entral high school is competing against northern high school in a backgammon match. each school has $3$ players, and the contest rules require that each player play $2$ games against each of the other school's players. the match takes place in $6$ rounds, with $3$ games played simultaneously in each round. in how many different ways can the match be scheduled?

Answer:

Therefore, the length of the hypotenuse of the 45°-45°-90° triangle is 32 centimeters.

Step-by-step explanation:

In a 45°-45°-90° triangle, the two legs are congruent, which means that each leg is equal to the length of the hypotenuse divided by √2.

Let h be the length of the hypotenuse. Then we have:

leg = h/√2

Given that one of the legs is 8√8 centimeters, we can substitute this value into the equation above to solve for h:

8√8 = h/√2

Multiplying both sides by √2, we get:

8√8 x √2 = h

Simplifying, we get:

h = 8√16

h = 8 x 4

h = 32

Therefore, the length of the hypotenuse of the 45°-45°-90° triangle is 32 centimeters.

Answer:

x = 6.464 and x = -0.464

Step-by-step explanation:

3/x + 6 = x

3 + 6x/x = x

3 + 6x = x²

x² - 6x - 3 = 0

x = 6 ± √36 - 4x - 3/2 = 6 ± √36 + 12/2

x = 6 ± √48/2 = 6 ± 4√3/2 = 3 ± 2√3

So x = 3 + 2√3 and 3 - 2√3

x = 6.464 and x = -0.464

The scale drawing of the mural would be 594.36 cm wide and 1097.28 cm tall.

A scale drawing is a drawing that shows an object or area at a scale that differs from the real size of the object or area. A scale, which is a ratio comparing the size of the drawing to the size of the actual item or location, is used to make scale drawings. A scale of 1:50, for instance, indicates that one unit on the design corresponds to fifty in real life.

In several disciplines, including architecture, engineering, and design, scale drawings are employed in real-world situations. Scale drawings are used by architects to construct building floor plans, elevations, and sections. Scale drawings are used by engineers to develop mechanical systems and machinery.

Given that the dimensions of the mural is 13 feet by 24 feet.

Converting into cm we have:

width = 13 feet * 30.48 cm/foot = 396.24 cm

height = 24 feet * 30.48 cm/foot = 731.52 cm

Now using the scale we have:

3cm : 2ft = x cm : 396.24 cm

Using cross multiplication we have:

2ft * x cm = 3cm * 396.24 cm

x = (3cm * 396.24 cm) / 2ft = 594.36 cm

For the height, we have:

3cm : 2ft = y cm : 731.52 cm

2ft * y cm = 3cm * 731.52 cm

y = (3cm * 731.52 cm) / 2ft = 1097.28 cm

Hence, the scale drawing of the mural would be 594.36 cm wide and 1097.28 cm tall.

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Answer: -1  1/3 (this is one and a third) or -4/3 (improper fraction)

Step-by-step explanation:

Solve for y by simplifying both sides of the equation then isolate the variable (y).

The sequence converges to ln 2 / ln 6 as n approaches infinity.

How to find limit?

To determine whether the sequence converges or diverges, we need to take the limit of the sequence as n approaches infinity.

a_n = (ln 2n) / (ln 6n)

We can simplify this expression by applying logarithm rules:

a_n = (ln 2n) / (ln 6n) = (ln 2 + ln n) / (ln 6 + ln n)

Now we can use the fact that for any constant a>1, ln n is dominated by ln a as n approaches infinity, i.e., ln n / ln a approaches infinity as n approaches infinity.

Thus, as n approaches infinity, we have:

a_n = (ln 2 + ln n) / (ln 6 + ln n) ≈ ln 2 / ln 6

Therefore, the sequence converges to ln 2 / ln 6 as n approaches infinity.

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The value of x that makes the expression 3√(53x) equivalent to 21√53 is 49.

