The arithmetic sequence 2, 4, 6, 8, 10,. . . Represents the set of even natural numbers. What is the 100th even natural number? a100 = What is the sum of the first 100 even natural numbers? S100 = Complete the sentence below with less than, greater than, or equal to. The sum of the first 100 even natural numbers is the sum of the first 101 odd natural numbers.

We can write the integral of f(x) as the sum of the integral of the even component, e(x), and the integral of the odd component, o(x). This gives us the following equation:  ∫f(x)dx = ∫e(x)dx + ∫o(x)dx

Integrals can be written as the sum of the integral of an odd function and the integral of an even function. This is because any function can be broken down into its even and odd components. Even functions are those that remain unchanged when reflected over the x-axis. This means that the result of evaluating the function for any x-value is the same as the result for its negative. Odd functions are those that change sign when reflected over the x-axis. This means that the result of evaluating the function for any x-value is the negative of the result for its negative.

The integral of an even function is the same regardless of whether it is written as the sum of the integral of an odd function and the integral of an even function, or if it is written just as an integral of the even function. The integral of an odd function is the negative of the integral of the even function when written as the sum of the two integrals.

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The bonus question asks for the application of the integral test to determine the convergence of the series given by 2n*e^(-a).

The integral test is a method used to determine the convergence or divergence of a series by comparing it to the integral of a related function. In this case, we are given the series 2n*e^(-a), and we can use the integral test because the terms of the series involve the variable 'n', and the function e^(-a) can be integrated.

To apply the integral test, we consider the integral of the function corresponding to the series. In this case, we integrate the function f(x) = 2x*e^(-a) from 1 to infinity. If this integral converges, then the series is also convergent. Conversely, if the integral diverges, then the series is divergent.

By evaluating the integral of f(x) and analyzing its convergence or divergence, we can determine whether the given series 2n*e^(-a) converges or diverges. Showing all the steps in evaluating the integral and discussing the convergence properties of the resulting integral will be necessary to receive full credit for this question.

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Answer:

x = number of bicycles = 35

y = number of cars = 55

Step-by-step explanation:

Let

x = number of bicycles

y = number of cars

x + y = 80 (1)

2x + 4y = 270 (2)

From (1)

x = 80 - y

Substitute x = 80 - y into (2)

2x + 4y = 270 (2)

2(80 - y) + 4y = 270

160 - 2y + 4y = 270

- 2y + 4y = 270 - 160

2y = 110

y = 110/2

y = 55

Substitute y = 55 into (1)

x + y = 80 (1)

x + 55 = 80

x = 80 - 55

x = 35

x = number of bicycles = 35

y = number of cars = 55

Step-by-step explanation:

In the figure below, determine the perimeter of AEFG.

26

26

DG

2x + 15

39 units

55 units

66 units

o

82 units

The minimum sample size needed for 95% confidence that the sample variance is within 5% of the population variance is given by n = (1.96² * σ²) / (0.05²).

The minimum sample size needed to be 95% confident that the sample variance is within 5% of the population variance can be calculated using the formula:

n = (Z² * σ²) / (E²)

where:

n is the minimum sample size,

Z is the z-score corresponding to the desired confidence level (in this case, 95% confidence corresponds to a z-score of approximately 1.96),

σ² is the population variance, and

E is the maximum allowable difference between the sample variance and the population variance (expressed as a proportion of the population variance).

The formula ensures that the desired confidence level is achieved while limiting the difference between the sample and population variances within the specified threshold.

In summary, to determine the minimum sample size needed to be 95% confident that the sample variance is within 5% of the population variance, you can use the formula n = (1.96² * σ²) / (0.05²), where σ² represents the population variance.

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Answer:

Step-by-step explanation:

Answer:

e (2,-1)

f (4,-1)

g (5,-4)

h (1,-4)

Answer:

it is 36.75

Step-by-step explanation:

Answer:4 length and 3 width

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf 22670.80 \ cm^3}\)

Step-by-step explanation:

Height = h = 20 cm

Diameter = d = 38 cm

Radius = d / 2 = 38 / 2 = 19 cm

Volume of cylinder:

\(= \pi r^2 h\\\\= (3.14)(19)^2(20)\\\\= (3.14)(361)(20)\\\\= 22670.80 \ cm^3\\\\\rule[225]{225}{2}\)

Solution:

Given:

First, let's find the radius of the cylinder as the radius of the cylinder is included in the formula.

\(\text{Diameter = 2(Radius)}\)

\(\text{Radius} = \dfrac{\text{Diameter}}{2}\)

\(\text{Radius} = \dfrac{38}{2}\)

\(\text{Radius} = 19 \ \text{cm}\)

Recall that the volume of a cylinder is πr²h. Now, let's use the formula to find the volume of the cylinder.

