Is the average of a sum the sum of the averages?.

The function has its graph to be represented by graph (a)

Table:

x  -2       -1      0     1      2

y  16/9   4/3   1     3/4   9/16

The equation that represents the function is given as

f(x) = (3/4)ˣ

Next, we extract the x values from the given table

These x values are represented as

x = -2, -1, 0, 1 and 2

Solving further, we need to calculate the function at the x values

So, we have the following computations

f(-2) = (3/4)⁻² = 16/9

f(-1) = (3/4)⁻¹ = 4/3

f(0) = (3/4)⁰ = 1

f(1) = (3/4)¹ = 3/4

f(2) = (3/4)² = 9/16

When these values are presented on a table, we have:

x  -2       -1      0     1      2

y  16/9   4/3   1     3/4   9/16

Some of the points on the table are

(0, 1), (1. 3/4) and (2. 9/16)

The graph that passes through these points is graph (a)

So, the

Hence, the graph of the function is graph (a)

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There are 99 students preferred pizza.

The students preferred pizza can be calculated as follows.

First, let’s make the equation.

Students preferred pizza is symbolized as P

Students preferred hotdogs is symbolized as H

P = 2.25H

Second, let’s put the number of student preferred hotdogs.

P= 2.25 x 44

= 99

Hence, there are 99 students preferred pizza.

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When testing a newly installed hydromatic propeller, the propeller is exercised by moving the governor control through its entire travel several times to free the dome of any entrapped air.

A hydromatic propeller uses a double-acting governor control utilizing oil pressure on both sides of the propeller piston. It was introduced in the 1930s as a substantial advancement over the counterweight, controllable pitch propeller. The application of oil pressure to both sides of the actuating piston provided improved capacity and the potential of feathering or unfeathering by a single control knob. It was designed for larger blades, faster rate of pitch change, and wider range of pitch control. A hydromatic propeller should be checked before, during, and after the operation of the engine. A newly installed hydromatic propeller should be checked by moving the governor along its travel numerous times to ensure that no air is entrapped in the dome.

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The Cartesian equation will be;

⇒ x² + y² - 4x - 5y = 0

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 polar equation will be;

⇒ r = 4 sin(θ) + 5 cos(θ)

Now,

Substitute r = √x² + y² , r sin θ = x, r cos θ = y in above equation, we get;

The polar equation will be;

⇒ r = 4 sin(θ) + 5 cos(θ)

⇒ r² = 4 r sin(θ) + 5 r cos(θ)

⇒ x² + y² = 4x + 5y

⇒ x² + y² - 4x - 5y = 0

Thus, The Cartesian equation will be;

⇒ x² + y² - 4x - 5y = 0

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The equation of the line in slope intercept form is y = 4/3x - 10/3.

What is a line in slope-intercept?

The equation of a line with a slope of m and a y-intercept of (0, b) is y = mx + b. To graph a slope-intercept line, do the following: On the coordinate plane, draw the y-intercept. Find another point on the line using the slope.

We have,

the line that passes through  (-3,-6) and slope m = -2/3.

Now using the slope and the point (-3, -6) the y-intercept is

m = -2/3.

y = mx + b

-6 = -2/3(-3) + b

6 = 6/3 + b

By further calculation,

b = 6 - 2

b = 4

By writing the equation in slope intercept form

y = mx + b

y = -2/3x - 4

Therefore, the equation of the line in slope intercept form is y = -2/3x - 4.

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Solution of the given expression 6a + 18ab after rewriting using a common factor is equal to :

A. 6a(1 + 3b).

As given in the question,

Given expression is equal to :

6a + 18ab

Find common factors of both the terms we get.

6 = 1, 2, 3, 6

18 = 1, 2, 3, 6, 9, 18

Highest common factor of 6 and 18 is equal to 6.

