1.45x + 1.25y =70.85

x + y = 53

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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Students must possess both the growth mindset necessary for problem-solving and strong reading skills. Some of the problem-solving methods are described.

The capacity to solve math word problems is an essential component of math fluency.

Concentrate on using mathematical key words and phrases.

Mark this sentence for deletion:

Promote Question-Asking:

Sketch the issue.

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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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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 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 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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[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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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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A pool is being drained by a pump at a rate of 4 gallon per minute, then the second pump affect the rate of drainage = 8 minutes

For two identical pumps in parallel the flow rate doubles compared to single pump,

Single pump flow rate = 4 gallons per minute

When two pump act at same time, drain rate will be double,

Drain rate = 8 gallons per minute

The first pump can drain in 8 minutes, therefore:

Rate of the first pump = 1/8

Working together, they can drain the pool in 4 minutes, therefore:

Rate of both pumps = 1/4

Let the time taken by the second pump =t

Rate of the second pump = 1/t.

So,

We can write,

[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{t}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{1}{t}[/tex] = [tex]\frac{1}{4} -\frac{1}{8}[/tex]

[tex]\frac{1}{t}[/tex] = [tex]\frac{2-1}{8}[/tex]

[tex]\frac{1}{t}[/tex] = [tex]\frac{1}{8}[/tex]

t = 8 minutes

Therefore,

A pool is being drained by a pump at a rate of 4 gallon per minute, then the second pump affect the rate of drainage = 8 minutes

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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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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

The numbers 2, -2, and -2 can replace the letters A, B, and C respectively in the table of values.

We use table of values when we have to graph out a linear equation. We can make use of the table of values to map out the corresponding values of x and y for a given line equation.

For y = x² - 3x - 2:

when x = -1;

y = (-1)² - 3(-1) -2

y = 1 + 3 - 2

y = 4 - 2

y = 2

when x = 0;

y = (0)² - 3(0) -2

y = 0 - 0 - 2

y = -2

when x = 3;

y = (3)² - 3(3) - 2

y= 9 - 9 - 2

y = 0 - 2

y = -2

Therefore, the values 2, -2, and -2 replace letters A, B, and C respectively in the table of values for y = x² - 3x - 2.

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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 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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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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Reason:

An increase of 95% will involve the multiplier 1.95

Think of it like saying 100% + 95% = 1 + 0.95 = 1.95

Therefore,

1.95*3.50 = 6.825 = 6.83 dollars

Answer:

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

The number of students that are majoring in Economics is 2592 whose percentage is 48% of the total.

What is the percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.

Examples of percentages are:

Now,

Total students=5400

Percentage of students doing majoring =48%

Hence,

           The number of students that are majoring in Economics

                                =48/100*5400

                               =2592

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Is the relation a function: C. No, because for each input there is not exactly one output.

In Mathematics, a function is typically used for uniquely mapping an independent value (input variable or domain) to a dependent value (range or output variable).

This ultimately implies that, an independent value represents the value on the x-axis of a cartesian coordinate while a dependent value represents the value on the y-axis of a cartesian coordinate.

Since the independent value (12) is mapped to multiple dependent values (-4 and -2), we can logically deduce that the relation does not represent a function.

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Answer:angle TSQ and angle UVX

Step-by-step explanation:

The equation of the graph is: y = -x.

The point where the graphs of two equations intersect has y-coordinate 0. If the y-coordinate is 0, that means that the x-coordinate of the point of intersection is the y-intercept of the equation.

The first equation is y = 3x + 3. Therefore, the slope of this equation is 3, and the y-intercept is 3.

The other equation we are trying to find is y = -1x + b, where b is the y-intercept.

Because the point of intersection has y-coordinate 0, the x-coordinate is the y-intercept of the second equation, which is b.

So, if we substitute 0 for y in the second equation, we get 0 = -1x + b

Therefore, b = 0

so the other equation is y = -1x + 0 which simplifies to y = -1x.

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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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A quadratic inequality is an equation that takes the form of ax^2 + bx + c ≤ 0 or ax^2 + bx + c ≥ 0, where a, b, and c are real numbers and a is not equal to 0.

Quadratic inequalities are used to represent a relationship between two variables and can be used to solve a variety of problems. They can be used to find the maximum or minimum value of a function, or to determine the range of values for which a given equation is true. They can also be used to find the number of solutions to an equation and to compare the values of two functions. Quadratic inequalities are used widely in mathematics and other sciences and can help us to understand and solve many real-world problems.

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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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By using pythagorean theorem, the length of the third side is 3 unit.

In mathematics, a number or an expression is said to be in its simplest radical form if it has no perfect square factors other than 1. For example, the square root of 12 can be simplified to 2√3 because 2 * 2 * 3 = 12, but 2 and 3 are not perfect squares. So the simplest radical form of √12 is 2√3.

what is pythagorean theorem?

The Pythagorean theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as:

c^2 = a^2 + b^2

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Answer: (x-2)(x+3)^2(x^2-16)

Step-by-step explanation:

(x+3)^2(x-2)

(x+3)(x^2-16)

(x+3)(x^2-16)=(x+3)(x+4)(x-4)

(x+3)^2(x-2)=(x+3)(x+3)(x-2)

LCM: (x+3)^2(x-2)(x^2-16)

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:

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