Six cars pull up to a red light, one at a time. At the light, there are three lanes, one left-turn lane, one straight-going lane, and one right-turn lane. How many ways can the cars stack up so that all three lanes are occupied

Solutions of a system of  an equations are given with the  values of the variables which  make all the equations true in which a solution of a system of given two linear equations is represented in  an ordered pair (x, y) as explained with example below:

An example of a system of two linear equations in an ordered pair , in order  to show the two equations that  are arranged  together to form a system of equations in an linear form .

let  , 2x + y = 7,

x- 2y = 6

A linear equation which consists of  two variables, as  2x + y = 7, has an infinite number of solutions. in which the  graph of a equation  is a line. we know that every point on the line is a required solution to the equation and every solution of an  equation is a point on the line.

To solve a system of two linear equations in an ordered pair , we want to find the values to particular  variables that are solutions to both  linear equations. In other words, we are expecting  for the ordered pairs (x, y) that make both equations valid . These type of equations are known as  solutions to a system of equations.

hence , the solutions of a system of equations are the values of the variables that make all the valid and obeyed equations are  true.  and solution of a system of two linear equations is represented always in an  ordered pair (x, y) .

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The length and width of the rectangle will be 2 and 8x + 12

Area of rectangle = 16x + 24.

A rectangle is a four-sided geometric shape having opposite sides that are equal in length and four right angles. The length and width of the rectangle are its opposing sides.

A rectangle's area is found by multiplying its length and width together, so:

Area = length x width

Calculating the length and width of the rectangle -

Factoring out 2 from the equation -

Therefore -

2 (8x+12)

Since, the area is the length times width, thus -

2 x (8x+12)

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1. The area of two concentric circles with radii 28 cm and 18 cm is 460π cm^2.

2. If the perimeter and the area of the circle are numerically equal then find the radius of the circle is 2 units.

What are concentric circles?

Concentric circles are those that share a common centre but have differing radii. It is described as two or more circles with the same centre, in other words.

The radii of two concentric circles are 28 cm and 18 cm.

The bigger circle has a radius of r1=28 cm and the smaller circle has the radius of r2=18 cm.

Area of two concentric circles is -

A = π[(r1)^2-(r2)^2]

A = π[(28)^2-(18)^2]

A = π[(28+18)(28-18)]

A = π[46 × 10]

A = 460π cm^2

Therefore, the area of concentric circle is 460π cm^2.

The formula for perimeter of the circle is 2πr, and the formula for the area of the circle is πr^2, where r is the radius of the circle.

Now, according to the data given the perimeter and area of the two circles are equal.

So, the equation will be 2πr = πr^2.

2πr = πr^2

2π = πr

r = 2 units

Therefore, the radius is 2 units.

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1. If radii of two concentric circle are 28 cm and 18 cm respectively. Find the area of the concentric circles.

2. If the perimeter and the area of the circle are numerically equal then find the radius of the circle​.

Answer:

It should be 6 because 6x6 is 36

Answer:

Step-by-step explanation:

fractions are division so just divide 36 by 6 and you will get 6 which is your answer

36/6 =

36 : 6 =

6

Therefore , the solution of the given question triangle comes out to be

triangle PQR to triangle ZXY is 3/2

You can link any three points in a plane to form triangles, which have three sides and three angles. They were among of the first geometric forms to be examined. Since triangles may be divided into any polygon, regardless of whether it has four, five, six, or n sides, they are very significant.

Here,

Consider PR and ZY as a point of comparison.

PR = 5

ZY = 14

Suppose the scaling factor is r and that

5 * r = 14

r = 14 / 5

r = 14/5

examining other sides

RQ to PR

right 5 * 12/3 = 20

To YX, QP

Correct answer is 4 * 9/3 = 12.

Thus,

triangle PQR to triangle ZXY

Therefore , Triangle PQR to Triangle ZXY equals 3/2, which is how the given question's solution is determined.

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The rule for the given set of data is y = 3x - 1.

The relationship between dependent and independent variables, expressed as an equation, is referred to as a function rule. In order to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, one must follow a specific function rule.

A function rule can be defined as the procedure that transforms an input value into an output in plain English.

Lets put two of the points in slope formula

y - y₁ = m(x - x₁)

29 - (-13) = m(10 - ( -4))

42 = m14

m = 42/14

m = 3

Now lets make the equation

y - 29 = m(x - 10)

y = 3x - 30 + 29

y = 3x - 1

Thus, the rule for the given set of data is y = 3x - 1.

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The area of bedroom rug is 15 square feet. the longer side measures 5 feet. his living room rug is twice as long and twice as wide as the bedroom rug.

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Answer:

I don't know I am sorry bro

A statement which correctly describes the solution set of the given inequality include the following: C. all rational-number values of n that are at least 0.5.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 12, 0.5, √16, etc.

