Enrique predicts that he can make additional money from sales of accessories and service for computer products sold by his store. The table at the right shows predicted percent returns for such sales. For example, if the store makes x dollars selling computer products, Enrique predicts the store with make 0.05x dollars from selling accessories. Part A In January and February of this year, the store made $2,500 from sales of accesories and services. Let x represent the amount the store with make from sales of computer products from March through December. Write an equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year. If Enrique predicts sales from accessories and services for the entire year will be $5,000, about how much money must be made from computer product sales from March through December? Explain.

The derivatives of y in each case is:

(a) \(dy/dx = u(dv/dx) + v(du/dx) = sin(x) * (-sin(x)) + cos(x) * cos(x) = -sin^2(x) + cos^2(x).\)

(b) \(dy/dx = u(dv/dx) + v(du/dx) = x * (cos(x^3) * 3x^2) + sin(x^3) * 1 = 3x^3*cos(x^3) + sin(x^3).\)

(a) y = sin(x)
To find the derivative of y with respect to x, use the chain rule. The derivative of sin(x) with respect to x is cos(x).
So, dy/dx = cos(x).

(b) y = sin(x) cos(x)
To find the derivative, use the product rule. Let u = sin(x) and v = cos(x).
The derivative of u with respect to x is du/dx = cos(x), and the derivative of v with respect to x is dv/dx = -sin(x).

Apply the product rule: \(dy/dx = u(dv/dx) + v(du/dx) = sin(x) * (-sin(x)) + cos(x) * cos(x) = -sin^2(x) + cos^2(x).\)

(c) y = x * sin(x^3)
Here, use the product rule again. Let u = x and v = sin(x^3).
The derivative of u with respect to x is du/dx = 1, and the derivative of v with respect to x requires the chain rule.

The outer function is sin(w) and the inner function is\(w = x^3. So, dw/dx = 3x^2 and dv/dw = cos(w).\)

By the chain rule, \(dv/dx = dv/dw * dw/dx = cos(x^3) * 3x^2.\)

Now, apply the product rule: \(dy/dx = u(dv/dx) + v(du/dx) = x * (cos(x^3) * 3x^2) + sin(x^3) * 1 = 3x^3*cos(x^3) + sin(x^3).\)

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Step-by-step explanation:

15x - 31 = 9x + 11

6x =42

x = 7

15(7) - 31 = 9(7) + 11

74 = 74

74 × 2 = 148

180-148=32

Answer:

I'm so sorry

Step-by-step explanation:

you have to re-enter in another format we can't all see the pictures

Answer:

runner 3

Step-by-step explanation:

Runner #1 runs 1 mile in 10 minutes

Runner #2 runs 1 mile in 12 minutes

Runner #3 runs 1 mile in 9.5 minutes

Leonie made a 125% profit on the cost of the coat.To determine Leonie's percentage profit on the cost of the coat, we need to calculate the original cost of the coat and then determine the profit made on that cost.

Let's start by finding the original cost of the coat. We know that the hat cost £6 and Leonie made a 300% profit on the hat. A 300% profit means she sold the hat for 4 times its original cost (£6 * 4 = £24).

Next, we can calculate the total cost of the hat and coat. Since Leonie made a 125% profit on the total cost, the total cost represents 100% + 125% = 225% of the original cost.

To find the original cost, we can divide the total cost (£45) by 225% (or 2.25 in decimal form): £45 / 2.25 = £20.

Now we can calculate the profit made on the coat. The total cost of the hat and coat was £20, and Leonie sold both items for £45, so the profit made is £45 - £20 = £25.

To find the percentage profit on the cost of the ccoatoat, we can divide the profit (£25) by the original cost of the coat (£20) and multiply by 100: (£25 / £20) * 100 = 125%.

Therefore, Leonie made a 125% profit on the cost of the coat.

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Measure of angle:

∠A  = 36.86°

∠B = 90°

∠C = 53.13 °

Measure of side ,

AB =  28

BC = 21

CA = 35

Given triangle ABC.

