Let d be a positive integer. Show that among any group of d+1 (not necessarily consecutive) integers there are two with exactly the same remainder when they are divided by d. HINT: Use the Pigeon-hole Principle!

Answer:

10x = 30

Step-by-step explanation:

We have 7x - 7 = 14.

Add 7 on both sides: 7x = 21

Divide 7 on both sides: x=3

So 10x is 10*3 = 30

Using these traces, we can sketch the surface as an ellipsoid in three dimensions centered at the origin, with semi-major axis of length 6 along the z-axis, semi-major axis of length 3 along the y-axis, and semi-major axis of length 2 along the x-axis.

To sketch the surface 9x^2 + 4y^2 + z^2 = 36 using traces, we can fix values of x, y, and z and plot the resulting curves. When we fix x = 0, we get 4y^2 + z^2 = 36, which is an ellipse in the yz-plane centered at the origin with semi-major axis of length 6 along the z-axis and semi-minor axis of length 3 along the y-axis.

When we fix y = 0, we get 9x^2 + z^2 = 36, which is also an ellipse in the xz-plane centered at the origin with semi-major axis of length 6 along the z-axis and semi-minor axis of length 2 along the x-axis. When we fix z = 0, we get 9x^2 + 4y^2 = 36, which is a horizontal ellipse in the xy-plane centered at the origin with semi-major axis of length 2 along the x-axis and semi-minor axis of length 3 along the y-axis.

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Answer:

100.8

I hope this helps:D

Answer:

100.8

Step-by-step explanation:

multiply 4 2.8 and 9 and you get 100.8

Answer: You need to multiply f(x) and g(x), then you get

3x^2 + 7x -6

Answer:

35, 31, 25, 18

Step-by-step explanation:

10 x 7/2 = 35

10 + 7 + 14 = 31

8 1/3 x 6/2 = 25

4 1/3 + 5 1/3 + 8 1/3 = 18

Answer:

OP and OR

Step-by-step explanation:

When the segments intersect, they do so at a 90-degree angle, implying they are perpendicular.

Based on the study results, there appears to be a difference among North American, European, and Asian organizations in the proportion of organizations that raised prices in response to unfavourable exchange rates.

Out of the surveyed sample, 46.67% of North American organizations (70 out of 150) raised prices, while 54.17% of European organizations (65 out of 120) and 30% of Asian organizations (30 out of 100) raised prices. Therefore, it can be concluded that a higher proportion of European organizations raised prices compared to North American organizations, while Asian organizations had the lowest proportion.

However, it is important to note that this study only represents a sample of organizations and may not necessarily reflect the entire population of each region.

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a) We have shown that for every positive integer k, 1/k = 1/(k+1) + 1/(k(k+1)). b) We have found integers a = 2, b = 3, and c = 6 such that 1 = 1/a + 1/b + 1/c. c) The every integer n ≥ 3, there exist n integers a₁, a₂, ..., aₙ such that 1 = 1/a₁ + 1/a₂ + ... + 1/aₙ.

(a) To prove that every positive integer k satisfies 1/k = 1/(k+1) + 1/(k(k+1)), we can start by manipulating the right-hand side of the equation:

1/(k+1) + 1/(k(k+1))

= (k/(k(k+1))) + 1/(k(k+1)) (finding a common denominator)

= (k + 1)/(k(k+1)) (combining the fractions with the same denominator)

= 1/k (canceling out the common factor of (k+1) in the numerator and denominator)

Thus, we have shown that for every positive integer k, 1/k = 1/(k+1) + 1/(k(k+1)).

(b) To prove that there exist integers a < b < c such that 1 = 1/a + 1/b + 1/c, we can choose specific values for a, b, and c. Let's choose a = 2, b = 3, and c = 6:

1/2 + 1/3 + 1/6

= 3/6 + 2/6 + 1/6

= 6/6

= 1

Therefore, we have found integers a = 2, b = 3, and c = 6 such that 1 = 1/a + 1/b + 1/c.

