in a school, the ratio of the number of boys to the number of girls is 2:3 and the ratio of the number of girls to the number of teachers is 7:3. what is the ratio of the number of students to the number of teachers

On solving the provided question, we can say that the inequality equation is -2y - 5 > 5/2 => -4y - 10 > 5 => -4y > 15 +. y > -15/4

An inequality in mathematics is a relationship between two expressions and or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

here,

the inequality equation is

-2y - 5 > 5/2

-4y - 10 > 5

-4y > 15

y > -15/4

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The postulate or theorem that proves that the two triangles are similar is: ΔFHK is similar to ΔGHJ by the SSS Similarity Theorem.

When the corresponding sides or measure of angles of two or more triangles have common properties, the triangles are said to be similar. This can be deduced on comparing the corresponding length of sides or measure of angles.

In the given question, comparing the corresponding sides of the triangle. We have;

HG/ HF = 10/ 22

            = 0.4545

Also,

HJ/ HK = 15/ 33

            = 0.4545

Since the two ratios are the same, it implies that the third sides of the two triangles would give the same answer. Thus they are similar.

Therefore, the postulate or theorem that proves that the two triangles are similar is: ΔFHK is similar to ΔGHJ by the SSS Similarity Theorem.

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The value of n is -1 < n < -4.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

-4>n or 3n+1>-2

now, solving the above inequality

3n+1>-2

3n > -2-1

3n > -3

n > -1

So, the value of n varies -1 < n < -4.

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Therefore, 2 with an exponent of 0 is equal to 1.

When a number is raised to an exponent of 0, the result is 1. This applies to any non-zero number, including 2. Therefore, 2 with an exponent of 0 is equal to 1.

The reason is that any number raised to the power of 0 is 1. This is because any number multiplied by 1 is itself, and any number raised to the power of 1 is itself. Therefore, raising a number to the power of 0 is the same as multiplying it by 1, so the result is 1.

It is also important to note that a number raised to the power of 1 is the number itself, so 2^1=2, 2^2=4, 2^3=8 and so on.

Therefore, 2 with an exponent of 0 is equal to 1.

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Where while feeding a patient, Nadine, a nurse's aide, twists her upper body as she turns to retrieve a piece of tissue to help the patient wipe hands. She sprains her neck muscles and so has to leave work and go home to rest. Note that Nadine could have correctly turned the body using the principles of body mechanics: "by moving her feet and hips along with the upper body" (Option D)

Employee well-being depends on maintaining good body mechanics at work. Every employee should adhere to the four body mechanics principles. They are as follows:

When these body mechanics principles are followed, employees are less likely to get injured at work and are more productive.

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The base value of a number can be changed by using a base conversion calculator. This calculator can convert a number from one base to any other base. It can also be changed manually by using the rules of base conversion.

Base conversion is the process of changing a number from one numerical base to another.

This can be done manually by using the rules of base conversion or by using a base conversion calculator. When using a calculator, the user will enter the number, the current base, and the desired base and the calculator will output the number in the desired base.

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The slope of the line is 60 The bus is traveling at a speed of 60 miles per hour.

A line's steepness is determined by its slope. Slope can be computed mathematically as "rise over run" (change in y divided by change in x). In the slope-intercept form, the equation for the line is expressed as follows: y = mx + b, where m denotes the slope and b the y-intercept. When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). Its y value of the y intercept point is represented by b in the equation.

Given that,

A line begins at ordered pair (0, 0) and goes through ordered pair (1, 60) and ordered pair (2, 120).

Slope of the line (m) = (y₂ - y₁) / (x₂ - x₁)

m = 120 - 60 / 2 - 1

m = 60

thus, slope of the line = 60

The bus is travelling at a speed of 60 miles per hour.

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If Lori made a fraction of 3/4 of a sketch, then she spent 9 minutes of sketching.

A fraction is a portion of something. Mathematics refers to a number as a quotient when the numerator and denominator are divided. Both are integers in a simple fraction. There is a fraction in the numerator or denominator of a complex fraction. The numerator and denominator of a proper fraction are different sizes.

Given the equation

m = 12s,

where

m is the number of minutes, and

s is the number of sketches.

Lori made 3/4 of a sketch i.e.

m = 12(3/4)

m = 9 mins

Thus, If Lori made 3/4 of a sketch, she spent 9 minutes sketching.

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Answer:

90 degrees

Step-by-step explanation:

The value of m = 2 results in the given equation having infinitely many solutions.

