Given the following functions, find (f- g)(x).
f(x) = 3x - 1
g(x) = 5x + 2

The moment of inertia (I) is a measure of an object's resistance to rotational motion around an axis. The moment of inertia of a cylinder can be calculated using the following formula:

I = (1/2) × m × r²

where:

I is the moment of inertia of the cylinder

m is the mass of the cylinder

r is the radius of the cylinder.

Here are the steps to calculate the moment of inertia for a cylinder:

Determine the mass of the cylinder. This can be done by weighing the cylinder on a scale or by using its density and volume. The formula for the mass of a cylinder is:

m = density × volume

Measure the radius of the cylinder. This is the distance from the center of the cylinder to its outer edge.

Substitute the values of m and r into the moment of inertia formula:

I = (1/2) × m × r²

Calculate the moment of inertia using a calculator.

Note that the moment of inertia of a hollow cylinder is different from that of a solid cylinder. To calculate the moment of inertia of a hollow cylinder, you need to subtract the moment of inertia of the hollow space from the moment of inertia of the solid cylinder using the parallel axis theorem.

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That's a general overview of how to use Solver in Excel to solve optimization problems. If you have a specific problem in mind, please provide the details, and I'll be happy to assist you further.

Excel Solver is an add-in tool in Microsoft Excel that allows you to find an optimal solution for a given problem by adjusting certain variables.

To use Excel Solver, you need to set up a model that includes the objective function to optimize and any constraints or limitations on the variables.

The Solver then iteratively adjusts the variables to find the optimal solution that maximizes or minimizes the objective function while satisfying the constraints.

Here's a step-by-step explanation of how to use Excel Solver:

Set up your Excel spreadsheet: Start by organizing your data in a spreadsheet.

You should have a section for input variables, the objective function, and any constraints.

This could be a mathematical formula or a cell reference in your spreadsheet.

Open Solver: Go to the "Data" tab in Excel and click on "Solver" in the "Analysis" group. The Solver Parameters window will appear.

Remember to round your answer according to the requirements of your specific problem.

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Answer:

1. 50 degrees.

2. 90 degrees

3. 50 degrees

Step-by-step explanation:

hope this helps!

The area of the rectangle would be 4.90 units which is shown in the given graph.

The area of a rectangle is defined as the product of the length and width.

The rectangle is given which has:

verticals at  A(-4,0), B(-3,1) C(0,-2) and D(-1,-3)

The length of segment AB = √ (-3 - (-4))² + (1 - 0)² = √ (1 + 1) = √2

The length of segment BC = √ (-3 - 0)² + (1 - (-2))² = √ (9 + 3) = √12

The area of the rectangle = length of segment AB x length of segment BC

The area of the rectangle = √2 x √12

The area of the rectangle = √24

The area of the rectangle = 4.90 units

Thus, the area of the rectangle would be 4.90 units

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well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

The collecting area of a telescope is proportional to the square of its diameter. This means that if the diameter of one telescope is two times that of another, its collecting area will be four times larger.

In mathematical terms, the collecting area of a telescope is given by the formula A = πr^2, where A is the collecting area and r is the radius of the telescope's aperture. Since the diameter of a telescope is twice its radius, we can rewrite this formula as A = π(d/2)^2, where d is the diameter of the telescope.

If the diameter of one telescope is two times that of another, then the collecting area of the larger telescope will be A = π(2d/2)^2 = 4π(d/2)^2 = 4A, where A is the collecting area of the smaller telescope.

Therefore, the collecting area of the larger telescope is four times larger than that of the smaller telescope.

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Answer:

it is 6 1/6

hope this helps.

