Please can someone help!

Rate of change of a bushel of corn in the current year is 8.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Part A :

Rate of change of a bushel of corn is found by finding the slope of the line given in the graph.

Consider two points (0, 0) and (3, 24).

Slope = (24 - 0) / (3 - 0) = 24 / 3 = 8

Rate of change of a bushel of corn in the current year is 8.

Part B :

Already, we have, price of the corn in the current year = 8

In the previous year,

Price of 3 bushels of corn = 21

Price of 1 bushel of corn = 21 / 3 = 7

Price of a bushel of corn in the current year is 1 dollar more than the price of a bushel of corn in the previous year.

Hence rate of change of a bushel of corn in the current year is 8 and price of a bushel of corn in the current year is 1 dollar more than the price of a bushel of corn in the previous year.

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9514 1404 393

Answer:

  114°

Step-by-step explanation:

Angles LOM and MON are a linear pair, so are supplementary.

  x + 66 = 180

  x = 180 -66 = 114

The measure of ∠x is 114°.

a) We have f−1(7) = 2.Thus, the value of f-1(7) is 2.

b) We can conclude that f( f−1(−3) ) = f(5) = −3.Thus, the value of f(5) is -3.

(a) Determine f-1(7)Given that f be a one-to-one function and f(2)=7.Since f is one-to-one, there exists a unique inverse function f−1. We have f(2) = 7, hence 2 = f−1(7). Therefore, we have f−1(7) = 2.Thus, the value of f-1(7) is 2.(b) Determine f(5)Given that f be a one-to-one function and f−1(−3) = 5.Since f is one-to-one, there exists a unique inverse function f−1. Hence, f( f−1(x) ) = x and f−1( f(x) ) = x for all x in the domain of f. Also, f(2) = 7, thus f−1(7) = 2. Therefore, we can conclude that f( f−1(−3) ) = f(5) = −3.Thus, the value of f(5) is -3.

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Step-by-step explanation: The values for a, b, and c come from the

coefficients on our 3 terms in the trinomial.

The value for a comes from the coefficient

on the x² term which in this case is 2.

So we say that a = 2.

The value for b comes from the coefficient

on the x term which in this case is -6.

So we say that b = -6.

The value of c comes from the

constant term which in this case is -4.

So we say that c = -4.

Answer:

system of function:

f(x)=.5x+6

f(x)=x^2; x > 2

Step-by-step explanation:

there's a screenshot attached. Explanation: I'm using desmos and just type the functions like what the screenshot did to graph the piecewise function made by two functions

Thermal conductivity can be expressed as 0.0003 W/cm⋅C.

In the given question, Khan academy 0.03 watts (W) per meter (m) per degree Celsius (C).

We have to find the batting's thermal conductivity value in W/cm⋅C.

A thermal conductivity of 0.03 watts (W) per meter (m) per degree Celsius is provided to us.

Therefore, Thermal conductivity = 0.03 W/m⋅C

However, we need the thermal conductivity of the batting in w/cm•c.

The metre and cm are the only differences.

Therefore, we must convert from meters to centimeters.

We are aware of 1 m = 100 cm

Thus, thermal conductivity can be expressed as = 0.03 W/1 m⋅C

We can change 1 m to 100 cm.

Thermal conductivity can be expressed as = 0.03 W/100 cm⋅C

Now simplifying it as,

Thermal conductivity can be expressed as = 0.0003 W/cm⋅C

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1) y=5

2) x=(10-5y)/2

3) y=(11-6x)/-3

4) x=0

5) x=(-y+6)/3

6) p=(8+m)/2

a) the inverse function is:

f-1(y) = (y-b)/a

b) f(x) is not one-to-one, it does not have a unique inverse function. Therefore, (F-1)(a) = DNE.

First, let's answer the first part of the question:

To determine whether the function f(x) = ar+b is one-to-one, we need to check if different inputs produce different outputs. Let's suppose that f(x1) = f(x2), where x1 and x2 are distinct inputs. Then, we have:

ar+b = f(x1) = f(x2) = ar+b

Subtracting ar+b from both sides, we get:

ar-ar+b-b = 0

Simplifying, we get:

a(x1 - x2) = 0

Since a is nonzero, this equation implies that x1 = x2, which contradicts our assumption that x1 and x2 are distinct. Therefore, the function f(x) = ar+b is one-to-one.