Next, we would translate the word problem into algebraic inequality and then solve for the value of n as follows;

5n + 1.5 ≥ 4

Subtracting 1.5 from both sides of the algebraic inequality, we have:

5n + 1.5 - 1.5 ≥ 4 - 1.5

5n ≥ 2.5

Dividing both sides of the algebraic inequality y 5, we have:

n ≥ 2.5/5

n ≥ 0.5

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The independent variable is h (the number of hours Neil works) and the dependent variable is B (the amount of Neil's bonus).

In this scenario, the amount of Neil's bonus (B) is dependent on the number of hours he works (h). The number of hours he works is the input or independent variable, while the amount of bonus he receives is the output or dependent variable. It can be said that the number of hours he works is the cause and the amount of bonus is the effect.

The equation is B = f(h) where f is the function that relates the two variables.

Thus, the independent variable is h (the number of hours Neil works) and the dependent variable is B (the amount of Neil's bonus).

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Complete Question is-

Neil works as a consultant at a software company and the amount of his annual bonus is based on the number of hours he works, which variable is independent and which is dependent? With B as the amount of Neil's bonus, and h as the number of hours Neil works.

The values of the variables are n = -17/31 and m = 23/93

From the information given, we have the equations;

To solve the simultaneous equation, we have to take the following steps

Make 'm' the subject from equation 1

9m = 1 + 4n

Divide both sides by 9, we get;

m = 1 -4n/9

Substitute the value into equation (2), we have;

11(1 -4n/9) - 2n = 5

expand the bracket

11 - 44n/9 - 2n = 5

find the LCM

11 - 44n - 18n  /9 = 5

cross multiply

11- 62n = 45

collect like terms

-62n = 45 - 11

-62n = 34

Make 'n' th subject

n = -34/62

n = - 17/31

Substitute the value into equation (3)

m = 1 - 4(-17/31)/9

m = 1+68/31 ÷9

m = 69/31 × 1/9

m = 69/279

m = 23/93

Hence, the values are n = -17/31 and m = 23/93

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Statement 1 is correct and Statement 2 is not correct.

As A, B and C represent distinct non-zero digits

For least value of x

Let A=1, B=2, C=3

The possible numbers that can be formed using 1,2,3 are 6 {using permutations}

123, 132, 213, 312, 231, 321

x is the sum of all possible 3-digit numbers formed by A, B and C without repetition so

x= 123+ 132+ 213+ 312+ 231+ 321

x=1332

So statement 1 is correct

statement 2 cannot be correct as least value of x is  4-digit so  greatest value of x cannot be a three digit number.

The 4-digit least value of x is 1332 so Statement 1 is correct and Statement cannot be correct.

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The required value of x is 17 for the given equation 11 = x - 6.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

11 = x - 6

We can determine the value of x by adding 6 to both sides of the equation.

As per the question, we have

⇒ 11 = x - 6

⇒ 11 + 6 = x - 6 + 6

⇒ x = 11 + 6

Apply the addition operation, and we get

⇒ x = 17

Therefore, the required value of x is 17.

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Answer:

Any ordered pair #(x, y)# that satisfies #x>=6+4y#Or, in set notation, #Solution={(x, y)|x>=6+4y}#Explanation:Now, there is a little problem here - it is that you never specified which ordered pair needs to be evaluated to satisfy the condition #0.5x-2y>=3# Allow me to explain.Below is a graph of the inequality of your question:graph{0.5x-2y>=3 [-10, 10, -5, 5]}To answer which point is in the solution set, well the answer is that any point that is on or within the shaded area is part of the solution set.

Step-by-step explanation:

The number of pecans in each bucket will be 20 and 35.

From the information, there are 55 pecans are put in 2 buckets where one has 15 more than the other. An expression show the relationship between the variables.

In this case, 55 pecans put them in 2 buckets where one has 15 more than the other.

This will be:

x + x + 15 = 55

2x + 15 = 55.

Collect the like terms

2x = 55 - 15

2x = 40

Divide

x = 20

The other number will be:

x + 15.

= 20 + 15

= 35

The numbers are 20 and 35.

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55 pecans are put in 2 buckets where one has 15 more than the other. What is the amount in each bucket.

The volume of water in the fish tank for the given time value is 0, 5, 7, 9, 11, and 13 liters.

The equation V = 3 + 2t expresses a time function, which represents the volume of fish tank as a function of time. It means that after t time, volume V is given by the equation. In the given table. t = 0,1,2,3,4,5. Hence, the volume can be determined by substituting the value of t in the equation.

