A new novel i elling for $17. 95. If it i on ale at 40% off, find the amount of dicount and ale price

To prove that gcd (n,n+2) is either 1 or 2 for any integer n, we can use a proof by contradiction. We can conclude that gcd (n,n+2) is either 1 or 2 for any integer n.

Suppose there exists an integer n such that gcd (n,n+2) is not 1 or 2, and let k be the gcd of n and n+2, where k ≥ 3. Then k is a common divisor of n and n+2, and k is not equal to 1 or 2.

Since k divides both n and n+2, we can write n = ka and n+2 = kb, where a and b are integers. Subtracting these equations gives 2 = kb - ka = k (b-a).

Since k is not equal to 1 or 2, it follows that k must be greater than or equal to 3. Therefore, k cannot divide 2, which implies that k (b-a) ≠ 2. This contradicts our assumption that gcd (n,n+2) is not 1 or 2.

Hence, we can conclude that gcd (n,n+2) is either 1 or 2 for any integer n.

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Answer:

  12√2 ≈ 16.97 units

Step-by-step explanation:

You want the diameter of the circle whose equation is ...

  x² -2x +8y = 55 -4x -y²

The equation can be rearranged to ...

  x² -2x +4x +y² +8y = 55

  (x +1)² +(y +4)² = 55 + 1 + 16

  (x +1)² +(y +4)² = 72

Comparing this to the standard form equation for a circle with center (h, k) and radius r, we se ...

  (x -h)² +(y -k)² = r²

  (h, k) = (-1, -4)  and  r² = 72

The diameter is twice the radius, so is ...

  d = 2r = 2√72 = 12√2

The diameter of the circle is 12√2 units.

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Answer:

  circumcenter

Step-by-step explanation:

You want to know the name of the point equidistant from the vertices of a triangle.

The circle that passes through the vertices of a triangle is called a "circumcircle". It circumscribes the triangle. Its center is equidistant from all points on the circle, so is equidistant from the triangle's vertices.

The point equidistant from the vertices of a triangle is the circumcenter.

__

Additional comment

The circumcenter is at the intersection of the perpendicular bisectors of the sides of the triangle.

The elasticity of demand at a price of $33 is inelastic. To increase revenue, it is advisable to raise prices.

To find the elasticity of demand at a specific price, we need to calculate the absolute value of the derivative of the demand function with respect to price (D'(p)) and then multiply it by the price (p) divided by the demand (D(p)). In this case, the demand function is given as D(p) = 200 - 4p.

First, we need to find D'(p) by taking the derivative of the demand function with respect to p:

D'(p) = -4.

Next, we can calculate the elasticity of demand at a price of $33:

Elasticity of Demand = |(D'(p) × p) / D(p)| = |(-4 × 33) / (200 - 4 × 33)| ≈ |-132 / 8| ≈ 16.5.

Since the elasticity of demand is less than 1 (inelastic), it means that a 1% change in price will result in less than a 1% change in demand.

To increase revenue, it is generally recommended to raise prices when demand is inelastic. This is because a price increase will lead to a proportionately smaller decrease in demand, resulting in higher total revenue. Therefore, to maximize revenue, it would be advisable to raise prices.

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Right triangles ABC and DEF are drawn to measure the slope of the line is:

a) run = 2 rise = 3 slope = 3/2

b) run = 6 rise = 9 slope = 9/6 = 3/2

c) Yes, they are similar because the 2 triangles are similar.

Two triangles are similar if they meet one of the following criteria. : Two pairs of corresponding angles are equal.

What is Right triangles?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

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Answer:

x=1.8 i think im wrong

Step-by-step explanation:

Answer

x=\(\frac{\sqrt{45} }{5}\)

Step-by-step explanation:

1) add 45 to both sides

5x^2=45

2) square root both sides

5x=\(\sqrt{45\)

3) Divide both sides by 5

x=\(\frac{\sqrt{45} }{5}\)

Answer:

it's A.

Step-by-step explanation:

a vertical translation, in the name, means you are moving the graph up or down the y axis. a horizontal translation is moving the graph left or right on the x axis. a reflection across the x axis is all the x values *-1. 180 counterclockwise rotation is rotating the graph top to bottom.

Answer:

A. Vertical translation

Step-by-step explanation:

A vertical translation means the object moves up or down without changing anything else of itself, such as size, rotation, reflection, etc.  Only movement up and down.

Reflection is where the object moves as though the axis is a mirror, where the object translates the same distance from the axis, but also flips across the axis, so if it is an x-axis, it flips upside down, and at a y-axis, flips left and right.

