Two bikers are riding a circular path.
The first rider completes a round in 12
minutes. The second rider completes
a round in 18 minutes. If they both
started at the same place and time
and go in the same direction, after
how many minutes will they meet
again at the starting point?

Please show working

The price of a single chicken is $8 and the price of a single duck is $5.

The prices can be determined by forming the linear equation in two variables.

Given that,

Michael sold last month, 50 chickens and 30 ducks for $550.

This month, he sold 44 chickens and 36 ducks for $532.

Let the price of single chicken be 'a' and the price of a single duck be 'b'. Then the linear equation will be:

50a+30b=550 ____________(1)

44a+36b=532 ____________(2)

Solving equation (1) for the value of 'b'.

b=550-50a/30

b=55/3 - 5a/3  ____________(3)

Putting the value of 'b' in equation (2).

44a+36(55/3 - 5a/3) = 532

128 = 16a

a=8

Putting the value of a in equation (3).

b= 55/3 - 5*8/3

b=5

Thus, The price of a single chicken is $8 and the price of a single duck is $5.

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Michael sold last month, 50 chickens and 30 ducks for $550.

This month, he sold 44 chickens and 36 ducks for $532.

50a+30b=550

44a+36b=532

Solving equation (1) for the value of 'b'.

b=550-50a/30

b=55/3 - 5a/3

Putting the value of 'b'

44a+36(55/3 - 5a/3) = 532

128 = 16a

a=8

Putting the value of a

b= 55/3 - 5*8/3

b=5

Thus, The price of a single chicken is $8 and the price of a single duck is $5.

Three parameters, start value, stop value, and step value, are required for the range() method in Python to function. After incrementing the values by the amount specified in the step value .

The range of values between a given data collection's top and lowest values is known as the statistical range. The difference between the highest and lowest observation is another method of expressing the range. By deducting the highest value from the lowest, one may calculate the sample interval. A crucial indicator of variability for continuous variables is the sample range.

here

startNumber (optional): The series of integers that are returned begins with this number.

stopNumber: The list of integers that range() provides comes to an end before this one.

stepValue (opportunity): a number that is an integer and represents the difference between each integer in the series.

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Yes, the given equation is quadratic equation.

Here it has been given that,

3x² - 5x + 9 = x² - 7x + 3

Now, after solving  above equation further we obtain,

2x² + 2x + 6 = 0

From the above equation the factor 2 is taken out as it is common and now the equation looks like : x² + x + 3 = 0

The coefficients of the quadratic equation are compared  and if it meets the criteria then it is quadratic equation otherwise not.

Now as we can see, the above equation clearly represents a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 1 and c = 3.

Hence, the above given equation is a algebraic quadratic equation.

Which of the following is quadratic equation 3x² - 5x + 9 = x² - 7x + 3 ?

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Therefore , we can calculate the side of the length of the square by finding the square root of the given area.

The square root of an integer, which is the outcome of multiplication alone, gives the initial number. Squares and square roots are a few of examples of exponents. Think about the number 36. Furthermore, this can be written as 6x6.

Here,

The base length times the height of any quadrilateral yields the area of that shape.

Since the shape is square, we can be certain that all of its sides are equal in length.

Using this information, we can work backwards to determine the length of one side by taking the square root of the area.

For example : Square having area of 25

We can find its length by taking square root of 25

Which comes out to be √25 = 5

Thus , 5 is a length of the side of the square.

Therefore , we can calculate the side of the length of the square by finding the square root of the given area.

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A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. 0 is not a positive integer and 1 is not greater than 1, so they are not considered a prime number.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

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The ordered pair for Point N is (6,9).

What is the ordered pair?

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples or 2-length sequences.

Here, we have

Given the graph and we have to find the coordinates of all points.

N = (6,9)

M = (5,7)

R = (9,8)

D = (2,6)

C = (1,4)

B = (2,1)

A = (6,2)

Q = (7,5)

Hence, the ordered pair for Point N is (6,9).