When t = 0

V = 3 + 2(0) = 3 liter

When t = 1

V = 3 + 2(1) = 5 liter

When t = 2

V = 3 + 2(2) = 7 liter

When t = 3

V = 3 + 2(3) = 9 liter

When t = 4

V = 3 + 2(4) = 11 liter

When t = 5

V = 3 + 2(5) = 13 liter

Note: The question is incomplete. The complete question probably is: A 40-liter fish tank is being filled with a faucet at a constant rate of 2 liters per minute. Before the faucet is turned on, the fish tank has a volume of 3 liters. The volume of water V in the fish tank is a function of time t. Time is measured in minutes and volume of water is measured in liters. Use the equation V = 3 + 2t to complete the function table.

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The angles of a 5-12-13 triangle are A = 81.19°, B = 48.76°, and C = 9.98°.

The angles of a triangle are determined by the triangle's side lengths. This is known as the Law of Cosines. To determine the angles of a 5-12-13 triangle, we can use the Law of Cosines formula:

Cos(A) = (b² + c² - a²) / 2bc

In this equation, A is the angle opposite side a, b is the angle opposite side b, and c is the angle opposite side c. In a 5-12-13 triangle, a = 5, b = 12, and c = 13.

Using the Law of Cosines formula, we can calculate the angle A:

Cos(A) = (12² + 13² - 5²) / 2(12)(13)

Cos(A) = (144 + 169 - 25) / 156

Cos(A) = 278 / 156

Cos(A) ≈ 1.78

Using a calculator, we can calculate the angle A:

A = cos-1 (1.78)

A ≈ 81.19°

Using the same Law of Cosines formula, we can calculate the other two angles of the triangle:

Cos(B) = (a² + c² - b²) / 2ac

Cos(B) = (5² + 13² - 12²) / 2(5)(13)

Cos(B) = (25 + 169 - 144) / 65

Cos(B) = 50 / 65

Cos(B) ≈ 0.77

Using a calculator, we can calculate the angle B:

B = cos-1 (0.77)

B ≈ 48.76°

We can also calculate the angle C:

Cos(C) = (a² + b² - c²) / 2ab

Cos(C) = (5² + 12² - 13²) / 2(5)(12)

Cos(C) = (25 + 144 - 169) / 60

Cos(C) = 10 / 60

Cos(C) ≈ 0.17

Using a calculator, we can calculate the angle C:

C = cos-1 (0.17)

C ≈ 9.98°

Therefore, the angles of a 5-12-13 triangle are A = 81.19°, B = 48.76°, and C = 9.98°.

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The percentage of increase in the number of points is 16 %

What Does Percent Mean?

A ratio or figure stated as a fraction of 100 is called a percentage. The percent marker is frequently used to indicate it,%

given the data,

The basketball team's total point total was 75.

The basketball team's enhanced point total was 87.

The difference between the basketball team's total points scored and its increased points are the increase in points.

The increase in points = 87 - 75

                                     = 12 points

So, the percentage increase in points = ( increase in points/number of points scored by the basketball team ) x 100

The percentage increase in points = ( 12 / 75 ) x 100

                                                         = 0.16 x 100

                                                         = 16 %

Therefore, the percentage increase is 16 %

Hence, the percentage of increase in the number of points is 16 %

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The perimeter of a shape with 4 sides is equal to the sum of its sides multiplied by itself, which in this case is 4 multiplied by 4, resulting in a perimeter of 16.

Step 1: Calculate the length of each side by multiplying 4 by 4.

Step 2: Add the lengths of each side together to get the perimeter.

Step 3: The perimeter of the shape with 4 sides is equal to 16.

The perimeter of a shape is the sum of the lengths of its sides. To calculate the perimeter of a shape with 4 sides, you need to find the length of each side. To do this, you can multiply the length of one side by itself. For example, if the length of one side is 4, the length of each side would be 4 multiplied by 4, which is 16. Therefore, the perimeter of a shape with 4 sides is equal to 16. To calculate the perimeter of a different shape with an unknown number of sides, you can add up the lengths of each side to get the total perimeter. This is a useful way to measure the size of a shape and can be used to calculate the area of a shape by dividing the perimeter by the number of sides.

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Answer: -37

Step-by-step explanation: -11-26

Answer:

  (x, {C and/or R}) = (5, 380)

Step-by-step explanation:

You want the break-even point when cost (C) and revenue (R) are given by ...

Profit is the difference between revenue and cost. The break-even point is the point at which profit is zero:

  P = R -C

  0 = 76x -(36x +200)

  0 = 40x -200 . . . . simplify

  0 = x -5 . . . . . . . . . divide by 40

  x = 5 . . . . . . . . . add 5

The break-even point is at x=5. Revenue and cost are both 380 at that point.

If you prefer to look at these values in a table, you can consider ...

  [tex]\displaystyle \begin{array}{ccc}x&C&R\\\cline{1-3}\vphantom{\^B}3&308&228\\4&344&304\\5&380&380\\6&416&456\end{array}[/tex]

We notice that cost and revenue are the same for x=5. They are both 380 for that value of x.