In mathematics, an expression is a combination of numbers, variables, and operations, typically written using mathematical symbols and/or mathematical notation. An expression can be a single number, variable, or combination of the two, or it can be a more complex combination of numbers, variables, and operators such as addition, subtraction, multiplication, division, exponentiation, or root extraction. Expressions can be used to represent a wide variety of mathematical concepts and relationships, such as equations, inequalities, functions, and geometric figures. They are an important part of mathematical language and are used to communicate mathematical ideas and concepts.

In mathematics, an equation is a statement that shows the equality of two expressions. It typically involves one or more variables and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or root extraction. The expressions on both sides of the equation are separated by an equal sign (=), indicating that they have the same value. The purpose of an equation is to find the value of the variable(s) that makes the equation true. Solving an equation involves manipulating the expressions on both sides of the equation to isolate the variable and determine its value. Equations are used in a wide variety of mathematical applications, such as solving problems in algebra, geometry, calculus, and physics.

We can start by equating the expression 3√(53x) to 21√53 and then solving for x.

3√(53x) = 21√53

Dividing both sides by 3√53, we get:

√x = 7

Squaring both sides of the equation, we get:

x = 49

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Answer: You can comment if this is wrong but I don't know what an area model is entirely I might just I don't remember

|\ |\

| \ | \

|  \|  \

|___\|___\

1/4  1/5

Step-by-step explanation:

1. Draw a rectangular area model with two sections.

2. Label the left section with 1/4 and the right section with 1/5.

3. Divide the left section into 4 equal parts by drawing lines horizontally and vertically

4. Divide the right section into 5 equal parts by drawing lines horizontally and vertically.

5. Count the number of parts in the left section (4 parts) and the number of parts in the right section (5 parts).

6. Multiply the parts in the left section by the parts in the right section, which gives 4 x 5 =20.

7. The answer is 20/4 = 5.

Geometric growth is a type of exponential growth where a quantity or value increases at a fixed percentage rate over a certain period of time.

Geometric growth is a type of exponential growth where a quantity or value increases at a fixed percentage rate over a certain period of time. This means that the growth rate is proportional to the current size or value of the quantity, resulting in a continuously increasing growth rate.

Geometric growth is commonly observed in natural and social systems, such as population growth, compound interest, and the spread of infectious diseases. It is represented mathematically by an exponential function, where the base of the exponent is greater than one, indicating an increasing rate of growth over time.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

What is geometric growth ?

Answer:

12.9cm

Step-by-step explanation:

Trapeziums QRVW and QRSP are similar because they share the same side 5.5 cm and their angles are corresponding to each other.

We can express the ratios of sides in both trapeziums to find WV.

Since side 5.5 is the same in each trapezium,

[tex]\frac{5.5}{WV}=\frac{5.5}{12.9}[/tex]

Thus, WV = 12.9cm

Hope this helps:)

the probability that 50 or more requests are made for pop songs is  0.0967, or about 9.67%.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

We can use the binomial distribution to model this situation, where the number of trials is 120 (the number of people at the party), and the probability of success (making a request for a pop song) is 0.37. Let X be the number of requests for pop songs. Then:

The mean of X is μ = np = 120 x 0.37 = 44.4

The standard deviation of X is σ = sqrt(np(1-p)) = sqrt(120 x 0.37 x 0.63) = 4.32

To find the probability that 50 or more requests are made for pop songs, we can use the normal approximation to the binomial distribution, which applies when np >= 10 and n(1-p) >= 10.

Let Z be a standard normal random variable, then:

P(X >= 50) = P((X - μ)/σ >= (50 - μ)/σ)

= P(Z >= (50 - 44.4)/4.32)

= P(Z >= 1.2963)

= 1 - P(Z < 1.2963)

= 1 - 0.9033

= 0.0967

Therefore, the probability that 50 or more requests are made for pop songs is approximately 0.0967, or about 9.67%.

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Answer: ∠1 and ∠2 are supplementary angles.