Now take 6a as a common factor from both the terms we get,

6a + 18ab

= ( 6a × 1 ) + ( 6a × 3b )

= 6a × ( 1 + 3b )

= 6a ( 1 + 3b )

Therefore, solution of the given expression 6a + 18ab after rewriting using a common factor is equal to :

A. 6a(1 + 3b).

The complete question is :

Rewrite 6a + 18ab using a common factor.

A.6a(1 + 3b)

B. 6a(0 + 3b)

C.6ab(0 + 3)

D. 6ab(1 + 18ab)

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Answer:  6a(1 + 3b)

Step-by-step explanation:  I took the test

Answer:

y=-3/4x+3

Step-by-step explanation:

(See picture)

The average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1] is 1/4( π - log4) - π²/48.

A function is a relationship between a number of inputs where each input has exactly one output, according to one definition. f is typically used to represent a function (x).

Given,

Function,

Region = [0,1] × [0,1]

Lˣ = 1/area of region ∫¹₀ ∫₀¹ f(xy) dx dy

Differentiating,

Lˣ

= 1/1 ∫₀¹ tan⁻¹ xy dxdy

= ∫¹₀ [ ∫¹₀ tan⁻¹(xy) dx ] dy

= ∫₀¹ [{x tan⁻¹ (xy) ¹₀ - 1/2 ∫ 2(x+y)/ 1 + xy₂ dx] dy

= ∫¹₀ tan⁻¹ y dy - ¹₀ log(y² + 1) 2y dy

= [ytan⁻¹ y - 1/2 log( y² + 1) ∫¹₀ - [1/4 log (y² +1) log y² +1/4log(y²+1)

= π/4 - 1/2 log 2 -π²/48

L = 1/4( π - log4) - π²/48

The average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1] is 1/4( π - log4) - π²/48.

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When a pair of dice rolled, the probability that the sum is either a multiple of 3 or a multiple of 4 is 5/9.

If an event A and an event B is independent to each other, then the probability A or B is:

P(A or B) = P(A∪B) = P(A) + P(B)

In the given problem:

The possible outcomes or the sample space of rolling a pair of dice = 6 x 6 = 36.

The maximum sum is 6 + 6 = 12

Multiple 3 or multiple 4 that ≤ 12 is {3, 4, 6, 8, 9, 12}

Possible outcomes for Sum = 3 are 1 + 2 and 2 + 1

Hence,

P(3) = 2/36

Possible outcomes for Sum = 4 are 1 + 3, 3 + 1, 2 + 2

Hence,

P(4) = 3/36

For Sum = 8,  2 + 6, 6 + 2, 3 + 5, 5 + 3, 4 + 4

Hence,

P(8) = 5/36

Similarly,

P(6) = 5/36

P(9) = 4/36

P(12) = 1/36

Therefore,

P(Multiple 3 or multiple 4) = P(3, 4, 6, 8, 9, 12)

                                          = 2/36+3/36+5/36+5/36+4/36+1/36

                                          = 20/36

                                          = 5/9

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The case mentioned above is resolved via multiplication.

Given information,

Linda can sell 12 magazine subscriptions per week and makes 4$ for each magazine subscription she sells. This means that Linda will make 48$ per week from magazine subscriptions.

To show it mathematically,

1 week ⇒ 12 magazines

Each of them costs $4;

⇒ 12 * 4$ = 48$ per week

By using multiplication we solve the above-given case.

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The prime multiples of 8 are number 2 and 4

The multiples of 8 are 1, 2, 4, 8.

The prime numbers are the numbers who can be divided only by 1 and itselves.

First we need the multiplies of 8

And then find their factors, if the number of factors is exactly two( that is 1 and the number itself) then it is prime.

The factors of 1 is 1

The factors of 2 are 1 and 2

The factors of 4 are 1, 2and 4

The factors of 8 are 1, 2, 4 and 8

The numbers which have only two factors are prime.

2 and 4 are prime multiples of 8

Therefore, the number 2 and 4 can be said as the prime multiples of 8

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The slope of the line that passes through the points (-3, 3), and (1, -5) is -2.