Right angled at B.

Now, using trigonometric ratios to find angle A , B , C .

Right angled at B : ∠B = 90°

Angle A,

SinA = 21/35

∠A = 36.86

Angle C,

SinC = 28/35

∠C = 53.13

Now measures of side.

To find the length of side use sine rule .

Sine rule:

a/sinA = b/sinB = c /sinC

a = opposite side of angle A .

b = opposite site of angle B .

c = opposite side of angle C.

AB = 28

BC = 21

CA = 35

Hence the sides and angles of the triangles are measured .

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The expression is equivalent to  2(a + 2b) minus a minus 2b expression and gives the same result as the given expression is \(a+2b\).

Equivalent expression are the expression whose result is equal to the original expression, but the way of representation is different.

Given information-

The given expression in the problem is,

\(2 (a+ 2 b)-a-2b\)

Let the expression which is equal to the given expression is \(f(a,b)\). Thus,

\(f(a,b)=2 (a+ 2 b)-a-2b\)

In the above expression the term inside the bracket is in multiple with the number two.

Thus open the bracket by multiplying each term inside the bracket with number 2 as,

\(f(a,b)=2\times a+ 2\times2 b-a-2b\\f(a,b)=2a+4b-a-2b\)

In the algebraic expression the term with same coefficient or variable added or subtract from each other.

In the above expression the solve the term a and b separately as,

\(f(a,b)=2a-a+4b-2b\\f(a,b)=a+2b\)

Thus the expression is equivalent to given expression and gives the same result as the given expression is \(a+2b\).

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Answer:

brainliest plss

Step-by-step explanation:

1. y = 35x

2. y = 30x + 1

3. y = 35x

   y = 30 x + 1

4. Its more convenient to substitute y because It's easier.

    35x = 30(x + 1)

5.  35x = 30x + 1

    35x = 30x + 30

    35x -30x = 30

    5x = 30

    x = 6    (30/5 = 6)

    35 x 6 = 210 (y)

6. Both people have read 210 pages and it takes amir 6 days to catch up.

Answer:

-2x

Step-by-step explanation:

x^2-10x+24

-20x+24

4x

x-6= -6x

4x-6x

4-6=-2

bring down the x and you get -2x

hope this helps

Quadrilaterals in the coordinate plane worksheet answer key. However, I can provide you with general information about quadrilaterals and their relationship to the coordinate plane. A quadrilateral is a polygon that has four sides, four vertices, and four angles.

Unfortunately, without the specific worksheet you are referring to, I cannot provide you with a direct answer to the Quadrilaterals in the coordinate plane worksheet answer key. However, I can provide you with general information about quadrilaterals and their relationship to the coordinate plane. A quadrilateral is a polygon that has four sides, four vertices, and four angles. The most common types of quadrilaterals are squares, rectangles, parallelograms, rhombuses, and trapezoids. These shapes can be identified in the coordinate plane by plotting their vertices using the x and y coordinates.
To plot a point in the coordinate plane, you use a pair of numbers, (x, y), where x is the horizontal distance from the origin, and y is the vertical distance from the origin. By plotting the vertices of a quadrilateral in the coordinate plane, you can determine its shape, size, and other properties.
When working with quadrilaterals in the coordinate plane, it is important to understand how to calculate the distance between two points using the distance formula and how to find the slope of a line. These skills will help you determine if a quadrilateral is a parallelogram, if its sides are parallel or perpendicular, and other important properties.
In summary, quadrilaterals in the coordinate plane involve plotting the vertices of the shape using x and y coordinates and using mathematical formulas to determine important properties such as distance and slope.

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Answer:

Congruence in two or more triangles depends on the measurements of their sides and angles. The three sides of a triangle determine its size and the three angles of a triangle determine its shape. Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

hope this helps mark me brainliest

Step-by-step explanation:

Answer: y= 100x +1500

Step-by-step explanation:

The 1500 value never changes, so it doesn’t need a variable

The 100 value will change based on how many he sells, so it needs a variable

Answer:

its the first one.