To find the inverse function of f(x) = ar+b, we can solve for x in terms of y:

y = ar+b

y-b = ar

r = (y-b)/a

x = (y-b)/a

Therefore, the inverse function is:

f-1(y) = (y-b)/a

Now, let's answer the second part of the question:

To find (F-1)(a) for f(x) = x2 + 2x - 1 and a = -4, we set y = -4 and solve for x:

y = x2 + 2x - 1

-4 = x2 + 2x - 1

x2 + 2x - 3 = 0

(x + 3)(x - 1) = 0

x = -3 or x = 1

Since f(x) is not one-to-one, it does not have a unique inverse function. Therefore, (F-1)(a) = DNE.

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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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The area of the region that lies inside the curve r = 11 cos θ and outside the curve r = 5 cos θ is \(48\int_{a}^{b}cos^2\theta d\theta\).

In the question, we are asked to find the area of the region that lies inside the curve, r = 11 cos θ and outside the curve, r = 5 cos θ.

The function r = n + a cos θ is a polar function, whose area under the curve can be calculated using integration with respect to dθ, with the formula, \(\int_{a}^{b}\frac{1}{2} r^2d \theta\), over the interval [a, b].

Thus, the area under the curve, r = 11 cos θ, using the stated formula, can be shown as:

\(\int_{a}^{b}\frac{1}{2} r^2d \theta\\=\int_{a}^{b}\frac{1}{2} (11 cos \theta)^2d \theta\\=\int_{a}^{b}\frac{121cos^2\theta}{2} r^2d \theta\)

The area under the curve, r = 5 cos θ, using the stated formula, can be shown as:

\(\int_{a}^{b}\frac{1}{2} r^2d \theta\\=\int_{a}^{b}\frac{1}{2} (5 cos \theta)^2d \theta\\=\int_{a}^{b}\frac{25cos^2\theta}{2} r^2d \theta\)

The area of the region that lies inside the curve, r = 11 cos θ, and outside the curve, r = 5 cos θ, can be shown as follows:

\(\int_{a}^{b}\frac{121cos^2\theta}{2} r^2d \theta - \int_{a}^{b}\frac{25cos^2\theta}{2} r^2d \theta\\=48\int_{a}^{b}cos^2\theta d\theta\)

Thus, the area of the region that lies inside the curve r = 11 cos θ and outside the curve r = 5 cos θ is \(48\int_{a}^{b}cos^2\theta d\theta\).

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Answer:

\(\cos \theta = -\frac{\sqrt{5}}{3}\)

Step-by-step explanation:

Draw a right triangle with angle \(\theta\). In all right triangles, the sine of an angle is equal to its opposite side divide by the hypotenuse of the triangle. Therefore, label the side opposite to \(\theta\) as 2 and the hypotenuse (longest side) of the right triangle as 3.

To find the last side, use the Pythagorean Theorem:

\(a^2+b^2=c^2\), where \(c\) is the hypotenuse of the triangle.

Solving for \(a\):

\(a^2+2^2=3^2,\\a^2+4=9,\\a^2=5,\\a=\pm\sqrt{5}\implies \sqrt{5}\)

In all right triangles, the cosine of an angle is equal to its adjacent side divided by the hypotenuse. However, the cosine of all angles in Quadrant III are negative. Therefore, the desired answer is \(\cos \theta=\boxed{-\frac{\sqrt{5}}{3}}\).

Verify:

\(\sin \theta =-\frac{2}{3},\\\\\theta=\arcsin(-\frac{2}{3}}),\\\\\cos(\arcsin(-\frac{2}{3}}))=-\frac{\sqrt{5}}{3}\checkmark\)

Answer:

C Subtraction property of equality

Step-by-step explanation:

You are subtracting 21 from both sides in step 3

Answer:

I would guess C

Step-by-step explanation:

I hope I'm correct, good luck.

The value of Sin2t is 1/4 and cos2t is (15/16)^1/2  and tan2t is 1/(15)^1/2.

According to the statement

we have given that the sint=1/8 then we have to find the exact value of

sin(2t) , cos(2t) , and tan(2t).

Here the value of Sint = 18

then sin2t becomes

sin2t = 2*1/8 then

sin2t = 1/4.

And

(Cos2t)^2 = 1 - (Sin2t)^2

(Cos2t)^2 = 1 - 1/16

(Cos2t)^2 = (16 - 1)/16

(Cos2t)^2 = 15/16

(Cos2t) = (15/16)^1/2

then

tan2t = sin2t/cos2t

tan2t = (1/4)/(15)^1/2 / 4

tan2t = 1/(15)^1/2

these are the values of given terms.