Steps to finding slope:

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Here,

m = slope of the line

x₁ = the x-coordinate of the first point

y₁ = the y-coordinate of the first point

x₂ = the x-coordinate of the second point

y₂ = the x-coordinate of the second point

Here, the given points are  (-3, 3), and (1, -5):

y₂ = -5, y₁ =3 , x₂ = 1, x₁ = -3

Substitute the values,

m = (y₂ - y₁) / (x₂ - x₁)

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

= -8 / (1+3)

= -8 / 4

m = -2

Hence, the slope of the line that passes through the points (-3, 3), and (1, -5) is -2.

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The first two events are not independent, with a probability P = 0.0637

The second pair of events are independent, and the probability is P = 0.0625

How is probability obtained?

First, the probability that any card will be picked at random will be the same for all cards in the deck, or p = 1/52.

A) If Lacy draws a diamond card first, there are now fewer cards in the deck (now there are 51 cards on the deck). As a result, there is now a higher chance than before of drawing a spade. In that case, the first two events are not random.

The Probability of getting the first diamond card is:

P = 13/52 (because there are 13 diamonds and a total of 52 cards).

The probability of drawing a spade after is:

Q = (13/51)

The joint probability is the product of the individual probabilities, this will give:p = P×Q = (13/52)×(13/51) = 0.0637

B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).

The probability of drawing a diamond is:

P = 13/52

Now we replace the diamond card drawn.

The probability of drawing a spade will be:

Q = 13/52

The joint probability is:

p = P×Q = (13/52)² = 0.0625

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By using the concept of cryptography, it can be concluded that

A solution that is now widely used to allow two parties to secretly exchange keys is Deffie - Hellman protocol

What is cryptography?

Cryptography refers to secure information and communication techniques derived from mathematical concepts and a set of rule-based calculations called algorithms, to transform messages in ways that are hard to decipher.

This is a concept of Cryptography

Diffie–Hellman key exchange establishes a shared secret between two parties which will be used for secret communication for exchanging data over a public network.

A solution that is now widely used to allow two parties to secretly exchange keys is Diffie - Hellman protocol

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he got the same answer i did

Step-by-step explanation:

There are basically three to four rules for angles of a triangle.

sum of all interior angle of triangle is 180°.

.

Angle in triangle

Triangles are one of the most basic geometric shapes and have a variety of well-studied properties. Triangle: Largest interior angle and sides facing each other. The same rules apply for minimum angles and sides, medium angles and medium sides.

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Answer:

x >= 2.25

x is greater than or equal to 2.25

Step-by-step explanation:

8x - 3 >= 15

add 3 to both sides

8x >= 18

divide 8 from both sides

x >= 2.25

Answer:

x≥6

Step-by-step explanation:

8x

3 less goes to 8x-3

then there is at least 15 which changes to

8x-3≥15

Then solve for x:

add 3 to the sides--> 3x≥15+3

3x≥18

Divide both of the sides by 3

x≥6

Hope this helped!

The coordinates of the point where y-4x=1 crosses on the axis is (0, 1).

The value of K is 6.5

An equation is an expression that shows the relationship between two or more numbers and variables.

a)  The graph will cross the y-axis at the y-intercept. We can find the value by putting the given equation into slope-intercept form (y = mx + b).

y - 4x = 1

y = 4x + 1

The y-intercept is (0,1).

b) We need to find c, or the y-intercept. This is given to us on the graph, where the line crosses the y-axis at (0,-3).

Therefore, our line is;

y = 2x - 3.

Then, we can plug in 10 for y from the point (k,10) and solve for k as;

10 = 2x - 3

13 = 2x

x = 6.5

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The bearing of the oil rig from the port is 28.61° west by north.

What are the trigonometric identities?

All trigonometric identities are based on the six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent are the functions. All of these trigonometric ratios are defined using the sides of a right triangle, specifically the adjacent, opposite, and hypotenuse sides.

We have,

First, the boat travels 55km toward the west,

and then it travels 30km toward the north.

