A and B together complete a work in 20days. They worked together for 5days and B leaves. How long will A takes to finish the remaining work if A alone can finish the work 36days.

The statements regarding the multiplicity of the numbers are classified as follows:

1. Nine is a factor of 777,777: False.

2. 3 is not a factor of 12,345: False.

3. 245+712 is a multiple of 5: False.

4. 3a+15b is divisible by 3 for any values of a and b: True.

5. 11 is not a factor of 11^3: False.

6. 555 is divisible by three but not by 9: True.

7. 2772 is a multiple of 9 but not of 3: False.

A number is divisible by 9 if the sum of the digits of the number is divisible by 9.

6 x 7 = 42 -> not divisible by 9 -> 9 is not a factor of 777,777.

A number is divisible by 3 if the sum of the digits of the number is divisible by 3.

1 + 2 + 3 + 4 + 5 = 15 -> divisible by 3 -> 3 is a factor of 12,345.

A number is a multiple of 5 if it finishes in either 0 or 5. 245+712 finishes in 7, hence it is not a multiple of 5.

3a+15b is divisible by 3 for any values of a and b, as the factors 3 and 15 are both divisible by 3.

11 is a factor of 11³, as:

11³/11 = 11².

As nine is a multiple of 3, all the multiples of 9 are also multiples of 3.

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Answer:

Step-by-step explanation:

The equation of the line passing through the points [tex](x_{1},y_{1} ) and (x_{2} ,y_{2} )[/tex] is

[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )[/tex]

plug the two points [tex](x_{1},y_{1} )=(-6,-4) and (x_{2} ,y_{2} )=(-5,-4)[/tex] into the equation.

[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\\y+4=\frac{-4-(-4)}{-5-(-6)} *(x+6)[/tex]

[tex]y-y_{1}=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}*(x-x_{1} )\\y+4=\frac{-4-(-4)}{-5-(-6)} *(x+6)\\y+4=0\\y=-4[/tex]

The equation of line that runs through the points (-6, -4) and (-5, -4) is y = -4.

The slope-intercept form is expresses as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line that passes through the points (-6, -4) and (-5, -4).

First, we find the slope.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( -4 - (-4) )/( -5 - (-6) )

Slope m = ( -4 + 4 )/( -5 + 6 )

Slope m = ( 0 )/( 1 )

Slope m = 0

Next, find the y-intercept b.

y = mx + b

Plug in slope m = = and point 1( -6, -4 )

-4 = 0(-6) + b

Solve for b

-4 =  b

b = -4

Now, plug slope m = 0 and y-intercept b = -4 into the slope intercept form to determine the equation of the line.

y = mx + b

y = 0(x) + -4

y = -4

Therefore, the equation of line is y = -4.

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The value of the variable, n is 5

An algebraic expression can simply be defined as an expression that is composed of variables, coefficients, factors, constants and terms.

These mathematical expression called algebraic expressions are also composed of arithmetic operations, such as;

Examples of algebraic expressions are;

2x + 18

2x² + 4

3y + 6

From the information given, we have that;

7n - 4 = 31

collect like terms

7n = 31 + 4

Add like terms

7n = 35

Make 'n' the subject of formula

n = 35/7

n = 5

Thus, the value is 5

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Answer:

sorry I posted this question and never got and never got an answer

The x-value of where the beam should be placed is X = (x1+x2)/2.

Given: the distance between the two trusses is 2 feet and the reinforcement beam will extend from one truss to the other.

We can set up an equation using the distance formula to determine the x-value of where the beam should be placed.

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²)

Let's assume that the trusses are located at point (x1, y1) and (x2, y2) and the beam is located at point (x, y).

We know that the distance between the trusses is 2 feet, so we can set d = 2.

We can use the coordinates of the trusses and the point where the beam is located to set up the equation:

d = √((x2 - x1)² + (y2 - y1)²) = 2

Since the trusses are located on the same line and only the x-coordinate changes, we can assume that y1=y2

Therefore the equation can be simplified to √((x2 - x1)²) = 2

Square both sides: (x2 - x1)² = 4

x2 - x1 = 2

Now we know that the difference between the x-coordinates of the two trusses is 2 feet.