An equation is the mathematical statement of two expressions situated on two sides connected with an equal to sign.

The two sides of an equation is usually called as left hand side and right hand side.

Given the equation,

2(x + 6) = mx + 12

Applying the distributive property a(b + c) = a b + a c on the left hand side,

2x + 12 = mx + 12

Two equations have infinitely many solutions when both the equations are same.

Left and right side are equal if m = 2.

Hence there are infinitely many solutions when m = 2.

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For the linear equations, cx – y = 2 and 6x – 2y = 4 will have infinitely many solutions; the value of c will be 3.

cx – y = 2     eqn(1)

6x – 2y = 4    eqn(2)

The condition for infinitely many solutions is

a₁/a₂ = b₁/b₂ = c₁/c₂    eqn(3)

Here, a₁ = c, b₁ = −1, c₁ = −2 and a₂ = 6, b₂ = −2, c₂ = −4

From eqn(3), we get

c/6 = −1/−2 = −2/−4

⇒c/6 = 1/2 and c/6 = 2/4

⇒c = 3 and c = 3

Hence, for the pair of equations that will have infinitely many solutions, the value of c will be 3.

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The sides 7 cm, 24 cm and 25 cm can form a right-angled triangle. The Pythagorean theorem can be used to verify this.

From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angles triangle.

Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. The equation can then be expressed as,

CA² = AB² + BC²

Now, let us check this rule for the above given sides of the triangle.

Longest side² = Sum of squares of other two sides

25² = 24² + 7²

625 = 625

Thus, the sides 7 cm, 24 cm and 25 cm can form a right-angled triangle.

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The answer to thus question is 140 degrees.

To solve this problem we must know about vertical angles,

Vertical angles are always congruent (congruent means having the same measure or size). Therefore, if one angle measures x degrees, the other angle also measures x degrees. If we know that one of the angles measures 40 degrees, we can use that information to find the measure of the other angle, which is x.

Since the angles are vertical angles, the sum of both angles will be equal to 180 degrees, therefore

x + 40 = 180

        x = 140

Therefore, the value of x is 140 degrees.

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The expression 3x − 6 = 2(x + 4) has one solution of x which is 10

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph

For the given problem, 3x − 6 = 2(x + 4) the solution is sort as thus

3x − 6 = 2(x + 4)

expanding the parenthesis

3x − 6 = 2x + 4

collecting like terms by subtracting 2x from both sides and adding 6 on both sides will result to the equation below

3x - 2x = 6 + 4

x = 10

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Answer:1.33333333 so B

Step-by-step explanation:16/12 = 1.33333333

Answer:

apples don't grow on maple trees

Step-by-step explanation:

Answer:

3:8

Step-by-step explanation:

The total number of t-shirts is 16. Out of the 16 t-shirts, 6 are blue. We can write this as 6:16, or 6 out of 16. You can simplify this further by dividing the ratio by 2 to get 3:8. I hope this helps!

Answer: a. To write a system of equations to find the family's costs for each kind of game according to the FCI, we can use the information provided in the problem. According to the FCI, a family of four would spend a total of $592.30 to attend two MLB games and one NBA game, and the family would spend $691.31 to attend one MLB and two NBA games. Let x be the cost of MLB games and y be the cost of NBA games. Then we can write the following system of equations:

x + y = 592.30 equation 1 represents the cost of attending two MLB games and one NBA game

2y + x = 691.31 equation 2 represents the cost of attending one MLB and two NBA games

b. We can solve the system of equations to find the cost for a family of four to attend each kind of game according to the FCI.

We can substitute equation 1 into equation 2

2y + (592.30 - y) = 691.31

2y + 592.30 - y = 691.31

2y = 691.31 - 592.30 = 99.01

y = 49.51

we know y represents cost of NBA games so 49.51 is cost of one NBA game for a family of four

x = 592.30 - y = 592.30 - 49.51 = 542.79

x represents cost of MLB games so 542.79 is the cost of one MLB game for a family of four

So, according to the FCI, a family of four would spend $542.79 to attend one MLB game, and $49.51 to attend one NBA game.

Step-by-step explanation:

The Triangle with length of the sides as 10.2 cm 5.8 cm and 4.5 cm is possible.

Triangle inequality is a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side; it is represented by the symbols a + b ≥   c. The basic tenet of the theorem is that a straight line connects any two places.

Given:

Sides of triangle is: 10.2 cm 5.8 cm and 4.5 cm

Now, using Triangle inequality "the sum of two sides is greater than the third side of the triangle."

