There are 12 people in a tennis tournament. Each player must play against every other player. How many games will be played?

The trigonometric ratios are given as follows:

a) cos(y) = -0.94.

b) sin(x) = 0.94.

The tree bisects an angle into two equal angle measures, one of which is of 70º and the other of which is of x.

Hence the measure of x is given as follows:

x = 70º.

The sine is given as follows:

sine of 70 degrees = 0.94.

The sum of the measures of the internal angles of a triangle is of 180º, hence the missing internal angle is of 20º.

An internal angle is supplementary with it's external angle, hence the value of y is given as follows:

y = 180 - 20

y = 160º.

Then the cosine is of:

cosine of 160 degrees = -0.94.

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Answer:3x+5x

Step-by-step explanation:

3x÷5 +x

3x+5x(multiply each term by 5)

the total area of all four square faces:  4 x 60.5 cm² = 242 cm²

To find the surface area of a rectangular prism, we need to calculate the area of each of its six faces and then add them up.

The two rectangular faces are congruent, so we only need to calculate one of them and multiply by 2.

The area of one rectangular face is:

6 cm x 5.5 cm = 33 cm²

Multiplying by 2 gives us the total area of both rectangular faces:

2 x 33 cm² = 66 cm²

The other four faces are also congruent, so we only need to calculate one of them and multiply by 4.

The area of one of the square faces is:

11 cm x 5.5 cm = 60.5 cm²

Multiplying by 4 gives us the total area of all four square faces:

4 x 60.5 cm² = 242 cm²

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Step-by-step explanation:

let length and width be increased by x>0

(10+x)(5+x)=6×10×5

50+10 x+5x+x²=300

x²+15x-250=0

x²+25 x-10x-250=0

x(x+25)-10(x+25)=0

(x+25)(x-10)=0

x=-25(rejected),10

so x=10

Therefore , the solution of the given problem of probability comes out to be the required probability is 0.05 or 1/20 and the correct option is c.

Probability theory is an area of mathematics that focuses on calculating the probability that a claim is valid or that a specific event will occur. Chance can be represented by any number between zero and 1, where range 1 is typically used to convey certainty and 0 is frequently used to denote possibility. The probability that a specific event will occur is displayed in a probability diagram.

Here,

The probability of randomly selecting an umbrella and a shaving kit in that order is equal to the probability of selecting an umbrella (with probability 1/5) multiplied by the probability of selecting a shaving kit from the remaining gifts (with probability 1/4,

since one gift has already been chosen and removed from consideration).

Therefore, the probability of selecting an umbrella and a shaving kit in that order is:

=>(1/5) x (1/4) = 1/20 or 0.05

So if you purchased Allure, the probability of randomly selecting an umbrella and a shaving kit in that order as your two free gifts is 1/20 or 0.05.

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Answer: The slope of the line between the points (-5, -4) and (1,-3) is 1/6 = 0.1667.

Step-by-step explanation:

To calculate the slope between two points, we apply the following formula:

[tex]\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff \ m=\dfrac{y_2-y_1}{x_2-x_1} }}[/tex]

where m is the slope of the line.

We identify the points:

     [tex]\boldsymbol{\sf{\diamond x_1=-5 \ \ \ \ \diamond y_1=-4 \ and \ x_2=1 \ \ \ \ \diamond y_2=-3 }}[/tex]

We substitute these points in the formula and solve:

          [tex]\boldsymbol{\sf{m=\dfrac{-3-(-4)}{1-(-5) }=\dfrac{1}{6}=0.1667 }}[/tex]

The slope of the line between the points (-5, -4) and (1,-3) is 1/6 = 0.1667.

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The right isosceles triangle PQR has vertices p(3,3), q(3,1) and r(x,y) and is rotated 90 degrees counterclockwise about the origin. the missing vertex of the triangle is r (5, 1)

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Properties are:

In a triangle, the angles that face the two equal sides are likewise equal.

An isosceles triangle has one base and two equal sides, which are known as the legs and the base, respectively.

