Ben’s aunt gives him $100 to spend on clothes. He buys 3 shirts that cost $16 dollars each and 1 pair of pants that cost $29. What is the total amount that Ben spends on shirt? How much more money does Ben spend on the 3 shirts than on the pair of pants? Ben also buys a baseball cap that is 4$ off the normal cost of 20$. Write an expression that shows how much Ben spends on all of his purchases. Explain hos you determinted your expression. Write an equcation that can be used to determine the amount of money Ben should have remaining after all of his purchases. Be sure to include a variable in your equaction. Sovle your equcation to find the amount of money Ben has remaining.

2x(3)-(-1) to the power 4 + 3x3 to the power of 2 x(-1) to the power 2 is 7raised to the power (-52).

The BODMAS rule states we should calculate the Brackets first, then any Division or Multiplication and finally any Addition or Subtraction.

while exponent is  a symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power

In the given problem the correct process of solving the problem is

firstly solve 2x(3)-(-1) = 6+1=7

solve 4+3x3=4+9=13

and then 2x(-1)= -2

Now moving as per the problem 2x(3)-(-1) to the  4 + 3x3 to the power of 2 x(-1) to the power 2=((7^13)^(-2))^2= 7^(-52)

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The number "three hundred and sixty-seven thousand seven hundred and fifty-two" can be written in numerical form as 367,752.

To understand how to convert this written form into a number, let's break it down step by step:

1. Starting from the left, we have "three hundred" which is represented by the digit 3 followed by two zeros, resulting in 300.

2. Moving on, we have "sixty-seven thousand." Here, "sixty" corresponds to the number 60, and "thousand" implies three zeros. Therefore, "sixty-seven thousand" becomes 67,000.

3. Finally, we have "seven hundred and fifty-two." "Seven hundred" is written as 700, and "fifty-two" can be represented by 52. Combining these two numbers, we get 752.

Now, we can put it all together. Combining 300 (from "three hundred"), 67,000 (from "sixty-seven thousand"), and 752 (from "seven hundred and fifty-two"), we obtain the final number: 367,752.

To summarize:
- "Three hundred" becomes 300
- "Sixty-seven thousand" becomes 67,000
- "Seven hundred and fifty-two" becomes 752

So, the written form "three hundred and sixty-seven thousand seven hundred and fifty-two" corresponds to the numerical value 367,752.

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Answer:

The answer is D. Variable. The "letters after the numbers" are always variables. A coefficient is the number that the variable is being multiplied by. An exponent would be something like this: \(x^{2} \\\) with the 2 being the exponent. A binomial is an algebraic expression of the sum or the difference of two terms.

The area of the given triangle is 87.55 square centimeter.

From the given triangle, base=17 cm and height=10.3 cm.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Here, area of a triangle = 1/2 ×17×10.3

= 87.55 square centimeter

Therefore, area of the given triangle is 87.55 square centimeter.

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The highest level of detailed information about social scientific findings can typically be found in academic journals. These journals publish peer-reviewed research articles written by experts in the field, ensuring a rigorous review process and a high level of quality and accuracy.

Academic journals provide detailed information about the methodology, data analysis, and results of social scientific studies. They often include statistical analyses, charts, and graphs to support the findings. Additionally, these journals may also provide in-depth discussions of the implications and limitations of the research, as well as suggestions for future studies.

Accessing academic journals can sometimes require a subscription or payment, but many universities, libraries, and research institutions provide access to these resources. Some journals also offer open access options, allowing anyone to read and download their articles free of charge.

It's important to note that when using information about social scientific findings from academic journals, it is crucial to properly cite and reference the original source to avoid plagiarism. Academic integrity is a fundamental principle in research and scholarly writing.

