Please help me I need to answer this before tomorrow!

Answer:

Sample response:

Both inequalities use the division property to isolate the variable, y. When you divide by a negative number, like –7, you must reverse the direction of the inequality sign. When you divide by a positive number, like 7, the inequality sign stays the same. The solution to the first inequality is y > -23, and the solution to the second inequality is y <>

The solution to the given Inequality is a > 12 and the graph is as attached.

We are given the Inequality as;

8a - 30 > 66

Now, use addition property of equality to add 30 to both sides to get;

8a - 30 + 30 > 66 + 30

8a > 96

Now, use division property of equality to divide both sides by 8 to get;

8a/8 > 96/8

a > 12

The graph of this is as attached.

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The arc length of the curve on the given interval is: arc length = ∫(sqrt(145)) dt, from a to b.

To find the arc length of the curve defined by the parametric equations, we need to evaluate the integral of the speed function with respect to the parameter over the given interval. The speed function is calculated as the square root of the sum of the squares of the derivatives of x and y with respect to the parameter.

Let's start by finding the derivatives of x and y with respect to t:

dx/dt = 8

dy/dt = -9

The speed function is given by:

speed = \(sqrt((dx/dt)^2 + (dy/dt)^2)\)

\(= sqrt((8)^2 + (-9)^2)\)

\(= sqrt(64 + 81)\)

\(= sqrt(145)\)

To find the arc length, we need to evaluate the integral of the speed function with respect to t over the given interval. The interval is not specified, so we'll assume it is from t = a to t = b.

arc length = ∫(sqrt(145)) dt, from a to b

Since the interval is not provided, we cannot provide an exact numerical value for the arc length. However, we can still express the arc length in terms of the parameter t.

Therefore, the arc length of the curve on the given interval is: arc length = ∫(sqrt(145)) dt, from a to b

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Answer:

3.398

Step-by-step explanation:

log(10) 2500 = log(10) (5^2*10^2) = log(10) 5^2 + log(10) 10^2 = 2*log(10) 5 + 2=3.398

Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

Answer:   \(\large \boldsymbol{\dfrac{1}{8 } (x^2-3)^4+c}\)

Step-by-step explanation:

\(\displaystyle \large \boldsymbol{} \int\limits {x(x^2-3)^2 } \, dx =\int\limits \frac{1}{2} {} \, (x^2-3)' (x^2-3)^3 dx =\frac{1}{8} (x^2-3)^4+c\)

Answer: 13.5 Miles an hour.

Step-by-step explanation:

Answer:

116°10"

Step-by-step explanation:

180°-63.9°=179°60"-63°50"=116°10"

Answer:

Step 2 should be division, not subtraction.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

8x = 24

Step 2: Solve for x

We see that 8x is actually 8 times x. Therefore, we would need to use the Division Property of Equality to isolate x and get our answer.

Answer:

PLEASE MARK AS BRAINLIEST AND GIVE THANKS

0.1007

Step-by-step explanation:

0.53 x 0.19 = 0.1007

Answer:

d. All of the above are true

Step-by-step explanation:

All of the following statements,

a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.

b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative.

C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant.

are true

answer:

423.5

step1.

you find the value of 3% by dividing over 100 because percentage is over 100 so 3/100

step2

multiply by $350

so 3/100×350=10.5

step3

we are told the investment is for 7years so we multiply 10.5 by 7 because 10.5 is only for 1year

10.5×7=73.5

step4

add the 73.5 to the 350 then you have your answer

Answer:

Answers are in bold

Data set A:

Mean: 7

Median: 7

Mode: 7

Range: 11

Data set B:

Mean: 78

Median: 95

Mode: No mode or all the numbers (85, 105, 95, 90, 115)

Range: 30

Data set C:

Mean: 13

Median: 13

Mode: 11 and 16

Range: 7

Step-by-step explanation:

I just answered this but you're welcome.

Answer: 62cm^2

Step-by-step explanation: 70-8=62

The roots of the auxiliary equation are r = (-1 ± √(1 + 16/x^2)) / x.