\(\pi r^{2} h = \text{Volume of cylinder}\)

\((\pi)( r^{2})( h) = \text{Volume of cylinder}\)

\((3.14)( 19^{2})( 20) = \text{Volume of cylinder}\)

\(\boxed{22670.8 \ \text{cm}^{3} = \text{Volume of cylinder}}\)

The right side of an ordered pair is y.

What is meaning of solution of a linear equation?

A specific point on the graph represents the solution of a linear equation in two variables, ax + by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.

The coordinates of one point in the coordinate system are included in an ordered pair. An ordered pair of the form of a point's name is (x, y). The x-coordinate is represented by the first integer, and the y-coordinate by the second.

The first element of the ordered pair (x,y) is x which lies on the left side of the ordered pair.

The second element of the ordered pair (x,y) is y which lies on the right side of the ordered pair.

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Louis total distance of 8/5 km. Louis rose his bicycle a total distance of 8/5 km.

Louis rose his bicycle a total distance of 1/2 km + 3/4 km + 7/10 km.

To find the total distance, we need to find a common denominator for the fractions: 2, 4, and 10.

The least common denominator is 20.

So, 1/2 km can be written as 10/20 km, 3/4 km can be written as 15/20 km, and 7/10 km remains the same.

Adding these fractions together, we have:

10/20 km + 15/20 km + 7/10 km = 32/20 km

Simplifying this fraction, we get:

32/20 km = 8/5 km

Therefore, Louis rose a total distance of 8/5 km.

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Louis rode a total distance of 8/5 km or 1 and 3/5 km

Louis rode his bicycle a total of 1/2 km to school, 3/4 km to a ball field, and 7/10 km back home. To find the total distance Louis traveled, we need to add up these three distances.

First, let's add 1/2 km and 3/4 km. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 2 and 4 is 4.

Converting 1/2 to have a denominator of 4, we get 2/4. Now we can add 2/4 + 3/4, which equals 5/4.

Next, we need to add 5/4 km and 7/10 km. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 4 and 10 is 20.

Converting 5/4 to have a denominator of 20, we get 25/20. Now we can add 25/20 + 7/10, which equals 32/20.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 32/4 and 20/4, we get 8/5.

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The author most clearly convey the sense that Dev is being playful as;

By including stage direction that indicates Dev's body language.

Gymnasium and word variations are terms in various European languages for secondary school that prepares for higher education at university.

The word "gymnasium" is a contraction of the gymnasium originally Latin for gymnastics school and comes from the Greek public place where gymnastics is practiced.

It is comparable to the US-British Term Prep High School. A good physical education class offers a variety of activities that improve coordination such as Throwing or catching a ball, swinging a bat, or aiming a bow and arrow.

In this game Shorts or sweatpants are the preferred attire for gyms, but in ancient Greece, it was common for men to exercise.

Also Flexibility is demonstrated in gymnastics such as splits jumps backbends and walkovers.

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Answer:

114

Step-by-step explanation:

Angle made at the center with same arc is always equal to the measure of the arc. so m_ FGH is 114

A posted speed limit of 55 mph means that: You may drive 55 mph only under favorable conditions.

Speed limits on road traffic, as used basically to set the legal maximum speed at which vehicles are permitted to utilize on a given stretch of road.

Now generally, speed limits are normally indicated on traffic signs reflecting the maximum allowable speed in kilometers per hour (km/h) or eevn miles per hour (mph). They are primarily set by the legislative bodies of national or provincial governments and then enforced by law enforcement agencies. This suggests that speed limits varies from road to road and is even absent in some certain areas.

Now, in this question we are told that the posted speed limit is 55 mph. Thus, from our definitions of speed limits above it is clear that A posted speed limit of 55 mph means that: You may drive 55 mph only under favorable conditions.

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The volume of the cuboid is 162 cubic centimeter.

Given that, a cuboid of side 3 cm.

We know that, the volume of a cube = a³.

So, volume of the cube is 3³=27 cubic centimeter

a) We know that, the volume of a cuboid = Length × Breadth × Height

Cuboid made with 6 of these cubes.

So, Length = 18 cm, Breadth = 3 cm and Height = 3 cm

Here, volume of cuboid = 18×3×3

= 162 cubic centimeter

b) Dimensions of cuboid of the base in the given figure are length = 12 cm, breadth = 3 cm and height = 3 cm

Surface area = 2(lb+bh+hl)

= 2(12×3+3×3+3×12)

= 2×81

= 192 square centimeter

Dimensions of cuboid of the top in the given figure are length = 9 cm, breadth = 3 cm and height = 3 cm

Surface area = 2(lb+bh+hl)

= 2(9×3+3×3+3×9)

= 2×63

= 126 square centimeter

Total surface area = 192+126

= 318 square centimeter

Therefore, the volume of the cuboid is 162 cubic centimeter.

