At a gathering of 10 people, there are 4 people who all know each other and 6 people who know no one. People who do not know each other shake hands. How many handshakes occur?

Answer:

7 and 35

Step-by-step explanation:

let the numbers be n and 5n , then when 21 is added to both they are

n + 21 and 5n + 21

Given that one is twice the other

5n + 21 = 2(n + 21)

5n + 21 = 2n + 42 ( subtract 2n from both sides )

3n + 21 = 42 ( subtract 21 from both sides )

3n = 21 ( divide both sides by 3 )

n = 7

and 5n = 5 × 7 = 35

The numbers are 7 and 35

First, locate the coordinate points given and join them.

Then, do the translation:

(x,y) = (x-9,y )

C' = (1-9 , 6 ) = (-8,6)

A'= (1-9,1) = (-8,1)

T'= (7-9 , 1 ) = ( -2,1)

Graph:

Finally reflect in x axis

(x,y )----> (x,-y)

C'' = (-8,-6)

A''= (-8,-1)

T''= (-2,-1)

Graph:

On solving the provided question, we can say that the random sampling is \(^5C_{2}\) = 4X5/ 2= 10

A simple random sample may be 25 employees chosen at random from a firm with 250 workers. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. The sampling technique of random sampling, also known as probabilistic sampling, enables the randomization of sample selection. It is crucial to keep in mind that populations as a whole are not always accurately represented by sampling. Sampling error is the term used to describe all variance.

population size, \(N = 5\)

sample size, \(n = 2\\\)

\(^5C_{2}\) = 4X5/ 2

= 10

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When creating flowcharts, we represent a decision with a diamond shape. Correct option is d.

The diamond shape is used to indicate a point in the flowchart where a decision or choice needs to be made. The decision typically involves evaluating a condition or checking a criterion, and the flow of the program can take different paths based on the outcome of the decision.

The diamond shape is commonly associated with decision-making because its sharp angles resemble the concept of branching paths or alternative options. It serves as a visual cue to identify that a decision point is being represented in the flowchart.

Within the diamond shape, the flowchart usually includes the condition or criteria being evaluated, and the two or more possible paths that can be followed based on the result of the decision. These paths are typically represented by arrows that lead to different parts of the flowchart.

Overall, the diamond shape in flowcharts helps to clearly depict decision points and ensure that the logic and flow of the program are properly represented. Thus, Correct option is d.

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Thus,  the proof of the identity cos^2(5x) - sin^2(5x) = cos(10x) involves the use of the double angle formula for cosine. This identity is useful in solving various problems related to trigonometry.

To prove the trigonometric identity cos^2(5x) - sin^2(5x) = cos(10x), we will use the double angle formula for cosine.

This formula states that cos(2θ) = cos^2(θ) - sin^2(θ). We can rewrite our identity as:
cos^2(5x) - sin^2(5x) = cos(2 * 5x)

Using the double angle formula, we get:
cos^2(5x) - sin^2(5x) = cos(10x)

This proves the given trigonometric identity.

To understand this identity better, let's break it down.

The left-hand side of the identity consists of two terms, cos^2(5x) and sin^2(5x).

These terms are known as the Pythagorean identity and state that cos^2(θ) + sin^2(θ) = 1.

We can rewrite cos^2(5x) as 1 - sin^2(5x) using this identity.

Substituting this value in the given identity, we get:
1 - sin^2(5x) - sin^2(5x) = cos(10x)

Simplifying this equation, we get:
cos^2(5x) - sin^2(5x) = cos(10x)

Therefore, we have successfully proven the given trigonometric identity.

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The porcelain pot is fired at 2552 degrees Fahrenheit.

The temperature at which porcelain pot is fired will be calculated firstly by forming the equation. Then we will perform mathematical operations as per the PEMDAS rule. Let us assume the temperature be t.