A rotation in any direction that is 180 degrees means that the object appears to be flipped opposite of what it started as.  For example, if A is at the top point, after rotation, A would be the bottom point.

A horizontal translation is the same as with a vertical translation, except the object moves left or right.

From each of these analyses I provided on each of the answer choices, we can clearly see that the correct answer is the first option, "A. Vertical translation," as the object did exactly as I described what a vertical translation is.

If I helped (and more clearly explained, hopefully, than the other answer), please make this answer brainliest ;)

Answer:

A.

Step-by-step explanation:

To find out how much 1 lunch costs, divide 33.75/15. You get 2.25. The first graph has the only answer that says one lunch is around 2.25.

Hope it helps!

In simple linear regression, the predictor variable is the independent variable, which is used to predict the value of the dependent variable. It is also referred to as the explanatory variable, as it is used to explain the variability in the response variable.

For example, in a study that examines the relationship between the hours studied and exam scores, the predictor variable is the number of hours studied, and the dependent variable is the exam score.

The predictor variable is plotted on the x-axis, while the dependent variable is plotted on the y-axis in a scatter plot. The relationship between the predictor and the dependent variable is represented by a straight line, which is determined by the regression equation.

The slope of the line represents the change in the dependent variable for each unit change in the predictor variable.

In summary, the predictor variable is the variable that is used to predict or explain the changes in the dependent variable in simple linear regression.

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Answer:

$1.25

Step-by-step explanation:

3.2/2.56=1.25

Answer:

1.25

Step-by-step explanation:

3.2/2.56=1.25 i know because i am the future

False. The expression \((3ab - 6a)^2\) is not the same as 2(3ab - 6a).

The expression\((3ab - 6a)^2\) is not the same as 2(3ab - 6a).

To simplify \((3ab - 6a)^2\), we need to apply the exponent of 2 to the entire expression. This means we have to multiply the expression by itself.

\((3ab - 6a)^2 = (3ab - 6a)(3ab - 6a)\)

Using the distributive property, we can expand this expression:

\((3ab - 6a)(3ab - 6a) = 9a^2b^2 - 18ab^2a + 18a^2b - 36a^2\)

Simplifying further, we can combine like terms:

\(9a^2b^2 - 18ab^2a + 18a^2b - 36a^2 = 9a^2b^2 - 18ab(a - 2b) + 18a^2b - 36a^2\)

The correct simplified form of \((3ab - 6a)^2 is 9a^2b^2 - 18ab(a - 2b) + 18a^2b - 36a^2\).

The statement that\((3ab - 6a)^2\) is the same as 2(3ab - 6a) is false.

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Gerry's beginning basis in the S corporation is $20,545.

To calculate Gerry's beginning basis in the S corporation, we need to consider the cost of the assets transferred and the additional expenses incurred for the conversion.

The cost of the assets transferred is given as $19,570. This represents the original cost of the assets when Gerry acquired them.

The adjusted basis of the assets is stated as $9,600. The adjusted basis takes into account any adjustments made to the original cost, such as depreciation or other deductions.

To calculate the beginning basis in the S corporation, we add the cost of the assets transferred ($19,570) to the adjusted basis ($9,600). This gives us a total of $29,170.

In addition to the assets, Gerry incurred an additional expense of $975 for the conversion to an S corporation. We include this amount in the calculation of the beginning basis.

Therefore, Gerry's beginning basis in the S corporation is $29,170 + $975 = $20,545.

This beginning basis is important for determining Gerry's tax consequences and future deductions within the S corporation structure.

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Answer:

W: (-4,5) W' -> (5,4)

X: (-1,4) X' -> (4,1)

Y: (-6,1) Y' -> (1,6)

Z: (-8,3) Z' -> (3,8)

Step-by-step explanation:

Let me give you a quick brief of how to master rotations!!

You need to understand the formula and positioning rules

The formulas shall be given by teachers or looked up!

*** BUT THE SHAPE POSITIONING RULES MATTER!!

-If the shape was in quadrant 2 which is where it is right now then a 90 degree turn clockwise would result in the shape being on quadrant 1, 180 quad 4, 270: quad 3, and 360 would be the original quad which is 2.

The formula for clockwise for this one is that you need to flip the (x,y) to (y,x)

The shape should be on quadrant 1 which is the one on the top right of the coordinate plane!

They want you to graph it by W'X'Y'Z

The ' is prime which is the new position/coordinate

W: (-4,5) W' -> (5,4)

X: (-1,4) X' -> (4,1)

Y: (-6,1) Y' -> (1,6)

Z: (-8,3) Z' -> (3,8)

That is the rotation 90 degrees clockwise coordinates!!