Step-by-step explanation:

the 1500 stays the same so it would be 100×how ever many tractors so 100z+1500

Answer: Just simply replace the letter with the number that it equals in the equation. Then solve the equation using PEMDAS order of operations, (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction).

Step-by-step explanation:

Stokes’ theorem is a vector calculus theorem that relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary of the surface.

Mathematically, it can be represented as:

\(∬ S curl F · dS = ∮ C F · dr\)

Where S is the surface that is bounded by the curve C, F is a vector field and curl F is the curl of that vector field. C is a simple closed curve that bounds S and is oriented according to the right-hand rule. dS is an element of area of the surface S and dr is an element of length of the curve C.

Now, given that F(x, y, z) = ⟨2xy, 6z, 14y⟩ and

C is the curve of intersection of the plane x + z = 6 and the cylinder x² + y² = 9 oriented clockwise as viewed from above,

we need to find the alternative integral to \(∫c F · dr\) using Stokes' theorem.

For this, we'll need to calculate curl F.

∴ curl F = ∇ × F = i (∂/∂y) (14y) − j (∂/∂z) (2xy) + k [(∂/∂x) (2xy) − (∂/∂y) (6z)] = 0 + 2xi − (-2yj) + 2k = ⟨2x,2y,2⟩

Now, let's find the boundary curve C of the surface S formed by the intersection of the cylinder and the plane.

First, we'll need to find the intersection points of the cylinder and the plane:

x + z = 6 and x² + y² = 9x² + y² + z² - 2xz + x² = 36z = 36 - 2x² - y²

Cylinder equation:

x² + y² = 9

At the intersection, we have:

x² + y² = 9 and z = 36 - 2x² - y²x² + y² + 2x² + y² = 45y² + 3x² = 15 → x²/5 + y²/15 = 1

This gives us an ellipse as the curve of intersection.

The boundary curve C is given by the ellipse, oriented clockwise as viewed from above.

Now, we can apply Stoke's theorem:

\(∬ S curl F · dS = ∮ C F · dr\)

The surface S is the portion of the plane x + z = 6 that lies inside the cylinder x² + y² = 9.

Its boundary curve C is the ellipse x²/5 + y²/15 = 1, oriented clockwise as viewed from above.

Therefore,

\(∫C​F·dr = ∬S​curl F·dS= ∬S​⟨2,2,2⟩·dS = 2∬S​dS = 2Area(S)\)

Thus, the alternative integral to ∫C​F · dr is 2 times the area of the surface S.

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The screen aspect ratio of a high-definition television is 16:9, which means the width is 16 units and the height is 9 units. We are given that the width of the HDTV is 41 inches.

To find the screen size, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the diagonal distance across the screen) is equal to the sum of the squares of the other two sides (width and height).

Let's assume the height is h inches. Using the Pythagorean theorem, we have:

(41^2) = (16^2) + (9^2) + (h^2)

Simplifying this equation, we get:

1681 = 256 + 81 + h^2

1681 = 337 + h^2

h^2 = 1681 - 337

h^2 = 1344

Taking the square root of both sides, we find:

h ≈ 36.65 inches

Therefore, the screen size of the HDTV is approximately 36.65 inches.

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The area of the triangle JHI is 8.75 square units.

From the given figure,

Area of a ΔJHI = Area of a rectangle - (Area of 3 triangles)

= 5×4 - (1/2 ×3×4 + 1/2 ×2×3 + 1/2 ×1×5)

= 20 - (6+3+2.5)

= 20 - 11.25

= 8.75 square units

Therefore, the area of the triangle JHI is 8.75 square units.