Forming and representing the equation with respect to t

t = 2×1409 - 266

Firstly performing multiplication on Right Hand Side of the equation to find the value of t

t = 2818 - 266

Now performing subtraction on Right Hand Side of the equation to find the value of t

t = 2552 degrees Fahrenheit

Hence, the temperature of porcelain pot based on the given information is 2552 degrees Fahrenheit.

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The volumes of the solids generated by rotating the given region around the given axis of rotation are 200π, 120π, 120π, and 80π, respectively.

Pappus' Theorem states that the volume of a solid generated by rotating a planar region about an external axis is equal to the product of the area of the region and the distance traveled by the centroid of the region during the rotation.

We can apply this theorem to find the volume of the solids generated by rotating the given region around the given axis of rotation.

a. When the region R is rotated around the x-axis, the distance traveled by the centroid is 2π(5) = 10π. Therefore, the volume of the solid is 20 × 10π = 200π.

b. When the region R is rotated around the y-axis, the distance traveled by the centroid is 2π(3) = 6π. Therefore, the volume of the solid is 20 × 6π = 120π.

c. When the region R is rotated around x=2, the distance traveled by the centroid is 2π(5-2) = 6π. Therefore, the volume of the solid is 20 × 6π = 120π.

d. When the region R is rotated around y=1, the distance traveled by the centroid is 2π(3-1) = 4π. Therefore, the volume of the solid is 20 × 4π = 80π.

Therefore,the solids generated by rotating the specified region around the specified axis of rotation have volumes of 200π, 120π, 120π, and 80π,  respectively.

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Answer:

-5y

Step-by-step explanation:

15 = 3×5

55 = 5×11

-15xyz = -1 × 3 × 5 × x × y × z

-55xy² = -1 × 5 × 11 × x × y²

-55yz = -1 × 5 × 11 × y × z

HCF = multiply all common factors with the lowest power amongst all 3 expressions

HCF = -1 × 5 × y = -5y

Answer:

y = -6x - 2

Step-by-step explanation:

Answer:

Yearly interest:

Yearly fees:

Total balance at the end of the year:

False, as negative income

Yearly interest:

Balance at the end of the year:

TRUE, as real income

False, the deals are different with +$10 and -$10

False, there is no restriction as long as it is a source of income

Answer:

Option B

. Bank B offers you a savings account with 2% annual interest rate and no fees

How?

Annual interest rate=2%

Hence annual interest

\(\\ \rm\longmapsto 500\times \dfrac{2}{100}\)

\(\\ \rm\longmapsto 5(2)\)

\(\\ \rm\longmapsto \$10\)

Now sum of money=$500+$10=$510

The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.

To understand this ratio, let's break it down using different units:

A. 1/3 part bleach and 2/3 part water:

If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.

B. 2 cups of bleach and 3 cups of water:

If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.

C. 3 cups of bleach and 2 cups of water:

If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.

Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

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The limit of the sequence (1) {2}, (2) {(-1)^n}, and (3) {n sin(n)}, converges to DNE (does not exist) or the sequence diverges. The limit of the sequence (4) {sin(nπ)} is undefined, as it oscillates between -1 and 1.

In the case of sequence (1) {2}, the limit is a constant value, and the sequence converges to that value. However, in the case of sequence (2) {(-1)^n}, the sequence oscillates between -1 and 1, and there is no single value that it approaches as n tends to infinity. Therefore, the limit does not exist, and the sequence diverges.

Sequence (3) {n sin(n)} also does not have a limit as n tends to infinity. The term n sin(n) oscillates between positive and negative values without approaching a specific value. Hence, the limit of this sequence is DNE, and it diverges.

In the case of sequence (4) {sin(nπ)}, the term sin(nπ) oscillates between -1 and 1 as n varies. Since there is no convergence to a specific value, the limit of this sequence is undefined.

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The function f(x) = \(5(3)^x+3\) is continuous everywhere on its domain, which is (-∞, ∞).

The function f(x) =  \(5(3)^x+3\)   is continuous everywhere because it is an exponential function with a base of 3, which is a positive number. Exponential functions with positive bases are continuous over their entire domain.