Another way to find the break-even point is to use a graph to plot cost and revenue on the same vertical axis. The point at which the lines cross is the break-even point. The break-even point coordinates are (5, 380).

Answer:

business plan proposal

Answer:

we have to make the denominator of both the fraction same so that we can compare.

We have to multiplybboth nominator and denominator by 6.then,

7×6/4×6=28/16

Now, comparing 28/6 and 28/6 we get to know that both the fraction are proportional.i.e.28/16=7/4

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The values of mean ,median, range and inter quartile range could be 23,23.5,22,14 respectively.

What is mean ?

mean can be defined as the ratio of sum of the total observations and the number of total observations.

Given set of data

11,13,17,20,22,25,27,31,31,33

Mean  =  11 +13+17+20+22+25+27+31+31+33/10

= 230/10

 =23

Hence  mean = 23

The (n/2)th term= the 5th term

                       =22

The  (n/2+1) term = The  6th term

= 25

The median = 22+25/2

                  =23.5

Range = Highest term - lowest term

          =33- 11

           =22

Here lower half {11,13,17,20,22}

The middle number of lower half is first quartile.

Q₁ = 17

And lower half is{25,27,31,31,33}

The middle number of upper half is third quartile.

Q₃=31

Interquartile Range =Q₃-Q₁

                               =31-17

                                =14

Hence, The values of mean ,median, range and inter quartile range could be 23,23.5,22,14 respectively.

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Answer:

Step-by-step explanation:

Find the prime factorization of 144

144 = 2 × 2 × 2 × 2 × 3 × 3

Find the prime factorization of 405

405 = 3 × 3 × 3 × 3 × 5

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 3 × 3

Answer = 9

Therefore, the measures of those two angles are 33° and 24°.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle."

Geometry is a branch of mathematics that studies the sizes, shapes, positions, angles, and dimensions of things.

We know, the sum of the angles in a triangle is always 180 degrees.

126 + x + y = 180

x + y = 54

Given that the two angles are in a ratio of 11:16, the proportion:

x/y = 11/16

Solving for x and y, we get:

x = 11y/16

We substitute this equation into the equation x + y = 54 and we get:

11y/16 + y = 54

Solving for y we get y = 24. Then we can use the proportion to find x:

x = 11 * 24 / 16 = 33.

So the two angles are 33° and 24°.

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Let x be the coefficient of y^2 in the expression 2x^2y+15xy^2-7y. So x=0.

What is co-efficient?

A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves.

Write an example of co-efficient.

As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.

The given algebraic expression is 2yx^2+15xy^2-7y.

The terms are xy^2, yx^2 any y^2

So the co-efficient of y^2 is 0

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On solving the provided question, we can say that Probability ( At least one of the students is a senior) = 0.4632 approx

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

P(All four players are senior) = 0.00033 approx

P(There is one each: freshman, sophomore, junior and senior) = 0.0944 approx.

P(There are 2 sophomores and 2 freshman) = 0.0568  approx

P( At least one of the students is a senior) = 0.4632 approx

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The required dimensions are solved using linear pair and vertical angle to get the result as

The value of x and y is calculated using linear pair theorem, the theorem implies that

solving for x

(3x + 5) + (x + 15) = 180

3x + x + 5 + 15 = 180

collecting like terms

4x = 180 - 15 - 5

4x = 160

x = 40

solving for y

(y + 20) + (4y - 15) = 180

y + 4y + 20 - 15 = 180

collecting like terms

5y = 180 - 20 + 15

5y = 175

y = 35

Angle AED

= 3x + 5

= 3 * 40 + 5

= 125 degrees

Angle AED = angle CEB = 125 degrees (vertical angles)

Angle DEB

= x + 15

= 40 + 15

= 55 degrees

Angle DEB = Angle AEC = 55 degrees (vertical angles)

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Read the link attached.

I have written it down on the word doc

If his growth spurt continued at the same rate Andrew will grow 26/7 inches per month during that growth spurt.

To calculate someone's age, you would subtract their birth year from the current year. For example, if someone was born in 1995 and it is now 2020, their age would be calculated as 2020 - 1995 = 25 years old.

If you have a birthdate, you can use a date calculator to find the exact age in years, months and days.

It's also important to note that, if the person's birthday hasn't occurred yet in the current year, you would subtract the birth year from the current year minus one.

We can start by converting the mixed number 4 1/3 to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 4 x 3 + 1 / 3 = 13/3

To find out how much Andrew grew per month, we need to divide the total growth by the number of months.

13/3 inches / 3 1/2 months = (13/3) / (7/2) = (13/3) x (2/7) = 26/7 inches/month.

So, Andrew grew 26/7 inches per month during that growth spurt.

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