Since the triangle is isosceles, the two legs have equal length. The coordinates of two vertices are given:

P(3,3)

Q(3,1)

Assuming that PQ and QR are the legs of equal length, the distance between Q and R must be the same as the distance between P and Q

d = √[(3-3)² + (3-1)²

d = 2

Therefore, the coordinates of r is: (5, 1)

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Trains make up approximately 49.04% of the total journeys across all modes of transportation.

We must divide the total number of train trips by the total number of trips made using all modes of transportation, then multiply the result by 100 to get the percentage that trains make up of the total.

There have been 2320 train trips overall, and there have been 4730 trips overall using all forms of transportation.

Trains therefore account for the following proportion of the total:

(2320 / 4730) x 100% = 49.04%

Train travel thus accounts for roughly 49.04 percent of all travels made using all modes of transportation.

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The union member worked 176 hours during the month of March.

Dues are the payment or obligation required by law or custom, it is like a monthly payment, fees or charges made by organizations.

Let h be the number of hours worked during the month of March by the union member.

According to the problem statement, the union charges monthly dues of $5.00 plus $0.15 for each hour worked during the month.

So, the total dues for the month of March can be expressed as -

Total dues = $5.00 + $0.15 x h

It is also given that the union member's dues for March were $31.40.

Set up an equation using this information as follows -

$31.40 = $5.00 + $0.15 x h

To solve for h, isolate the variable on one side of the equation.

Start by subtracting $5.00 from both sides -

$31.40 - $5.00 = $0.15 x h

Simplifying the left side gives -

$26.40 = $0.15 x h

To solve for h, divide both sides by $0.15 -

h = $26.40 / $0.15

h = 176

Therefore, the number of hours is 176.

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The required, we need to pay $0.132 in tax on the item that cost $3.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
To calculate the amount of tax, we need to multiply the cost of the item by the tax rate. The tax rate is 4.4% or 0.044 as a decimal.

So, the amount of tax on the item is:

0.044 × $3 = $0.132

Therefore, we need to pay $0.132 in tax on the item.

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The point slope equation with the point (x1, y1) is given as (y - y1) = m (x - x1).

As a line has length but no width, it is a one-dimensional figure in geometry. A line is constructed from a collection of points that can be stretched indefinitely in opposite directions. In a two-dimensional plane, it is determined by two points. In a two-dimensional coordinate plane, there are various ways to express line equations. The general or standard form of the equation of a line, the slope-intercept form, and the point-slope form are the three most often used ways. The point-slope form, as its name implies, combines a line's point with the straight-line slope. The equations of infinite lines with a specified slope can be written, however when we specify that the line passes through a certain point, we obtain a singular straight line.

The point slope equation with the point (x1, y1) is given by the formula:

(y - y1) = m (x - x1)

Here, (x1, y1) are the coordinates of the point on the graph.

m is the slope of the line.

Hence, the point slope equation with the point (x1, y1) is given as (y - y1) = m (x - x1).

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The fraction of the teams that raised the extra money, given the number of teams laps needed to be walked, is D.  1 / 3

To find the fraction of teams that raised the extra money, you need to count the number of teams who were able to walk more than 50 laps. The number of teams who walked more than 50 laps walked:

53, 63, 63, and 65 miles so 4 teams did so.

The total number of teams is the number of leafs which is 12 teams.

The fraction of teams who raised the extra money is :

= 4 teams / 12 total teams

= ( 4 ÷ 4 ) / ( 12 ÷ 4 )

= 1 / 3

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The amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ equals 1.1 then the probability is 0.9979.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.

a) What is the probability that a randomly selected male college freshman will gain more than 5.6 kg?

To answer this question, we can use the z-score formula to calculate the z-score for a gain of 5.6 kg. The z-score formula is:

z = (x - μ) / σ

where x is the gain of 5.6 kg, μ is the mean of 1.1 kg, and σ is the standard deviation of 4.5 kg.