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On solving the provided question, we can say that - If you put all the numbers together by digits, the total must be a multiple of three. so answer is 17

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

[tex]51, 54, 57\\60, 63, 66, 69\\72, 75, 78\\81, 84, 87\\90, 93, 96, 99[/tex]

If you put all the numbers together by digits, the total must be a multiple of three. so answer is 17

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We calculated the domain of this function is all the real numbers of independent variable X such as 0, 1, 2, 3, 4, 5, 6 etc.

An expression that indicates a relationship between an independent variable and dependent variable. A function consists of two variables with or without numbers. A function has symbols but equal sign is mandatory.

The domain of a function is the set of all possible value of independent variables. It is also called the input of a function.

In the above function, the domain is all real number of independent variable x.

For each value of x that means for each domain, we get a value of y. The set of y values are called ranges.

we put x= 0, 1, 2, 3, 4, 5, 6 and so on.

we get y = 3×0-1 = -1

     y = 3×1-1 = 2

   y =3×2-1 = 5

  y = 3×3-1 = 8

 y= 3×4-1 = 11

y = 3×5-1 = 14

y= 3×6-1= 17

The set of domains are {0, 1, 2, 3, 4, 6}

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Answer:

AB = 6.71

Step-by-step explanation:

See the attached worksheet.

Find the lengths of the two sides of the right triangle:

 CB = (5 - (-1)) = 6

 CA = (6-3) = 3

Use the Phythagorean Theorem to find AB.

6^2 + 3^2 = AB^2

AB^2 = 45

AB = 6.71

Answer:

[tex]x {}^{3} + 2x {}^{2} y + 2xy {}^{2} + y {}^{2} [/tex]

Step-by-step explanation:

Greetings !

[tex](x + y)( x{}^{2} + xy + y {}^{2}) [/tex]

Distribute parentheses

[tex] = xx {}^{2} + xxy + xy {}^{2} + yx {}^{2} + y {}^{2}x + y {}^{2} [/tex]

[tex] = x {}^{3} + x {}^{2} y + xy {}^{2} + yx {}^{2} + y {}^{2} x + y {}^{2} [/tex]

Collect Like terms and further simplification

[tex] = x {}^{3} + 2x {}^{2} y + 2xy {}^{2} + y {}^{2} [/tex]

Hope it helps!!!

If you have any questions and suggestions tag it on the comments. thanks

The product of (x+y)(x²+xy+y²) gives x³ + 2x²y + 2xy² + y³.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

(x+y)(x²+xy+y²)

Multiplying the terms

= x(x²+xy+y²)) + y(x²+xy+y²)

= x³ + x²y + xy² + yx² + xy² + y³

= x³ + 2x²y + 2xy² + y³

Hence, the expression gives x³ + 2x²y + 2xy² + y³.

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A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself, so 1 is not consider as a prime number.

Therefor 1 is not the biggest prime number.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

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The solution to both inequality is 2 ≥  -x and -x≥ 14

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

We have the equation 1≥-x-1 and -x-1≥ −13

Let us solve the inequality

1 ≥ - x - 1

1 + 1 ≥ -x

2 ≥  -x

Now, let us solve the inequality

-x-1≥ −13

-x+13 ≥ -1

-x≥ 14

Therefore the solution to both inequality is 2 ≥  -x and -x≥ 14

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Answer:

Step-by-step explanation:

If Z1 = (x1, y1) and Z2 = (x2, y2) are complex numbers, then their sum is given by:

Z1 + Z2 = (x1 + x2, y1 + y2)

For example, if Z1 = (3, 4) and Z2 = (-2, 5), then their sum is:

Z1 + Z2 = (3 + (-2), 4 + 5) = (1, 9)

In general, to add two complex numbers, we add their real parts and their imaginary parts separately.

The value of  [tex]z_1[/tex] +  [tex]z_2[/tex]  = ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex])

Complex Numbers. Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a imaginary number called a "iota."

