math:John is buying new shoes. He finds the shoes he wants on sale for 30%, and the original price is $88. How much will he pay for the shoes?

Answer:

\(fg(x) = f(x)g(x) = {e}^{2x} {e}^{a} = {e}^{2x + a} \)

To find the absolute maximum value of the function g(x)=−2x^2/x−1 over the closed interval [−3,5], we will use the Extreme Value Theorem (EVT).EVT states that if a function is continuous over a closed interval, then the function will have an absolute maximum and minimum over that interval.

So, for finding the absolute maximum value of the given function, we will follow these steps:Step 1: Check the function's domain.We know that the denominator of the function g(x) is x - 1, so the function is not defined at x = 1. However, the closed interval we are working with is [-3, 5], which does not include x = 1. Hence, the function is defined over this interval.Step 2: Find the critical points of the functionTo find the critical points, we need to differentiate the function g(x) and equate it to zero:g'(x) = (-4x(x-1) + 2x^2)/(x-1)^2= 2x(3-x)/(x-1)^2=0So, the critical points of g(x) are x = 0 and x = 3.Step 3: Find the end-point values of the functiong(-3) = -2/5, g(5) = -50/9.

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Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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The deflection angle of light by the white dwarf star is approximately \(\(0.00108 \times 206,265 = 223.03\)\)arcseconds (rounded to two decimal places).

To calculate the deflection angle of light by a white dwarf star, we can use the formula derived from Einstein's theory of general relativity:

\(\[\theta = \frac{4GM}{c^2R}\]\)

where:

\(\(\theta\)\) is the deflection angle of light,

G is the gravitational constant \((\(6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}\)),\)

M is the mass of the white dwarf star,

c is the speed of light in a vacuum \((\(299,792,458 \, \text{m/s}\)),\) and

(R) is the radius of the white dwarf star.

Let's calculate the deflection angle using the given values:

Mass of the white dwarf star, \(\(M = 1.2 \times \text{solar mass}\)\)

Radius of the white dwarf star, \(\(R = 0.0088 \times \text{solar radius}\)\)

We need to convert the solar mass and solar radius to their respective SI units:

\(\(1 \, \text{solar mass} = 1.989 \times 10^{30} \, \text{kg}\)\(1 \, \text{solar radius} = 6.957 \times 10^8 \, \text{m}\)\)

Substituting the values into the formula, we get:

\(\[\theta = \frac{4 \times 6.67430 \times 10^{-11} \times 1.2 \times 1.989 \times 10^{30}}{(299,792,458)^2 \times 0.0088 \times 6.957 \times 10^8}\]\)

Evaluating the above expression, the deflection angle \(\(\theta\)\) is approximately equal to 0.00108 radians.

To convert radians to arcseconds, we use the conversion factor: 1 radian = 206,265 arcseconds.

Therefore, the deflection angle of light by the white dwarf star is approximately \(\(0.00108 \times 206,265 = 223.03\)\)arcseconds (rounded to two decimal places).

Hence, the deflection angle is approximately 223.03 arcseconds.

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The solutions to the equation \(x^2 - 2 = 6x - 3\) are x = 3 + 2√2 and x = 3 - 2√2. The equation \(x^2 - 2 = 6x - 3\)can be solved using the quadratic formula, which is (-b ± √(b² - 4ac))/(2a).

The given equation, \(x^2 - 2 = 6x - 3\), is a quadratic equation in the form \(ax^2 + bx + c = 0\), where a = 1, b = -6, and c = 1.

To solve this equation, we can use the quadratic formula, which states that for any quadratic equation \(ax^2 + bx + c = 0\), the solutions for x can be found using the formula (-b ± √(b² - 4ac))/(2a).

Applying the quadratic formula to the given equation, we have x = (-(-6) ± √((-6)²- 4(1)(1)))/(2(1)). Simplifying this further, we get x = (6 ± √(36 - 4))/2, which becomes x = (6 ± √32)/2.

To simplify the expression under the square root, we can rewrite √32 as √(16 * 2), which is equal to 4√2. Therefore, x = (6 ± 4√2)/2, which can be further simplified to x = 3 ± 2√2.

Hence, the solutions to the equation \(x^2 - 2 = 6x - 3\) are x = 3 + 2√2 and x = 3 - 2√2.