Step-by-step explanation:

Complementary angles are two angles that add up to 90 degrees.

Supplementary angles are angles that add up to 180 degrees.

∠1 + ∠2 = 180 degrees, so it is a supplementary angle.

In order to be within a 1% margin of error at a 95% confidence level, the candidate would need to survey 9604 people in the community. The size of the sample is 9604.

We have a political candidate who wants a 1% margin of error at a 95% confidence level. To find the size of the sample, we use the formula given below;

n = [ Z (α/2) / E ]²

Where,

n = the sample size required

Z (α/2) = the value obtained from the standard normal distribution for the given level of confidence

E = the margin of error

Here, α = 1 - 0.95 = 0.05

Z (α/2) = Z (0.025), is the z-value corresponding to 0.025 in the normal distribution table. It is found to be 1.96.

Now, substituting the given values in the formula,

n = (1.96² * 0.5 * 0.5) / 0.01² ⇒ 9604

Hence, the sample size required for the poll is 9604.

However, this is not feasible, as it would be very expensive and time-consuming. Therefore, we will round the answer to the nearest whole number as we are looking for a practical solution. Thus, the candidate would need to survey 9604 people in the community (rounded to the nearest whole number).

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Answer:

The equation for the width is:

1056 = (2w+4) * w

And the solution is:

Width: 22 inches

Length: 48 inches

Step-by-step explanation:

Area of a rectangle = length * width

1056 = h * w   Eq. 1

h = 2w + 4         Eq. 2

h = length

w = width

Replacing Eq. 2 in Eq. 1:

1056 = (2w+4) * w

1056 = 2w*w + 4*w

1056 = 2w² + 4w

2w² + 4w - 1056 = 0

w = {-4±√((4²)-(4*2*-1056))} / (2*2)

w = {-4±√(16 + 8448)} / 4

w = {-4±√8464} / 4

w = {-4±92} / 4

Is a geometric figure, therefore, only the positive value will be obtained

w = {-4+92}/4

w = {88} / 4

w = 22

From Eq. 2:

h = 2w+4

h = 2*22+4

h = 44+4

h = 48

Check:

From Eq. 2

1056 = h * w

1056 = 48 * 22

Answer:

a. 4

b. -2

c. 0,5

it js wants u to say what the number line represents

Step-by-step explanation:

You paid the total amount of $1257 at the end of 5 years.

Let us assume that c represents the cost per month.

So, c = $20.95

and let t represents the total number of months.

We know that there are 12 months in a year.

so, the number of months in 5 years would be:

12 × 5 = 60

So, t = 60 months

Using unitary method the total amount paid at the end of five years :

s = c × t

s = 20.95 × 60

s = $1257

Therefore, the total amount is $1257

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Answer:

Step-by-step explanation:

y = –5x + 10

y = –3x + 2

–5x + 10= –3x + 2

2x= 8

x=4

y= -5(4)+10

y= -20+10

y=(-10)

Answer:

Step-by-step explanation:

[tex]-5x + 10= -3x + 2[/tex]        (since both equal y)

            [tex]10=2x+2[/tex]          ([tex]+5x[/tex] both sides)

             [tex]8=2x[/tex]                 (-2 both sides)

             [tex]x=4[/tex]                   (÷2 both sides)

Sub [tex]x=4[/tex] to find y:

      [tex]y=-5(4)+10=-10[/tex]

Solution: x=4, y= -10

The set notation that represents the shaded portion in the given Venn-diagram​ is: A ∪ B − (A ∩ B).

The union of the sets A and B simply denotes everything which is in either A or B, as represented by the shaded region in the given venn diagram. The intersection of two sets is that which is in both sets, as represented by the unshaded region in the following Venn diagram

The union of A and B is the entirety of all that is in either A or B, as represented by the shaded area inside the given venn diagram.

The intersection of  sets is  in each sets, as represented via way of means of the magenta shaded area withinside the following Venn diagram.