Given:

[tex]Z_1=(x_1,y_1)[/tex] and [tex]Z_2=(x_2,y_2)[/tex]

Also, we know by Complex number

[tex]z_1[/tex] = [tex]x_1[/tex] + i [tex]y_1[/tex]

and, [tex]z_2[/tex] = [tex]x_2[/tex] + i [tex]y_2[/tex]

Then, [tex]z_1[/tex] +  [tex]z_2[/tex]

= ( [tex]x_1[/tex] + i [tex]y_1[/tex]) + ( [tex]x_2[/tex] + i [tex]y_2[/tex])

= ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex])

Hence, the addition gives  ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex]).

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Answer:

let x= amount she earn for each delivery

6(16.5) = 11x

99 = 11x

x = 9

$16.5 per hour * 6 hours = $99

11 deliveries * $9 = $99

Step-by-step explanation:

Yes, the given equation is a quadratic equation.

The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given is an equation, 2x²-7x = 0

As we know that, a quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

On comparing equation 2x²−7x=0 with standard form of quadratic equation

ax ²+bx+c=0:

We get, a=2,b=−7,c=0

Hence, the equation 2x²−7x=0  is a quadratic equation.

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The slope of the linear equation y = -3x + 4 is -3, and the y-intercept is 4.

To calculate the slope of a linear equation, the formula is m = (y2 - y1) / (x2 - x1). The slope is calculated by selecting two points on the line, (x1, y1) and (x2, y2), and then subtracting the first point's y-value from the second's and dividing the result by the first point's x-value minus the second's. For the equation y = -3x + 4, the y-intercept is 4, which is the b-value in the equation y = mx + b. The y-intercept is the point where the line crosses the y-axis. To calculate the y-intercept, set x = 0 and solve for y. For the equation y = -3x + 4, when x = 0, y = 4. Therefore, the y-intercept is 4.

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Answer:

y=1/2x+-2

Step-by-step explanation:

Answer:

Number 5

Step-by-step explanation:

When the net is folded, 3 will be folded left and up, with 4 being the base. 6 will be folded right, with 2 being the top of the cube.

So, we have pairs

2 and 4

6 and 3

1 and 5

So, the opposite of the number 1 is the number 5

No. of teeth on the pinion(TP)=17.

Diametral pitch(pd)=8 teeth/in.

Rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.

Rotational speed of the gear(NG)=544 rev/min or 544 rpm.

To calculate:

No. of teeth on gear(TG) & theoretical centre to centre distance(C).

Solution:

We know that;

Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear

For pinion,

pd=TP/DP  

Pittiong the values in above eq.

8 teeth/in =17/DP    =>DP=17/8 in.

or DP=2.125 in.

Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)

=>(NP/NG)=(TG/TP)

=>1120/544 =TG/17 =>TG=35

No. of teeth the gear(TG)=35 {Ans}

Also from gear ratio formula,

(NP/NG)=(DG/DP)

=>1120/544=DG/2.125

=>DG=4.375 in.

In the next fig. I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre to centre distance(C)

centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}

=>C=(DP+DG)/2

Diameter =2*radius}

=>C=(2.125+4.375)/2 in. =3.25 in.

Theoretical centre to centre distance (C)=3.25 in.

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Answer:

All three angles must add up to 180 degrees

Step-by-step explanation:

The equation that shows the number of plates that is remaining would be = Y = (Total salad plate/X) - 4.

A banquet hall is a building constructed is a way that various celebrations and functions can be held in such a place such as wedding receptions.

The total number of salad plates available = 144

The number of salad plate per every table set = 10

The number of salad plates remaining = y

The number of tables set by Duncan = x.

If 1 table = 10

X tables = 144

make X tables the subject of formula;

X tables = 144/10

X tables = 14 tables (approximately)

But 14 × 10 = 140 salad for the 14 tables

The remaining salad plates is 4 plates.

Y = (Total salad plate/X) - 4

Therefore, the number of salad plates remaining which is 4 depends on the number of tables Duncan sets which is 10.

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Answer:

transversitile multistelular projection

Answer:

Step-by-step explanation:

The perimeter of triangle ACD that is formed by two right-angle triangles ACB and DCB, approximated to 1 decimal place is: 40.1 cm.

The zeros of the polynomial are 1/2√2 and -3/√2.