(c) To prove that for every integer n ≥ 3, there exist n integers a₁, a₂, ..., aₙ such that 1 = 1/a₁ + 1/a₂ + ... + 1/aₙ, we can use the following construction:

Choose a₁ = 2, a₂ = 3, and a₃ = 6 as shown in part (b) above.

Now, for the remaining integers a₄, a₅, ..., aₙ, we can choose them to be equal to the least common multiple (LCM) of a₁, a₂, ..., aₙ₋₁. This guarantees that each term 1/aₖ, where k > 3, will have the same denominator and can be added to the other terms.

Since the LCM is a multiple of each of the previous integers, it is guaranteed that the sum of the reciprocals will be equal to 1.

Therefore, for every integer n ≥ 3, there exist n integers a₁, a₂, ..., aₙ such that 1 = 1/a₁ + 1/a₂ + ... + 1/aₙ.

The complete question is:

(a) Prove that every positive integer k satisfies 1/k=1/(k+1) + 1/ (k(k+1)).

(b) Prove that there exist integers a <b<c such that 1 = 1/a + 1/b + 1/c.

(c) Prove that for every integer n ≥ 3 there exist n integers \(a_1,a_2,.....,a_n\) such that \(1=1/a_1+1/a_2+.....1/a_n\)

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Yes, the table contains the solution of the system of equations, and the solution is (7, 6).

Here we have a table that defines a system of equations of the form:

ya = f(x)

yb = f(x)

And a solution of that system is a point of the form:

yb = f(x) = ya

So we wan to find a pair such that for the same value of x, the values of ya and yb are the same ones.

We can see that when x = 6 that happens, then yes, the table has the solution to the system of equations, and the solutions is (6, 7)

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Answer:

the answer is (x+1)(3x-5)

Answer:

X=-1,-\(\frac{5}{3}\)

Step-by-step explanation:

Given function in the question is,

        g(x) = |x + 1| - 5

Rules to remember for the translation a function,

        g(x) = |x - h|

        h(x) = |x + h|

        k(x) = |x| + k

        p(x) = |x| - k

Using these rules,

Function 'f' will be translated 1 units left and and 5 units down to form the image function 'g'.

       Therefore, Margo made an error to interpret that the function is translated 1 units right.

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Answer:

What is asked: How much does she spend

Given: 3-2-68p

Operation: Addition

Solution: 3 + 2 = 5

If its wrong im domb

Answer:

B and D.

Step-by-step explanation: Just took the test.

Answer:

it is b and d trust

Step-by-step explanation:

edge2020

distribution of the total number of tumors produced in the whole population over a one-year period by this kind of radiation is 0, 1, 2, ..................104000.

let, x denote the total number of hits,

y denotes the number of hits by a particle in a year or an individual,

one per week ⇒ 52 per year

therefore, rate = 52 per year

since it is very rare to hit all individuals, we can use Poisson distribution.

therefore by using the formula p (x = x) = (e^(-rate) × rateˣ) ÷ x! ; x = 0, 1, 2, ............( 2000 × 52)

p (x = 2) = (e⁻⁵² × 52ˣ) ÷ x! ; x = 0, 1, 2, ............104000

now each hit has a harm of probability 10⁻⁵.

so p(total no. of tumors produced over a one year period)

= {e⁻⁵² × 52ˣ} ÷ x! × 10⁻⁵ ; x = 0, 1, 2, ............104000

therefore total no. of tumors = 2000 × (e⁻⁵² × \(52^{x.10^{-5} }\) ) ÷ x!  × xⁿ ; x = 0, 1, 2, ............104000

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(complete question)

Assume that each of the 2000 individuals living near a nuclear power plant is exposed to particles of a certain kind of radiation at an average rate of one per week. Suppose that each hit by a particle is harmless with a probability of 1 - 10⁻⁵, and produces a tumor with a probability of 10⁻⁵. Find the approximate distribution of the total number of tumors produced in the whole population over a one-year period by this kind of radiation.