Thus, it is A ∪ B − (A ∩ B).

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The length of PQ in triangle PQR is 110.

What are similar triangles ?

Similar triangles are two triangles that have the same shape but may differ in size. In other words, their corresponding angles are equal, and their corresponding sides are in proportion. This means that if you were to resize one triangle by a constant factor, the resulting triangle would still be similar to the original triangle.

For example, if you take a triangle and multiply all its side lengths by a factor of 2, you will end up with a triangle that is twice as large but still similar to the original triangle.

According to the question:
Since the triangles XYZ and PQR are similar, their corresponding sides are in proportion. That is:

XY/PQ = XZ/PR = YZ/QR

We can use this property to find the length of the missing side QP.

First, let's find the ratio of corresponding sides:

XY/PQ = XZ/PR

48/PQ = 55/110

Simplifying this equation, we get:

PQ = 48*110/55 = 96

So, PQ is 96.

Alternatively, we could use the other pair of corresponding sides:

XZ/PR = YZ/QR

55/110 = 73/146

Simplifying this equation, we get:

QP = 55*146/73 = 110

So, QP is also 110.

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An equation is formed of two equal expressions. The maximum height reached by a rocket, to the nearest tenth of a foot is 1542.82 feet.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

To find the maximum height through which the rocket will reach, we need to differentiate the given function, therefore, we can write,

y=-16x²+173x+140

dy/dx = -16(2x)+173

Substitute the value of dy/dx as 0, to get the value of x,

0 = -32x + 173

173 = 32x

x =5.406

Substitute the value of x in the equation to get the maximum height,

y=-16x²+173x+140

y=-16(5.406²) +173(5.406) +140

y= 467.59 + 935.23 + 140

= 1542.82 feet.

Hence, the maximum height reached by the rocket, to the nearest tenth of a foot is 1542.82 feet.

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Answer:

[tex]\frac{4}{3}[/tex]

Step-by-step explanation:

You consumed approximately 69 calories from the 9 cashews you ate.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

A nutrition label typically provides information about the nutrient content of a food item per serving size. In this case, the label states that 28 grams of dry roasted cashews contain 161 calories.

To determine the number of calories in a smaller portion of cashews, we need to use a proportion or ratio.

We start by calculating the number of calories per gram of cashews by dividing the total number of calories by the total weight of cashews:

161 calories / 28 grams = 5.75 calories per gram of cashews

This means that each gram of cashews contains about 5.75 calories.

Next, we need to figure out how many grams of cashews you ate. The question states that you ate 9 cashews, which weighed a total of 12 grams.

To find out the number of calories you consumed, we simply need to multiply the weight of the cashews (12 grams) by the number of calories per gram (5.75):

5.75 calories per gram x 12 grams = 69 calories

Therefore, you consumed approximately 69 calories from the 9 cashews you ate.

Complete question is:

A nutrition label shows that there are 161 calories in 28 grams of dry roasted cashews. You eat 9 cashews totaling 12 grams. How many calories did you consume?

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Answer:

To subtract two-digit numbers, use column form. Subtract one column at a time, starting with the Ones column. We regroup, or borrow. To regroup, take 1 from the Tens column and add 10 to the Ones column.

Step-by-step explanation:

The probability that between 6 and 9 (both inclusive) bulbs from the sample are defective is 0.5362

This is a binomial distribution problem, where the probability of success (defective bulb) is 0.2 and the probability of failure (non-defective bulb) is 0.8. We need to find the probability that between 6 and 9 (both inclusive) bulbs out of 16 bulbs in the sample are defective.

We can use the binomial probability formula to solve this problem

P(6 ≤ X ≤ 9) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)

where X is the number of defective bulbs in the sample.

P(X = k) = (n choose k) × p^k × (1-p)^(n-k)

where n is the sample size, k is the number of defective bulbs, p is the probability of a defective bulb, and (n choose k) is the binomial coefficient.

