Only six players on the tennis team showed up for practice today. If each player plays every other player one game, then how many games the team played total today?

Answer:

The solution to the system will be in the point where the two lines intersect.

Step-by-step explanation:

The solution to the system will be in the point where the two lines intersect.

Answer:

It's 4

Step-by-step explanation:

Trust the math

Answer: 4

Step-by-step explanation:

With the pythagorean theorem, a²+b²=c².

C² is always the hypotenuse, which in this case is [tex]2\sqrt 5\\[/tex]. The length of the base, a², is 2, ad we don't know b so we'll substitute it as "x".
So...
(2)²+(x)²=[tex](2\sqrt{5} )^2[/tex].

Simplify to get 4+(x)²=([tex]2\sqrt{5} \\[/tex])².

Now, to write as a single radical, we need to square the two ("undoing" the square root). So, we get ([tex]\sqrt{4} *\sqrt{5\\[/tex] )², which is ([tex]\sqrt{20}[/tex])². Since we're squaring a square root, the square root almost "cancels out", leaving just the 20.

Now going back to our pythagorean theorem equation,

4+(x)²=20. Now we can subtract 4, getting (x)²=16. Hence, x= ± 4, and since a side can't be egative, it's just 4.

VERIFICATION: (4)²+(2)²=20, =16+4=20 ✓

The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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After simplifying the total cost is $78

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas. The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given, that each pair of wings is made with 3/4 yard of fabric. Since the fabric costs $8 per yard. Therefore:

1) 3/4 x $8 will give us the cost of the amount required for 3/4 yard of fabric.  3/4 x $8 = $6 each

2) Now, we are told that Mr. Townsend needs to make 13 pairs of butterfly wings and as such:

Amount needed to make 13 pairs is expressed as; 3/4 x $8 x 13 = $78

3) Treat 1 yard of fabric like the fraction 4/4.

Now, if this 1 fabric is equal to $8, then it means that 3/4 of the fabric will be $6. That is for one pair of butterfly wings, there's 13 of those so multiply $6 by 13.

This is easier  because we know how much 1 fabric costs, but we don't know what 3/4 of it does, so we treat 1 yard of fabric as the fraction 4/4.

4) Simplifying the expression gives: $78

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The solutions of the quadratic equation:

x^2 + 8x = -15

are

x = -5

x = -3

So here we have the following quadratic equation:

x^2 + 8x = -15

First, we can rewrite the equation as:

x^2 + 8x + 15 = 0

The solutions are given by the quadratic formula:

[tex]x = \frac{-8 \pm \sqrt{8^2 - 4*1*15} }{2} \\\\x = \frac{-8 \pm \sqrt{4} }{2}\\\\[/tex]

Then the two solutions are:

x = (-8 - 2)/2 = -5

x = (-8 + 2)/2 = -3

Y assume that the options are for another question, or the quadratic equation is written incorrectly.

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2 kg of pebbles we can purchase by using $10.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that there is a sale for pebbles

1KG of pebbles cost is $4.50.

We need to find how many kilograms of pebbles we can purchase by 10.

Let x be the pebbles we purchase for $10.

Let us form an equation

4.5/1=10/x

x=10/4.5

x=2.2

Hence, 2 kg of pebbles we can purchase by using $10.

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a) An equation that relates the area of the desktop components is w(w+3) = w(7-w).

b) The value of w is 2.

c) The combined area of the desktop components is 20 square feet.

What is an area of an object?

The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area. Draw a square on a piece of paper with a pencil. It is a two-dimensional figure. The area of the shape on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Given that two components joined together to make the desktop.

The width of both components is w ft.

The length of one component is 3+w ft.

The length of the other component is (7-w) ft.

The area of the first component is w(3+w) sq. ft.

The area of the second component is w(7-w) sq. ft.

The area of the components are equal.