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Answer:

the slope is -1/3

Step-by-step explanation:

The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.

To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.

For Division A:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($230,000 / $2,120,000) * 100

Profit Margin ≈ 10.85%

For Division B:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($34,700 / $381,000) * 100

Profit Margin ≈ 9.11%

To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.

Net Income = Profit Margin * Sales

Net Income = 7% * $1,220,400

Net Income = $85,428

Return on Assets = Profit Margin * Asset Turnover

Return on Assets = 7% * 2.7

Return on Assets = 18.9%

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Step-by-step explanation:

consumers?

Producers undergo the photosynthesis/chemosynthesis and cellular respiration. On the other hand, consumers undergo cellular respiration only. Therefore, cellular respiration occurs in both producers and consumers, whereas photosynthesis/chemosynthesis only happen in producers.

The rules of the calculation are:

The complete question is added as an attachment

The equation is given as:

0.738 × 0.28 = 0.20664

When approximated, we have:

0.738 × 0.28 ≈ 0.21

The above approximation can mean any of the following:

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Answer:

24

Step-by-step explanation:

Step 1: Define

x = 2

y = 4

16x + 2x² - y²

Step 2: Substitute and Evaluate

16(2) + 2(2)² - 4²

32 + 2(4) - 16

16 + 8

24

A parabola is a U-shaped curve that can be formed by intersecting a cone with a plane that is parallel to one of its sides.

To find an equation of a parabola given the vertex and focus, we can use the following formula:

For a parabola with vertex (h, k) and focus (h, k + p), the equation is:

(x - h)^2 = 4p(y - k)

where p is the distance from the vertex to the focus.

If the focus is at (h + p, k), then the equation is:

(y - k)^2 = 4p(x - h)

where p is the distance from the vertex to the focus.

what is distance?

In the context of a parabola, the distance is the distance between the vertex and the focus, which is also known as the focal length. It is a constant value that determines the shape and size of the parabola.

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Answer:$46.75

Step-by-step explanation:

The total is the whole or 100%

55=100%

x=15%

Multiply across

100%*x=55*15%

x=8.25

Now we minus 8.25 from 55=

$46.75

Answer:

Assuming

\(y = -2x + 6x - 1\\y = 4x - 1\)

Step-by-step explanation:

See Graph

the solution to the boundary-value problem is y(x) = (1/3)\(e^{3x}\) - (1/2)\(e^{(-2x) }\)

To solve the boundary-value problem, we first need to solve the associated second-order linear homogeneous differential equation, which is y″ + 5y′ − 6y = 0. We assume a solution of the form y(x) = e^(rx), where r is a constant. Substituting this into the differential equation, we obtain the characteristic equation \(r^{2}\) + 5r − 6 = 0. Solving this quadratic equation, we find two distinct roots: r = 1 and r = -6.

The general solution to the differential equation is y(x) = \(c1e^{x}\) + \(c2e^{-6x}\)^, where c1 and c2 are constants.

To determine the specific solution that satisfies the boundary conditions, we substitute the values of the boundary points into the equation. From the condition y(0) = 0, we find c1 + c2 = 0. From y(2) = 1, we find \(c1e^{2}\) + \(c2e^{-12}\) = 1. Solving these equations simultaneously, we find c1 = (\(e^{-2}\) - \(e^{-12}\))/(1 - \(e^{-10}\)) and c2 = -(\(e^{-12}\) - \(e^{2}\))/(1 -\(e^{-10}\) ).

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Answer:

(- 3, 12 ) and (5, 28 )

Step-by-step explanation:

Given the 2 equations

y = x² + 3 → (1)

y - 2x = 18 → (2)

Substitute y = x² + 3 into (2)

x² + 3 - 2x = 18 ( subtract 18 from both sides )

x² - 2x - 15 = 0 ← in standard form

(x + 3)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 5 = 0 ⇒ x = 5

Substitute these values into (1) for corresponding values of y

x = - 3 : y = (- 3)² + 3 = 9 + 3 = 12 ⇒ (- 3, 12 )

x = 5 : y = 5² + 3 = 25 + 3 = 28 ⇒ (5, 28 )

Answer:

11.7

Step-by-step explanation:

add all the numbers then divide the answer with the number of how many numbers they are