Using this formula, we can calculate the probability for each value of X and sum them up to get the probability for the range 6 to 9.

P(X = 6) = (16 choose 6) × 0.2^6 × 0.8^10 = 0.0881

P(X = 7) = (16 choose 7) × 0.2^7 × 0.8^9 = 0.1409

P(X = 8) = (16 choose 8) × 0.2^8 × 0.8^8 = 0.1606

P(X = 9) = (16 choose 9) × 0.2^9 × 0.8^7 = 0.1462

Therefore, the probability that between 6 and 9 (both inclusive) bulbs from the sample are defective is

P(6 ≤ X ≤ 9) = 0.0881 + 0.1409 + 0.1606 + 0.1462 = 0.5362

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Equation one can be solved by additive property two by subtractive property.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

7=m+1.2

m=7-1.2

6.8

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Explanation:

2 freshmen + 3 sophomores + 2 juniors + 2 seniors = 9 students total.

Let's consider the cases where we have the same number of juniors and seniors. We'll then take the complement of this to get the final answer.

-----------

Case A: There is 1 junior and 1 senior

There are 2 ways to pick a junior and 2 ways to pick a senior. That's 2*2 = 4 ways so far.

Then we have 9-4 = 5 students left to pick from (i.e. 2 freshmen+3 sophomores = 5 students left) and we have 5-2 = 3 seats to fill. Order doesn't matter on the committee since each person has equal rank.

We use the nCr combination formula.

n = 5 students

r = 3 seats to fill

n C r = (n!)/(r!(n-r)!)

5 C 3 = (5!)/(3!*(5-3)!)

5 C 3 = (5!)/(3!*2!)

5 C 3 = (5*4*3!)/(3!*2!)

5 C 3 = (5*4)/(2!)

5 C 3 = (5*4)/(2*1)

5 C 3 = (20)/(2)

5 C 3 = 10

There are 10 ways to fill the remaining 3 seats when we pick from the freshmen and sophomores only.

To recap everything so far:

Therefore, we have 4*10 = 40 different combinations possible for case A. We'll refer to this value later.

-----------

Case B: We pick 2 juniors and 2 seniors

Since there 2 juniors to pick from, and 2 junior seats to fill, there's only 1 way to do this. Likewise, there's only 1 way to pick the 2 seniors to fill the 2 seats.

In total so far there is 1*1 = 1 way to pick the 2 juniors and 2 seniors in any order you like.

Then we have 9-4 = 5 students left that are freshmen or sophomores. This is the number of choices we have for the final 5th seat.

We have 1*5 = 5 ways to have case B happen.

----------

Summary so far:

There are 45 ways to have the same number of juniors as seniors (either 1 of each or 2 of each).

Now we must calculate the number of total combinations possible on this committee. We'll turn to the nCr formula again.

n = 9 students

r = 5 seats

n C r = (n!)/(r!(n-r)!)

9 C 5 = (9!)/(5!*(9-5)!)

9 C 5 = (9!)/(5!*4!)

9 C 5 = (9*8*7*6*5!)/(5!*4!)

9 C 5 = (9*8*7*6)/(4!)

9 C 5 = (9*8*7*6)/(4*3*2*1)

9 C 5 = (3024)/(24)

9 C 5 = 126

There are 126 different five-person committees possible.

Of those 126 committees, 45 of them consist of cases where we have the same number of juniors and seniors.

That must mean there are 126-45 = 81 combinations where we do not have the same number of juniors and seniors. This is where the concept of "complement" comes in.

the orthogonal projection of a point P onto a line L can be expressed as: projection  L(P) = ((P . u) ×u)·

Orthogonal projection is a mathematical operation that involves projecting a vector or point onto another vector or line in a way that the projection is perpendicular (or orthogonal) to the vector or line.

In mathematical notation, the orthogonal projection of a point P onto a line L can be expressed as:

projection L(P) = ((P . u) × u)

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Answer: B

Step-by-step explanation: