Mr. Chaplin measured his son’s rectangular bedrooms for new carpeting. Whose bedroom has the greatest area?


George’s bedroom 3.5 meters by 4.4 meters
Steven’s bedroom 3.8 meters by 3.8 meters
Andy’s bedroom 3.6 meters by 4.1 meters

This is a credit balance problem. Listed the previous balance, finance charge, new purchases, payments, and credits, the new balance can be calculated by summing up the previous balance, finance charge, and new purchases then subtracted to the sum of payments and credits. Applying this calculation, the new balance for the credit card is

Answer: B. $111.00

Answer:

\(\huge\boxed{GCF:6x^3y}\)

\(\huge\boxed{Factored: 6x^3y(2x+5)}\)

Step-by-step explanation:

Look at both terms separately, and isolate each "part."

i.e. 12x^4y^2 becomes 12, x^4, y^2

So the problem becomes:

12, x^4, y^2 and

30, x^3, y^1

Then, find the GCF of each term,

30 and 12 - 6

x^4 and x^3 - x^3

y^2 and y^1 - y^1

Hope it helps :) and let me know if you want me to elaborate.

a) The ratio of similitude of triangle PQR to triangle STU is the ratio of their corresponding sides.

b) The ratio of the perimeter of triangle PQR to triangle STU is the same as the ratio of their corresponding sides.

a) Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. The ratio of similitude of triangle PQR to triangle STU is the ratio of their corresponding sides, which means that the length of each side of PQR is multiplied by the same factor to get the corresponding side of STU.

b) Since the corresponding sides of similar triangles are proportional, the ratio of the perimeter of triangle PQR to triangle STU is the same as the ratio of their corresponding sides. In other words, if the ratio of the sides of PQR to STU is x:y, then the ratio of their perimeters is also x:y.

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a) The ratio of similitude of triangle PQR to triangle STU is the ratio of their corresponding sides.

b) The ratio of the perimeter of triangle PQR to triangle STU is the same as the ratio of their corresponding sides.

a) Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. The ratio of similitude of triangle PQR to triangle STU is the ratio of their corresponding sides, which means that the length of each side of PQR is multiplied by the same factor to get the corresponding side of STU.

b) Since the corresponding sides of similar triangles are proportional, the ratio of the perimeter of triangle PQR to triangle STU is the same as the ratio of their corresponding sides. In other words, if the ratio of the sides of PQR to STU is x:y, then the ratio of their perimeters is also x:y.

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The given expression is

- 36 > 6x + 12

By subtracting 12 from both sides of the inequality, we have

- 36 - 12 > 6x + 12 - 12

- 48 > 6x

Dividing both sides of the inequality by 6, we have

- 48/6 > 6x/6

- 8 > x

We can write this as

x < - 8

Answer:

25.5

Step-by-step explanation:

He sells 15 and 3/4 bushels each day.

After 6 days he has sold

15 and 3/4 * 6

Change 15 and 3/4 to an improper fraction

15 and 3/4 = 63/4

Thus he sold 63/4 * 6 = 378/ 4 bushels

                                = 94.5

As a result, the farmer would have only 120 - 94.5 = 25.5 bushels for sale

I'm guessing the change in the number of bushels for sale after 6 days would be 94.5

Answer:

y -17 = 17/10(x + 13)

Step-by-step explanation:

Answer: 3 ft

Step-by-step explanation:

l=length. w=width. h=height. V=volume

V=l*w*h

24=4*w*2

24=8*w

8w=24

w=3 ft

Answer:

150

Explanation:

Alright so basically, 150 x 40 = 6000, right? So you want to find out how to find it using the division process. It is a whole number with no fractional part. As division with remainder the result of 6000 ÷ 40 = 150 R 0.

6000 divided by 40 ⇒ 150.

Here given that,

6000 is divisible by 40

since we know that,

Division is a process of repeated subtraction. It is the inverse action of multiplication. It is characterised as the formation of equal groupings. When we divide numbers, we split them down into smaller amounts so that the multiplication of those smaller numbers equals the larger number taken.

6000 is divisible by 40 we get,

⇒ 6000/40

⇒ 150

So, the quotient is 150

Hence,

After dividing 6000 by 40 we get 150.

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Answer:

EG = 84

Step-by-step explanation:

Here, we want to get the length of EG

Mathematically, we will be considering two triangles

these are EFJ and EHG

These two triangles are similar as can be seen

when two triangles are similar, the ratio of their corresponding sides are equal

Thus, we have it that;

EH/EG = EJ/EF

let us represent EF by x

so; EG is (x + 72)

EH = 3 + 18 = 21

Hence, we have it that;

21/x+ 72 = 3/x

21(x) = 3(x + 72)

21x = 3x + 216

21x-3x = 216

18x = 216

x = 216/18

x = 12

EG = 12 + 72 from EG = x + 72

EG = 84

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

Given the equation x^2 = 2y.

The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:

To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].

Now we need to find the value of x that will minimize this expression.

We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.

Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T

he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

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The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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To determine a reasonable range for the function h(t) = -16t^2 + 48t + 36, we need to consider the physical context of the problem.

Since the function represents the height of a ball thrown into the air, the range of the function should be the set of all possible heights that the ball can reach. In this case, the ball is thrown upward and then falls back down due to gravity.

The vertex of the parabolic function can give us some insights. The vertex of the parabola h(t) = -16t^2 + 48t + 36 occurs at the value of t = -b/2a = -48 / (2 * -16) = 1.5 seconds. Plugging this value into the function, we find h(1.5) = 54 feet.

Therefore, a reasonable range for the function is all heights from 0 feet up to a maximum height of 54 feet. In interval notation, the range can be expressed as [0, 54].

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Applying the Pythagorean theorem, the length of the missing side is: x ≈ 18.3 units.

The Pythagorean theorem that is applied to a right triangle with c as the longest side and a and b as the lengths of the other legs is expressed as:

c² = a² + b².

Apply the Pythagorean theorem to find the value of x, where:

a = x

b = 17

c = 25

Plug in the values:

25² = x² + 17²

625 = x² + 289

625 - 289 = x² + 289 - 289

336 = x²

x² = 336

x = √336

x ≈ 18.3 units

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Answer:

\(a^2+2ab+b^2\)

Step-by-step explanation:

If we have \((a+b)^2\) we can calculate this as:

\((a+b)*(a+b)\)

So, applying distribution property, we get:

\((a+b)*(a+b)=a*a+a*b+b*a+b*b\)

Where:

\(a*a=a^{2}\)

 \(b*b=b^2\)

\(a*b=b*a=ab\)

so:

\((a+b)*(a+b)=a^2-ab+ab+b^2\\(a+b)*(a+b)=a^2+2ab+b^2\)

Answer:

9/4 *(x-2)

Step-by-step explanation:

Replace xa and y in the given function then solve for y

a) Bisection Method MATLAB code for equation \(x^3 + 4x^2 - 10 = 0\) in the interval [0,5]:

function root = bisection_method()

   f = \(x^3 + 4*x^2 - 10\);

   a = 0;

   b = 5;

   tol = 1e - 6;

   while (b - a) > tol

       c = (a + b) / 2;

       if f(c) == 0

           break;

       elseif f(a) * f(c) < 0

           b = c;

       else

           a = c;

       end

   end

   root = (a + b) / 2;

end

b) Bisection Method MATLAB code for equation \(x^3 - 6x^2 + 10x - 4 = 0\) in the interval [0,4]:

function root = bisection_method()

   f = \(x^3 - 6*x^2 + 10*x - 4\);

   a = 0;

   b = 4;

   tol = 1e-6;

   while (b - a) > tol

       c = (a + b) / 2;

       if f(c) == 0

           break;

       elseif f(a) * f(c) < 0

           b = c;

       else

           a = c;

       end

   end

   root = (a + b) / 2;

end

c) Newton's Method MATLAB code for equation \(x^3 + 3x + 1 = 0\) in the interval (-2,0]:

function root = newton_method()

   f = \(x^3 + 3*x + 1\);

   df =  \(3*x^2 + 3\);