So the boat forms the right triangles, see in the image attached,

tanθ = 33/55

θ = tan⁻¹ (33/55)

θ = 28.61°

28.61° west by north.

Hence, the bearing of the oil rig from the port is 28.61° west by north.

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Yes, there is sufficient evidence at the α = 0.05 level to conclude that less than 20% of the parts are being painted with an error.

We have,

There is sufficient evidence at the α = 0.05 level to conclude that less than 20% of the parts are being painted with an error.

The calculated P-value of approximately 0.023, which is less than the significance level of 0.05.

The P-value indicates the probability of observing a test statistic as extreme as or more extreme than the observed value of -2.00 under the null hypothesis.

Since the P-value is smaller than the significance level, we reject the null hypothesis and conclude that the proportion of parts with an error is significantly less than 20%.

The fact that 16% is less than 20% also supports this conclusion.

Thus,

Yes, there is sufficient evidence at the α = 0.05 level to conclude that less than 20% of the parts are being painted with an error.

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The required number of two positive consecutive integers are 35 and 36.

Consecutive integers are the whole numbers that follow each other without gaps. consecutive  integers are even, and odd integers.

consecutive even integers that differ from previous integer by difference of 2 and each integer is divisible by 2.

consecutive odd integers that differ from previous integer by difference of 2 and each integer is an odd number.

let the first positive integer be x

Therefore the second positive integer be (x+1)

Given that the sum of two consecutive positive integer is 71:

x+(x+1)=71

open the bracket

x+x+1=71

Add the similar terms

2x+1=71

2x=71-1

2x=70

x=35

Finding the second integer Substituate the value of x=35 in (x+1):

x+1=35+1

x+1=36

The required number of two positive consecutive integers are 35 and 36.

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The surface area of the given rectangular prism with a length 7cm , width 2cm and height 6cm is equal to 136cm².

As given in the question,

Dimensions for a given rectangular prism are:

Length = 7cm

Width = 2cm

Height = 6cm

Surface area of the given rectangular prism is equal to

= 2 ( length × width + width × height + height × length )

Substitute the value in the formula we get,

= 2 ( 7 × 2 + 2 × 6 + 6 × 7 )

= 2 ( 14 + 12 + 42 )

= 2 ( 68 )

= 136 cm²

Therefore, the surface area of the rectangular prism is equal to 136cm².

The complete question is :

Hannah has a rectangular prism with a length of 7 cm, a width of 2 cm,

and a height of 6 cm.

What is the surface area of Hannah's rectangular prism?

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The ratio of tubes of blue paint to all of the tubes of paint used was 75/10000 = 0.0075.

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.

Given,

          red paint= 666 tubes

          yellow paint = 222 tubes

          white paint = 131313 tubes

          blue paint= 999 tubes  

Total paint tubes = 666+222+131313+999 = 133200

The ratio of blue paint tubes to all of the paint tubes = 999/133200

                                                                                        = 75/10000.

The ratio of tubes of blue paint to all of the tubes of paint used = 75/10000 = 0.0075.

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Yes, you can still get from one city to another even if a road is closed for maintenance.

How is it feasible to get from one city to another if one road is closed for repairs?

It is sufficient to show that even with route AB closed, we can still get from point A to point B. In the connected component that contains vertex A, all the vertices would be even if this weren't the case.

When a connected component has exactly one odd vertex, the "A graph must have an even number of odd vertices" condition is violated.

Therefore, even if one of the roads is closed for maintenance, it is still possible to go from Point A to Point B by another road or city.

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The given question is improper. Proper question is given below;

in a certain country, 40 roads lead out of each city. when all roads are open, it is possible to travel from any city to any other. each road leads from one city to another; there are no dead end roads. if one road is closed for repairs, is it still necessarily possible to travel from any city to any other? prove your answer.

Okay here is step by step.

2x + 8 = 15

2x = 15 - 8

2x = 7

7/2 = 3.5

3.5 = x

Because we use the laws of substitution switching the numbers to the other side, which is allowed because they still mean the same thing.

