since the probability of getting two heads in a row (HH) is 1/4, which is the same as the probability of getting tails and heads (TH), it is less likely for Martin to achieve the pattern HH before the pattern TH. Therefore, Martin is less likely to win the game compared to Gale.

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The representation of given graphs are as following:

I. Identity

II. Reciprocal

III. Absolute value

IV. absolute function

According to the given graphs we have:

For graph 1:

This graph is  represents a equation of line,

Which is of the form,

y  = x

Then at x = 1 we get y = 1

         at x = 2 we get y = 2

Hence,

This graph represents an identity function.

For graph 2:

This graph represents the graph of inverse functions ,

y = 1/x

Which represents a graph of reciprocal function.

For graph 3:

This graph is representation of mod function

y = |x|

Which is nothing but absolute function.

For graph 4:

This graph represents,

y = [x]

Which represents the graph of  greatest integer function.

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