Answer:

∴Given Δ ABC is not a right-angle triangle

a= AB = √45 = 3√5

b = BC = 12

c = AC = √45 = 3√5

Step-by-step explanation:

Given vertices are A(3,3) and B(6,9)

           AB =

Given vertices are  B(6,9) and C( 6,-3)

            =  

   BC = 12

Given vertices are  A(3,3) and C( 6,-3)

AC² = AB²+BC²

45  = 45+144

45  ≠ 189

∴Given Δ ABC is not a right angle triangle

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

trust

Answer:

Step-by-step explanation:

Answer:

£22.33

Step-by-step explanation:

calculate the cost of an album and a single track using simultaneous equations.

let a represent an album and s a single track , then

3a + 4s = 18.13 → (1)

2a + 5s = 13.93 → (2)

multiplying (1) by - 2 and (2) by 3 and adding will eliminate a

- 6a - 8s = - 36.26 → (3)

6a + 15s = 41.79 → (4)

add (3) and (4) term by term to eliminate a

0 + 7s = 5.53

7s = 5.53 ( divide both sides by 7 )

s = 0.79

substitute s = 0.79 into either of the 2 equations and solve for a

substituting into (1)

3a + 4(0.79) = 18.13

3a + 3.16 = 18.13 ( subtract 3.16 from both sides )

3a = 14.97 ( divide both sides by 3 )

a = 4.99

that is album costs £4.99 and single track £0.79

then cost to Charlotte is

cost = (4 × £4.99) + (3 × £0.79) = £19.96 + £2.37 = £22.33

The cost of 4 albums and 3 single tracks is £22.33

Let the cost of 1 album = £x

and let the cost of 1 single track = £y

Now, the cost of 3 albums and 4 single tracks = £3*x + £4*y

and cost of 2 albums and 5 single tracks= £2*x + £5*y

Given that,

£3*x + £4*y = £18.13  -------->(1)

£2*x + £5*y = £13.93 -------->(2)

Multiply (1) equation by 2 and (2) equation by 3 then solve for x and y.

On applying the substitution method we have,

x = £4.99 and y = £0.79

Now, we have to calculate the value of 4 albums and 3 single tracks.

It can be written as 4*x +3*y

£4*4.99 + £3*0.79 = £22.33

So, the cost of 4 albums and 3 single tracks is £22.33

This question is based on a linear equation in two variables. Here, we used two equations based on two variables and then solved them with the help of the substitution method.

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Answer: The value of x is 38.4

Answer:D

Step-by-step explanation:

At the 0.1 level of significance, the conclusion we come up with is to reject the null hypothesis.

we are given that a random sample of 150 people was taken. 98 of the people in the sample favored the candidate, were it to determine whether or not the proportion of the population in favor of candidate a is significantly more than 57%.So we need to find the test statistic, which is 1.98  determined from the z score, here the rejection region is the number more than 1.28, and 1.98 is greater than 1.28, so it is better to simply reject the null hypothesis.

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Answer:

\(P(Not\ hobbit\ or\ Not\ Umbrella) = \frac{14}{15}\)

Step-by-step explanation:

Your question is poorly formatted (See comment section for complete question)

Given

\(x = \{elf, hobbit, human\}\) ---- characters

\(n(x) =3\)

\(y = \{Magic,Sword,Shield,Slingshot,Umbrella\}\) --- tools

\(n(y) = 5\)

Required

The probability that your character won't be a hobbit or your tool won't be an umbrella?

First we calculate the probability of choosing a hobbit.

\(x = \{elf, hobbit, human\}\)

\(n(hobbit) = 1\)

So:

\(P(hobit) = \frac{n(hobbit)}{n(x)}\)

\(P(hobit) = \frac{1}{3}\)

Using the complement rule, we calculate the probability of not choosing a hobbit

\(P(Not\ hobbit) = 1 - P(hobbit)\)

\(P(Not\ hobbit) = 1 - \frac{1}{3}\)

\(P(Not\ hobbit) =\frac{2}{3}\)

Next, we calculate the probability of choosing an umbrella.