Therefore,

w(3+w) = w(7-w)

3w + w² = 7w - w²

3w + w² - 7w + w² = 0

2w² - 4w = 0

2w(w - 2) = 0

Either                         or,

2w = 0                            w - 2 = 0

w = 0                                w = 2

Since the length of width is never zero, Thus w = 2.

The area of the component is w(3+w) +  w(7-w)  sq. ft

Putting w=2 in w(3+w) +  w(7-w)  sq. ft:

A = 2(3+2) +  2(7-2)  sq. ft

A = 10 +10  sq. ft

A = 20  sq. ft

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An equation of the line of best fit in slope-intercept form include the following: y = -10x + 105.

If the trend continues, the number of pairs of shoes that would be left in stock 10 days after the shipment arrived is 5 pairs of shoes.

In order to write an equation of the line of best fit in slope-intercept form, we would use the given data points. Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would determine the slope by using the given data points as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (45 - 95)/(6 - 1)

Slope, m = -50/5

Slope, m = -10.

At point (1, 95), an equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - 95 = -10(x - 1)

y - 95 = -10x + 10

y = -10x + 10 + 95

y = -10x + 105

For the number of pair shoes left in stock 10 days, we have:

y = -10(10) + 105

y = -100 + 105

y = 5 pairs of shoes.

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Calculate the row tension by measuring down your knitting tension square.

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Answer:

18, -16, 22, 24

Step-by-step explanation:

(4,-1)

4p - 2q  Substitute 4 for p and 1 for q

4(4) - 2(-1)

16 - (-2)

16+ 2

18

(-3,2)

4p - 2q

4(-3) - 2(2)

-12 - 4

-16

(7,3)

4(7) -2(3)

28 - 6

22

(5,-2)

4(5) - 2(-2)

20 - (-4)

20 + 4

24

Answer:

x = 6

Step-by-step explanation:

5x + 3 = 33

     - 3.   - 3

5x = 30

5.      5

X = 6

Step 1: subtract 3 (3-3 & 33-3)

Step 2: divide by 5 (5x/5 & 30/5)

Step 3: answer is x = 6

Answer:

4 (x + 3.3) = 28

Distribute the 4:

4x + 13.2 = 28

Subtract 13.2 to both sides:

4x = 14.8

Divide by 4 on both sides:

x = 3.7

The method for calculating an angle depends on the information available to you. Here are a few typical methods for determining an angle θ:

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Answer:

y=x+1

Step-by-step explanation:

because the rise is 13 and the run is 13, x is 1 or just x. The y intercept is 1 so y=x+1

The time that Siobhan’s family should leave for the trip to the Grand Canyon, if they plan to arrive at 3 : 30 pm, is 7 : 30 am.

If the trip will take 5 hours of driving and three 1-hour stops, then the total time spent on the road is 5 hours + 3 hours = 8 hours.

If the family wants to arrive at the Grand Canyon at 3:30 pm, then they need to subtract the time spent on the road from their arrival time to determine the time they need to leave.

3:30 pm - 8 hours = 7:30 am

In conclusion, Siobhan's family should plan to leave at 7:30 am to arrive at 3:30 pm

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Answer:

Graphing, Substitution, and Elimination.

Step-by-step explanation:

Graphing: Graphing is the best method to use when introducing a new student to solving systems of two equations in two variables because it gives them a visual to recognize what they are looking for. Graphing is less exact and often takes more time than the other methods. I only recommend graphing to find a solution if the problem comes with a graph already drawn and the intersection appears to be on an exact coordinate.

Substitution: Substitution gives the advantage of having an equation already written for the second variable when you find the first one. Substitution is best used when one (or both) of the equations is already solved for one of the variables. It also works well if one of the variables has a coefficient of 1.

Elimination: Elimination is the method that I use almost every time. If you are not sure which method to use, I recommend that you use elimination. Elimination is best used when both equations are in standard form (Ax + By = C). Elimination is also the best method to use if all of the variables have a coefficient other than 1.