Close ties between the members of the group typically are formed during the norming stage of group development.

The norming stage of group development is the third stage, where the group begins to establish a sense of cohesion and unity. During this stage, members start to accept each other's ideas and opinions, develop relationships with one another, and establish patterns of communication and interaction. As a result of these positive developments, close ties between the members of the group often begin to form.

In the norming stage, group members also start to identify common goals and work together to achieve them. This shared sense of purpose can further strengthen the bonds between group members and contribute to the formation of close ties.

Overall, the norming stage is an important period of transition for groups as they move from the early stages of forming and storming to a more cohesive and productive group dynamic. The close ties formed during this stage can help to foster a supportive and collaborative environment that benefits the group as a whole.

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The graph of the inequality y > x² - 9 is given by the image presented at the end of the answer.

The inequality for this problem is given as follows:

y > x² - 9.

For the curve y = x² - 9, we have that:

Due to the > sign, the values greater than the inequality, that is, above the inequality, are shaded.

As the inequality does not have an equal sign, the parabola is dashed.

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Answer:

Construct an angel bisector

Answer: 75.2

Step-by-step explanation:

Well, if it isn't the most confusing question ever.

First of all, what is P?

I'll assume its the perimeter...

2*(1.2*2)+4*(8.8*2)

Or

2*2.4+4*17.6

75.2

The simplified form would be (r - 24).

What is a simplification in mathematics?

Simplification in mathematics refers to the process of making a mathematical expression or equation easier to understand and work with. This can involve combining like terms, factoring expressions, or reducing fractions. The goal is to get a simpler and more manageable expression without changing its value or meaning.

\(X = r+2\\Y = 2r-9 $ and\\Z = r^2+17r+30\\X.Y = (r+2).(2r-9)\\X.Y = r(2r-9) + 2(2r-9)\\X.Y = 2r^2-5r-18\\X.Y-Z=2r^2-5r-18-(r^2+17r+30)\\X.Y-Z=r(r-24)+2(r-24)\\X.Y-Z = (r+2)(r-24)\\\)\(\frac{(X.Y-Z)}{X} = \frac{(r+2)(r-24)}{r+2}\\\\\frac{(X.Y-Z)}{X} = r-24\\\\Hence, the simplified form [X.Y - Z]/X = r-24.\)

Hence, the simplified form would be (r - 24).

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Using the volume x³ + 10x² + 19x  - 30, the missing side of the rectangular prism is (x + 6)

Two sides of a rectangular prism are x + 5 and x - 1. The volume of the rectangular prism is given as x³ + 10x² + 19x  - 30.

Let's find the missing side of the rectangular prism.

Therefore,

volume of a rectangular prism = lwh

where

Therefore,

volume of the prism = x³ + 10x² + 19x  - 30

Let's factorise it to find the missing side length

x³ + 10x² + 19x  - 30  = 0

(x - 1)(x² + 11x + 30)

let's factorise x² + 11x + 30

x² + 11x + 30

x² + 5x + 6x + 30

x(x + 5) + 6(x + 5)

(x + 6)(x + 5) = 0

Therefore, the side length of the rectangular prism are (x - 1), (x + 5) and (x + 6)

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A critical value, z subscript alpha (zα), denotes the boundary or cutoff point for a statistical test where the level of significance, also known as alpha (α), is set.

A critical value, z subscript alpha (zα), denotes the value at which the probability of observing a test statistic in the tail(s) of the sampling distribution equals the pre-determined significance level (alpha).

The critical value can be defined as the value that is compared with the parameter value in the hypothesis test to determine whether the null hypothesis will be rejected. If the value of the parameter is less than the critical value, the null hypothesis is rejected.

However, if the measured value is higher than the critical value, reject the null hypothesis and accept the alternative hypothesis. In other words, cropping divides the image into acceptable and unacceptable areas. If the value of the index falls within the rejection range, the rejection of the fact is rejected, otherwise the negative hypothesis is rejected.