Suppose such a triangle is possible.

4.5 + 5.8 > 10.2

5.8 + 10.2 > 4.5

10.2 + 4.5 > 5.8

Hence, the triangle is possible.

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Number of functions. It is an important topic in sets and relation. A relation in which each input has a specific output is called a function. If f is a function from set A to set B, then each element of A will be plot with only one element in B.

1. Number of possible functions: If a set A has j elements and set B has k elements, then the number of functions possible from A to B is j ^k.

2. Number of Injective Functions (One to One): If set A has j elements and set B has k elements, j ≥k, then the number of injective functions or one to one function is given by j! / (j-k)!

3. Number of Bijective functions: If there is bijection between two sets A and B, then both sets will have the same number of elements. If n(A) = n(B) = m, then number of bijective functions = m!

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A day has 24 hours, so 4 days have 4 * 24 = 96 hours.

The factory produces 350 smartphones per hour, so in 96 hours it can produce 350 * 96 = 33600 smartphones.

Therefore the factory can produce 33600 smartphones in 4 days.

The simplified expressions are given as follows:

1. 3n³/8 + 2.

2. 2.4y² + 7.6y - 0.5.

The expressions are simplified combining the like terms.

The first expression is given as follows:

(7/8)n³ + 2 - (1/2)n³.

The like terms are given as follows:

Hence the simplified expression is:

3n³/8 + 2.

The second expression is defined as follows:

1.4y² + 3.6y + 8y - 0.5 - 4y + y².

The like terms are given as follows:

Hence the simplified expression is:

2.4y² + 7.6y - 0.5.

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To find out how much time the campers took to get downstream, we can use the formula:

time = distance / speed

where distance is the distance they paddled downstream (in this case, 2 km) and speed is their average speed (in this case, 12 km/h). So we can substitute in the values we know to get:

time = 2 km / 12 km/h

To solve for the time, we can divide the distance by the speed:

time = 2/12 hours = 0.17 hours or approximately 10.2 minutes

So it takes 10.2 minutes for Nick and Chloe to get downstream.

Answer: The student got the wrong answer. ✅

Step-by-step explanation: When you add 364 and 728 together, you get 1092. To make it easier to understand, it is like having 3 piles of 100, 6 piles of 10, and 4 ones on one side, and 7 piles of 100, 2 piles of 10, and 8 ones on the other side, when you put them together you get 10 piles of 100, 8 piles of 10 and 12 ones.

To find the biggest number they have in common, you can divide both numbers by 2 and you get 182 and 364.

So the correct way to rewrite 364 + 728 is 364 * (3+2) ✅

The equation y = 2x + 2 is a function. This can be determined by observing that for each x-value, there is exactly one corresponding y-value. In other words, the graph of the equation passes the vertical line test, which states that a graph represents a function if no vertical line intersects the graph more than once.

Additionally, as the given points (1,0), (0,2), (1,4), (2,6) all fall on the same line, all with a slope of 2 and y-intercept of 2, so this confirms that the equation is indeed a function.

Therefore , the solution of the given problem of expressions comes out to be ΔH = ΔU.

By changing each variable with the a number and running arithmetic operations, an algebraic equation must be checked. Since 79 + 8 = 87 , the answer variable in the aforementioned example is the same as 6. We can substitute the variables values with those we know in order to evaluate the expression.

Here,

Given:

During a procedure that takes place in a closed vessel, ΔH = ΔU.

ΔV = 0 denotes that there are no gaseous reactants or products in the reaction, or

that the amount of moles for gaseous products equals the number of molecules of gaseous reactants.

Therefore , the solution of the given problem of expression comes out to be ΔH = ΔU.

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Noah's total score is 17 out of 20 since he answered 3 questions wrong.

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 multiple choice questions = 20

The score of answering one question correctly = 1

Total number of questions Noah wrongly answered = 3

Therefore, his score out of 20 = 20 - 3 = 17

Thus, Noah's total score is 17 out of 20 since he answered 3 questions wrong.

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Answer:

(1, -2)

The solution to a system of equations is the point where the 2 lines intersect.

Examine the graph. Where do the 2 lines intersect?

(1,-2)

The answer is:

Work/explanation:

This system has been solved by the graphing method; both equations have been graphed, and to find the solution, I need to find the point where both graphs intersect. And the graphs are the lines.

The x co-ordinate of the point is the solution for x, and the y co-ordinate of the point is the solution for y.

In our case, the lines intersect at (1, -2), which means that the value of x is 1, and the value of y is -2.