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Based on the graph, a possible solution for the system of inequalities is 5 and 4.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of hamburgers purchased and number of tacos purchased respectively, and then translate the word problem into algebraic equation as follows:

Since this restaurant sold hamburgers for $5 each and tacos for $2.50 and Kevin has $35 to spend, a linear inequality to describe this situation is given by:

5a + 2.50y ≤ 35 ⇒ y ≤ 14 - 2a

Additionally, Kevin and his children must buy a minimum of 9 hamburgers and tacos altogether:

a + y ≥ 9 ⇒ y ≥ 9 - a

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Answer:

A. {x,y}={-2,-3}

// Solve equation [2] for the variable  x

 [2]    x = 2y + 4

// Plug this in for variable  x  in equation [1]

  [1]    (2y+4) - y = 1

  [1]    y = -3

// Solve equation [1] for the variable  y

  [1]    y = - 3

// By now we know this much :

   x = 2y+4

   y = -3

// Use the  y  value to solve for  x

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

B.   [1]           3x=3y-6

 [2]           y=x+2

Equations Simplified or Rearranged :

  [1]    3x - 3y = -6

  [2]    -x + y = 2

Solve by Substitution :

// Solve equation [2] for the variable  y

 [2]    y = x + 2

// Plug this in for variable  y  in equation [1]

  [1]    3x - 3•(x +2) = -6

  [1]    0 = 0 =>  Infinitely many solutions

C.Step by Step Solution

More Icon

System of Linear Equations entered :

  [1]    4x - y = 2

  [2]    8x - 2y = 4

Solve by Substitution :

// Solve equation [1] for the variable  y

 [1]    y = 4x - 2

// Plug this in for variable  y  in equation [2]

  [2]    8x - 2•(4x-2) = 4

  [2]    0 = 0 =>  Infinitely many solutions

Answer:

Step-by-step explanation:

a) y = -1/4x    --------------(I)

x + 2y = 4 -----------------(II)

Substitute y = (-1/4)x in equation (I)

\(x + 2*\dfrac{-1}{4}x=4\\\\\\x -\dfrac{1}{2}x=4\\\\Multiply \ the \ entire \ equation \ by \ 2 \\\\2x -x = 8\\\\x=8\)

\(Substitute \ x = 8 \ in \ equation \ (I)\\\\y=\dfrac{-1}{4}*8\\\\\\y = -2\)

Answer: x = 8  ; y = -2

b) y = -x - 2 --------------(i)

   3x + 3y = 6   -----------(ii)

Divide equation (ii) by m

x + y = 2

  y = -x + 2  ----(iii)

From (i) and (iii), it shows that these lines have same slope. So, they are parallel lines

Answer: No solution

3) -8x + 2y =4

            2y = 8x + 4

Divide the entire equation by 2

             y = 4x + 2 -------------(i)

            y = 4x + 2 ----------------(ii)

From (i) and (ii), we come to know that these lines coincide.So, they have infinite solutions.

Answer:

subtract 1.1j from both sides

Step-by-step explanation:

The true statement about isolating the variable j is (d) Subtract 1.1j from both sides.

Equations which are the expressions that have equal values, when compared with the "=" sign. An equation can be stated as a  mathematical statement that is made up of two expressions connected by an equal sign.  In its normal form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

The equation is given as:

5.6j – 0.12 = 4 + 1.1j

The variable in the equation is j, and it can be isolated by subtracting 1.1j from both sides of the equation.

So, we have:

5.6j – 0.12 - 1.1j = 4 + 1.1j - 1.1j

we get,

4.5j - 0.12 = 4

Hence, the true statement is (d) Subtract 1.1j from both sides.

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Answer:

1385.4

Step-by-step explanation:

Volume=pi*r^2*h=pi*49*9=1385.4

The equation of the line that passes through the two points (5, 4) and (4, - 1) will be 5 x - y = 21.

We have the points:

(5, 4)

(4, - 1)

We need to find the equation of the line that passes through the two points (5, 4) and (4, - 1).

So, slope of the line will be:

m = (4 + 1) / (5 - 4)

m = 5

Now, the equation of the line will be:

y - y₁ = m (x - x₁)

y + 1 = 5 (x - 4)

y + 1 = 5 x - 20

5 x - y - 20 - 1 = 0

5 x - y = 21

Therefore, we get that, the equation of the line that passes through the two points (5, 4) and (4, - 1) will be 5 x - y = 21.