   \(x_0\) = -1;

   tol = 1e-6;

   while abs(f(\(x_0\))) > tol

       \(x_0 = x_0 - f(x_0) / df(x_0)\);

   end

   root = \(x_0\);

end

d) Fixed-Point Method MATLAB code for equation \(x^3 - 2x - 1 = 0\) in the interval (1.5,2]:

function root = fixed_point_method()

   g = \((x^3 - 1) / 2\);

   \(x_0 = 2\);

   tol = 1e-6;

   while abs(\(g(x_0) - x_0\)) > tol

       \(x_0 = g(x_0)\);

   end

   root = \(x_0\);

end

e) Secant Method MATLAB code for equation 1 - 2*exp(-x) - sin(x) = 0 in the interval (0,4]:

function root = secant_method()

   f = 1 - 2*exp(-x) - sin(x);

   \(x_0\) = 0;

   \(x_1\) = 1;

   tol = 1e-6;

   while abs(f(\(x_1\))) > tol

       \(x_2 = x_1 - f(x_1) * (x_1 - x_0) / (f(x_1) - f(x_0))\);

       \(x_0 = x_1\);

       \(x_1 = x_2\);

   end

   root = \(x_1\);

end

f) Secant Method MATLAB code for equation \(2 - x^3 + 4*x^2 - 10 = 0\) in the interval [0,4]:

function root = secant_method()

   f = \(2 - x^3 + 4*x^2 - 10\);

   \(x_0 = 0\);

   \(x_1 = 1\);

   tol = 1e-6;

   while abs(f(\(x_1\))) > tol

       \(x_2 = x_1 - f(x_1) * (x_1 - x_0) / (f(x_1) - f(x_0))\);

       \(x_0 = x_1\);

       \(x_1 = x_2\);

   end

   root = \(x_1\);

end

MATLAB provides several numerical methods for solving equations. In this case, we have used the Bisection Method, Newton's Method, Fixed-Point Method, and Secant Method to solve different equations.

The Bisection Method starts with an interval and iteratively narrows it down until the root is found within a specified tolerance. It relies on the intermediate value theorem.

Newton's Method, also known as Newton-Raphson Method, approximates the root using the tangent line at an initial guess. It iteratively refines the guess until the desired accuracy is achieved.

The Fixed-Point Method transforms the equation into an equivalent fixed-point iteration form. It repeatedly applies a function to an initial guess until convergence.

The Secant Method is a modification of the Newton's Method that uses a numerical approximation of the derivative. It does not require the derivative function explicitly.

By implementing these methods in MATLAB, we can numerically solve various equations and find their roots within specified intervals.

These numerical methods are powerful tools for solving equations when analytical solutions are not feasible or not known.

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Answer:

1148

Step-by-step explanation:

Multiply to get 1148.16, then round.

Answer:

(- 110, - 22 )

Step-by-step explanation:

since the dilatation is centred at the origin , then multiply the coordinates of the point by 22

(- 5, - 1 ) → (- 5(22), - 1(22)) → (- 110, - 22 )

Answer:

8 feet

Step-by-step explanation:

It is given that, a 3 ft tree casts a 10 ft. shadow.  It means that 1 ft long shadow will cast by \(\dfrac{3}{10}\) feet long tree.

Let 26 ft tall tree will cast x feet long shadow. To find it using unitary method we get :

\(x=\dfrac{3}{10}\times 26\\\\x=7.8\ \text{feet}\)

or

x = 8 feet

So, 8 feet long is the shadow of a 26 feet tall tree.

Answer:The cost for each person is not always the same. It is not a linear relationship between number in group and cost in dollars. Since we have only 4 rows it's difficult to make an accurate prediction for cost of $50, In addition, we don't have any formula or equation that can represent this data set.

