The ratio of three numbers is 7 : 3 : 2. These three numbers have a sum of 228. What is the difference between the largest and the smallest of these three numbers?.

Answer:

Step-by-step explanation:

(a) 1.653 x 10^12 / 87 * 10^6

= (1.653 / 87) x (10^12 / 10^6)

= 0.019 x 10^6

= 1.9 x 10^4

or 19,000 days.

(b) 6 billion / 87 million

= 6,000,000,000 / 87,000,000

= 6000/87

= 69 days.

The second step required to solve the given system of equations using elimination method is to add or subtract the modified system of equations.

As given in the question,

Steps required to solve the given system of equations by elimination method :

Let us consider two system of equations are :

2x + 3y = 1  __(1)

3x + 2y = 1  __(2)

1. Multiply 3 to (1) and 2 to (2)  to eliminate the x-term.

6x + 9y = 3  __(3)

6x + 4y = 2   __(4)

2. Now in second step subtract (4) from (3) to get the value of y.

6x + 9y = 3  

6x + 4y = 2

0x + 5y = 1

⇒ y = 1/5

3.  Multiply 2 to (1) and 3 to (2)  to eliminate the x-term

4x + 6y = 2 __(5)

9x + 6y = 3  __(6)

4. Now in subtract (5) from (6) to get the value of x.

9x + 6y = 3

4x + 6y = 2

5x = 1

⇒ x = 1/5

Therefore, the second step in the given system of equation using elimination method is add or subtract the modified equations.

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The linear equation for this scenario is y = 2x + 10 and $20 was charged for 5 ATM transactions

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the total cost for x monthly transactions.

$10 is charged monthly plus $2 per transaction, hence:

m = 2, b = 10

y = 2x + 10

For 5 ATM transactions:

y = 2(5) + 10 = $20

The linear equation for this scenario is y = 2x + 10

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The percentage error is 8.3%. ((60 - 55) / 60) x 100 = 8.3%.

(60 - 55) / 60 = 0.083

0.083 x 100 = 8.3

Brianna estimated that he would spend $60 hopping for school supplies before the start of the school year. However, she actually spent $55. To calculate the percent error for her estimate, we first subtract the actual amount spent ($55) from the estimated amount ($60). This gives us 0.083, which is then multiplied by 100 to get 8.3%. This means that Brianna's estimate was 8.3% off from the actual amount spent. This result can help her understand how close her estimate was to the actual amount spent and can help her improve her estimating skills in the future.

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Your monthly payment for this house will be $1689.5 if your mortgage payment is $1345, your annual insurance premium is $678, and your real estate taxes are $3456.

Describe the mortgage payments in brief?

Principal and interest payments make up your monthly mortgage payments. You must purchase private mortgage insurance if your down payment is less than 20%, which raises your monthly payment. Real estate or property taxes are also included in some payments. Early on in the mortgage, the borrower pays more interest, whereas the principle balance is favored in the latter stages. A greater down payment will directly increase your home's equity.

To find the total monthly payment for the home, we need to divide the annual costs by 12.

Total monthly payment = Mortgage payment + (Annual insurance premium / 12) + (Annual real estate taxes / 12)

= $1345 + ($678 / 12) + ($3456 / 12)

= $1345 + $56.5 + $288

= $1689.5

So the total monthly payment for the home is $1689.5

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Your monthly payment for this house will be $1689.5 if your mortgage payment is $1345, your annual insurance premium is $678, and your real estate taxes are $3456.

Principal and interest payments make up your monthly mortgage payments. You must purchase private mortgage insurance if your down payment is less than 20%, which raises your monthly payment. Real estate or property taxes are also included in some payments. Early on in the mortgage, the borrower pays more interest, whereas the principle balance is favored in the latter stages. A greater down payment will directly increase your home's equity.

To find the total monthly payment for the home, we need to divide the annual costs by 12.

Total monthly payment = Mortgage payment + (Annual insurance premium / 12) + (Annual real estate taxes / 12)

= $1345 + ($678 / 12) + ($3456 / 12)

= $1345 + $56.5 + $288

= $1689.5

So the total monthly payment for the home is $1689.5

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Answer: f(2) = g(2)

Step-by-step explanation:

Well, this is kind of a comparison so you can do this by putting "2" as x value for both functions.

If you do that for both functions:

[tex]f(x) = 4x^{5}\\f(2) = 128 = (2^{7}) \\----------\\g(x) = 8.4^{x} = 2^{2x + 3}\\g(2) = 128[/tex]

So, this shows that f(2) = g(2).

The table for given phrase shows non-linearity.

The complete explanation is given below.

The graph of a linear function is a straight line. The following is the form of a linear function.

a + bx = y = f(x).