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a. The equation for the line tangent to the graph is W(0.4) ≈ 3 + 3(0.4) = 4.2°C.

b. The particular solution to the differential equation with the initial condition W(0) = 3 is W(t) = 3e^(3sin(t/2)).

c. To find the cost of operating the refrigerator for the 24-hour interval, an expression involving an integral would be ∫[0, 24] 0.001(W(t) - 20) dt.

a. To find the equation for the line tangent to the graph of W(t) at t = 0, we can find the derivative dW/dt and evaluate it at t = 0. We have dW/dt = 3cos(t/2)W. Evaluating it at t = 0 gives dW/dt = 3cos(0/2)W = 3W. This represents the slope of the tangent line. Using the point-slope form, we get the equation for the tangent line as W(t) ≈ 3 + 3t. Plugging in t = 0.4, we find W(0.4) ≈ 3 + 3(0.4) = 4.2°C as an approximation for the temperature inside the refrigerator at t = 0.4 hours.

b. To find the particular solution to the differential equation dW/dt = 3cos(t/2)W with the initial condition W(0) = 3, we can separate variables and integrate both sides. After solving the integral, we arrive at the particular solution W(t) = 3e^(3sin(t/2)).

c. The cost of operating the refrigerator accumulates at a rate of $0.001 per hour for each degree that the temperature in the kitchen exceeds the temperature inside the refrigerator. Let's denote the cost as C(t). To find the cost for the 24-hour interval, we need to calculate the accumulated cost over that period. This can be expressed as the integral of the rate of accumulation, which is 0.001 multiplied by the difference between the kitchen temperature (20°C) and the temperature inside the refrigerator W(t), integrated from t = 0 to t = 24. Thus, the expression involving an integral to find the cost of operating the refrigerator for the 24-hour interval is ∫[0, 24] 0.001(W(t) - 20) dt.

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Answer: line segment

Step-by-step explanation:

A line segment is a ray that extends from one point to another. Hope this helps!

Answer:

line segment

Step-by-step explanation:

If a portion of a line has two endpoints (two little black dots on its end), then it is a line segment.

If it has one dot and an arrow, its a ray. This has an endpoint and goes on forever in the direction of the arrow.

Answer:B cointerior

Step-by-step explanation: if you look the angle make a C or backward C pattern and are both on the inside of parallel lines. the are supplementary which means they will add to 180. there is also Z and F patterns that create equal angles

The reason why Verifone Systems would have a valuation allowance almost equal to its deferred tax assets is to avoid the risk of having a significant deferred tax liability.

In 2015, Verifone Systems reported deferred tax assets of $398 million and a valuation allowance of $332 million.

A valuation allowance is an accounting approach that is used to create a contra-asset account on a company's balance sheet. A contra-asset account is a ledger account that offsets the balance of another account. A valuation allowance is used to account for the uncertainty regarding the recoverability of a deferred tax asset.

In essence, a valuation allowance serves as an offsetting contra account to the deferred tax asset that is created when a company has more tax deductions or credits than it has taxable income.

This is why Verifone Systems reported a valuation allowance almost equal to its deferred tax assets.

The rationale behind using a valuation allowance is to ensure that a company does not have a significant deferred tax liability that could affect its financial position. It also ensures that a company's balance sheet accurately reflects the tax consequences of its transactions.

A valuation allowance can also be used to show that a company has reduced its deferred tax assets, which can be beneficial for tax planning and compliance purposes.