***REMEMBER EACH ROTATION RULE HAS A DIFFERENT FORMULA!!**

Counterclockwise is pretty similar but the opposite direction with different rules!

**POSITION OF THE SHAPE IS THE MOST IMPORTANT!!!**

Answer: x = 5.5

Step-by-step explanation: Since a midpoint divides a segment into two congruent segments, ST and TU are congruent to each other.

This means that you can set up the equation 14x-6=12x+5 to isolate x. x=5.5

144. Use the formula for the volume of a cone, since the answer is in terms of pi disregard the pi in the formula and solve using (r^2)(h/3) which will give you the answer in terms of pi.

When presenting chunks of information, bar charts should be used. As long as there aren't too many categories to contrast, vertical bar charts can be useful for comparing several discrete or categorical variables, such as age groups, courses, and schools. For time series data, they are also highly beneficial.

Why would one use a bar chart?

To show a frequency distribution for qualitative data, bar charts are frequently employed.

                   The axis used to measure the bars should always begin at zero, unless there is a valid reason for doing otherwise.

                  Otherwise, the axis can be stretched to magnify differences in the lengths of the bars. A title and the axis labels are required for bar charts.

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The probability of being dealt a nine and an eight from a standard 52-card deck is 1/663.

To find the probability of being dealt a nine and an eight, we need to determine the number of favorable outcomes (getting a nine and an eight) and the total number of possible outcomes (all the cards in the deck).

In a standard 52-card deck, there are four nines and four eights. When we are dealt one card, the probability of getting a nine on the first draw is 4/52, as there are four nines out of the total 52 cards.

Now, for the second draw, assuming the first card was not replaced, there are three remaining nines and 51 remaining cards in the deck. The probability of getting an eight on the second draw, given that a nine was already drawn, is 4/51.

To find the overall probability of being dealt a nine and an eight, we multiply the probabilities of each draw:

P(Nine and Eight) = (4/52) * (4/51) = 16/2652 = 1/663.

Therefore, the probability of being dealt a nine and an eight from a standard 52-card deck is 1/663.

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Answer:Irrational,2/9,22/100 11/50, Irrational, No Fraction Given, Perfect Square, Non-Perfect Square

Step-by-step explanation:Best fit options for each question.

Answer:

side of base, a = 10.1 inches, height, h = 40.1 inches

Step-by-step explanation:

Volume of rectangular solid, V = 4096 cubic inches

Let the side of base is a and the height is h.

\(V = a^2h\\\\4096 = a^2 h ..... (1)\)

surface area of the solid  

\(S = 2a^2 + 4 ah \\\\S = 2a^2 + 4 \times a \times \frac{4096}{a^2} from (1)\\\S = 2a^2 + \frac{4096}{a}\\\\\frac{dS}{da}= 4 a - \frac{4096}{a^2}\\\\4 a - \frac{4096}{a^2} = 0 \\\\a^3 = 1024\\\\a =10.1 inches\)

So, h = 40.2 inches

Answer:

  0.253 m/s

Step-by-step explanation:

You want to know the horizontal component of motion of a passenger riding a Ferris wheel when they are 1/27 of the way around the circle and their rate of rise is 0.06 m/s.

The wheel makes one revolution in 27 minutes, so the angular displacement is changing at the rate of (360°)/(27 min) = 13 1/3°/min.

After 1 minute, the passenger is following a path that has an angle of elevation of 13 1/3°.

The ratio of vertical speed to horizontal speed will be the tangent of the angle of elevation:

  Vv/Vh = tan(13 1/3°)

Then the horizontal speed will be ...

  Vh = Vv/tan(13 1/3°) = (0.06 m/s)/0.237004

  Vh ≈ 0.253 m/s

The passenger's horizontal motion is about 0.253 m/s.

Answer:

x=12

Step-by-step explanation:

since it is an equilateral triangle the angle r all the same the angle have to equal 60

Since it's a equilateral triangle.

\(\\ \sf\longmapsto 5x+5x+5x=180\)

\(\\ \sf\longmapsto 15x=180\)

\(\\ \sf\longmapsto x=12\)

No. of ways of selecting the 5 member committee by combination= 1981

What are the number of ways of selecting the 5 member committee ?