The zeros of a polynomial are all the x-values that make the polynomial equal to zero.

Given, the polynomial is 4x² + 5√2x - 3.

We have to find the zeros of the polynomial,

Let 4x² + 5√2x - 3 = 0

On factoring,

= 4x² + 6√2x - √2x - 3

= 2√2x(√2x + 3) - (√2x + 3)

= (2√2x - 1)(√2x + 3)

Now, 2√2x - 1 = 0

2√2x = 1

x = 1/2√2

Also, √2x + 3 = 0

√2x = -3

x = -3/√2

Therefore, the zeros of the polynomial are 1/2√2 and -3/√2.

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The pool holds about 245,000 gallons. Therefore, option (c) 244,596 gal is correct.

To find the number of gallons of water the pool holds, we need to convert the volume in cubic feet to gallons.

One cubic foot is equal to 7.4805194805 gallons, so to find the number of gallons in the pool, we can multiply the volume in cubic feet by the conversion factor:

1 cubic foot= 7.4805194805 gallons

gallons = 32,700 cubic feet * 7.4805194805 gallons/cubic foot

= 244,999.99968 gallons

Rounded to the nearest gallon, the pool holds about 245,000 gallons.

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One cubic foot is equal to 7.4805194805 gallons, so to find the number of gallons in the pool, we can multiply the volume in cubic feet by the conversion factor:

1 cubic foot= 7.4805194805 gallons

gallons = 32,700 cubic feet * 7.4805194805 gallons/cubic foot

= 244,999.99968 gallons

Rounded to the nearest gallon, the pool holds about 245,000 gallons.

Mean is calculated to get an idea of the average of the observations in the data set.

The average value of the observations in a data set is called the mean or average . It is calculated by dividing the sum of observations by the number of observations i.e.

u = (x1 + x2 + x3 + .... + xn)/n

where u is the mean , x1 , x2 ...,  xn are data observations and n is the number of observations.

For example, we have values as 1,2,3,4,5 and we want to calculate the mean . Then it is calculated by

u = (1+2+3+4+5) / 5 = 3.

So, the mean is 3.

Therefore, mean is calculated to get an average or an idea of a certain number of observations.

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Therefore ,the collar remain effective for 26.44 days.

In mathematics, there are numerous ways to use the word "order." It most frequently refers to the quantity of elements in (for example, conjugacy class order, graph order, group order, etc.) or describes the biggest term (for example, curve order, surface order, or polynomial order) that appears in a mathematical object.

Here,

=>Rate of evaporation=k=dr/dt

=> amount still present=R.

Thus ,It's a first order reaction.

So, half life=0.693/k.

20=0.693/k.

=> k=0.0346

Now,

60% of active ingredient has been evaporated.

So, 40% left.

Time taken=T=(2.303/k)log(R/0.4R)

T=(2.303/0.0346)log(5/2)

T=66.56(log5-log2)

T=66.56(0.699-0.301)

T=66.56(0.398)

T=26.44 days.

Therefore ,the collar remain effective for 26.44 days.

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Among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.

For the first part of the problem, we can prove that the game must end after at most n(n+1)/2 turns by induction. Base case: When there is only one bowl, Marvin can remove the single marble in one turn, so the game ends after one turn.

Inductive step: Suppose the game ends after at most k(k+1)/2 turns when there are k bowls. We will show that the game ends after at most (k+1)(k+2)/2 turns when there are k+1 bowls. If Marvin removes a marble from a bowl, then the number of bowls decreases by one and the game must end after at most k(k+1)/2 turns by the inductive hypothesis.

If Marvin moves a marble from bowl A to bowl B, where bowl A has at least one marble and bowl B has at least as many marbles as bowl A, then the number of marbles in bowl A decreases by one and the number of marbles in bowl B increases by one. Since bowl B has at least as many marbles as bowl A, the number of bowls remains unchanged. Thus, the game must still end after at most k(k+1)/2 turns.

In either case, the game ends after at most k(k+1)/2 turns, so the game must end after at most (k+1)(k+2)/2 turns when there are k+1 bowls, as desired.

