If 1/4 of the dozen eggs were
cracked, how many eggs were
not cracked? Plz hurry

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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The mathematical model that can be used to express the verbal statement of the proportional relationships are;

10. y = k/x²

11. P = k/V

12. P = k·V·I

A proportional relationship is one in which the output variable is a multiple of the input variable and a constant (the constant of proportionality).

10. The verbal statement is; y varies inversely as the square of x

The inverse relationship indicates that a variable is related to the reciprocal of the other variable, therefore;

The mathematical model for the statement can be presented as follows;

y ∝ 1/x²

The constant of proportionality k can therefore be applied as follows;

11. The verbal statement is; For a constant temperature, the pressure P of a gas is inversely proportional to the volume V of the gas

The mathematical model of the proportional relationship is; P ∝ 1/V

Therefore;

12. The verbal statement is; The electric power P of a direct current circuit is jointly proportional to the voltage V and the electric current I

The mathematical model is therefore;

P ∝ V·I

Therefore;

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The solution of the expression, \(x^{\frac{9}{7} }\) is \(\sqrt[7]{x^{9} }\).

An expression is a combination of numbers, variables, functions such as addition, subtraction, multiplication or division etc.

Therefore, let's rewrite the expression to it's equivalent expression.

An equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.

Therefore, using indices rule

\(x^{\frac{9}{7} }\) = \(\sqrt[7]{x^{9} }\)

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Answer:

x=9

Step-by-step explanation:

step one pull out the factors

 3x - 27  =   3 • (x - 9)

and step two: Equations which are never true

2.1      Solve :    3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

so x-9=0 and add both sides to 9 and to equal 9

5 years longer then Bill, 2x5=10.

10+2=12.

12-5=7

Hoang has be there for 12 years. Bill has for 7 years.

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

output = 23

Step-by-step explanation:

x = -4

f(x) = 3ǀ2x - 1ǀ + x

f(x) = 3ǀ2(-4) - 1ǀ + (-4)

f(x) = 3ǀ2(-4) - 1ǀ - 4

f(x) = 3ǀ-8 - 1ǀ - 4

f(x) = 3ǀ-9ǀ - 4

f(x) = 3(9) - 4

f(x) = 3(9) - 4

f(x) = 27 - 4

f(x) = 23

Answer:

2.865

Step-by-step explanation:

pls rate five stars, thanks  :)

Answer:

3 and 17

7 and 13

Step-by-step explanation:

Three odd numbers add up to 25

This means that

\(x + y + z = 25\)

One of the numbers is 5

Using \(z = 5\)

We have that:

\(x + y + 5 = 25\)

\(x + y = 20\)

Then

We need to find two prime numbers which add to 20.

The prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, ...

So the possible options are:

3 and 17

7 and 13

The exact values of sin(θ), sec(θ), and tan(θ) are -3/√13, -√13/2 and 3/2 respectively.

Suppose a segment is formed starting from the origin to a certain point, this terminal point's coordinates can help determine the values of the trigonometric functions of the angle this segment forms with the positive x-axis. For a point (x,y), the trigonometric functions of the angle are as follows.

sinθ=y/r,cosθ=x/r, tanθ=y/x, cscθ=r/y, secθ=r/x, cotθ=x/y

We are given the point (x,y)=(−3,7) and we are asked to determine certain values of the trigonometric functions of the angle, θ between the positive x-axis and the line segment formed by connecting the origin and the given point. It would help if we find the value of r first using the Pythagorean theorem then plug them into the formulas above.

r=√(-2)²+(-3)²

=√13

sinθ=y/r= -3/√13  secθ=r/x= -√13/2 and tanθ=y/x= 3/2

Therefore, the exact values of sin(θ), sec(θ), and tan(θ) are -3/√13, -√13/2 and 3/2 respectively.

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Answer:

Each notebook cost $3 and each binder cost $4.

Step-by-step explanation:

Do some trial and error when plugging in certain numbers for each notebook and each binder.  You should get $3 and $4 when plugging it in.