One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.

Given:

There were 50 mosquitos near a pond.

The population doubles every month.

For 4 next four months, the population of mosquitos,

Number of months (x) → Population (y)

1  →  50

2 →  100

3 →  200

4 →  400

If the table shows linear relationship,

then its first difference is constantly equal.

That means,

100 - 50 = 50

200 - 100 = 100

400 - 200 = 200

First difference is not equal.

Therefore, the table shows non-linearity.

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Using the formula x=-b/2a, find the quadratic's vertex, and then substitute the result for y in the original equation.

Three points produce a quadratic function of the formula f(x) = ax^2 + bx + c. A quadratic function can be determined by finding a, b, and c algebraically given three locations on the graph. Because two points do not define a particular parabola, it is not possible.

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The function y whose graph is a horizontal shrink of f(x) = 5x + 8 by a factor of 1/5 is given as follows:

y = 25x + 8.

The function for this problem is defined as follows:

f(x) = 5x + 8.

For the horizontal shrink by a factor of a, the function is defined as follows:

f(x/a).

The parameter a for this problem is given as follows:

a = 1/5.

Hence the shrunk function is defined as follows:

y = f(x/(1/5)) = f(5x) = 5(5x) + 8 = 25x + 8.

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A 3x4 matrix is ​​a matrix with 3 rows and 4 columns is a rectangular matrix. The number of solutions in a matrix depends on the context in which it is used.

When the matrix is ​​used to represent a system of linear equations, the number of solutions to the system depends on the rank of the matrix, which is the number of linearly independent rows or columns.

A 3x4 matrix has no solutions because it is not a square matrix and does not have a well-defined inverse. A square matrix has the same number of rows and columns and can be inverted if and only if its determinant is nonzero. A non-square matrix, on the other hand, has no inverse and cannot be inverted.

It should be noted that in the case of the rectangular matrix, the solution depends on the context of the problem and by using other techniques, such as the linear least squares method.

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Step-by-step explanation:

22 pounds for $11.

we could now calculate how many pounds we can buy for $1.

that would be 22/11 = 2 pounds.

or we can calculate as requested how much (how many $) he needed to pay for 1 pound.

that would be 11/22 = 1/2 = $0.50

and as you can see, both answers work prefectly together. they are just different views of the same basic problem.

we have to pay $0.50 per pound, and so we can buy 2 pounds with $1.

The equation that represents the situation in terms of x is 4x = 50 -13.5,

and there will be 9 whole pieces of wire of 4 feet.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Given the total length of wire = 50 feet

length used = 13.5 feet

length of wire left = 50 - 13.5

A. wire is cut into 4 feet pieces

let there are x pieces,

expression for the pieces is

4x = 50 -13.5

B. 4x = 50 - 13.5

4x = 36.5

x = 36.5/4

x = 9.125

the whole number is 9

so there will be 9 pieces in a whole.

Hence the expression is 4x = 50 -  13.5,

and there will be 9 pieces of wire.

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force = M × A

115 = M × 0.657

make M which is the mass the subject by dividing by 0.657 on both sides

115/0.657 = 0.657M/0.657

M = 115/0.657

M = 175.0380518

M = 175kg

Her gross pay is $850.

Commission, also known as sales commission, is a payment given to employees based on the sales they make. Create invoices for free with SumUp Invoices. Commission is often calculated as a percentage of the value of a sale.

Gross salary is the amount received by an employee without any tax deductions. Net salary is the amount that an individual receives after all deductions have been taken out.

Salary of Carly = $720

Commission of Carly = 4%

Amount of products sold by Carly = $3250

Commission of Carly on the goods sold = 4% of $3250 = $130

Hence gross pay of Carly = $720 + $130 = $850

Carly hence gets $850 at the end of the week.

Her gross pay is her salary plus her commission.

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A 45-45-90 triangle is an isosceles right triangle, meaning that it has two congruent sides and one right angle. To find the area and perimeter of a 45-45-90 triangle, use the following formulas:

Area:

(1/2) * (side length)^2

Perimeter:

2 * (side length) + (side length) * √2

Note that the perimeter of a 45-45-90 triangle is equal to twice the length of one of its sides plus the length of the hypotenuse.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The F-14 Tomcat was created as a long-range naval interceptor and air superiority fighter, allowing it to perform the roles of an escort attack aircraft when equipped with Sparrow missiles and a fleet air defense loitering interceptor when equipped with Phoenix missiles.

The F-14 was equipped with the capacity to shoot down ANY enemy aircraft, anywhere in the globe. No other Cold War aircraft could dispatch two nuggets on a "normal" mission from the CV and capture two Aces a few hours later. Incredible combat capabilities were made possible by the AIM-54 and the AWG-9.