The general solution of the differential equation is y(x) = c_1 x^4/16 + c_2 x^(-1/2) cos(ln x) + c_3 x^4/16 + c_4 x^(-1/2) sin(ln x), where c_1, c_2, c_3, and c_4 are arbitrary constants

The auxiliary equation for the given differential equation is obtained by assuming a solution of the form y(x) = e^(rx), where r is a constant. Substituting this solution into the differential equation, we get:

x^2(e^(rx))'' + x(e^(rx))' - 16(e^(rx)) = 0

Differentiating twice, we get:

r^2x^2 e^(rx) + 2rx e^(rx) + x e^(rx) + x e^(rx) - 16 e^(rx) = 0

Simplifying and factoring out e^(rx), we get:

e^(rx) (r^2x^2 + 2rx - 16) = 0

For nontrivial solutions, we must have e^(rx) ≠ 0, which implies that the quadratic expression in the parentheses must be zero. Thus, we need to solve the equation:

r^2x^2 + 2rx - 16 = 0

Using the quadratic formula, we get:

r = [-2x ± √(4x^2 + 64x^2)] / (2x^2) = [-x ± √(x^2 + 16)] / x

The roots of the auxiliary equation are therefore:

r = (-1 ± √(1 + 16/x^2)) / x

To solve the differential equation, we need to find two linearly independent solutions. Since the roots of the auxiliary equation are complex when x > 0, we can write the solutions in terms of exponentials of complex numbers as follows:

y_1(x) = x^4/16 + x^(-1/2) cos(ln x)

y_2(x) = x^4/16 + x^(-1/2) sin(ln x)

Thus, the general solution of the differential equation is:

y(x) = c_1 x^4/16 + c_2 x^(-1/2) cos(ln x) + c_3 x^4/16 + c_4 x^(-1/2) sin(ln x)

where c_1, c_2, c_3, and c_4 are arbitrary constants determined by the initial conditions of the problem.

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The area of the largest rectangle is 46.47 square root.

Consider a semi-circle with a rectangle ABCD inscribed in it.

Let, O = centre of the semi-circle

A and B lies on the base of the semi-circle

OA = OB = x

D and C lie on the semi-circle

BC = AD = y

AB = CD = 2x

By Pythagorean theorem,

CB² + OB² = OC²

⇒ y² + x² = (6)²

⇒ y² = 36 - x²

⇒ y = √(36 - x²)

Now, area of rectangle in terms of x,

Area, A = 2x × y

= 2x × √(36 - x²)

Differentiating,

A' = 2 × √(36 - x²) - 2x²/(36 - x²)

When x = 0, y = 6 and when x = 6, y = 0, area = 0.

It implies that area is maximum when the value of x lies between 0 and 6.

This will occur where A’ = 0.

⇒ 2 × √(36 - x²) - 2x²/(36 - x²) = 0

⇒ 2 × √(36 - x²) = 2x²/(36 - x²)

On simplification, we get,

⇒ 2 × (36 - x²) = 2x²

⇒ 36 - x² = x²

⇒ 2x² = 36

⇒ x² = 36/2

⇒ x = √36/2

Now, y = √(36 - x²) becomes

⇒ y = √(36 - (√36/2)²)

⇒ y = √(36 - 36/2)

⇒ y = √(96 - 36)/2

⇒ y = √60/2

Maximum area = 2xy

= 2(√36/2)(√60/2)

= 46.47

Therefore, the area of the largest rectangle = 46.47 square units.

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The number of car stereos with a CD player only is 65.

Step-by-Step Explanation:

To find out the number of car stereos with a CD player only, we need to follow these steps:

Identify the total number of car stereos sold, which is given as 320.

Identify the number of car stereos with a CD player, which is given as 108.

Identify the number of car stereos with both a CD and a cassette player, which is given as 43.

Now, we need to subtract the number of car stereos with both a CD and a cassette player from the number of car stereos with a CD player to find the number of car stereos with a CD player only.

108 - 43 = 65

So, 65 car stereos had a CD player only. Therefore, the correct answer is (e) 65.

Answer: There were 65 car stereos with a CD player only out of the total 320 car stereos sold.

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Answer:

The million dollar cube will be 10.79 cm tall

Step-by-step explanation:

Let the sides of the gold cube representing the tallness of the cube  be s

volume of the gold cube V = s³

Then :

\(\mathbf{s = \sqrt[3]{V} }\)  --- (1)

Similarly; we know that , density ρ = mass m/Volume V

making volume the subject of the formula, then ;

V = m/ρ

Replacing that into (1) above , we have:

\(\mathbf{s = \sqrt[3]{\dfrac{m}{\rho}} }\)

Given that:

At the time, gold is selling for $1282 per troy ounce

∴ In a million-dollar cube of gold, the number of troy ounce that can be bought with a million dollar = 1000000/1282 = 780.03 troy ounce