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Answer:

6.39 m

Step-by-step explanation:

( for a right triangle such as this)

Sin (theta) = opp leg / hypotenuse = AB / x    

sin (54) = AB / 7.9

7.9 * sin 54 = AB = 6.39 m

Answer:

60

Step-by-step explanation:

The function of time x(t) corresponding to the Laplace transform 1/(s^2 + 9), Re{s} > 0, is x(t) = (1/3π) sin(3t) e^(st).

To compute the inverse Laplace, transform of 1/(s^2 + 9), we can use the formula for the inverse Laplace transform of a rational function:

L^-1{F(s)} = (1/2πi) ∫γ+σ-iγ+σ+ iF(s)e^(st) ds

where γ is a real number greater than the real part of all singularities of F(s), σ is a positive real number such that the contour of integration lies to the right of all singularities of F(s), and the contour of integration γ+σ is a line parallel to the imaginary axis.

In this case, the Laplace transform of 1/(s^2 + 9) is:

F(s) = L{1/(s^2 + 9)} = 1/[(s + 3i)(s - 3i)]

which has singularities at s = ±3i. Since Re{s} > 0, we can choose γ = 0 and σ > 3. Then, the inverse Laplace transform of F(s) is:

L^-1{F(s)} = (1/2πi) ∫γ+σ-iγ+σ+ iF(s)e^(st) ds
= (1/2πi) ∫γ+σ-iγ+σ+ i [1/((s + 3i)(s - 3i))] e^(st) ds

We can use partial fraction decomposition to express F(s) as:

F(s) = A/(s + 3i) + B/(s - 3i)

where A = 1/(2(3i)), B = -1/(2(3i)), and we get:

L^-1{F(s)} = (1/2πi) [∫γ+σ-iγ+σ+ i A/(s + 3i) e^(st) ds + ∫γ+σ-iγ+σ+ i B/(s - 3i) e^(st) ds]
= (1/2πi) [A e^(-3it) ∫γ+σ-iγ+σ+ i e^(su) du + B e^(3it) ∫γ+σ-iγ+σ+ i e^(sv) dv]
= (1/2πi) [(A e^(-3it) + B e^(3it)) ∫γ+σ-iγ+σ+ i e^(su) du]

where u = s - 3i, v = s + 3i, and we can evaluate the integral using the residue theorem:

∫γ+σ-iγ+σ+ i e^(su) du = 2πi Res[e^(su)/(u + 3i), u = -3i]
= 2πi e^(-3it)/(2(3i))
= -i/3 e^(-3it)

Therefore, we have:

x(t) = L^-1{F(s)} = (1/2πi) [(A e^(-3it) + B e^(3it)) ∫γ+σ-iγ+σ+ i e^(su) du]
= (1/2πi) [(1/(2(3i)) e^(-3it) - 1/(2(3i)) e^(3it)) (-i/3) e^(st) ds]
= (1/6π) [e^(-3it) - e^(3it)] e^(st) ds
= (1/3π) sin(3t) e^(st)

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The length of the cuboid is 16 mm

In this question, we have been given a  cuboid having height of 42 mm

and a width of 8 mm.

Also, the volume of the cuboid is 5376 mm³.

We know that, the volume of the cuboid is V = length × width × height

Here, width = 8 mm

height = 42 mm

V = 5376 mm³

We need to find the length of the cuboid.

V = length × width × height

5376 = length × 8 × 42

length = 5376 / 336

length = 16 mm

Therefore, the length of the cuboid is 16 mm

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Answer:

The top of the cake is 25.12 in²

Step-by-step explanation:

Hello!

So you are dealing with a circumference question! And because the diameter is 2x the radius, we know the radius is actually 4.

Lets write out the circumference formula and use that to help us.

c = 2\(\\\pi\) x r

pi is 3.14....

But lets use 3.14

c = 2(3.14) x 4

Plus this into a calculator and we get 25.12 as the answer.

Answer:

≈50.265 \(in^{2}\)

Step-by-step explanation:

You first have to find the radius since the formula for the area of a circle is  A=\(\pi r^{2}\).