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Answer:

1st pic:

x = 61

left angle = 125 degrees

right angle = 55 degrees

2nd pic:

n = 14

left angle = 78 degrees

right angle = 102 degrees

Step-by-step explanation:

1st pic:

use the following equation ⇒ 2x + 3 + x - 6 = 180

combine like terms ⇒ 3x - 3 = 180

add 6 on both sides ⇒ 3x - 3 + 3 = 180 + 3 ⇒ 3x = 183

divide both sides by 3 ⇒ \(\frac{3x}{3} = \frac{183}{3}\)

x = 61

solve the angles by subtituting 61 for x

left angle = 2x + 3 ⇒ 2 x 61 + 3 ⇒ 125 degrees

right angle = x - 6 ⇒ 61 - 6 ⇒ 55 degrees

2nd pic:

use the following equation ⇒ 4n + 22 + 8n - 10 = 180

combine like terms ⇒ 12n + 12= 180

subtract 12 on both sides ⇒ 12n + 12 - 12 = 180 - 12 ⇒ 12n = 168

divide both sides by 12 ⇒ \(\frac{12n}{12} = \frac{168}{12}\)

n = 14

you can find the angles by substituting 14 for n:

left angle = 4n + 22 ⇒ 4 x 14 + 22 =78 degrees

right angle: 8n - 10 ⇒ 8 x 14 - 10 = 102 degrees

Answer:

  a.  $110,700

Step-by-step explanation:

You want to know the value of a $141,000 house after 15 years, if it declines in value 1.6% each year.

The value multiplier each year is ...

  1 - 1.6% = 1 -0.016 = 0.984

When the house value is multiplied by this factor 15 times, it becomes ...

  $141,000×0.984^15 ≈ $110,700

Russell's house is worth about $110,700.

Answer:

slope = -2

Step-by-step explanation:

Use the slope formula which is: (y2-y1)/(x2-x1) (also referred to as "rise over run")

It doesn't matter which coordinate pair is x1 and y1 or x2 and y2.

To plug in the coordinates:

(4-0)/(2-4) = -2

slope = -2

\(\huge\boxed{\boxed{Hello~there!}}\)

We are given 2 points that the line passes through, so we can find the slope of the line using this formula:

\(\displaystyle\frac{y2-y1}{x2-x1}\)

In this case, y₂=4, y₁=0, x₂=2, x₁=4

Now, plug in the values:

\(\displaystyle\frac{4-0}{2-4}\)

\(\displaystyle\frac{4}{-2}\)

Divide:

\(\huge\boxed{\boxed{\sf{Answer:{\boxed{\tt{Slope=\:\:-2}}}}}}\)

Hope it helps!

Enjoy your day!

Please feel free to ask if you have any doubts.

-Sparkle-

Answer:

A. Even

Step-by-step explanation:

Even Function

A function is "even" when:

\(f(x) = f(-x) \;for\; all\; x\\\\\)

Stated in other terms, the function graph is symmetric about the vertical(y-axis). The right part of the function graph about the y-axis is a reflection of the left part of the function graph  about the y-axis

Looking at the function graph, we see it is indeed symmetric about the y-axis

Hence an even function

Answer: = 3 acres per day

Showing Work

This is a fraction equal to

3 acres ÷ 1 days

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 1

3 acres ÷ 1

__________

1 days ÷ 1

=

3 acres

_____

1 day

=

3 acres

______

day

= 3 acres per day

False. The columns of matrix P are not necessarily eigenvectors of matrix A. While the diagonal matrix D contains the eigenvalues of A, the eigenvectors are not explicitly determined by the columns of P.

False. The columns of matrix P are not guaranteed to be eigenvectors of the transpose of matrix A (A.T).

In the given equation, \(a = PDP^(-1),\)

where D is a diagonal matrix and P is an invertible matrix.

The diagonal elements of D represent the eigenvalues of matrix A, while the columns of P correspond to the eigenvectors of A.

When considering the transpose of matrix A (A.T), we have \((A.T) = (PDP^(-1)).T = (P^{(-1)})^T D^T P^T.\)

Taking the transpose of a product involves reversing the order of the matrices and transposing each matrix individually.

Therefore, we have \((A.T) = P^T D^T (P^{(-1)})^T.\)

Since P is an invertible matrix, its transpose \(P^T\) is also invertible. Similarly, the transpose of the inverse of \(P, (P^{(-1)} )^T,\) is also invertible.

However, the key point is that the diagonal matrix\(D^T\) is not guaranteed to have the same eigenvalues as matrix A.

The eigenvalues of A are present in D, but they may not remain on the main diagonal after transposing.