12 +15+ 6+ 8 +12+17 +10+8+ 7+ 13+ 14 +16 +8+18+11=175

175/15=11.6666666667

round the answer to the nearest whole number=11.7

The probability of the sets are solved and

a) n(P U Q) = 85%

b) n(P ∩ Q) = 20%

c) n(only P) = 35%

d) n(only Q) = 30%

Given data ,

P and are the subsets of universal set U

And , n (p) = 55% n (Q) = 50% and n(PUO)complement = 15%

Now , we'll use the formula for the union and intersection of sets:

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(only P) = n(P) - n(P ∩ Q)

n(only Q) = n(Q) - n(P ∩ Q)

We're given that:

n(P) = 55%

n(Q) = 50%

n(P U Q)' = 15%

To find n(P U Q), we'll use the complement rule:

n(P U Q) = 100% - n(P U Q)'

n(P U Q) = 100% - 15%

n(P U Q) = 85%

Now we can substitute the values into the formulas above:

(i)

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(P ∩ Q) = 55% + 50% - 85%

n(P ∩ Q) = 20%

(ii)

n(P ∩ Q) = 20%

(iii) n(only P) = n(P) - n(P ∩ Q)

n(only P) = 55% - 20%

n(only P) = 35%

(iv)

n(only Q) = n(Q) - n(P ∩ Q)

n(only Q) = 50% - 20%

n(only Q) = 30%

Hence , the probability is solved

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The perimeter is 34 , if I have to multiply each number by 2 and then add them, if not it is 17.

Answer:

The final balance is $23,232.33.

The total compound interest is $3,232.33.

Answer:1,041

Step-by-step explanation:

The surface area of the tetrahedral die is 1353 square millimeters

To find the surface area of the tetrahedral die, we need to find the area of each of the four equilateral triangular faces and add them together.

The formula for the area of an equilateral triangle is A = (√(3)/4) x s², where s is the length of the side.

In this case, the base edge of the tetrahedral die is 26 millimeters, so the length of each side of the equilateral triangles is also 26 millimeters.

Using the formula for the area of an equilateral triangle, we can find the area of one face:

A = (√(3)/4) x 26²

A = 338.3 square millimeters (to the nearest tenth)

Since there are four faces, we can multiply the area of one face by 4:

4 x 338.3 = 1353.2 square millimeters

Therefore, the surface area of the tetrahedral die is approximately 1353 square millimeters (to the nearest ten square millimeters).

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Answer:

rational. BRAINLIEST??

Step-by-step explanation:

Answer: A Rational

Step-by-step explanation:

A rational number is one that can be written as an integer over an integer, with non-zero denominator. ie. all your fractions. An irrational number cannot be expressed as a ratio of integers and include numbers such as π,e,√2,ln2 , etc

The value of the total number of yellow chips are, 35

We have to given that;

In each pile there are green and yellow chips.

Here, In one pile, the ratio of the number of green chips to the number of yellow chips is 1 : 2.

And, In the second pile, the ratio of the number of green chips to the number of yellow chips is 3 : 5.

For one pile;

Number of green chips = x

And, Number of yellow chips = 2x

For second pile;

Number of green chips = 3x

And, Number of yellow chips = 5x

Here, Thelma has a total of 20 green chips,

Hence, We get;

x + 3x = 20

4x = 20

x = 5

Thus, Number of yellow chips are,

= 2x + 5x

= 7x

= 7 x 5

= 35

Thus, The value of the total number of yellow chips are, 35

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The sampling frame is: All adults with residential telephones

An opinion poll calls 2000 randomly chosen residential telephone numbers, then asks to speak with an adult member of the household. The interviewer asks, "How many movies have you watched in a movie theater in the past 12 months?"The question is asking for the sampling frame which means it is looking for the subset of the population from which the sample is selected. It is important to define the sampling frame because it is necessary to determine how to obtain a representative sample.Here in the given statement, the sampling frame would be All adults with residential telephones. This is because the poll calls randomly chosen residential telephone numbers and then asks to speak with an adult member of the household. It is unclear whether the poll only includes adults who have watched movies in the past 12 months.

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The type of r.v.R is a continuous random variable, since its possible values form a continuous interval [0,1].