I hope this gives you some idea about which method you should use. All three methods will give the same solution. Also, you should always check your answer in both equations to make sure it is correct.

For any chi-square goodness-of-fit test, the number of degrees of freedom is equals to

(k - 1), where k is number of categories. So, second option is correct.

Chi-square goodness test : The chi-square goodness test is used to check whether the observed data distribution matches with the expected distribution. Since this is a non-parametric test, the data are divided into classes or groups, and the number of values that fall into those groups is compared to the expected number of values that fall into those groups. The chi-square test of goodness has

degrees of freedom equal to the number of groups minus one i.e., (k −1), where

k --> Number of classes or categories, the data is divided into.

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The equation of circle does not have any solution

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The circumference of a circle C with a radius of r units is approximately given by the linear equation C = 6.3r.

We need to find two solutions of this equation

The circumference of circle is 2πr

2πr= 6.3r.

The equation does not have solutions

Hence, the equation of circle does not have any solution

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A two-sample t-test is the inferential statistical test that would be best suitable to this situation.

The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A t-test is a method for evaluating hypotheses that involve examining the means of one or more populations. A t-test can be used to determine if one group deviates from a predetermined value, whether two groups diverge from one another (an independent two-sample t-test), or whether paired measurements reveal a statistically significant difference.

According to the question, we can say

With 12 technicians each, there are two techniques. To put it another way, the sample sizes are really small. Aside from that, there is no connection between the two samples. A two-sample t-test should be used as a result.

Thus, a two-sample t-test is the inferential statistical test that would be best suitable to this situation.

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The probability that they can be arranged into a group of three consecutive cards, all of the same suit, is 0.002.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.

If 3 cards are chosen at random from a standard 52-card deck, then the total number of possible outcomes is:

52C3 = 22100

For a single suit, there are 11 possible ways for three cards to be consecutive cards. So, the total number of desired outcomes is:

11 x 4 = 44

Solve for the probability.

p = 44 / 22,100 = 0.002

Therefore, the probability is 0.002.

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The fractions () function in R is used to create a fractional number from a numeric vector. It takes a numeric vector and returns a fractional number based on the elements of the vector. It is useful when working with fractional numbers, such as when working with probabilities or financial calculations.

The fractions () function in R is used to create a fractional number from a numeric vector. It takes a numeric vector as its argument, and returns a fractional number based on the elements of the vector. The fractions () function is useful when working with fractional numbers, such as when working with probabilities or financial calculations. To use the fractions () function, you must first create a numeric vector that contains the values you want to use to create a fractional number. Next, you can call the fractions () function with the vector as the argument. The fractions () function will then return a fractional number that is equal to the sum of the elements in the vector. For example, if you had the vector c(1, 2, 3), the fractions () function would return the fractional number 6/1. This fractional number can then be used in any further calculations. The fractions () function in R is an easy and convenient way to create fractional numbers from numeric vectors.

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R's fractions () function can be used to convert a numeric vector into a fractional number. It accepts a numeric vector as input and outputs a fractional number based on the vector's elements.

A fractional number can be produced from a numeric vector using R's fractions () function. It accepts a numeric vector as an argument and outputs a fractional number based on the vector's components.

When working with fractional numbers, such as when working with probability or financial computations, the fractions () function is helpful. You must first generate a numeric vector containing the numbers you intend to utilise to construct a fractional number before using the fractions () function.

The vector can then be used as a parameter when calling the fractions () function. The sum of the items in the vector will subsequently be returned by the fractions () function as a fractional number.

The fractions () function, for instance, would return the fractional number 6/1 if you had the vector c(1, 2, 3). Then, you can use this fractional value in any subsequent calculations. The fractions () function in R makes it simple and practical to convert numeric vectors to fractional numbers.

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The sample variance is the most accurate point estimate of the population variance sigmasquared.