Since 1.0000 troy ounce equals 31.1035 g

∴ 780.03 troy ounce = 780.03  × 31.1035 g

= 24261.66 g

From the tables 12.1 of Gold , the density of Gold is obtained as 19.3 g/cm³

∴

\(\mathbf{s = \sqrt[3]{\dfrac{m}{\rho}} }\)

\(\mathbf{s = \sqrt[3]{\dfrac{24261.66}{19.3}} }\)

\(\mathbf{s = \sqrt[3]{1257.080829} }\)

\(\mathbf{s = 10.79 \ cm }}\)

The million dollar cube will be 10.79 cm tall

Answer:

n-3

Step-by-step explanation:

Im not 100% sure this is correct but im pretty sure that it is its the only answer that would make sense.

when n is input then output is n-3.

A number system is defined as a system of writing to express numbers.

The given table is

Input          5         6         9        n

Output       2         3          6       x

We need to find the value of x

By observing the data,

When input is five, output is two.

It means 3 is decreased from input.

When input is six, output is three.

It means 3 is decreased from input.

6-3=3

When input is nine, output is six.

It means 3 is decreased from input.

9-6=3

When input is n the output is x

n-3 is the output when n is input.

Hence when n is input then output is n-3.

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Answer:

Para descomponer 132 en decenas y unos, se deben identificar cuántas decenas contiene el número primero, y luego determinar el número de unidades restantes.

En este caso, el número 132 contiene 13 decenas y 2 unidades. Por lo tanto, se puede escribir como 13 decenas y 2 unidades, o como 130 + 2 = 13(10) + 2.

Answer:

4+2d

Step-by-step explanation:

2(3+d-1)

6+2d-2=6+(-2)+2d

=4+2d

The inverse of f is a function which takes any value x and divides it by 4, then adds 7 to the result.

The inverse of a function is the opposite of the original function, meaning that it takes the output of the original function and turns it back into the input. In this case, the original function is f(x)=1/4x+7. To find the inverse, we need to solve for x in the equation, which can be done by subtracting 7 from both sides and then multiplying both sides by 4. This gives us x=(x+7)/4, which is the inverse of the original function. To put it simply, the inverse of f takes any output of the original function, adds 7 to it, and then divides it by 4 to get the original input.

example;

If f(x)=1/4x+7 and x=3, then

f(3) = (1/4)3 + 7

7.75

The inverse of f is f^-1(x) = (x + 7) / 4.

If f^-1(7.75) = (7.75 + 7) / 4, then

f^-1(7.75) = 14.75 / 4

3.6875

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For the segments to be congruent, x should be 13/2.

This is a case of congruency of segments. We know that two segments are congruent if and only if they have equal lengths.

Now, here the two line segments JK and RS have lengths 2x-9 and 30-4x respectively.

So, to be congruent, JK and RS must be of equal length.

Or in other words, 2x-9 = 30-4x

or 6x= 30 + 9 =39

i.e. 6x = 39.

Dividing both sides by 3, we get

2x=13 , which implies , x =13/2 or 6.5

Thus, for JK and RS  to be congruent  , x =13/2.

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For the segments to be congruent, x should be 13/2.

This is a case of congruency of segments. We know that two segments are congruent if and only if they have equal lengths.

Now, here the two line segments JK and RS have lengths 2x-9 and 30-4x respectively.

So, to be congruent, JK and RS must be of equal length.

Or in other words, 2x-9 = 30-4x

or 6x= 30 + 9 =39

i.e. 6x = 39.

Dividing both sides by 3, we get

2x=13 , which implies , x =13/2 or 6.5

Thus, for JK and RS  to be congruent  , x =13/2.

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Answer:

A

Step-by-step explanation:

Every input (x value) can have only ONE ouput (y value) to be a function, y- values can be repeated but x- values cannot

Hope that helps

\(f(x,y) =tan(x) + y\) and u is the unit vector in the direction of (-2,0). Then

(a) \(f(x,y) = tan(x) + y - sqrt(4)\)

(b) \(f(0.9, 9) = 7.813\)

(c) \(fu = (-1.077,-0.5)\)

The gradient of f at the point (4,4) is \((∂f/∂x, ∂f/∂y)\) evaluated at (4,4), which is \((sec^2(4), 1)\).