The sample space of R is the interval [0,1], since the distance from the origin to any point inside the unit circle is between 0 and 1.
To find P(R < r), we need to find the probability that the randomly selected point falls inside a circle of radius r centered at the origin. The area of this circle is πr^2, and the area of the entire unit circle is π, so the probability is P(R < r) = πr^2/π = r^2.
The cdf of R is the function F(r) = P(R ≤ r) = ∫0r 2πx dx / π = r^2, where the integral is taken over the interval [0,r]. This is because the probability that R is less than or equal to r is the same as the probability that the randomly selected point falls inside the circle of radius r centered at the origin, which has area πr^2. The cdf of R is a continuous and increasing function on the interval [0,1].

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Answer:

okay?... and...?

Step-by-step explanation:

The dimensions of his model of the train station would be

3 inches by 6 inches by 4 inches.

Scale factor is a dimensionless constant value that is used to compare the size of two objects. It is denoted by [K]. Mathematically -

K = O[1]/O[2]

Given is Lewis who is building a train layout and wants to build a model of the train station in his city. He wants it to be exactly to scale to match his engine. The engine measures 8 inches long and is the model of a train that is 80 feet long. The station in his city is 30 feet by 60 feet by 40 feet.

Now, it is given here that Lewis assumed a dilation model in which 80 feet is 8 inches long. Then -

80 feet = 8 inches

So one feet will be -

1 ft = 8/80 = 1/10 inches

Now, the dimensions of station in Lewis native city is 30 feet by 60 feet by 40 feet.

Now, dilating the dimensions with a scale factor of 1/10 inches, we get -

30 feet = 30 x 1 feet = 30 x 1/10 = 3 inches

60 feet = 60 x 1 feet = 60 x 1/10 = 6 inches

40 feet = 40 x 1 feet = 40 x 1/10 = 4 inches

Therefore, the dimensions of his model of the train station would be

3 inches by 6 inches by 4 inches.

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The critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:  θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

To find the critical numbers of g(θ) = 4θ - tan(θ) on the interval 0 ≤ θ < 2π, we need to find the values of θ where the derivative of g(θ) is equal to 0 or undefined.

First, we find the derivative of g(θ) using the chain rule and quotient rule:

g'(θ) = 4 - sec²(θ)

To find where g'(θ) is equal to 0, we set the derivative equal to 0 and solve for θ:

4 - sec²(θ) = 0

sec²(θ) = 4

Taking the square root of both sides, we get:

sec(θ) = ±2

Since sec(θ) = 1/cos(θ), we can rewrite this as:

cos(θ) = ±1/2

We know that on the interval 0 ≤ θ < 2π, the cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants.

Therefore, we need to find the values of θ in the first and fourth quadrants where cos(θ) = 1/2, and the values of θ in the second and third quadrants where cos(θ) = -1/2.

For cos(θ) = 1/2, we have:

θ = π/3 or 5π/3 in the first quadrant
θ = 7π/3 or 11π/3 in the fourth quadrant

For cos(θ) = -1/2, we have:

θ = 2π/3 or 4π/3 in the second quadrant
θ = 8π/3 or 10π/3 in the third quadrant

Therefore, the critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:

θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

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Answer:

a: f= 24y−17 /3y−1

b: x=−23

Step-by-step explanation:

The maximum and the least grossing movies are the combinations of movies A & B and movies C & D, respectively

The grossing amounts are given as:

The selection of two movies could be any of the following selections

Selection = AB, AC, AD, BC, BD, and CD

The gross of each selection is:

AB = $700 million + $680 million = $1.38 billion

AC = $700 million + $610 million = $1.31 billion

AB = $700 million + $420 million = $1.12 billion

BC = $680 million + $610 million = $1.29 billion

BD = $680 million + $420 million = $1.10 billion

CD = $610 million + $420 million = $1.03 billion

In the above computation, the maximum and the least gross amounts are:

AB = $1.38 billion

CD = $1.03 billion

Hence, the maximum and the least grossing movies are the combinations of movies A & B and movies C & D, respectively

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Answer:

mean of A, C = 655

mean of B, C = 645

mean of C, D = 515

Step-by-step explanation:

you just take whatever the 2 numbers are (for A, B, C, D) and find the mean between them both,, also correct on edge