So, The value of Sin2t is 1/4 and cos2t is (15/16)^1/2  and tan2t is 1/(15)^1/2.

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The coplanar points in plane U are

Point P

Point W

Point S

Point L

Coplanar points are three or more points which all lie in the same plane

Collinear points are the points that lie on the same straight line or in a single line.

In the image attached, points A, B, C, and D are coplanar points. This is because they all lie on the same plane.

Now,

In the given image, points P, W, and S all lie on the same straight line. Thus, they are collinear.

and

Points P, W, S, and L all lie on plane U. This means the points are coplanar.

Hence, the coplanar points in plane U are

Point P

Point W

Point S

Point L

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To solve the given problem using the Delta Learning Rule method, we have the following data: X₁: -2, -1, 1

d₁: -1
W₁₀: 0.5
c (learning rate): 0.1
Transfer function: 2 / (1 + e^(-net))
The Delta Learning Rule is an iterative algorithm used to adjust the weights of a neural network to minimize the error between the predicted output and the target output. Let's go through the steps to find the updated weights:

1. Initialize the weights:
We start with the given initial weight W₁₀ = 0.5.
2. Calculate the net input (net):
net = W₁₀ * X₁
net = 0.5 * X₁

3. Apply the transfer function:
Using the given transfer function, we have:
y = 2 / (1 + e^(-net))
4. Calculate the error (δ): δ = d₁ - y
5. Update the weights:ΔW₁₀ = c * δ * X₁
W₁new = W₁₀ + ΔW₁₀

By repeating these steps for each data point, we can iteratively adjust the weights to minimize the error. The process continues until the error converges to an acceptable level or a maximum number of iterations is reached. The specific calculation and iteration process depend on the number of data points and the complexity of the problem. Without additional data points and a clear objective, we cannot provide a detailed step-by-step solution.

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Answer:

7

Step-by-step explanation:

Multiply 10.5 by 2/3 to find x, since those sides are corresponding.

10.5(2/3)

= 7

So, x is equal to 7.

The ending dollar balance in inventory, using the FIFO method, is $973.

The cost of each sold unit must be tracked according to the sequence of the unit's purchase if we are to use the FIFO (First-In, First-Out) approach to calculate the ending dollar balance in inventory.

Let's begin by utilizing the FIFO approach to get COGS or the cost of goods sold. In order to attain the total number of units sold, we first sell the units from the earliest purchase (First Purchase) before moving on to the units from the second purchase (Second Purchase).

First Purchase:

Number of Units: 130

Cost per unit: $3.1

Second Purchase:

Number of Units: 451

Cost per unit: $3.5

We compute the cost based on the cost per unit from the First Purchase until we reach the total amount sold to estimate the cost of goods sold (COGS) for the 303 units sold:

Units sold from First Purchase: 130 units

COGS from First Purchase: 130 units × $3.1 = $403

Units remaining to be sold: 303 - 130 = 173 units

Units sold from Second Purchase: 173 units

COGS from Second Purchase: 173 units × $3.5 = $605.5

Total COGS = COGS from First Purchase + COGS from Second Purchase

Total COGS = $403 + $605.5 = $1,008.5

To calculate the ending dollar balance in inventory, we need to subtract the COGS from the total cost of inventory.

Total cost of inventory = (Quantity of First Purchase × Cost per unit) + (Quantity of Second Purchase × Cost per unit)

Total cost of inventory = (130 units × $3.1) + (451 units × $3.5)

Total cost of inventory = $403 + $1,578.5 = $1,981.5

Ending dollar balance in inventory = Total cost of inventory - COGS

Ending dollar balance in inventory = $1,981.5 - $1,008.5 = $973

Therefore, the ending dollar balance in inventory, using the FIFO method, is $973.

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Answer:

16400$

Step-by-step explanation:

Persent invest value= 4100$

Compound intrest rate=8.5% or 0. 085 (annual)

Time period =17 years

According to compound interest formula

Future valve (fv) =persent value(pv) (1+r)^n

Substitute all values

Fv=4100$(1+0.085)^17

Fv=4100$(1.085)^17

Fv=4100 * 4.00

Fv= 16400 $ answer

The problem involves a subspace P2 of continuous functions over the interval (0, 2). It requires showing that the evaluation map Ev is invertible, determining coefficients for a quadrature formula, and discussing whether the formula holds for every function in C|0,2).