No. of women faculty in the mathematics department = 7

No. of men faculty in the mathematics department = 7

Total number of faculty members = 14

Condition - at least one woman must be on the committee

No. of ways of selection = C (14, 5) - C (7, 5)

We know that combination C(n , r) = \(\frac{n!}{(n-r)!r!}\)

Consider the total combination C (14, 5),

\(C (14, 5)=\frac{14!}{9!5!} \\\\=\frac{14 *13* 12 *11 *10 *9!}{9!* 5!} \\\\=\frac{14 *13* 12 *11 *10}{120} \\\\= \frac{240240}{120} \\\\= 2002\)              

Consider the combination of men C (7, 5) ,

\(C (7, 5)=\frac{7!}{2!5!} \\\\=\frac{7*6*5!}{2!* 5!} \\\\=\frac{7*6}{2} \\\\= 7*3\\\\=21\)

No. of ways of selection = C (14, 5) - C (7, 5)

                                        = 2002 - 21

                                        =1981

No. of ways of selecting the 5 member committee of the department with least one woman by combination= 1981

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Answer:$96.98

Step-by-step explanation: all you just do is to add it all up to the total amount.

Answer: $105.47

I hope you get the job!!!!!

Step-by-step explanation:

We are to get the expression for the following statements;

1) The difference of nine times a number x and the quotient of that number and 5.

The product of nine and a number x is expressed as;

\(=9 \times x\\= 9x\)

The quotient of that number and 5.

\(= \frac{x}{5}\)

The difference between both expression;

\(9x - \frac{x}{5}\)

Hence, the difference of nine times a number x and the quotient of that number and 5 is expressed as \(9x - \frac{x}{5}\)

2) Eight more than the quotient of twelve and a number n

Quotient of twelve and a number n is expressed as:

\(\frac{n}{12}\)

Eight more than the resulting function is;

\(\frac{n}{12}+8\)

Hence eight more than the quotient of twelve and a number n is expressed as \(\frac{n}{12}+8\)

3) The product of a number and the quantity 'six minus the number' plus the quotient of eight and the number.

Let the number be x:

six minus the number is expressed as;

\(6-x\)

product of a number x and the quantity 'six minus the number is;

\(x(6-x)\)

quotient of eight and the number is;

\(\frac{8}{x}\)

Taking the resulting sum of the last two expression

\(x(6-x) + 8x\)

Hence the product of a number and the quantity 'six minus the number' plus the quotient of eight and the number is expressed as;

\(x(6-x) + 8x\)

4) Sum of three consecutive even integers. 2x + (2x + 2) + (2x + 4).

Let the first even number be 2x

The consecutive even numbers are gotten by adding 2 to the preceding number. The two consecutive even integers are 2x+2 and 2x+2+2

the sum of three consecutive even integers is expressed as;

\(= 2x +(2x+2)+(2x+2+2)\\= 2x+(2x+2)+(2x+4)\)

Answer: 1st , 2nd, and 3rd!

Step-by-step explanation:

Answer:

\(f^{-1}(x)=6x - 5\)

Step-by-step explanation:

Invert the operations done onto x and their order:

f(x)                     |      f^-1(x)

add 5                |      subtract 5

divide by 6       |      multiply by 6

f(x) = (x + 5) / 6

f^-1(x) = 6x - 5

The particle's motion is therefore periodic, with a period of\(2\pi\), and its path is an ellipse centered at the origin with major axis of length 4 and minor axis of length 3 in case of parametric equations.

The given parametric equations define the motion of a particle in the xy-plane, which are;4 cos(t)3 sin(t), where t represents the time in seconds. Parametric equations. In mathematics, a set of parametric equations is used to describe the coordinates of points that are determined by one or more independent variables that are related to a number of dependent variables by way of a set of equations.

When an independent variable is altered, the values of the dependent variables change accordingly.ParticleIn classical mechanics, a particle refers to a small object that has mass but occupies no space. It is used in kinematics to describe the motion of objects with negligible size by assuming that their mass is concentrated at a point in space. Therefore, a particle in motion refers to a moving point mass.The motion of a particle can be represented using parametric equations. In the given equation \(4 cos(t) 3 sin(t)\), the particle is moving in the xy-plane and its path is given by the equation x = \(4 cos(t)\) and y = \(3 sin(t)\).

The particle's motion is therefore periodic, with a period of \(2\pi\), and its path is an ellipse centered at the origin with major axis of length 4 and minor axis of length 3.

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The volume of the smaller figure is 990 in³.

The  volume of the smaller figure is calculated by applying similar figure theorem.

The surface area of the smaller figure is given as 522 in²

The surface area of the larger figure is given as 1450 in²

The volume of the larger figure is given as 2750 in³

The volume of the smaller figure is ?

The volume of the smaller figure is calculated as follows;

V/2750 = 522/1450

V = 2750 (522 / 1450 )

V = 990 in³

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Answer: y = 1/2x+15/2

Step-by-step explanation:

If you need any more help let me know!! I will try to answer every question you post!

Answer:

first one is A

second one is A

Step-by-step explanation:

yeah-ya.... right?