The best way to find out how many people will go to movie with $50 is by looking at the table.

So the answer is, We don't have any information that can give us a prediction of number in group for a cost of $50,

Step-by-step explanation:

Answer:

12.75

Step-by-step explanation:

if 10.2 /y= 0.8,

then 10.2/y = 0.8/1.

( cross multiply ), we have that

10.2*1=9.8*y

so,10.2=0.8y

(divide both sides by the coefficient of y)

y=10.2/0.8

y = 12.75

After dividing 10.2 by an unknown number gives 0.8. The unknown number is 12.75.

It is described as the process through which we add, subtract, multiply, and divide numerical values. It has the fundamental operators +, -, ×, and ÷.

The order in which arithmetic operations must be performed in an equation is referred to as PEMDAS. This rule states that operations must be performed as follows: parentheses, exponents, multiplication, or division, followed by addition or subtraction.

Let the unknown number be x,

10.2 / x= 0.8

10.2/x = 0.8

10.2×1=9.8×x

10.2=0.8x

x=10.2/0.8

x= 12.75

Hence, after dividing 10.2 divided by an unknown number gives 0.8. The unknown number is 12.75.

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The 25th number in the arithmetic sequence is 197.

The sequence starts with the number 5 and counts by 8s. To find the 25th number in the sequence, we need to find the number that comes after the 24th number.

To do this, we can use the formula for the nth term of an arithmetic sequence, which is given by the formula:

aₙ = a₁ + (n - 1)d

In this case, a₁ is the first term of the sequence (5), n is the number of terms (25), and d is the common difference (8). Plugging these values into the formula, we get:

a₂₅ = 5 + (25 - 1) * 8

Simplifying this expression, we get:

a₂₅ = 5 + 24 * 8
    = 5 + 192
    = 197

Therefore, the 25th number in the sequence is 197.

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Answer:

\(p=- \frac{15}{2}\)

\(p=2\)

Step-by-step explanation:

\(2p^2+11p=30\)

Subtract 30 on both sides.

\(2p^2+11p-30=30-30\)

\(2p^2+11p-30=0\)

Factor left side of the equation.

\((2p + 15)(p-2)=0\)

Set factors equal to 0.

\(2p+15=0\)

\(2p=-15\)

\(p=\frac{-15}{2}\)

\(p-2=0\)

\(p=2\)

a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Answer:

the answer to this certain question is 5

The one-line answer statement for the optimum solution regarding the number of trucks to be produced per day by Green Vehicle Inc. is: Number of trucks to be produced per day = Any positive value or infinity.

To determine the optimum solution for the number of trucks to be produced per day by Green Vehicle Inc., we need to consider the objective function and maximize the objective value.

Let's denote the number of trucks to be produced per day as "x". Since it takes 1/25 of a day to paint a truck and 1/45 of a day to assemble a truck, the total time required to process "x" trucks in the paint shop and assembly shop would be (1/25)x and (1/45)x, respectively.

The profit per truck for a T1 truck is $300. Therefore, the total profit from the production of "x" trucks can be calculated as 300x.

To maximize the objective value, we need to maximize the total profit. Hence, the objective function would be:

Objective function: Total Profit = 300x

Now, to find the optimum solution, we need to consider any constraints or limitations provided in the problem statement. If there are no constraints or limitations on the production capacity, we can produce an unlimited number of trucks.

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Answer:

Two imaginary solutions.

Step-by-step explanation:

In order to simplify the equation, we square root both sides. As the argument (value in the root) is negative, and we know that the square root function's domain is only positive numbers, we would have two imaginary solutions.

This would be positive/negative \(3i\sqrt{5}\).

Another way to visualize this is by looking at the parabola's graph. Through algebraic manipulation, we know that the parabola is z^2 + 45. This parabola never crosses the x-axis. Therefore there are two solutions that are imaginary.

I hope this helps!