The best point estimate of the population variance is the sample variance. This is because the sample variance is an unbiased estimator of the population variance, meaning that it is the most accurate estimate of the population variance. The sample variance is calculated by taking each individual data point, subtracting the sample mean, squaring the result, and then summing the results. The sample variance then is the sum of these squared differences divided by the number of data points minus one. This is a consistent estimator, meaning that it will always produce the same result even if the sample size is different. This is why the sample variance is the best point estimate for the population variance.

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x²= 9² + 7²

x =√81+49

x=√130

x≈11.40

Answer:

x=11.40

Step-by-step explanation:

Answer:

Step-by-step explanation:

If we complete the shape it will be square of side of 8 miles.

The added part is a rectangle of 5×2 miles.

The figure will have the area of their difference:

The line segment joining the points (1/2, -2) and (1, 1) cuts the line 3x + 4y = 7 at the point of intersection of the line defined by the points and the line 3x + 4y = 7.

To find the ratio of the line segment at this point of intersection, we first need to find the point of intersection. We can do this by solving the system of equations defined by the line 3x + 4y = 7 and the line defined by the points (1/2, -2) and (1, 1).

Once we have the point of intersection (x,y), we can use the following formula to find the ratio:

(x - 1/2) : (y + 2) = (x2 - x1) : (y2 - y1) = (x - x1) : (y - y1)

Where (x1, y1) and (x2, y2) are the coordinates of the two points defining the line segment

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The value of a makes quadrilateral tuvw a parallelogram is 1.

What is the quadrilateral bisect?

If a quadrilateral is a parallelogram, then its diagonals bisect each other. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

It should be noted that a quadrilateral simply means a four sides polygon that has four edges and four vertices, when the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

We have,

tx=13a and vx=a+12,

To find the value of a that makes quadrilateral tuvw a parallelogram.

As the diagonal of quadrilateral bisects each other:

tx = vx

13a = a+12,

13a - a  = 12

a  = 12/12

a = 1,

Hence, the value of a makes quadrilateral tuvw a parallelogram is 1.

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The Formula for finding the surface area of hexagonal prism is written as [tex]6sh + 3\sqrt{3} s^{2}[/tex] .

What is a Hexagonal Prism ?

A hexagonal prism is a type of prism which contains a hexagonal base and top .

(i) The hexagonal prism contains two hexagons where one is base and other on top and it has 6 rectangles that connects the hexagonal faces .

(ii) The hexagonal prism has 12 vertices , 8 faces and 18 edges .

Let the side of the hexagonal base of the hexagonal prism be = s ;

let height of hexagonal prism be denoted by "h" ;

So , Surface Area of hexagonal prism  =  [tex]6sh + 3\sqrt{3} s^{2}[/tex] .

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Displacement is calculated as the shortest distance between starting and final point which prefers a straight-line path over curved paths.

Displacement is the distance between two different positions of an object in m motion. So, it depends on the initial position and its final position. Also, displacement is the minimum distance between the starting and final positions.

Suppose a body is moving in two different directions x and y then the Resultant Displacement will be S=√x²+y²

Example 1: The path distance from the garden to a school is 5 m west and then 4 m south. A builder wants to build a short-distance path for it. Find the displacement length of the shortest path.

Solution: Distance to the west x = 5 m

Distance to the south y = 4 m.

Displacement is given by S=√x²+y²

s = 6.403 m.

The builder can build a path for a displacement length of 6.7 m.

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The formula to solve the displacement is written as Δx  = xf − xi

The term displacement is defined as  the change in the position of any point or object. It has a direction and magnitude, so it is a vector quantity and it is shown with an arrow that points from the starting position to the final position.

In order to find the displacement by determining the object’s initial and final position.

Therefore, the displacement formula is written as,

=> Δx  = xf − xi

Here xf refers the final position,

And the variable xi is the initial position, and

Then the term Δx is the change in the position of the object.

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