Hope this helps.

The correct answer is 4 km per hour Lashonda would swim if there were no current.

Here, we'll suppose that Lashonda is moving at x km/hr. in the absence of any current.

Speed of the current is 2 km/hr.

Distance swim against current is 5km

Time taken to swim against current is  5 ÷ (x - 2)

Distance swim with current is 15km

Time is taken to swim with current is 15 ÷ (x + 2)

Now,

Given that  if the time taken in both instances are the same, So, the equation will be 5 ÷ (x - 2) = 15 ÷ (x + 2)

After solving for x we will be solving;

⇒ 5 ÷ (x + 2) = 15 ÷ (x - 2)

⇒ 5x + 10 = 15x - 30

⇒ 10 + 30 = 15x - 5x

⇒ 40 = 10x

⇒ x= 40 ÷ 10 = 4 km per hour

Hence, 4 km per hour Lashonda would swim if there were no current.

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One of the two identical halves of a chromosome that has been replicated in preparation for cell division is referred to as a chromatid. The two "sister" chromatids are united at the centromere, a restricted portion.

A chromatid is an individual of two together alike halves of a deoxyribonucleic acid that has been copied imminent for the formation of cells by dividing. The two “twin” chromatids are linked at an inhibited domain of the chromosome named the centromere. The establishment of chromatids is a main become involved in cellular division guaranteeing that each new girl cell has the correct complement of DNA at the end of the formation of cells by dividing.

Cell division is the process by which a person's container divides into two woman cells. Cell division frequently happens as few the best container phase at which point the cell evolves and replicates allure deoxyribonucleic acid before separating.

There are two types of cell division: the formation of cells by dividing and the formation of cells by dividing. Most of the time when nations are concerned with “cellular division,” they mean the formation of cells by dividing, the process of making new carcass containers.

Sister chromatids differ from chromatids in that sister chromatids are two copies of a single chromosome and are products of the S phase of the cell cycle. The centromere links sister chromatids together.

During the early stages of cell division, chromatids are produced. Non-sister chromatids appear during metaphase I of meiosis, whereas sister chromatids replicate from the same chromosome.

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By using the concept of Population and sample, it can be concluded that

The above data would be a population of weights because they represent all of the football players.

The first option is correct

What is population and sample?

Population is the set where all item are the members of the sets and from where the set of items can be drawn for statistical study

Subset of population is called sample

Here the data would be a population of weight because they represent all of the football players .

This is not a subset. So the question of sample will not come into existance here

So the first option is the correct option

The above data would be a population of weights because they represent all of the football players.

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Complete Question

The statistical data has been given below

Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year. 176; 202; 212; 212; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230; 250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265

Answer:

  The ratio (center to focus)/(semi-major axis) is the greatest

Step-by-step explanation:

Given various foci coordinates and major axis lengths, you are asked to identify the ellipse with the highest eccentricity.

The eccentricity of an ellipse can be defined as the ratio of distance between foci to the length of the major axis. A high value of eccentricity corresponds to a longer, narrower ellipse.

The attached graph plots the locations of the given foci. They are color coded to correspond with the color of the resulting ellipse. (We have used the given r-value as the semi-major axis, not the major axis.)

The blue focal points (A, A') of the blue ellipse give the "flattest" of the bunch, so corresponds to the highest eccentricity. Its parameters are those of the first answer choice.

If we assume the given r-value is the semi-major axis, the eccentricity represented by each of the answer choices is ...

The numerator in each case is the distance from the center (0, 0) to one focus.

The solution of the given differential equation u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2 be,

u''x^6 u'x^5

Given, a differential equation

u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2

we have to find the solution of the given differential equation

on integrating both the sides, we get

u''x^6 u'x^5

So, we get u''x^6 u'x^5 as a solution of the given differential equation on solving by the reduction method.

Hence, the solution of the given differential equation u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2 be,

u''x^6 u'x^5

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