So, to find the x-value of the point where the reinforcement beam should be placed, we can take the average of the x-coordinates of the two trusses.

x = (x1+x2)/2

We don't know the values of x1 and x2, so we can't solve for x. But we know that the reinforcement beam should be placed exactly in the middle of the trusses.

Thus, The x-value of where the beam should be placed is X = (x1+x2)/2.

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The smallest y - intercept for the given equations is, (0, -6).

What is y - intercept?

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.

There are four function are given.

We have to find which function having smallest y - intercept.

Since, to find y - intercept we have to plug x = 0 in each equation.

Consider, the functions

1. g(x) = 2x - 6

Plug x = 0

g(0) = 0 - 6

g(0) = -4

⇒  The y - intercept is (0, -4).

2. f(x) = √x - 2

Plug x = 0

f(0) = 0 - 2

f(0) = -2

⇒  The y - intercept is (0, -2).

3. For 3 we get the equation, y = 2x + 1

Plug x = 0

y = 0 + 1

⇒  The y - intercept is (0, 1).

4. From graph the y - intercept is (0, -2).

Hence, the smallest y - intercept for the given equations is, (0, -6).

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Therefore ,when the problem of expression is solved, we may state that the necessary inequality statement is 4.50x+1.75y 50.

An expression in mathematics consists of a statement, two or more variables or integers, but one or more mathematical functions. Numbers can be multiplied, divided, added, or subtracted using this mathematical operation. The construction of an expression is as follows: Expression: Math operator, variable or number, and math operator.

Here,

Cost per assignment is $4.50.

Therefore, "x" assignment cost equals 4.50x.

Cost per assignment: $1.75

Assignment "Y" cost is therefore 1.75Y.

Consequently, the sum of 4.50x+1.75y must be $50 or less.

Therefore, 4.50x+1.75y ≤ 50 is the necessary inequality statement.

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Answer:

4/9 in the simplest form

Step-by-step explanation:

When dividing by a negative number the sign of the quotient changes. so if the quotient is negative when the divisor and dividend have the same sign, it becomes positive when they have opposite sign. In this case -12 and -25 have opposite signs and the quotient will be positive, that's why the negative signs cancel out.

-12 / (-25) = 12/25 =  4/9 in the simplest form

Endpoint A has coordinates (3,12) since the slope of AB is 1/3 and B is (9,4). Point P has coordinates (7,8) since P is 5/6 the directed path of BA.

Point P divides BA in the ratio of 5:6.

How much of one quantity is in the other can be found by comparing two amounts of the same unit and calculating the ratio. Ratios can be categorized into two groups. Part to part ratio is the opposite of part to whole ratio. A two distinct things or groupings are related to one another as shown by the part-to-part ratio. For instance, the boy-to-girl ratio in a class is 12:15, but the part-to-whole ratio describes how one group of people compares to the total population. For instance, five out of ten people say they like to read. The ratio of the part to the whole is therefore 5: 10, which indicates that 5 out of every 10 people enjoy reading.

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Answer:

8 hours

Step-by-step explanation:

The rate at which the candle burns is:

5.5 in/11 hr = 0.5 in/hr

The 4 in candle burns at the same rate.  Find the time for a 4 in candle to burn down:

time = (4 in) / (0.50 in/hr) = 8 hr

Answer:

[tex]0.7 \ m/s^2[/tex]

Step-by-step explanation:

      From the graph, final speed = 9m/s

                                   initial speed =  2 m /s

                       Time taken = 10 m

[tex]\sf \boxed{Acceleration=\dfrac{final \ speed - initial \ speed}{time \ taken}}[/tex]

                       [tex]\sf = \dfrac{9-2}{10}\\\\\\=\dfrac{7}{10}\\\\= 0.7 \ m/s^2[/tex]

The measure of angle S = 29 degrees, angle T= 29 degrees, and angle U = 122 degrees.

A triangle is a straightforward closed curve made up of three-line segments. An angle inside the form is known as an interior angle. The inner angles add up to a constant 180 degrees.

The sum of internal angle of the triangle is 180 degrees.

(x + 4) + (x + 4) + (5x - 3) = 180

7x + 5 = 180

7x = 175

x = 25

Substitute the value of x in each of the angle to find the measure of each angle as follows:

The value of angle S = x + 4 = 25 + 4 = 29 degrees.

The value of angle T = x + 4 = 25 + 4 = 29 degrees.