Therefore, z = (5.6 - 1.1) / 4.5 = 2.8

The probability that a randomly selected male college freshman will gain more than 5.6 kg is 1 - the cumulative probability of a z-score of 2.8. This can be found using a z-table. The probability is 0.9979.

b) What is the probability that a randomly selected male college freshman will gain between 1.1 kg and 5.6 kg?

To answer this question, we can use the z-score formula to calculate the z-scores for a gain of 1.1 kg and a gain of 5.6 kg.

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The solutions of the system of inequalities are:

(0, 3)

(6, 2)

Here we have the graph of a system of inequalities, the solutions are all the points on the area where the two shaded regions intercept (it would be on the purple area).

And we can see that one line is solid, the points on that line are solutions, the other line is dashed, the points on that line are not solutions.

Then the points that are solutions are:

(0, 3)

(6, 2)

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The solution of the inequality 3|x|+4≥1 in interval notation is {x | -1 ≤ x ≤ 1}.

An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words. The numbers in between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all values between 0 and 5 is the set of numbers x satisfying 0 x 5.

Given that the inequality is:

3|x|+4≥1

Subtract 4 from both sides of the equation:

3|x| + 4 - 4 ≥ 1 - 4

3 |x| ≥ -3

Divide 3 from both sides of the equation:

|x| ≥ -1

We know that, |x| can be written as x and -x thus,

x ≥ -1

-x ≥ -1 or x ≤ 1

Hence, the solution of the inequality 3|x|+4≥1 in interval notation is {x | -1 ≤ x ≤ 1}.

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Answer:

$448.25

Step-by-step explanation:

For her medical expenses, it has to be more than 7.5% of her gross income of $32,500 => 7.5% of $32,500 = $2437.5.

so her deduction for medical expenses is $19,500 - $2437.50 = $17,062.5

so her total itemized deduction is $6,320.00 + $17,062.50 = $23,382.50

Given Kristina will file a single so her standard deduction for 2022 is $12,950.

If she uses standard deduction, her taxable income is 32,500 - 19,500 = 13,000

For the first 10,000 taxed at 10% so it is 10,000 x 10% = $1,000

The next $3000 taxed at 12% = $360

Her total tax is $1,000 + $360 = $1,360

If she uses itemized deduction, her taxable income is 32,500 - 23,382.50 = 9117.5

For the first 10,000 taxed at 10% so it is 9117.5 x 10% = $911.75

The tax saved is $1,360 - $911.75 = $448.25

Hope this helps.

Answer:

The economy car weighs 800 pounds.

The monthly cost for 39 minutes of calls is $14.30.

Let's start by using the given information to find the slope and y-intercept of the linear function that gives the monthly cost in terms of the total calling time. We can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

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

Using the points (34, 14.69) and (57, 17.68), we get:

m = (17.68 - 14.69) / (57 - 34) = 0.09

To find the y-intercept, we can use the point-slope form with either of the two points:

y - 14.69 = 0.09(x - 34)

y - 14.69 = 0.09x - 3.06

y = 0.09x + 11.63

So the monthly cost (y) is a linear function of the total calling time (x) with a slope of 0.09 and a y-intercept of 11.63.

To find the monthly cost for 39 minutes of calls, we simply substitute x = 39 into the equation:

y = 0.09(39) + 11.63 = 14.30

Hence, the monthly cost for 39 minutes of calls is $14.30.

What is cost price ?

Cost price refers to the amount of money that is paid to purchase an item or produce a good. It includes all the costs incurred in the production or acquisition of an item, such as the cost of raw materials, labor, and other expenses. Cost price is important for businesses because it helps determine the profit margin on a product, which is the difference between the selling price and the cost price. A business needs to set a selling price that covers the cost of producing or acquiring a product and leaves room for profit.

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Answer: The answer is 6.

Step-by-step explanation:

The value of x when we solve the equation 6/ -4.5 = 8/4x is x = - 1.5.

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. Another well formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's equivalents in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French.

The given equation is:

6/ -4.5 = 8/4x

Using the method of cross multiplication or butterfly method of multiplication we have:

6(4x) = (8)(-4.5)

24x = -36

x = -1.5

Hence, the value of x for the equation 6/ -4.5 = 8/4x is x = - 1.5.