To see why, consider the definition of continuity: a function f(x) is continuous at a point x = c if the limit of f(x) as x approaches c exists and is equal to f(c). For an exponential function with a positive base, as x approaches c, the function values either increase to infinity or decrease to 0, depending on whether the exponent is positive or negative, respectively. In either case, the limit exists and is equal to the function value at c, so the function is continuous at c. Since this holds for all points in the domain, the function is continuous everywhere it is defined.

The domain of f(x) is all real numbers, so the function is continuous on the interval (-infinity, infinity), or in interval notation, the domain is (-∞, ∞).

In summary, the function f(x) = 5(3)ˣ +3 is continuous everywhere on its domain, which is (-∞, ∞).

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Answer:

Step-by-step explanation:

Here we see regrouping of the multiplied numbers.

Relevant property is given below

Answer:

Your answer is C

Step-by-step explanation:

1.   4x − 2y = 10 and 2x − y = 5

Lines are coincident.

2.  y = 2x − 3 and −2x + y = −5

Lines are parallel.

3.  2x − 5y = 14  and 3x + 4y = 10

Lines are intersecting.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

1.   4x − 2y = 10 and 2x − y = 5

2.  y = 2x − 3 and −2x + y = −5

3.  2x − 5y = 14  and 3x + 4y = 10

\(\rm \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2} \ \ \ \ \ \ \ \ \ \ \ Lines\ are\ intersecting\\\\\rm \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}\ \ \ \ Lines \ are\ parallel\\\\\rm \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2} \ \ \ \ Lines\ are\ coincident\)

1.   4x − 2y = 10 and 2x − y = 5

Lines are coincident.

2.  y = 2x − 3 and −2x + y = −5

Lines are parallel.

3.  2x − 5y = 14  and 3x + 4y = 10

Lines are intersecting.

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The relationship between the x- and y-coordinates is described by a linear equation in two variables known as the equation of a line.

A line's slope and y-intercept are expressed in its slope intercept form as y = m x + c. Where the line meets the y-axis is known as the y-intercept.

y = 5 x is the equation for the given line.

Adding 0 to RHS and writing it in the slope-intercept form results in.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

A line's equation is written as ax + by + c = 0. Here, the variables x and y are the variables, while the constant term c is the coefficients. Slope-intercept form, point-slope form, two-point form, intercept form, and normal form are a few additional ways to determine and describe a line's equation.

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Full Question = What is the slope and the y-intercept of the equation y=5x?

Answer:

Your answer, many solutions is correct!

Step-by-step explanation:

The answer one solution is incorrect because there is more than one solution to this equation.

The answer no solution is incorrect because there is a solution to this equation so clearly, this one is incorrect.

The answer many solutions is correct because there are two solutions to this equation, \(y=-3,\:x=\frac{9}{2}\).

hope this helps!!!

(Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.)

Answer:

yeah correct

Step-by-step explanation:

8400000cm

84 kilometer is 8400000 centimeter.

Here given 84 km ,

We know that 1 km = 1000 meter

               so 84 km  = 84 x 1000 meter

                                 = 84000 meter

 and 1 meter = 100 cm

 so here 84000 meter = 84000 x 100 cm

                                       = 8,400,000 Centimeters

∴ 84 km = 8400000cm

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\((4d)(6d)(0.25d)=d^3[(4)(6)(0.25)]=\boxed{6d^3}\)

Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

The value of x that makes this equation (X-2)/2= (X+4)/4  to be true is 8.

An equation ca be described as the mathematical terms which can contains different digits as well we a as alphabet and it can simplified so that a particular expression or term can be found, in the given equation we were told to find the value of x by simplify the equation which is done below.

(X-2)/2= (X+4)/4

Then if we cross multiply we will have

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

then we can simplify further and collect the like terms which is

2x=16

x=8

There, the correct option is B

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The formula to calculate the common sum of the interior angles of an n-sided polygon is as follows: Sum = (n-2) × 180The problem states that the polygon is regular. As a result, all angles in the polygon have the same degree.