During the war, the F-14 was credited with one air-to-air victory. On February 6, 1991, a VF-1 F-14A employing an AIM-9 Sidewinder brought down an Iraqi Mil Mi-8 helicopter. Budget cuts that came into effect in 1991, after the conclusion of both the Cold War and the Persian Gulf War, forced the early retirement of the Tomcat.

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The 4 systems of equations are Quadratic Equation, Linear Equation,

Exponential Equation and Rational Equation.

Linear Equations: Each term involved in the linear equation is either a constant, a single variable, or a product of a constant. The general form of this equation with two variables is shown by

Y = mx + c,   m ≠ 0

Where m is the slope

C is the intercept of the y-axis

Quadratic Equations: The quadratic equation is a second-order equation in which any one of the variables contains a power of 2. The general form is

px² + qx + r = 0, p ≠ 0

Exponential Equations: This math equation contains the variables in place of exponents. By using the properties, an exponential equation can be solved.

[tex]a^{x}=a^{y}[/tex] ⇒x = y

Rational Equations: A rational math equation involves rational expressions.

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Answer:

13.5 blocks

12 blocks

Step-by-step explanation:

Each division on the number line represents half a block.

From inspection of the number line:

Therefore, the distance between John's house and Liam's house is:

From inspection of the number line:

Therefore, the distance between Katie's house and Trina's house is:

The number of small boxes it is carrying is 60 and the number of large boxes it is carrying is 50.

The first step is to form a system of equations using the information in the question:

l + s = 110 equation 1

60l + 30l = 4800 equation 2

Where:

l = number of large boxes

s = number of small boxes

The elimination method would be used to solve these equations.

Multiply equation 1 by 60

60l + 60s = 6,600 equation 3

Subtract equation 2 from equation 3:

30s = 1800

Divide both sides of the equation by 30

s = 1800 / 30

s = 60

Substitute for s in equation 1

l + 60 = 110

l = 110 - 60

l = 50

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Yes, 35 and 36 are co-prime numbers. The factors of 35 are 1,,5, and 7 while for 36 it is 1,3,4,6,9, and 12. They share only 1 as factor hence they are coprime

The only two numbers that have 1 in common are known as co-prime numbers. From 1 to 100, some of these Co-Prime Numbers include: There are numerous pairs of Co-Primes from 1 to 100 that adhere to the aforementioned characteristics. The following are a few of them: (1, 99), (14, 15), (28, 57), (29, 31), (23, 1), (59, 97), etc. Sets of numbers that are coprime with one another are referred to as coprime numbers. Each and every prime number is a co-prime: One and the number itself are the only two factors that each prime number has, so the only factor that two prime numbers will have in common is 1. Two prime numbers are, for instance, 11 and 17.

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Radical 3, also known as the cube root of 3, is a number that when multiplied by itself three times equals 3. It is denoted as ∛3. To find the value of radical 3, one way is to use a calculator with a cube root function.

Another way to find the value of radical 3 is to use a process called prime factorization. It involves breaking the number down into its prime factors and then taking the cube root of the result. In the case of ∛3, we have:

∛3 = ∛(3)

Since 3 is a prime number, we don't need to factor it further, and thus the cube root of 3 is just 3^(1/3) = 3^(1/3) = ∛3.

It's important to note that cube roots can be negative or positive and in this case, ∛3 is positive.

∛3 is an irrational number, which means that it cannot be expressed as a ratio of two integers, and its decimal representation is non-repeating and non-terminating. But it can be approximated to some decimal values.

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Jackson's company $1.2 more than Micaela's.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Micaela charges a $3.50 pickup fee and $1.30 per mile.

And, The table represents what Jackson's company charges.

Now, Micaela charges a $3.50 pickup fee and $1.30 per mile.

Hence, The equation that represents Mathew's charges is given as,

⇒ y = 1.30x + 3.50  .. (i)

And, From table,

The equation that represents Jackson's charges is given as:

Take two points (x, y) = (10, 30.50) and (30, 88.50)

Hence, The equation is,

⇒ y - 88.50 = (88.50 - 30.50)/(30 - 10)  (x - 10)

⇒ y - 88.50 = 50/20 (x - 10)

⇒ y - 88.50 = 2.5 (x - 10)

⇒ y - 88.50 = 2.5x - 25

⇒ y = 2.5x + 88.50 - 25

⇒ y = 2.5x + 63.50  .. (ii)

We know that;

A linear equation is represented as:

⇒ y = mx + b

Where: m represents the slope/rate.

Hence, Jackson's company $1.2 more than Micaela's.

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We know that 1 hour = 60 minutes.