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The sinusoidal function is y = sin(2/3x) - 5

The general form of a sinusoidal function is given by:

y = A sin(Bx + C) + D

where:

We know that the period is 3π and the amplitude is 1.

So, we have

A = 1

B = (2π)/(3π) = 2/3

So, we have

y = sin(2/3x + C) + D

The point (-3π/2, -5) implies that, the function is shifted down by 5 units

So, we have

y = sin(2/3x) - 5

Hence, the function is y = sin(2/3x) - 5

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Answer:

Step-by-step explanation:

For the 3-year loan at 6% simple interest:

Interest = Principal x Rate x Time

Interest = 12,000 x 0.06 x 3

Interest = $2,160

For the 5-year loan at 7.5% simple interest:

Interest = Principal x Rate x Time

Interest = 12,000 x 0.075 x 5

Interest = $4,500

The difference in the amount of interest Hannah would have to pay on these two loans is:

$4,500 - $2,160 = $2,340

So the answer is (B) $2,340.

The exponential function that is represented by the graph is f(x) = 2(2x).

This is because the graph shows a function with a base of 2 and an exponent of x. The function f(x) = 2(2x) has a base of 2 and an exponent of x, so it matches the graph.

To verify this, we can plug in some values of x into the function and see if they match the points on the graph. For example, when x = 0, the function gives us f(0) = 2(2^0) = 2(1) = 2, which matches the point (0, 2) on the graph. Similarly, when x = 1, the function gives us f(1) = 2(2^1) = 2(2) = 4, which matches the point (1, 4) on the graph.

Therefore, the correct answer is f(x) = 2(2x).

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Answer:

Step-by-step explanation:

In the context of communication, a medium is a substance or material through which information or messages are conveyed from a sender to a receiver. Examples of media include photographs, newspaper articles, paintings, videos, radio broadcasts, and so on. These media carry information from the person or organization that created them to the people who consume them, whether it be to inform, entertain, or educate.

A cookbook, on the other hand, may not be considered a medium in the same way as the other options, as it is not primarily used to convey information or messages from a sender to a receiver. While a cookbook contains information, such as recipes and instructions for preparing food, this information is not usually communicated from one person to another in the same way as, for example, a photograph or a newspaper article. A cookbook is more like a reference book or guidebook, which people use to obtain information rather than as a means of transmitting information.

All of the options given could be considered examples of media. However, if we interpret "medium" as a substance or material through which something is transmitted or conveyed, then "cookbook" might not be considered a medium. A cookbook is a book that provides instructions on how to prepare food and does not necessarily serve as a substance through which information is transmitted or conveyed. So the answer would be C. Cookbook.

Answer:

C. Cookbook

Step-by-step explanation:

The other answer choices represent examples of communication medium. A communication medium is  a system or channel through which information disseminated to others.

A cookbook is a set of instructions for a specific task and therefore does not fall under the generalized category of medium.

Answer:The volume would be 8,341,984

Step-by-step explanation:

4.3cm is the measure of the unknown side

According to the theorem, the product of the measurements of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment if two secant segments are drawn to a circle from an exterior point.

Applying the rule to the question;

3(y+3)= 2(2+9)

3y + 9 = 22

Subtract 9 from  both sides

3y = 22- 9

3y = 13

y = 13/3

y = 4.3cm

Hence the measure of y to the nearest tenth is 4.3cm

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A linear model (equation of line) that describes the growth of the organism for the time period given is y = 46/5(x) + 16.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided, we have the following equation that represents the relationship between the number of hours and the weight;

y = mx + c

y = 46/5(x) + 16

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Answer:

10 2/3

Step-by-step explanation:

The common ratio is 2.  Each term is being multiply by 2 to get to the next term.

To find the 7th term you take the first term and multiply that by the common ratio to the n-1 or 6th power.

[tex]1/6(2)^{6}[/tex] = 10 2/3