What is the remainder when x 2 2x 1 is divided by x 1?.

The diameter of the Ferris wheel is equal to 95 ft.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a function that models the height of a seat on a Ferris wheel after [t] minutes.

We have the following function -

f(t) = 95 cos(π/10)t

The diameter of the Ferris wheel would be the maximum height reached by the wheel. We have -

f(t) = 95 cos[(π/10)t]

df/dt = 95 x - sin[(π/10)t] x (π/10)

df/dt = -(95π/10) sin[(π/10)t]

For maximum height -

df/dt = 0

- (95π/10) sin[(π/10)t] = 0

sin[(π/10)t] = 0

sin[(π/10)t] = sin (0)

(π/10)t = 0

t = 0

Put t = 0, in f(t) = 95 cos[(π/10)t], we get -

f(max) = 95 cos(0) = 95 ft

Therefore, the diameter of the Ferris wheel is equal to 95 ft.

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Answer: Option C (190 ft)

Step-by-step explanation:

Trigonometric functions, rational functions, hyperbolic functions, and log functions are some examples of having inverse.

The inverse of a function is basically a reverse function or undo of the function.

For example y = f(x) then the inverse will be x = f(y).

It means in the inverse function we need to interchange x and y.

Suppose a function,

y = sinx here x is the angle while y is the real number.

Now, x = sin⁻(y) here sin⁻(y) is a function of x as inverse.

Another example y = 2x

x = 2/y if x is output then it will be inverse.

Hence "Trigonometric functions, rational functions, hyperbolic functions, and log functions are some examples of having inverse".

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There are 4 fundamental main properties of numbers: commutative, associative, distributive, and identity. You must be acquainted with every of those.

Commutative Property: a. Addition. When numbers are added, the sum is the equal irrespective of the order wherein the numbers are added. b. Multiplication. When all numbers are accelerated together, the product is the equal irrespective of the order wherein the numbers are accelerated. Identity Property. Addition. The sum of any wide variety and 0 is that wide variety.

Associative Property : a. Addition. When 3 or greater numbers are added, the sum is the equal irrespective of the manner wherein the numbers are grouped. b. Multiplication. When 3 or greater numbers are accelerated, the product is the equal irrespective of the manner wherein the numbers are grouped. Distributive Property: The sum of numbers instances a 3rd wide variety is identical to the sum of every addend instances the 1/3 wide variety.

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#6

z =(-2,-3)

y =(-1,-1)

b =(-3,1)

w =(-4,-2)

#7

r =(3,-2)

j =(4,-4)

e =(3,-4)                                                          

#8

v = (-1,-5)

c = (0,0)

r = (-3,-3)

#9

z = (2,0)

l = (4,-3)

n =(1,-4)

#10

r =(-3,-2)

z =(0,-2)

j =(-1,3)

y =(2,2)

Hope those are all correct! Good luck on the HW!

A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits.

In the given question we have to explain about 2-digit special number.

A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits.

Take the number's initial and last digits out, then add and multiply each digit independently. After that, multiply the two-digit number by the sum and product of its digits and then compare the result to the original value. If they match, it qualifies as a special two-digit number; otherwise, it does not.

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The surface area of the square pyramid that has the above stated dimensions is: 112 in.².

A square pyramid is a three-dimensional geometric shape that is made up of one square base and four triangular faces that meet at a vertex point.

The diagram attached below shows what a typical square pyramid looks like.

The formula for the surface area of a square pyramid (SA) = A + 1/2Ps, where:

Given the following:

Length of a side of the base (b) = 4 in.

Base area (A) = 4²

A = 16 in.²

Perimeter of the base (P) = 16 in.

Slant height (s) of the square pyramid = 12 in.

Surface area (SA) = 16 + 1/2(16)(12)

SA = 16 + 96

Surface area of the square pyramid = 112 in.²

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The gravitational force on one sphere due to the three of square is 1042.18 ×10⁻¹¹N

We are given that ,

Mass = m = 7.5 kg

Side = d = 0.6 m

Due to the square's three corner there will be up , right and diagonal three forces acting on the system,

Fup = G(m²/d²)

Fright =  G(m²/d²)

Fdia = G (m²/(√2d)²)cos45°+ G (m²/(√2d)²)sin45°

To calculate the force on the left sphere in the lower left corner. From the symmetry of the problem the net forces in the x and y direction will be the same and θ = 45°

Therefore, the force will be,

Fx =Fright +Fdia

Fx =  G(m²/d²) +G (m²/(√2d)²)(1/√2)

Fx = G(m²/d²)[(1+(1/2√2)]

Thus, Fy = Fx =G(m²/d²)[(1+(1/2√2)]

By the Pythagorean combination of the two component forces , due to symmetry the the net force will be along the diagonal of the square,

F = √Fx +Fy= Fx√2

F = G(m²/d²)[(1+(1/2√2)]√2

F = (6.67 ×10⁻¹¹ Nm²/kg²)(7.5kg)²/(0.6m)²

F = 1042.18 ×10⁻¹¹N

The force at points are the center of the square.