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Answer:

C

Step-by-step explanation:

Add like terms to get

4.5a + 4b + 3.5c

Answer:

x=2

Step-by-step explanation:

2-6x=-10

-2     -2

____________-

-6x=-12

÷-6    ÷-6

______________

x=2

Hope this helps :D

Step-by-step explanation:

-4x=-10

divide both sides by -4

therefore the answer is 2.5

False. very few tools are available to assist system analysts and end users in analyzing data.

There are many tools available to assist system analysts and end users in analyzing data. Some commonly used tools include spreadsheets (such as Microsoft Excel), data visualization software (such as Tableau or Power BI), statistical analysis software (such as R or SPSS), and business intelligence software (such as SAP or Oracle).

These tools allow analysts and end users to process, manipulate, and visualize large volumes of data, as well as to perform complex statistical analyses and modeling. Additionally, with the advent of big data technologies, such as Hadoop and Spark, analysts and end users can now analyze vast amounts of data in real-time, using distributed computing systems.

In summary, there are many tools available to assist system analysts and end users in analyzing data, and these tools continue to evolve and improve over time.

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Answer:

$214.

Step-by-step explanation:

30 hrs x 5 = 150.

Any hours above 30 = $8

8x8=64.

150+64=214

Answer:$214

Step-by-step explanation: To get 214 dollars we first find how much money Josi makes before exceeding 30 hrs which is 30 x 5 = $150

Then 38-30= 8hr extra so, if $8 per extra hour means 8 x 8 = $64 over time

Finally 150 + 64 =$214

Answer:

10x

Step-by-step explanation:

Answer: The slop is -2 and the y-intercept is (0,4/5)

Step-by-step explanation:

Here is the graph, I hope this helps, have a great school day! :D

Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

The average rate of change of f(x) over the interval [-4, -1], with coordinates, (-4, -3) and (-1, 3) is 2

The average rate of change of a function over an interval is found from the change in the output values of the function over the period indicated, divided by the change in the input values of the function over the specified interval.

Average rate of change = \(\dfrac{\Delta y}{\Delta x}\)

The interval over which the average rate of change of the function is required = [-4, -1]

The formula for the average rate of change over the interval, [-4, -1], can be presented as follows;

Average rate of change = \(\dfrac{\Delta y}{\Delta x}\)  =  \(\dfrac{f(-1) - f(-4)}{\left(-1 - (-4)\right)}\)

The coordinates of the points of the graph of the function in the indicated range are; (-1, 3), and (-4, -3)

f(-1) = 3, f(-4) = -3, therefore;

Average rate of change = \(\dfrac{3 - (-3)}{-1 - (-4)}\) = 2

The average rate of the function over the specified interval is 2

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Answer:

C

Step-by-step explanation:

The base number is 2, and it's being multiplied 7 times, so 7 is the exponent

Hope this helps!

If \(MU_{x}/P_{x}\)=30 and \(MU_{y} /P_{y}\)=40 then the consumer should buy the commodity y to maximise utility.

Given that \(MU_{x}/P_{x}\)=30 and \(MU_{y} /P_{y}\)=40 of commodities x and y.

Marginal utility is the additional utility that a consumer gets from consuming additional units of commodity. For maximising the utility of the consumer,the ratio of marginal utilities must be equal to the ratio of the products.

There can be two situations in our case:

Because \(MU_{x}/P_{x}\)<\(MU_{y} /P_{y}\)

So to equalise the ratio we need to reduce \(MU_{y} /P_{y}\). To reduce the utility of y the consumer needs to increase the consumption of y because as the consumption of commodity y increase it decreases the utility of commodity y.

Hence if \(MU_{x}/P_{x}\)=30 and \(MU_{y} /P_{y}\)=40 then the consumer should buy the commodity y to maximise utility.

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Answer:

B

Step-by-step explanation:

Using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

\(a^{0}\) = 1

Given

\(9^{c}\) × \(9^{-c}\)

= \(9^{(c-c)}\)

= \(9^{0}\)

= 1 → B

Answer: 405 students

Step-by-step explanation:

From the question, Banneker Middle School has 750 students and we are told that Lynn surveys a random sample of 50 students and finds that 27 have pet dogs. The number of students at the school that are likely to have pet dogs goes thus:

Since out of 50 students surveyed, 27 have pet dogs, this means we multiply the fraction by 750. This can be mathematically written as:

= 27/50 × 750

= 27 × 15

= 405

This means 405 students are expecting to have pet dogs.

Converse: If a number is divisible by 4, then it is divisible by 2.

Inverse: If a number is not divisible by 2, then it is not divisible by 4.

Contrapositive: If a number is not divisible by 4, then it is not divisible by 2.

In the given figure, m∠2 and m∠7 are "Alternate Exterior Angles" and they are always congruent (equal).

So we can equate them and solve for x.

So, m∠2 is

According to the straight-line angle property, the sum of m∠1 and m∠2 must be equal to 180°

Therefore, the measure of m∠1 is 147°

Answer:

x = 4 or x = -4 is your answer