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The cost of each music video is $1.99.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Given total cost of 2 music videos, a TV series and a movie is $42.95

and TV series cost 2 times as much as the movie,

cost of the movie = $12.99

cost of  TV series = 2*12.99

cost of  TV series = $25.98

let the cost of a video be x

so according to condition,

2x + cost of  TV series + cost of the movie = $42.95

2x + 25.98 + 12.99 = 42.95

2x = 42.95 - 25.98 - 12.99

2x = 3.98

x = 3.98/2

x = $1.99

Hence the cost of a music video is $1.99.

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A circle inside a semicircle is depicted in the diagram. The circle measures 10 cm in diameter. The semicircle has a 20 cm diameter. Calculate the shaded area. Give a precise response to the nearest decimal point.

The area of the shaded region is 39.3\(cm^{2}\).

Given the diagram shows a circle inside a semicircle.

Every point in the plane of a circle, which is a closed, two-dimensional object, is evenly separated from the center. All lines that cross the circle join together to produce the line of reflection symmetry. Every angle also possesses rotational symmetry about its center.

Area of a circle = \(\pi r^{2}\).

Semicircle is when a line travelling through the center of a circle reaches its two ends, a semicircle is created. Thus, a circle can be formed by combining two semicircles.

Area of a semicircle = \(\frac{1}{2} \pi r^{2}\).

The circle has a diameter of 10 cm. The semicircle has a diameter of 20 cm.

Semicircle:

\(r_{1}=\frac{d_{1} }{2}=\frac{20}{2}=10cm\\S_{1}=\frac{ \pi r_{1}^{2} }{2} =\frac{ \pi \times 10^{2} }{2} =50\pi cm^{2}\)

Circle:

\(r_{2}=\frac{d_{2} }{2}=\frac{10}{2}=5cm\\S_{2}=\pi r_{2}^{2} = \pi \times 5^{2} =25\pi cm^{2}\)

So,

\(S=\frac{S_{1} -S_{2}}{2} \\S=\frac{50\pi -25\pi}{2}\\S=\frac{25\pi}{2} \\S=39.3cm^{2}\)

Therefore, The area of the shaded region is 39.3\(cm^{2}\).

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The equation in spherical coordinates is a) 3sin²ϕ - 2sinϕcosθ/ρ - 3cos²ϕ = 0

b) 2sinφcosθ + 4sinφsinθ + 5cosφ = 1/ρ

a) The equation in Cartesian coordinates is 3x² - 2x + 3y² - 3z² = 0. To convert to spherical coordinates, we use the following substitutions:

x = ρsinϕcosθ

y = ρsinϕsinθ

z = ρcosϕ

Substituting these values into the Cartesian equation gives:

3(ρsinϕcosθ)² - 2(ρsinϕcosθ) + 3(ρsinϕsinθ)² - 3(ρcosϕ)² = 0

3ρ²sin²ϕcos²θ - 2ρsinϕcosθ + 3ρ²sin²ϕsin²θ - 3ρ²cos²ϕ = 0

3ρ²sin²ϕ(cos²θ + sin²θ) - 2ρsinϕcosθ - 3ρ²cos²ϕ = 0

3ρ²sin²ϕ - 2ρsinϕcosθ - 3ρ²cos²ϕ = 0

Simplifying and dividing by ρ² gives:

3sin²ϕ - 2sinϕcosθ/ρ - 3cos²ϕ = 0

(b) The equation in rectangular coordinates is 2x + 4y + 5z = 1. To write it in spherical coordinates, we use the same conversion formulas as before:

2(ρsinφcosθ) + 4(ρsinφsinθ) + 5(ρcosφ) = 1

Simplifying and dividing by ρ, we get:

2sinφcosθ + 4sinφsinθ + 5cosφ = 1/ρ

This is the equation in spherical coordinates.

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Step-by-step explanation:

look at the picture i have sent

The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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