a) To show that the evaluation map Ev is invertible, we need to demonstrate that it is both injective (one-to-one) and surjective (onto). Injectivity means that different functions in P2 map to different points in R², and surjectivity means that every point in R² has a pre-image in P2. By examining the properties of P2 and the evaluation map, we can prove its invertibility.

b) The problem asks to find specific coefficients a₀, a₁, and a₂ that satisfy the given quadrature formula. We need to solve the equation ∫(0 to 2) [a₀ + a₁p(1) + a₂p(2)]p(c) dt = f₀p(0) + f₁p(1) + f₂p(2) for all polynomials p in P2. By substituting specific values for c and solving the resulting equations, we can determine the explicit values of a₀, a₁, and a₂.

c) The question inquires whether the quadrature formula holds for every function in C|0,2]. To justify our answer, we need to analyze the properties of the quadrature formula and determine if it provides accurate approximations for any arbitrary function in C|0,2]. This analysis involves considering the convergence properties of the formula and whether it can accurately capture the behavior of functions beyond polynomials.

The explanation provides an overview of the problem's components, including showing invertibility, finding coefficients for the quadrature formula, and discussing its applicability to functions in C|0,2]. It emphasizes the need for proofs, equations, and analysis to support the conclusions. The word count exceeds the minimum requirement of 100 words to provide a comprehensive explanation of the problem.

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The value of x is 3 and y is 6 when that satisfy the equation xy = 18 and have a minimum feasible sum of 2x + y.

Given that,

We have to find two positive values, x and y, that satisfy the equation xy = 18 and have a minimum feasible sum of 2x + y. What is this 2x + y minimum value.

We know that,

Take the xy=18

y= 18/x

Now,

S =2x + y

S =2x + 18/x

S' =2 - 18/x²        (differentiation)

Now take S'=0

2 - 18/x²=0

- 18/x²=0-2

- 18/x²=-2

18/x²=2

2x²=18

x²=18/2

x²=9

x=3

Substitute in xy=18

3y=18

y=18/3

y=6

Therefore, The value of x is 3 and y is 6 when that satisfy the equation xy = 18 and have a minimum feasible sum of 2x + y.

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The percentage decrease of the function y = -6 is 0%.

The function y = -6 represents a horizontal line with a constant value of -6. Since there is no change in the y-value as x varies, the percentage increase or decrease is 0%.

To calculate the percentage increase or decrease, we use the formula:

Percentage Change = (New Value - Old Value) / Old Value * 100

In this case, the old value and the new value are both -6. Plugging in the values into the formula, we get:

Percentage Change = (-6 - (-6)) / (-6) * 100

= 0 / (-6) * 100

= 0 * 100

= 0%

Therefore, the percentage increase or decrease of the function y = -6 is 0%. This indicates that the function remains constant and does not experience any change in its value as x varies.

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===================================================

Explanation:

We could add 9 to both sides, and then apply the square root to both sides. Don't forget about the plus minus

x^2 - 9 = 0

x^2 = 9

x = sqrt(9) or x = -sqrt(9)

x = 3 or x = -3

To check these answers, you replace x with those values we found. I'll show you how to check x = 3

x^2 - 9 = 0

(3)^2 - 9 = 0

9 - 9 = 0

0 = 0

So that confirms x = 3. The confirmation for x = -3 is nearly the same. Keep in mind that (-3)^2 = (-3)(-3) = 9. You'll be squaring the negative as well.

------------------

Another method you could do is to use the difference of squares rule

x^2 - 9 = 0

x^2 - 3^2 = 0

(x - 3)(x + 3) = 0

Now apply the zero product property. This effectively means you set each factor equal to zero and solve for x

x-3 = 0 or x+3 = 0

x = 3 or x = -3

We end up with the same solution set.

Yet another method you could use is the quadratic formula, but that may be overkill. It's still good practice to do.

Graphing is a visual way to find the answers. You'll graph y = x^2 - 9 and look to see where the curve crosses or touches the horizontal x axis.

Answer:

A) No solution

Step-by-step explanation:

Both linear equations have the same slope of 3, but different y-intercepts. Therefore, there will be no solutions because the lines will never intersect each other.

the answer is b because you add the two numbers together x + x y + y

Answer:

Its a

Step-by-step explanation:

Edge 22

Answer: 90°

Step-by-step explanation:

A full rotation on a clock would be 360° like a normal circle and this would represent a full hour.

When it comes to 15 minutes therefore, to find the number of degrees the time would turn, find out the proportion of an hour that 15 minutes is then relate it to 360°.