The value of angle U = 5x - 3 = 125 - 3= 122 degrees.

Hence, the measure of angle S = 29 degrees, angle T= 29 degrees, and angle U = 122 degrees.

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170 out of 300 students in the school own a dog.

A word problem is a short passage presenting a "real-life" situation where an issue has to be solved using math.

Word problems are seen as an essential component of learning in the elementary curriculum because they require students to apply their understanding of various concepts to situations that are representative of "real-life" situations.

Given that,

Total number of students surveyed = 30

Total number of students that own a dog = 17

Total number of students in the school = 300

In order to find the equivalent of 17/30 with the bottom number 300

we get, 10 times of 30 is equal to 300 so based on this,

17/30 times 10/10 = 170/300

Thus, 170 out of 300 students in the school own a dog.

Correct question: Out of 30 students surveyed, 17 have a dog. Based on these results, predict how many of the 300 students in the school have a dog.

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Answer: 9

Step-by-step explanation:

The names of the terms of m/5+4.6 are m/5 and 4/6

From the question, we have the following parameters that can be used in our computation:

m/5 + 4.6

Considering an expression a + b

The terms of the expression are a and b

This means that the terms of the expression m/5 + 4.6 are m/5 and 4/6

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For the number -(4 / 7), the additive inverse would be (4 / 7).

The additive inverse of a number is the number that when added to the original number, the result is 0. In other words, it is the opposite of the original number.

To see this, let's add -(4 / 7) and (4 / 7) together:

-(4 / 7) + (4 / 7) = 0

This is because the negative sign in front of the fraction indicates that the fraction is the opposite of (4 / 7). So adding the two fractions together cancels out the opposite and results in 0.

In summary, the additive inverse of -(4 / 7) is (4 / 7) because adding the two fractions together results in 0, which is the definition of an additive inverse.

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Answer:

hypotenuse = 55

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse c is equal to the sum of the squares on the other 2 sides, that is

c² = 33² + 44² = 1089 + 1936 = 3025 ( take square root of both sides )

c = [tex]\sqrt{3025}[/tex] = 55

The angle that the golfer has between the spectator and the hole is cos^-1((a^2 + b^2 - c^2)/(2ab))

The angle that the golfer has between the spectator and the hole can be found using the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we know that a = 140 (the distance from the golfer to the spectator), b = 200 (the distance from the golfer to the hole), and C = 120 (the angle between the golfer and the spectator).

We can use these values to solve for c, which is the distance from the spectator to the hole. Once we have this value, we can use the Law of Cosines again to find the angle between the golfer and the hole.

c^2 = 140^2 + 200^2 - 2 * 140 * 200 * cos(120)

c = sqrt(140^2 + 200^2 - 2 * 140 * 200 * cos(120))

Now we can use this value of c to find angle A:

A = cos^-1((a^2 + b^2 - c^2)/(2ab))

Note that the angle A is what we're looking for, the angle between the golfer and the hole.

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[nΣk=1]k/(k+1)! is the notation of the summation .

The summation notation is a compact way of expressing the sum of a series of terms. In this case, the series of terms is the expression "1/2! + 2/3! + 3/4! + ...+ n/(n+1)!" which can be represented using the summation notation as [nΣk=1]k/(k+1)!. It is saying the sum of all k/(k+1)! where k = 1, 2, 3, ...., n. The summation notation consists of three parts, the n, Σ and the k=1. The n represents the upper limit of the summation, the Σ (sigma) represents the summation operator and the k=1 represents the lower limit of the summation.

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Enter the data value to be searched for in the Search text area. Choose the database to search in from the Database drop-down menu.

The length of the sequence is the number of ordered elements (which could be infinite). Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of sequences you need to be familiar with. A list of numbers connected by a rule is known as a number sequence. You can determine the subsequent numbers in the sequence if you figure out the rule. The difference in this instance between each number is 6.

given

Enter the data value to be searched for in the Search text area.

Choose the database to search in from the Database drop-down menu.

Select the tables and views you want to search in from the Select objects to search tree, or leave them all checked.

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The equation of the linear function represented by the table  is y = - x + 2 .

What is linear Equation ?

Linear equation can be defined as the equation in which the highest degree is one.