\(y = \{Magic,Sword,Shield,Slingshot,Umbrella\}\)

\(n(Umbrella) = 1\)

So:

\(P(Umbrella) = \frac{n(Umbrella)}{n(y)}\)

\(P(Umbrella) = \frac{1}{5}\)

Using the complement rule, we calculate the probability of not choosing an umbrella

\(P(Not\ Umbrella) = 1 - \P(Umbrella)\)

\(P(Not\ Umbrella) = 1 - \frac{1}{5}\)

\(P(Not\ Umbrella) = \frac{4}{5}\)

The required probability is calculated using:

\(P(A\ or\ B) = P(A) + P(B) - P(A)P(B)\)

In this case;

\(P(Not\ hobbit\ or\ Not\ Umbrella) = P(Not\ hobbit) + P(Not\ Umbrella) -\) \(P(Not\ hobbit)*P(Not\ Umbrella)\)

\(P(Not\ hobbit\ or\ Not\ Umbrella) = \frac{2}{3} + \frac{4}{5} - \frac{2}{3} * \frac{4}{5}\)

\(P(Not\ hobbit\ or\ Not\ Umbrella) = \frac{2}{3} + \frac{4}{5} - \frac{8}{15}\)

Take LCM

\(P(Not\ hobbit\ or\ Not\ Umbrella) = \frac{10+12-8}{15}\)

\(P(Not\ hobbit\ or\ Not\ Umbrella) = \frac{14}{15}\)

To eliminate X in the system of equations. use the method of equivalent equations, which is to manipulate one of the equations so that it has the opposite coefficient of the variable that you want to eliminate, and then add or subtract them to eliminate that variable.

There are different methods to eliminate a variable in a system of equations, but one common method is to use the property of equivalent equations.

To eliminate x in the given system of equations:

4x + 3y = 20 (equation 1)

3x + 2y = 12 (equation 2)

1. Multiply equation 1 by 3, this will result in 12x + 9y = 60.

2. Multiply equation 2 by -4, this will result in -12x - 8y = -48.

3. Add the two equations 12x + 9y = 60 and -12x - 8y = -48. This will give you y = 12.

This is how we eliminated x in the system of equation by using the method of equivalent equations.

Now that we have the value of y, we can substitute it to any of the two equations and solve for the value of x.

4x + 3y = 20 (equation 1)

4x + 3(12) = 20

4x = -16

x = -4

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The factors of the given Quadratic Equation 2x² - x - 120 = 0 is 8 and -15/2.

What are zeros ?

zeros denotes the factors of the given equation in other words the zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.

Polynomial roots are the same as polynomial zeros, so they can be found by factoring the quadratic equation into two linear factors, after which they can be equating to zero.

Now, considering the given Quadratic Equation to find x :

2x² - x - 120 = 0

writing the above equation into two linear factors as :

2x² - 16x + 15x - 120 = 0

2x(x-8) + 15(x-8) = 0

(x-8)(2x+15) = 0

Now, equating each linear equation to zero to find the factors:

(x-8) = 0 and (2x+15) = 0

x = 8 and x = -15/2.

Therefore, the factors of the given Quadratic Equation is 8 and -15/2.

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Answer:

2(8 x 4) + 2(4 x 10) + 2(8 x 10)

Step-by-step explanation:

the expression represents the surface area, because it is finding the area of the three different sizes of sides, doubling them, then adding them together

Answer:

30

Step-by-step explanation:

60(highest) - 30(lowest) = 30(range)

Answer:

Step-by-step explanation:

Let the number of pastries  is x.

We have an inequality:

The least whole number for x is 131.

Correct choice is D

Let that be n

Atleast 131

Answer:

y= 1-x

Step-by-step explanation:

● (a^2x)/a^(x-y) = a

This means that:

● 2x-(x-y) = 1

● 2x - x +y = 1

● x + y = 1

Substract x from both sides

● x+y -x = 1-x

● y = 1-x

The perimeter of the composite shape is: (3π + 12)mm

A semicircle is a part of a circle cut through its diameter.

Analysis:

perimeter of a semicircle = πr

where r = 6/2 = 3mm

perimeter of a semicircle = π(3)  = 3π

perimeter of incomplete rectangle = L+2B, L = 6mm, B = 3mm

perimeter of rectangle = 6mm +2 x 3= 12mm

perimeter of shape = (3π+12)mm

In conclusion, the perimeter of the rectangle is (3π+12)mm

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Answer:

The answer is \(\sqrt{x} 101\)

Step-by-step explanation:

Answer:

D.\(\sqrt{101}\)

Step-by-step explanation:

The formula is = \(\sqrt{(x2-x1)^{2}+(y2-y1)^{2}\)

So, x1=-2 ; y1=3; x2=8; y2=2

putting these values in the formula the result will be \(\sqrt{101}\)

Hope, this helps you.