Set equal proportions for both Laisha and Jefford to find the distance x and y they bike in 60 minutes:

Laisha will bike farther by:

In this situation, it is true that the population who go to the movie theater, and the sample is the first 150 people of the theater.

In statistics and related fields, the population can be considered as the whole or the complete group that is being studied. On the other hand, the sample is a fraction taken from the whole population.

The purpose of a sample is to make the process of studying the population easier as studying every individual of the population is too complicated.

Based on this, the population are all customers going to the theater but the sample are the 150 people.

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Due to its peculiar ratio of 1:2:3  , the  30-60-90 triangle is referred to as a special right triangle. Any triangle with a ° angle is considered to be a right triangle in this context.

A unique type of right triangle known as  30-60-90 a  triangle always has angles of

30-60 and -90 ,

The length of the hypotenuse is twice the length of the shortest side and the length of the other side is √ times the length of the shortest side in a  30-60-90  Triangle.

The above theorem can be written mathematically as the 30-60-90  Triangle Formula as

√  which is the ratio of the three sides of the  30-60-90 Triangle.

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The area of the major sector is 2807. 1 cm²

The perimeter of a sector given by the formula:

P = θ/360 × 2πr

where r is the radius and θ is the angle subtended at the centre

Since the perimeter of a major sector is 168cm and the angle subtended by the minor arc is 72 degrees. We can say:

angle subtended by the major arc  = 360 -72 = 288 degrees

P = θ/360 × 2πr

168 = 288/360 × 2πr

210 = 2πr

r = 210/2π

r = 33.42 cm

Thus, the radius of the major arc is 33.42 cm

The area of a sector given by the formula:

A = θ/360 × πr²

A = (288/360) × π × 33.42²

A = 2807. 1 cm²

Thus, the area of the major sector is 2807. 1 cm²

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Equation of the form are considered quadratic equations: ax² + bx + c = 0, where a, b and c are constants. The most straightforward method of solving a quadratic equation by factoring is to express the equation in its factored form, and then solve for the values of x that make it true.

To solve, start by setting the equation equal to zero. This will simplify the equation and make it easier to factor.

The equation has to be factored after that. To do this, you will need to identify the factors of c that add up to b. For example, if c = 15 and b = 6, the factors are 3 and 5, since 3 + 5 = 6.

Once you have identified the factors, you can rewrite the equation in its factored form. For example, if c = 15 and b = 6, the equation can be rewritten as (x+3)(x+5) = 0.

Finally, you can solve the equation by setting each factor equal to zero. For instance, if the equation is (x+3)(x+5) = 0, then x+3 = 0 and x+5 = 0. Solving each equation separately, you get x = -3 and x = -5. Therefore, the solutions to the equation are x = -3 and x = -5.

In conclusion, to solve a quadratic equation by factoring you will need to set the equation equal to zero, identify the factors of the constant c that add up to the coefficient b, and then rewrite the equation in its factored form. Finally, you can solve for the values of x that make the equation true by setting each factor equal to zero.

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The quadratic formula, factoring, using the square roots, and completing the square are the four methods for solving a quadratic equation.

The quadratic formula x = [-b(b2 - 4ac)] / (2a) provides the solutions of the quadratic equation ax2 + bx + c = 0. Therefore, to use the quadratic formula to solve a quadratic equation, simply transform the equation into its standard form, ax2 + bx + c = 0, and then apply the quadratic formula.

A quadratic equation is a second-order equation written as ax2 + bx + c = 0, where a is a real number and b and c are real number coefficients.

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Answer:

4 hours

Step-by-step explanation:

We know

Mr. Bagnulo charges $60 per hour for the labor, and you must pay $100 for the part. Let C represent the cost and x represent the number of hours; we have the equation

C = 60x + 100

Now put 340 in for C and solve

340 = 60x + 100

240 = 60x

x = 4 hours

So, Mr. Bagnuoto take 4 hours to fix your car,

The equivalent fractions of 3/4 are 6/8, 9/12, 12/16, and 15/20.

Equivalent fractions are fractions that represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake. If you cut a cake into eight equal pieces and eat four of them, you will still have eaten half the cake. These are equivalent fractions.

To find the equivalent fractions for any given fraction, multiply the numerator and the denominator by the same number. For example, to find an equivalent fraction of 3/4, multiply the numerator 3 and the denominator 4 by the same number, say, 2. Thus, 6/8 is an equivalent fraction of 3/4. We can find some other equivalent fractions by multiplying the numerator and the denominator of the given fraction by the same number.

3/4= 3×3/4×3

=9/12.

3/4=

3/4= 3×4/4×4

=12/16

3/4= 3×5/4×5

=15/20

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