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Using the Indifference curve , the slope of ambrose indifference curve is -2.

Indifference Curve

A bunch of places of consumption where consumer tastes are indifferent is an indifference curve. Indifference curves are usually convex towards the origin.

Rewriting algebraically the equation of the indifference curve U(t, y)=c in the form y=g(t, c),

where g(t, c) is a decreasing convex function of t for c given .

Indifference curve is given by:

x₂ = C − 4x₁¹/²

Slope of the indifference curve = dx₂/dx₁

Hence, Slope of the Ambrose indifference curve = dx₂/dx₁ = -(1/2)(4/x₁¹/²)

=> Slope of the Ambrose indifference curve = -2/x₁¹/²

At (1,6), Slope of the Ambrose indifference curve = -2/x₁¹/² = -2/1= -2

Hence, Slope of the Ambrose indifference curve = -2

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The correct statement is option (B) the market for paper is growing faster than the market for all other

The given statement is

Paper production accounts for approximately 40 percent of the world's industrial use of wood, and the market for paper is growing faster than it is for all major wood products.

The first option is a sentence that in the question but its not conveying the proper meaning of the given statement. Option C, D and E is not saying about the paper market, therefore it is not conveying the correct meaning of the statement

Hence, the correct statement is option (B) the market for paper is growing faster than the market for all other

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To graph an inequality, consider the < or > sign to be a = sign and graph the equation. If the inequality is < or >, draw a dotted line to represent the equation.

Graph the equation as a solid line if the inequality is ≤ or ≥, This line divides the xy-plane into two regions: one that meets the inequality and one that does not.

When inequalities are graphed on a coordinate plane, the solutions are found in a region of the plane that is shaded. If the points on the line satisfy the inequality, as in the case of and, the boundary line for the inequality is drawn as a solid line.

Linear inequalities are not the same as linear equations, but what you know about equations can help you understand inequalities. Equations and inequalities are both mathematical statements that compare two values. 

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The equivalent expression of 4(x + 2) + 4. is 4x + 12.

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.

Therefore, let's find the equivalent expression of 4(x + 2) + 4.

Let's simplify the expression to find it's equivalent.

4(x + 2) + 4 = 4x + 8 + 4 = 4x + 12

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Option(4) The different decisions in both study 1 & study 2 are possible because the second test was associated with a greater power to detect an effect.

In statistics, power is the probability of rejecting a null hypothesis when, in fact, it is true. An error of Type II is less likely to occur when power is high. In the event of a false null hypothesis, power is the probability of making the correct decision (to reject the null hypothesis).

The power of a test of significance is the likelihood that an effect will be found. In the event of a deviation from the null hypothesis, power is the probability that the test of significance will detect it.

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The required an equation for the perpendicular bisector of the line segment joining (1,2) and (-5,12) is y = 3x/5 + 41/5.

Equation of the lines which are even or lined up with the X-pivot is y = a, where an is the y - direction of the focuses on the line. Essentially, the condition of a straight line which is vertical or lined up with the Y-hub is x = a, where an is the x-direction of the focuses on the line.

Mid point of the line passing through the points (1,2) and (-5,12).

mid point = [tex](\frac{1-5}{2} , \frac{2+12}{2} )[/tex] = (-2, 7)

So, the line perpendicular to given line is passing through  (-2, 7)

Slope of line of points (1,2) and (-5,12).

Slope(m) = [tex]\frac{12-2}{-5-1}=-\frac{5}{3}[/tex]

Then slope of perpendicular bisector of this line is negative and reciprocal of Slope(m).

slope of perpendicular bisector(n)  = 3/5

Now, equation of line is

[tex](y-y_{1})=n(x-x_{1})[/tex]

(y - 7) = 3/5(x + 2)

y = 3x/5 + 41/5

Thus required equation of perpendicular bisector is y = 3x/5 + 41/5

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The marginal revenue in the interval between six and seven jet skis is $300.