For the second part of the problem, we can prove that for every positive integer k, there is an n such that Marvin can make the n-bowl game last for at least kn turns by constructing a strategy.

Suppose Marvin wants to make the n-bowl game last for at least kn turns. He can do this by making sure that there are always at least k marbles in each bowl. To do this, Marvin can start by placing k marbles in the first bowl, k-1 marbles in the second bowl, and so on, down to 1 marble in the nth bowl.

On each turn, Marvin can choose a bowl with at least k marbles and move one marble to a bowl with fewer than k marbles. For example, if there are k+1 marbles in the first bowl and k marbles in the second bowl, Marvin can move one marble from the first bowl to the second bowl. This keeps the number of marbles in each bowl at least k. Since Marvin can take at least one turn per bowl, the game will last for at least kn turns.

For the third part of the problem, we can prove that among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.

Let n be a positive integer. We will show that either Marvin has a winning strategy for the n-bowl game or Marisa has a winning strategy for the (n+1)-bowl game.

If Marvin has a winning strategy for the n-bowl game, then he can win the n-bowl game by following his winning strategy.

If Marvin does not have a winning strategy for the n-bowl game, then Marisa has a winning strategy for the n-bowl game. In this case, Marvin can adopt Marisa's winning strategy for the n-bowl game as his own winning strategy for the (n+1)-bowl game.

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Step-by-step explanation:

A number is divisible by 11 if and only if the difference between sum of alternate digits is divisible by 11.

Here the number is x557x55. The difference between the sum of alternate digits is,

[tex]\longrightarrow S=(x+5+x+5)-(5+7+5)[/tex]

[tex]\longrightarrow S=2x-7[/tex]

By statement, the number x557x55 is divisible by 11 if and only if [tex]S=2x-7[/tex] is divisible by 11.

Let,

[tex]\longrightarrow 2x-7=11a[/tex]

[tex]\longrightarrow 2x=11a+7\quad\dots(1)[/tex]

We separate the RHS as the following.

[tex]\longrightarrow 2x=10a+a+6+1[/tex]

[tex]\longrightarrow 2x=10a+6+a+1[/tex]

[tex]\longrightarrow 2x=2(5a+3)+(a+1)[/tex]

In this question, the LHS is an even integer since x is a digit, i.e., integer. So RHS should also be an even integer.

Since [tex]2(5a+3)[/tex] is even, [tex]a+1[/tex] must be even. So let,

[tex]\longrightarrow a+1=2k[/tex]

[tex]\longrightarrow a=2k-1[/tex]

Then (1) becomes,

[tex]\longrightarrow 2x=11(2k-1)+7[/tex]

[tex]\longrightarrow 2x=22k-4[/tex]

[tex]\longrightarrow x=11k-2\quad\dots(2)[/tex]

So this is expression for x, for any integer k.

As x is a digit of x557x55, x is a single digit integer, so its value lies in between 1 and 9 [x ≠ 0 because it is also the left most digit of x557x55], i.e.,

[tex]\longrightarrow 1\leq x\leq 9[/tex]

From (2),

[tex]\longrightarrow 1\leq 11k-2\leq 9[/tex]

Adding 2,

[tex]\longrightarrow 3\leq 11k\leq 11[/tex]

Dividing by 11,

[tex]\longrightarrow\dfrac{3}{11}\leq k\leq 1[/tex]

Since k is an integer, we get,

[tex]\longrightarrow k=1[/tex]

Then from (2),

[tex]\longrightarrow x=11(1)-2[/tex]

[tex]\longrightarrow\underline{\underline{x=9}}[/tex]

Hence the value of x is 9.

The process of finding the discontinuity of a hole is explained below.

The term discontinuity in statistics is defined as a point on the graph that is undefined or is unfit for the rest of the graph.

In order to find the discontinuity of the hole we have to perform the following steps,

The first and foremost thing is to factor out the numerator and the denominator

Next we have to determine the common factors in the numerator and the denominator

After that we have to set the common factors equal to zero and find the value of x.

Then the final steps is to plot the graph and mark the point with a hole

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