Answer:

below

Step-by-step explanation:

Here's a completed table based on the information provided:

Category Amount (in dollars)

Transportation  36% * 2,300 * .70%

Snacks                   X

Rewards                   Y

Transportation: 36% * 2,300 * .70% = 82.32

Let X = amount spent on snacks

Let Y = amount spent on rewards

Since more money was spent on snacks than rewards, we have X > Y

The total spent on transportation, snacks, and rewards must be equal to 36% of the yearly budget:

82.32 + X + Y = 36% * 2,300 = 828

Therefore, X + Y = 828 - 82.32 = 745.68

Since X > Y, we can set X = 400 and Y = 345.68, for example. These are just possible amounts of money Mrs. Smith could have spent in each category.

The x and y are of t, if y = x4 5x and dx/dt = 4, when x = 3, the rate of change of y with respect to t is 436

Using the chain rule, we can find the derivative of y with respect to t as:

dy/dt = (dy/dx) * (dx/dt)

We are given that dx/dt = 4 and y = x^4 + 5x. Taking the derivative of y with respect to x, we get:

dy/dx = 4x^3 + 5

Substituting x = 3, we get:

dy/dx (at x=3) = 4(3)^3 + 5 = 109

Now, substituting dx/dt = 4 and dy/dx = 109 into the chain rule formula, we get:

dy/dt = (dy/dx) * (dx/dt) = 109 * 4 = 436

Therefore, when x = 3, the rate of change of y with respect to t is 436

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x= -21 / 40

I hope it will help you

We have shown that if a and b are odd integers, then c must be even. Since a, b, and c are integers, it follows that at least one of a and b must be even. Therefore, we have proved that for all integers a, b, and c, if a²b²=c², then a or b is even.

We have to prove that for all integers a, b, and c, if a²b²

=c², then a or b is even.Given that a, b, and c are all integers, and that a²b²

=c², we must show that either a or b must be even.To prove this, we'll use proof by contradiction by supposing both a and b are odd.Since a is odd, it can be expressed as a

=2m+1 for some integer m, while b can be expressed as b

=2n+1 for some integer n. Therefore, a²

=(2m+1)² and b²

=(2n+1)².Substituting these values into the equation a²b²

=c², we get (2m+1)²(2n+1)²

=c², which can be simplified to (4mn+m+n)²

=c². This equation can also be written as 4mn+m+n

=c/d for some integers c and d.Let k

=m+n. Then 4mn+m+n

=4mn+2k

=2(2mn+k). We know that 2mn+k

=c/d, so 4mn+2k

=2(2mn+k)

=2(c/d), which is even because c/d is an integer. Therefore, the left-hand side of the equation is even, which means that the right-hand side of the equation must also be even. Since c/d is an integer, c must be even.We have shown that if a and b are odd integers, then c must be even. Since a, b, and c are integers, it follows that at least one of a and b must be even. Therefore, we have proved that for all integers a, b, and c, if a²b²

=c², then a or b is even.

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Answer:

uhh oh thaaaaaaat's such a pain

Answer:

If the steak is between 8 and 12 pounds, inclusive, cook the steak for 7 minutes.

If the steak is more than 12 pounds but less than or equal to 13 pounds, then cook the steak for 8 minutes.

If the steak weighs more than 13 pounds but is less than or equal to 14 pounds, cook the steak for 9 minutes.

If the steak weighs more than 14 pounds but is less than or equal to 15 pounds, cook the steak for 10 minutes.

Finally, if the steak is more than 15 pounds but less than or equal to 16 pounds, cook the steak for 11 minutes.

Answer:

AB = 15

Step-by-step explanation:

6(6 + x + 6) = 7(7 + 11)

72 + 6x = 126

6x = 126 - 72 = 54

x = 54/6

   = 9.

So AB = 9 + 6 = 15.