Here we are given that total revenue from six jet skis is $2,400

and total revenue from seven jet skis is $2,700

Now, marginal revenue is defined as the revenue gained or lost by producing one more additional unit of a good.

Here, the total revenue increases from $2,400 to $2,700 as we go from producing 6 jet skis to 7 jet skis.

Thus, the change in total revenue will be-

2700 - 2400

= 300

This means that the gain in revenue is $300.

Thus, the marginal revenue in the interval between six and seven jet skis is $300.

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Step-by-step explanation:

Let's say that the you have to found the mean of 5, 2, and 8

first you would have to add up all of the number 5+2+8 which equals to 15

now you would have divide 15 by the amount of the data points which is 3, so your mean in this problem is 5.

here is an example by only using numbers:

(5+2+8) ÷ 3 = 5

A power function with two points can be written by substituting the values of the two points in the given function.

To given an example, let f(x) = aˣ b;

Taking natural logs on both sides:

ln f(x) = ln (aˣb);

ln f(x) = ln (aˣ) + ln (b);

ln f(x) = xln (a) + ln (b);

Taking Exponential both sides

then,  

Let the two points be P (x₁, y₁) and Q (x₂, y₂)

The we get two equations:

(i) ln f(y₁) = x₁ ln (a) + ln (b);

(ii) ln f(y₂) = x₂ ln (a) + ln (b);

Subtracting (ii) from (i)

ln f(y₁) - ln f(y₂) = x₁ ln (a)  - x₂ ln (a) + ln (b) - ln (b);

ln f(y₁)/f(y₂) = ln a( x₁ - x₂)

[ln f(y₁)/f(y₂)]/ [( x₁ - x₂)] = ln a

Taking exponential both side

let f(y₁)/f(y₂) = s

let ( x₁ - x₂)= r

[tex]e^{ \frac{ln s}{r} } = e^{ ln a}[/tex]

[tex]e^{ \frac{ln s}{r}[/tex] = a

On solving both the equations we get two values of b

f(y₁) = aˣ₁ . b

f(y₂) = aˣ₂ . b

ln f(y₁) = ln (aˣ₁) + ln (b); --(1)

ln f(y₂) = ln (aˣ₂) + ln (b); --(2)

subtracting (2) from (1)

ln f(y₁) - ln(y₂) = ln([tex]e^{\frac{ln s}{r}^x1}[/tex]) - ln([tex]e^{\frac{ln s}{r}^x2}[/tex]) + ln(b) - ln(b)

ln f(y₁)/f(y₂) = (ln s/r)ˣ₁ - (ln s/r)ˣ₂

ln f(y₁)/f(y₂) = x₁ ln s/rˣ₁ - x₂ ln s/rˣ₂

rˣ₁rˣ₂ ln f(y₁)/f(y₂) = x₁ rˣ₂ ln s - x₂ rˣ₁  ln s

ln [tex]f(y1)/f(y2)^{r^{x1} r^{x2}}[/tex] = ln [tex]s^{x1 r^{x2}}[/tex] - ln [tex]s^{x2 r^{x1}}[/tex]

ln [tex]f(y1)/f(y2)^{r^{x1} r^{x2}}[/tex] = ln [tex]\frac {s^{x1 r^{x2}}}{s^{x2 r^{x1}}}[/tex]

Taking exponential both sides.

let [tex]f(y1)/f(y2)^{r^{x1} r^{x2}}[/tex] = w

let [tex]\frac {s^{x1 r^{x2}}}{s^{x2 r^{x1}}}[/tex] t

then,

[tex]e^{ln w} } = e^{ ln t}[/tex]

w = t

[tex]f(y1)/f(y2)^{r^{x1} r^{x2}}[/tex] = [tex]\frac {s^{x1 r^{x2}}}{s^{x2 r^{x1}}}[/tex]

Solving this equation we get the value of x by putting the values given

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The slope of this line is given as 1/2

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane. Calculating the slope of a line is similar to finding the slope between two different points. In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.

Taking two points from the graph;

The slope of the line is calculated as

m = y₂ - y₁ / x₂ - x₁

Substituting the values into the formula above;

m = -3 - (-1) / 1 - 5

m = -2 / - 4

m = 1/2

Slope = 1/2

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Yes, angry is considered to be a tone in a paper.