Since the radius is half the diameter, just divide 8 by 2 which will give you 4.

r=4

Now plug in the radius into the formula and simplify.

A=\(\pi 4^{2}\)

\(A=\pi 16\)

≈50.265 \(in^{2}\)

Answer:

75%

Step-by-step explanation:

150/200 × 100 =75

Divide 150 by 200:

150/200 = 0.75

Multiply by 100:

0.75 x 100 = 75%

The answer is 75%

Answer:

201.53\(m^{2}\)

Step-by-step explanation:

That is a hexagonal pyramid, which means it consists of one hexagon and six triangles.

Let's first find the hexagonal base.

The formula to find the area of a hexagon is \(\frac{3\sqrt{3}}{2}a^{2}\), where a is the length of one side of the hexagon. In this question, a = 6m

Solve that to find that the area of the hexagon is 93.53m^2.

Now, on to the triangles. The area of one triangle is the base times the height, then halved. We know that the base of the triangle is 6m as it shares the base with a side of the hexagon, and the question states that the height is also 6m.

6 * 6 = 36

36 / 2 = 18

Hence, the area of one triangle is 18m^2

However, there are six triangles - not just one!

6 * 18 = 108

Adding everything up:

93.53 + 108 = 201.53

The answer is 201.53m^2

The floodplain that was submerged in the 1993 imagery was about 150 km wide

In 1993, a major flood occurred in the Mississippi River Basin. This flood was caused by excessive rainfall that lasted for a long time. The flood resulted in massive flooding and millions of dollars in property damage.

During the flood, the floodplain, which is the area adjacent to a river that gets flooded during heavy rains or when the river overflows its banks, was submerged.

The floodplain that was submerged in the 1993 imagery was about 150 km wide. This flood was one of the most significant in the history of the United States. It affected over 9 million acres of farmland, destroyed homes and other buildings, and caused the displacement of thousands of people.

The flood had a significant impact on the economy of the United States and led to the development of new flood management strategies to prevent future occurrences. Today, there are many measures in place to help mitigate the effects of flooding, such as levees and other structures that can divert water away from populated areas.

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Answer:

34.51

Step-by-step explanation:

It would be 98.60*65% and then subtract that answer with 98.60.

So, we get 34.51

Answer:

$34.51

Step-by-step explanation:

65% discount means 0.65 off

0.65× 98.60=64.09

Meaning $64.09 off

Sale price= 98.60-64.09

$34.51

22.22 was spent on a pass and lunch for each student.

Now, According to the question:

Total money spend on passes = 674.73

Total no. of people = 47 + 2

                                = 49

Money spend on pass for each person  = 674.73/49

                                                                  = 13.77

Total money spend on lunch = 414.07

Total no. of students = 49

Money spend on lunch for each student = 414.07/49

                                                                  = 8.45

Total = 13.77 + 8.45

       = 22.22

Hence, 22.22 was spent on a pass and lunch for each student.

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Answer:

a= 20

b=20

Step-by-step explanation:

9b-6a-20 = b+a

or, 8b-7a-20 = 0

or, 8b = 20+7a

or, b = (20+7a)/8

now

a-2b+34 = 9b-10a+34

substituting b's value as (20+7a)/8

or, a-2(20+7a)/8+34 = 9(20+7a)/8-10a+34

or, a-(20+7a)/4 = (180+63a)/8-10a

or, (4a-20-7a)/4 = (180+63a-80a)/8

or, -3a-20 = (180-17a)/2

or, -6a-40 = 180-17a

or, 11a=220

a = 20

now

b=(20+7a)/8

or, b = (20+7×20)/8

or, b = (20+140)/8

or, b = 160/8

so, b = 20

Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, 4 ) and (x₂, y₂ ) = (2, - 1 )

m = \(\frac{-1-4}{2-(-3)}\) = \(\frac{-5}{2+3}\) = \(\frac{-5}{5}\) = - 1 → A