(a) \(f(x,y) = tan(x) + y - sqrt(4)\)

(b) \(f(0.9, 9) = tan(0.9) + 9 - 2 = 7.813\)

(c)\(fu = (0.9,9) = (∂f/∂x, ∂f/∂y) . u = (sec^2(0.9) * (-2), 1) . (-2/sqrt(4)) = (-1.077,-0.5)\)

The gradient of f at a point (x,y) is defined as the vector\((∂f/∂x, ∂f/∂y\)).

At the point (4,4), the partial derivative of f with respect to x,\((∂f/∂x),\) is \(sec^2(4)\) and the partial derivative of f with respect to y,\((∂f/∂y)\), is 1. Therefore, the gradient of f at (4,4) is \((sec^2(4), 1)\).

The gradient of a function gives the direction of maximum increase at a point and is orthogonal to the level curves (contours) of the function.

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The text discusses a production function and addresses various aspects of a firm's decision-making. It covers profit maximization, factor demand functions, supply function, profit function, Hotelling's lemma, cost minimization, conditional factor demand functions, and the cost function. These concepts are derived using mathematical calculations and formulas. Hotelling's lemma is verified, and the cost function is determined.

(a) The firm's profit maximization problem can be stated as follows: Maximize profits (π) by choosing the optimal levels of inputs (z and zo) that maximize the output (y) given the prices of output (p) and inputs (w, w₂).

(b) To derive the firm's factor demand functions, we need to find the conditions that maximize profits.

The first-order condition for input z is given by:

∂π/∂z = p * (∂f/∂z) - w = 0

Substituting the production function f(z) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/4 * z^(-3/4) / z^(1/2)) - w = 0

Simplifying, we get:

p * (1/4 * z^(-7/4)) - w = 0

Solving for z, we find:

z = (4w/p)^(4/7)

Similarly, for input zo, the first-order condition is:

∂π/∂zo = p * (∂f/∂zo) - w₂ = 0

Substituting the production function f(zo) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Simplifying, we get:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Solving for zo, we find:

zo = (2w₂ / (pz^(1/4)))^(2/3)

(c) To derive the firm's supply function, we need to find the level of output (y) that maximizes profits.

Using the production function f(z), we can express y as a function of z:

y = z^(1/4) / z^(1/2)

Given the factor demand functions for z and zo, we can substitute them into the production function to obtain the supply function for y:

y = (4w/p)^(4/7)^(1/4) / (4w/p)^(4/7)^(1/2)

Simplifying, we get:

y = (4w/p)^(1/7)

(d) The firm's profit function is given by:

π = p * y - w * z - w₂ * zo

Substituting the expressions for y, z, and zo derived earlier, we have:

π = p * ((4w/p)^(1/7)) - w * ((4w/p)^(4/7)) - w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

(e) To verify Hotelling's lemma, we need to calculate the partial derivatives of the profit function with respect to the prices of output (p), input z (z₁), and input zo (z₂).

Hotelling's lemma states that the partial derivatives of the profit function with respect to the prices are equal to the respective factor demands:

∂π/∂p = y - z * (∂y/∂z) - zo * (∂y/∂zo) = 0

∂π/∂z₁ = -w + p * (∂y/∂z₁) = 0

∂π/∂z₂ = -w₂ + p * (∂y/∂z₂) = 0

By calculating these partial derivatives and equating them to zero, we can verify Hotelling's lemma.

(f) The firm's cost minimization problem can be stated as follows: Minimize the cost of production (C) given the level of output (y), prices of inputs (w, w₂), and factor demand functions for inputs (z, zo).

(g) To derive the firm's conditional factor demand functions, we need to find the conditions that minimize costs. We can express the cost function as follows:

C = w * z + w₂ * zo

Taking the derivative of the cost function with respect to z and setting it to zero, we get:

∂C/∂z = w - p * (∂y/∂z) = 0

Simplifying, we have:

w = p * (1/4 * z^(-3/4) / z^(1/2))

Solving for z, we find the conditional factor demand for z.

Similarly, taking the derivative of the cost function with respect to zo and setting it to zero, we get:

∂C/∂zo = w₂ - p * (∂y/∂zo) = 0

Simplifying, we have:

w₂ = p * (1/2 * z^(1/4) * zo^(-3/2))

Solving for zo, we find the conditional factor demand for zo.

(h) The firm's cost function is given by:

C = w * z + w₂ * zo

Substituting the expressions for z and zo derived earlier, we have:

C = w * ((4w/p)^(4/7)) + w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

This represents the firm's cost function.

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