The tone of writing appears an author’s attitude or intent. The tone is the essence of the voice, which is how a writer passes on their thoughts to the peruser. Tone can be found through particular words, expressions, and sentence structure. The tone is broadly depicted as the author’s demeanor toward his or her subject. It can be enthusiastic, far off, irate, and cheerful, among numerous other possibilities. Tragically there are as well numerous possibilities for us to cover, and without knowing your subject, we cannot allow the foremost particular advice possible. The obvious pitfalls incorporate sounding condescending or silly, whereas sounding energetic and eager could be a definite positive. An angry tone is ordinarily utilized when the author needs to communicate a sense of frustration or outrage. It can take diverse forms such as passive-aggressive, protective, or sarcastic.

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Carpetland not $8,000 in step with week in earnings. Vice President, proposes a plan with new selling incentives with the want that the plan will increase the not earnings in step with earnings are more than $8,000 in step with week.

It implies, The null hypothesis, H: μ≤$8,000 in step with week. The possibility hypothesis, H: μ>$8,000 in step with week where μ is the whole not unusual place earnings in step with week.

Type II mistakes is defined due to the fact the opportunity of now now not rejecting the false-null hypothesis i.e. now now not rejecting the null whilst it is false. Therefore, if we do now now not reject that the not earnings are a great deal much less than or same to $8000 (and end that the not unusualplace earnings may be a great deal much less than same to $8000) whilst in fact it is more than $8000 then we are growing a type II mistakes.

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Percentage of the sales price to the given purchase price is equal to 180% .

As given in the question,

Purchase price of the each coat bought by owner is equal to  $55

Selling price of each coat sold by owner is equal to  $99

Percentage of sales price of purchase price is equal to

= ( Selling price / Purchase price )  × 100

Substitute the value of the selling price and the purchase price we get,

= ( 99 / 55 ) × 100

= ( 1.8 ) × 100

= 180%

Therefore, the sales price is 180 percent of the given purchase price.

The complete question is:

Owner buys coats for $55 each and sell them for $99 each. The sales price is what % of the purchase price.

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The required value of the given function  f(a) = -2a^2 - 5a + 4 at a = -3 is 1

Function is characterized as a connection between a bunch of data sources having one result each. In straightforward words, a capability is a connection between inputs where each info is connected with precisely one result. Each Function has a domain and co-domain or range. A capability is by and large meant by f(x) where x is the information.

Function, f(a) = -2a^2 - 5a + 4

To find value of f(-3),

f(a) = -2a^2 - 5a + 4

Put a = -3 in th function

F(-3) = -2(-3)^2-5×-3+4

F(-3) = -18+15+4=1

F(-3) = 1

Thus, required value of f(-3) is 1

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Coorect Question:

What is f(-3) for the function f(a) = -2a2 - 5a + 4?

The equation in closed form for the sequence {aₙ: n ≥0} that each of the exponential generating functions below represents.

b. x²e³ˣ is aₙ=(3ⁿ.xⁿ⁺²)/n!, n≥0

d. (eˣ)⁴ is aₙ=x⁴ⁿ/n!,  n≥0

Given that,

We have to give an equation in closed form for the sequence {aₙ: n ≥0} that each of the exponential generating functions below represents.

b. x²e³ˣ

d. (eˣ)⁴

We have to find the simplified form.

First take the

b. x²e³ˣ

=x²[1+3x+(3x)²/2!+(3x)³/3!+(3x)⁴/4!....]

=x²+3x³+3².x⁴/2!+3³.x⁵/3!+3⁴/x⁶/4!....]

aₙ=(3ⁿ.xⁿ⁺²)/n!, n≥0

d. (eˣ)⁴

=1+x⁴+(x⁴)²/2!+(x⁴)³/3!+(x⁴)⁴/4!....

aₙ=x⁴ⁿ/n!,  n≥0

Therefore, The equation in closed form for the sequence {aₙ: n ≥0} that each of the exponential generating functions below represents.

b. x²e³ˣ is aₙ=(3ⁿ.xⁿ⁺²)/n!, n≥0

d. (eˣ)⁴ is aₙ=x⁴ⁿ/n!,  n≥0

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The estimated kilowatt usage when the temperature is 90° outside is 1132.5.

Here we have to find the point estimate kilowatt usage when the temperature is 90° outside.