To discover the degree of each angle, divide the sum of the angles by the number of angles in the polygon.

Say, for instance, that the polygon has 150 sides. The formula for the sum of the interior angles of a polygon with 150 sides is:S = (n-2) × 180 = (150-2) × 180 = 148 × 180 = 26640 degrees

To determine the size of each interior angle, we must now divide the sum by the number of angles in the polygon: Each angle size = S/n = 26640/150 = 177.6 degrees Therefore, each interior angle in a regular 150-sided polygon has a degree of 177.6.

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Answer:

How does one find use partial quotients for subration

Step-by-step explanation:

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

Answer:

(-4, -1)

Step-by-step explanation:

The midpoint formula is [ (x1+x2/2,y1+y2/2) ]

(-1+(-7)/2, 2+(-4)/2)

(-8/2, -2/2)

(-4, -1)

Best of Luck!

Step-by-step explanation:

3m is the answer.

hope it helps

Answer:

3 meters

Step-by-step explanation:

The train starts at (0, 0) and ends at (6, 3). So the train travels in 6 seconds (6 - 0) 3 meters (3 - 0).

Using the concepts of probability, we got that that Stratified sampling is the experiment design which an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs.

In the question, actually the insurance company intends to study and understand the relationship between the health care cost of the customers and the provision of incentives for the preventative care by two groups, each having one of  two given attributes under study, which are;

a) One group consist of the customers having high health care cost and offered incentives for preventative care

b) The other group consist of the customers having only high health care cost without incentives

Therefore, the insurance company customers are stratified into the groups based on health care cost and again into the groups that have high health care cost and are offered preventative care and those that have only the high heath care cost, which is the process used to implement the stratified sampling technique.

Hence, an insurance company which wants to study whether offering incentives for preventative care reduces overall health care costs, by selecting a random sample of 200200200 of their customers and using a random number generator to select 100100100 customer account numbers to offer the incentive, the experiment design is named as  Stratified sampling.

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(a) The equation that estimates the population t years after 2010 is

P(t) = 5655(1.014)^t.

(b) Population of the town in 2022 is 6,681.

We have given that the population of a town was 5655 in 2010.

And the population grow at a rate of 1.4% annually.

(a) We have to find equation that estimates the population t years after 2010.

We know the formula for exponential growth,

P(t) = P₀(1 + r)^t

where P₀ is the initial population,

r is the relative growth rate,

t is the time unit.

Putting the values in above equation we get,

P(t) = 5655(1 + 0.014)^t

P(t) = 5655(1.014)^t

(b) Now we have to find population of the town in 2022.

Here t = 2022 - 2010 = 12

Therefore equation of growth will become,

P(12) = 5655(1.014)^12

P(12) = 6681

Hence the population of the town in 2022 is 6,681.

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Respuesta:

-4;

-1

Explicación paso a paso:

Dado :

-2- | -2 | - | -3 | +3

Los números entre barras verticales son valores absolutos y se tratan como positivos:

-2 - +2 - +3 + 3 = - 2-2-3 + 3 = - 4

| -1 | + | -1 | - | -3 |

Los números entre barras verticales son valores absolutos y se tratan como positivos

1 + 1 - + 3 = 1 + 1-3 = - 1

A unit vector u in the direction opposite of ⟨−6,−3,−1⟩ is ⟨6/√46, 3/√46, 1/√46⟩. To find a unit vector in the opposite direction of ⟨−6,−3,−1⟩.

We first need to find the magnitude of this vector:
||⟨−6,−3,−1⟩|| = √((-6)^2 + (-3)^2 + (-1)^2) = √46
Then, to find the opposite direction, we simply negate each component ⟨6, 3, 1⟩. Finally, to find the unit vector in this direction, we divide by the magnitude:
u = ⟨6/√46, 3/√46, 1/√46⟩

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