Thus, the columns of matrix P, which correspond to the eigenvectors of A, may not necessarily be the eigenvectors of A.T.

In conclusion, the statement is false.

The columns of matrix P do not have to be eigenvectors of the transpose of matrix A (A.T).

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Answer:

Jimmy spent 4/25 of his $5,000 budget on hotel accommodation, which is equal to $2,000. He spent 3/20 of his budget on airfare, which is equal to $1,500, 1/10 of his budget on shopping, which is equal to $500, and 1/5 of his budget on the remainder, which is equal to $1,000. This means that Jimmy spent $2,000 on hotel accommodation, which is $500 more than he spent on food.

Population: The population for this survey question would be the parents of the students at Rosedale Academy.

Sample: To obtain a representative sample of the parents' opinions, a stratified random sampling approach can be used. The school can divide the parents into different strata based on relevant factors such as grade level, nationality, or language spoken at home. Then, a random sample of parents can be selected from each stratum. This approach ensures that the sample represents the diversity within the parent population at Rosedale Academy. For example, if there are parents from different grade levels (e.g., elementary, middle, high school), the school can randomly select a proportionate number of parents from each grade level. Similarly, if there are parents from different nationalities or language backgrounds, the school can randomly select a proportionate number of parents from each group. By using stratified random sampling, the survey will capture the opinions of parents from different segments of the population, leading to a more comprehensive understanding of how parents at Rosedale Academy feel about visiting Canada.

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The percentage increase in the cost of a gallon of gas according to the description given is; 80%.

It follows from the task content that the percentage increase in the cost of a gallon of gas is to be determined.

Since the percent increase is given by the formula;

%increase = (∆price/initial price) × 100%

= (6.30 - 3.50)/3.50 × 100%

= 2.80/3.50 × 100%

= 80%.

Ultimately, thee required percentage increase in the cost per gallon of gas is; 80%.

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Answer:

(x+2)(3x+2)(3x−2)

Answer:

Total number of chips = 720 Favorable cases = 720 - 568

Answer:

Every ordered pair within this region will satisfy the inequality y ≥ x. Incorrect. The boundary line here is y = x, and the correct region is shaded, but remember that a dotted line is used for < and >. The inequality you are graphing is y ≥ x, so the boundary line should be solid.

The theorem that corresponds to the given scenario is the Fundamental Theorem of Line Integrals.

The Fundamental Theorem of Line Integrals states that if F is a vector field with a continuous first derivative in a region containing a smooth curve C parameterized by r(t), where t ranges from a to b, and if F is the gradient of a scalar function f, then the line integral of F over C is equal to the difference of the values of f at the endpoints A and B:

∫[C] F · dr = f(B) - f(A)

In the given scenario, it is stated that F = Pi + Qj + Rk is a vector field with continuous components and has a potential f in a region containing the curve C. Therefore, the line integral of F over C, denoted as ∫[C] F · dr, is equal to f(B) - f(A).

Hence, the theorem that corresponds to the given scenario is the Fundamental Theorem of Line Integrals.

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Write tan in terms of sin and cos.

\(\displaystyle \lim_{t\to0}\frac{\tan(6t)}{\sin(2t)} = \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)}\)

Recall that

\(\displaystyle \lim_{x\to0}\frac{\sin(x)}x = 1\)

Rewrite and expand the given limand as the product

\(\displaystyle \lim_{t\to0}\frac{\sin(6t)}{\sin(2t)\cos(6t)} = \lim_{t\to0} \frac{\sin(6t)}{6t} \times \frac{2t}{\sin(2t)} \times \frac{6t}{2t\cos(6t)} \\\\ = \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right)\)

Then using the known limit above, it follows that

\(\displaystyle \left(\lim_{t\to0} \frac{\sin(6t)}{6t}\right) \times \left(\lim_{t\to0}\frac{2t}{\sin(2t)}\right) \times \left(\lim_{t\to0}\frac{3}{\cos(6t)}\right) = 1 \times 1 \times \frac3{\cos(0)} = \boxed{3}\)