We have to find the linear regression model:

Creating the table with the following:

∑y; ∑x; ∑xy; ∑x²; ∑y²

Now use these equations to find coefficients a and b:

a = (∑y) (∑x²) - (∑x) ( ∑yx) / n(∑x²) -(∑x²)

b = n( ∑xy) - (∑x ) (∑y) / n( ∑x²) -(∑x²)

Now substitute this in the equation:

y = a + bx

The linear regression equation is:

y = -2004 + 34.85x

Here it is asked for the temperature at 90°

So we take x = 90°

y = -2004 + 34.85× 90

y = 1132.5

Therefore the estimated kilowatt is 1132.5.

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The complete question is:

The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a point estimate Kilowatt usage when the Temperature is 90 degrees outside.

Temperature(x)                       Kilowatts(y)

       73                                         680

       78                                         760

       85                                         910

       98                                         1510

       93                                         1170

       83                                         888

       92                                         923

       81                                          837

       76                                         600

     105                                        1800

The total cheese production in 2006 was about 7.7 billion pounds and the total cheese production in 2014 was about  9.7 billion pounds

The function that can be used in our computation is given as

y = 7(1.03)ˣ

Such that

x = Number of years after 2003 and y is the amount of cheese

The value of x can be calculated using

x = year - 2003

Substitute 2006 for year

x = 2006 - 2003

Evaluate

x = 3

Substitute x = 3 in the equation y = 7(1.03)ˣ

y = 7(1.03)³

Evaluate

y = 7.7

In the year 2014, the value of x is calculated as

x = Current year - 2003

So, we have

x = 2014 - 2003

Evaluate

x = 11

Substitute x = 11 in the equation y = 7(1.03)ˣ

y = 7(1.03)¹¹

Evaluate

y = 9.7

Hence, the amount of cheese is 9.7 billion pounds

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The scale factor used to create the travel version of the piece is 1: 0.16

0.6 is the scale factor used to reduce the dimensions of the original piece having sides measuring 3 inches each.

Scale factor is calculated by dividing the new reduced scale by original scale. Hence:

0.5/3 = 0.166

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Scale Factor = New Shape Dimension / Original Shape Dimension

Enlarging a small form into a huge one is known as scaling up. Upscaling always uses a scale factor greater than 1. A scale factor 2 means the figure is enlarged twice the original figure's size.

A large number gets scaled down in order to become a smaller one. Scaling down always results in a scale factor less than 1.

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The average of numbers from 8 to 49 will be 21.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The numbers 8 to 49.

Now,

The average of numbers from 8 to 49 is calculated as;

⇒ Average = (n + 1) / 2

Where, n is the numbers in between 8 to 49.

Hence, n = 49 - 8

               = 41

Thus, We get;

⇒ Average = (n + 1) / 2

                  = (41 + 1) / 2

                  = 42/2

                  = 21

Therefore, The average of numbers from 8 to 49 will be 21.

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The feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

With the constraint that x and y are both non-negative, the second constraint has only one point in common with each of the first and third constraints; and those two points are different.

The feasibility region is empty; so nothing can be optimized.

Plots x + 2y = 30 (red),  2x + 2y = 30 (green)  and  2x+y = 30 (blue)

The feasibility area, according to the condition, is the area of the first quadrant

   - above the red line,

   - below the green line,

   - above the blue line.

It can be seen from the plot that this set is empty.

Therefore, the feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

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Disclaimer

The question given by you is incomplete, so the above solution is of a similar question, and the question is

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT

Maximize p = x + y subject to

x + 2y ≥ 30

2x + 2y ≤ 30

2x + y ≥ 30

x ≥ 0, y ≥ 0.

p=

(x, y)=

The "correct" statement is that the odds ratio appears statistically significant when the whole 95% confidence interval is much less than 1.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values a predetermined percentage of the time.

Thus, the "correct" statement is that the odds ratio appears statistically significant when the whole 95% confidence interval is much less than 1.

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The area of grass that the horse has access to is 314 square-foot

From the question, we are to determine how much grass the horse have access to.

From the given information,

"A horse is tied with a 10 -foot-long rope to a pole"

This means the horse has access to a circular area of radius 10 feet.

Now, we will calculate the area of a circle with radius 10 feet.

Using the formula for calculating the area of a circle,

A = πr²

Where A is the area of the circle

and r is the radius of the circle

Substitute r = 10 into the equation,

A = π × 10²

A = 100π

Take π = 3.14

Then,

A = 100 × 3.14

A = 314 square foot

Hence, the area is 314 square foot

Learn more on Calculating area here: https://brainly.com/question/13004107

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