Given points,

(-1, 3), (1, 1), (3, -1), (5, -3)

Slope-intercept form:

y = mx + b

Finding the slope using slope formula and the first two points:

m = (1 - 3)/(1 - (-1))

= -2 / 2 = -1

Finding y-intercept using the slope and the first point:

3 = (-1)*(-1) + b

3 = 1 + b

b = 3 - 1

b = 2

Hence, The equation of the linear function represented by the table  is

y = - x + 2 .

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Answer:

24 pens

Step-by-step explanation:

Answer: the answer is actually 288

Step-by-step explanation:

you multiple 12 by 12 to get 144 then you multiply that by 2 to get 288

Answer:

the reduced price must be increased by 32% to have a 12% higher price than the original price

The percentage that must the reduced in the reduced price so that the new price is 12% higher than the original price is 40%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Let the price of the suit = 100

Reduced = 20%

Now,

The reduced price of the suit.

= 100 - (20% of 100)

= 100 - (20/100 x 100)

= 100 - 20

= 80 _____(1)

Now,

New price.

= 100 + (12% of 100)

= 100 + 12

= 112

Now,

From (1)

100% = 80

Multiply 112/80 on both sides.

112/80 x 100% = 112

140% = 112

This means,

40% increased

Thus,

40% increase in the reduced price.

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The surface areas for each of the cylinders are;

1) S = 10178.8 millimeters squared

2) S = 955.0 inches squared

3) S = 157.1 centimeters squared

4) S = 351  square inches

The formula for surface area of a cylinder is;

S = 2πr² + 2πrh

1) We are given;

radius; r = 30 mm

height; h = 24 mm

Thus;

S = 2π(30)² + 2π(30*24)

S = 10178.8 millimeters squared

2) We are given;

radius; r = 8 in

height; h = 11 in

Thus;

S = 2π(8)² + 2π(8*11)

S = 955.0 inches squared

3) We are given;

radius; r = 1 cm

height; h = 9 cm

Thus;

S = 2π(1)² + 2π(1*9)

S = 157.1 centimeters squared

4) We are given;

radius; r = 4 in

height; h = 10 in

Thus;

S = 2π(4)² + 2π(4*10)

S = 351  square inches

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A z-score is used to measure how many standard deviations an individual value is from the mean of a given set of data.

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the required probability is 0.1

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: 3 students study for an hour and total students are 30

Thus P(1 hour) =3/30

                          =0.1

Hence, the required probability is 0.1

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The rational function to define this situation would be p = 3.45 + 0.33c.

A rational function in mathematics is any function that can be expressed as a rational fraction, which is an algebraic fraction in which the denominator and numerator are both polynomials. It is not necessary for the polynomials' coefficients to be rational numbers; they can be taken from any field K.

In this instance, a rational function and a rational fraction over K are used. The variables' values can be entered into any field L that contains K. In this case, L is the codomain and the domain of the function is the collection of variable values for which the denominator is not zero.

They charge $3.45 to develop a roll of film and $0.33 for each photo that it prints.

The rational function define this situation would be

p = 3.45 + 0.33c

Thus, the rational function to define this situation would be p = 3.45 + 0.33c

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Therefore , the solution of the given problem of inequality comes out to be x > 6/5  and y > -13/5.

In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are. Many fundamental inequality problems can be addressed by flipping the two aspects until only the variables are left

Here,

Given :

=> y ≤ 2x-5

=> y > -3x + 1

and

=>  y  ≤ 2x-5

=>  2x - 5  > -3x + 1

=> 2x + 3x > 1 +5

=> 5x > 6

=> x > 6/5

=> y > -3(6/5) + 1

=>  y > -18/5 + 1

=> y > -13/5

Therefore , the solution of the given problem of inequality comes out to be x > 6/5  and y > -13/5.

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Answer:

y = 5 + √-3 + x

y = 5 - √-3 + x

Step-by-step explanation:

X=3+(y-5)^2

Let's simplify, and we will get

x = 3 + (y^2 -10y + 25)

x = 3 + y^2 - 10y + 25

x = y^2 - 10y + 28

0 = y^2 - 10y + 28 - x

We use the formula

-b ± √ b^2 -4(ac) / 2a

10 ± √(-10)^2 - 4 · (1 ( 28 - x) ) / 2

The answer will be

y = 5 + √-3 + x

y = 5 - √-3 + x