Answer:

there is no slope

Step-by-step explanation:

cause both x variables are the same

Answer:

C) 22 units

Step-by-step explanation:

2x(9-1)=16

2x(5-2)=6

16+6=22

Answer: maybe 0 if i sound unreasonable then I'm really sorry I'm only in 4th grade.

Step-by-step explanation: -10 + 10 + -10 + 10

Answer:

33

Step-by-step explanation:

333333333333333333333

Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

Answer:

approx. 9.06 for one pound

Step-by-step explanation:

Answer:

D) 48

Step-by-step explanation:

Let s = Scott

Let j - James

s = 5

s + 43 = j  Substitute 5 for s

5 + 43 = j

48 = j

The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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Answer:

A, She added before multiplying.

Step-by-step explanation:

First, start off by using GEMDAS.

Grouping

Exponents

Multiply

Divide

Add

Subtract

You work from left to right - so you obviously divide first, which Amanda did successfully. Then, you multiply, which is exactly where Amanda went wrong. She was supposed to multiply before adding the 3 with 4.

Not sure if this made sense,

Answer:

(i) 8b-32

(ii) 7z^3+12z^2-20z

(iii) –q+p

(iv) a+ab

(v) 8x^2y+8xy^2-4x^2-7y^2

(vi) 4y^2-3y

Step-by-step explanation:

Answer: c

Step-by-step explanation:

The number of cows are 9 and the number of chickens are 13.

Given that, a farm has 22 cows and chicken altogether.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let the x be the number of cows and y be the number of chicken.

Now, x+y=22 -------(I)

The farmer counted 62 legs total.

So, 4x+2y=62 -------(II)

Multiply equation (I) by 2, we get

2x+2y=44 -------(III)

Subtract equation (III) from equation (II), we get

4x+2y-(2x+2y)=62-44

⇒ 2x=18

⇒ x=9

Substitute x=9 in equation (I), we get

9+y=22

⇒ y=13

Hence, the number of cows are 9 and the number of chickens are 13.

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Answer:

100 lightbulbs

Step-by-step explanation:

Basically find the percentage of lightbulbs that are bad. 5/136. So about 3. 6 percent. I'm going to use a more exact form of this percent for my calculations though. Now use the decimal for of this (0.036....) and multiply it by 2720. Using my exact decimal, the answer just so happened to be exactly 100. So there will be 100 defective lightbulbs per day. (Teachers are a stickler for units, so don't forget them if it's for a teacher)

Hope this helps!

Answer:

81

Step-by-step explanation:

25 and 27 are not perfect squares so they can not be the answer.

36 and 81 are both multiples of 3, but only 81 is not even, so the answer is 81

Answer:

9

Step-by-step explanation:

3+3+3=9

Answer:

9

Step-by-step explanation:

3

6

9

Answer:

Step-by-step explanation:

Given that the total distance of the school from home is 6km

converting 6km to meters we have 6,000m

Since the bus stopped at 4750 meters from his home.

The remaining distance is the distance the bus is from his school

i.e \(6000-4750= 1250 meters\)

Answer: C

Step-by-step explanation:

The rest of the quadrilaterals provided have 2 pairs of parallel lines.

The choice is:

Explanation:

The quadrilateral that has exactly one pair of parallel lines is called a trapezoid.

Here's what a trapezoid looks like :

\(\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(1,3)\qbezier(5,0)(5,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(8.2,0)(0,0)\put(-0.5,-0.3){$\sf A$}\put(5.3,-0.3){$\sf B$}\put(4.2,3.1){$\sf C$}\put(0.6,3.1){$\sf D$}\end{picture}\)

Answer:

30.57%

Step-by-step explanation:

Dylan bought it for 3600.

Kirtim bought it from Dylan for 3600+205 = 3805

Aayush bought it from Kirtim for 4968.

that difference (profit for Kirtim) = 4968 - 3805 = 1163

Kirtim's initial 100% = 3805

1% = 100%/100 = 3805/100 = 38.05

now we want to know how many % in relation to his buying cost this 1163 selling profit is.

that means we need to see how often 1% fits into that amount.

%profit = profit / 1% cost = 1163 / 38.05 = 30.57%

=>

Kirtim made a profit of 30.57%.