= 15 mins / 60 mins

= 1/4 hours

If an hour is 360°, 1/4 hours must be:

= 1/4 * 360

= 90°

He has eaten \(\frac{5}{8}\) pizza altogether.The total pieces of pizza was 8.Marco ate 3 for lunch and 2 for dinner.So, he ate 5 pieces of pizza out of 8.

What is fraction?

A fraction is a numerical value that is a part of whole number.In this numerator divided by denominator .In simple term both are integers.The word fraction means to break.

there are many types of fraction.Proper fraction, improper fraction,mixed fraction,whole fraction, like fraction, unlike fraction and unit fraction.

Total pieces of pizza =8

Marco ate for lunch =3

He ate for dinner =2

Total he ate =3+2

                     =5

Now remaining pieces of pizza=8-5

                       =3

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Answer:

5/8

Step-by-step explanation:

Answer:

168 ft²

Step-by-step explanation:

The equation for the lateral area of a square pyramid is LA = (Pl/2)

Plug in the values LA = (24(14)) / 2

LA = 336/2

LA = 168 ft²

The lateral surface area of the given pyramid whose base is an equilateral triangle is 126 square feet.

The lateral surface area of a triangular pyramid is 1⁄2(perimeter of the base × slant height) which further becomes 3⁄2(side × slant height).

Given that, slant height is 14 ft and the length of each side of the triangular base is 6 ft.

The equation for the lateral area of a square pyramid is 3/2 (6×14)

= 3×3×14

= 126 square feet

Therefore, the lateral surface area of the given pyramid whose base is an equilateral triangle is 126 square feet.

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Since f is both injective and surjective, it is a bijective homomorphism. Therefore, ⟨C*,⋅⟩ is isomorphic to K.

To prove that K is a subgroup of the group of 2x2 invertible matrices, we need to show that it satisfies the three conditions of being a subgroup:

1. Closure: We need to show that for any two matrices A and B in K, their product AB is also in K. Let A and B be matrices in K, then A = (a1 b1; -b1 a1) and B = (a2 b2; -b2 a2), where a1, b1, a2, b2 are real numbers. The product AB is given by (a1a2 - b1b2  a1b2 + b1a2; -(a1b2 + b1a2) a1a2 - b1b2). Since a1a2 - b1b2 and a1b2 + b1a2 are real numbers, AB is also in K.

2. Identity: We need to show that the identity element of the group of 2x2 invertible matrices is in K. The identity matrix I is given by (1 0; 0 1), which can be written as (1 0; 0 -1). Since 1 and -1 are real numbers, I is in K.

3. Inverse: We need to show that for any matrix A in K, its inverse A^(-1) is also in K. Let A = (a b; -b a) be a matrix in K. The inverse of A is given by A^(-1) = (a/(a^2 + b^2) -b/(a^2 + b^2); b/(a^2 + b^2) a/(a^2 + b^2)). Since a^2 + b^2 is not zero, A^(-1) is in K.

Therefore, K is a subgroup of the group of 2x2 invertible matrices.

To prove that ⟨C*,⋅⟩≅K, we need to show that there exists a bijective homomorphism between the multiplicative group of non-zero complex numbers and K.

Let f: ⟨C*,⋅⟩ -> K be defined as f(z) = (Re(z) Im(z); -Im(z) Re(z)), where Re(z) represents the real part of z and Im(z) represents the imaginary part of z.

To show that f is a homomorphism, we need to show that f(xy) = f(x)f(y) for all x, y in ⟨C*,⋅⟩. Let x = a + bi and y = c + di be non-zero complex numbers, where a, b, c, d are real numbers. Then f(x) = (a b; -b a) and f(y) = (c d; -d c). The product xy is given by (ac - bd) + (ad + bc)i. The image of xy under f is (ac - bd ad + bc; -(ad + bc) ac - bd). This is equal to the product of f(x) and f(y), so f is a homomorphism.

To show that f is bijective, we need to show that it is both injective and surjective.

To show injectivity, we need to show that if f(x) = f(y), then x = y. Let f(x) = f(y), then (a b; -b a) = (c d; -d c). This implies a = c and b = d, which means x = a + bi = c + di = y. Therefore, f is injective.

To show surjectivity, we need to show that for every matrix A in K, there exists a non-zero complex number z such that f(z) = A. Let A = (a b; -b a) be a matrix in K. We can find a non-zero complex number z = a + bi such that f(z) = (a b; -b a).

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