The arithmetic sequence 2, 4, 6, 8, 10, . . . represents the set of even natural numbers. What is the 100th even natural number? a100 =

Answers

Answer 1

You can use this rule to find any even natural number. Multiply the position of the number by 2 to find the number. In this example, you would take 100 times 2 to get 200. I used the given pattern to figure this out. 2 x 2 = 4, 2 x 3 = 6, 2 x 4 = 8, 2 x 5 = 10, etc....

Answer 2

Answer: The 100th even natural number is 200.

Step-by-step explanation: Given that the following arithmetic sequence represents the set of natural numbers :

2, 4, 6, 8, 10, . . ..

We are given to find the 100th even natural number, i.e., the 100-th term of the sequence.

We know that

the n-th term of an arithmetic sequence with first term a and common difference d is given by

[tex]a_n=a+(n-1)d.[/tex]

For the given sequence, we have

a = 2 and d = 4 - 2 = 6 - 4 = . . . =2.

Therefore, the 100-th term of the sequence will be

[tex]a_{100}=a+(100-1)d=2+99\times2=2+198=200.[/tex]

Thus, the 100th even natural number is 200.

Related Questions

Can someone answer B please???

Answers

a)

150 were surveyed, possible outcomes, and 132 said they prefer dogs, favorable outcomes, 132/150 or 22/25 or 0.88, now 0.88 * 100 is just 88, namely 88% is the probability.

b)

since we know is 88%, what is 88% of 100? (88/100) * 100, 0.88 * 100, or just 88 students.

c)

18/150 or 3/25 or 0.12 namely 12%,

what's 12% of 300? (12/100) * 300, or 0.12 * 300, so just 36 students.

What is the circumference of circle p? Express your answer in terms of pi , ab = 14

Answers

C=2πr hope this helps have a great day

Answer:

14 pi in.

Step-by-step explanation:

hop this helps!

Let x be a random variable that takes integer values and is symmetric, that is, p(x = k) = p(x = âk) for all integers k. what is the expected value of y = cos(xÏ) and y = sin(xÏ)?

Answers

Without knowing how [tex]X[/tex] is distributed, or what its PMF happens to be, we can't completely answer the question. However, recall that

[tex]\cos(-kx)=\cos kx[/tex]
[tex]\sin(-kx)=-\sin kx[/tex]

If [tex]Y=\cos(\pi X)[/tex], then

[tex]\mathbb E[Y]=\displaystyle\sum_{k\in\mathbb Z}\cos(k\pi)\,\mathbb P(X=k)[/tex]

By the symmetry of [tex]X[/tex],

[tex]\mathbb E[Y]=\mathbb P(X=0)+2\displaystyle\sum_{k\ge1}\cos(k\pi)\,\mathbb P(X=k)[/tex]

Splitting on the even and odd [tex]k[/tex], and using the fact that [tex]\cos(k\pi)=(-1)^k[/tex] for [tex]k\in\mathbb Z[/tex], we can write this as

[tex]\mathbb E[Y]=\mathbb P(X=0)+2\displaystyle\sum_{\ell\ge1}\bigg(\mathbb P(X=2\ell)-\mathbb P(X=2\ell-1)\bigg)[/tex]

but without knowing how [tex]X[/tex] is distributed, we can't go any further as far as I'm aware.

For [tex]Y=\sin(\pi X)[/tex], we would have

[tex]\mathbb E[Y]=\mathbb E[\sin(\pi X)]=\displaystyle\sum_{k\in\mathbb Z}\sin(k\pi)\,\mathbb P(X=k)[/tex]

but [tex]\sin(k\pi)=0[/tex] for all integers [tex]k[/tex]. Thus [tex]\mathbb E[\sin(X\pi)]=0[/tex].

Final answer:

The expected value of y = cos(xÏ) is 0 and the expected value of y = sin(xÏ) is also 0, due to the symmetry of the random variable x.

Explanation:

The expected value (mean) of y = cos(x Ï) is 0.

The expected value (mean) of y = sin(x Ï) is also 0.

Since the random variable x is symmetric, the probability of both positive and negative values cancel out, resulting in an expected value of 0 for both cosine and sine functions.

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Hayden is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complete the project in 8 hours. Kaitlyn can complete the project in 6 hours. Hayden wants to know how long it will take them to complete the project together.

Write an equation and solve for the time it takes Cody and Kaitlyn to complete the project together. Explain each step.

Answers

Answer: 3.4 h

Explanation:

1) The basis to solve this kind of problems is that the speed of working together is equal to the sum of the individual speeds.

This is: speed of doing the project together = speed of Cody working alone + speed of Kaitlyin working alone.

2) Speed of Cody

Cody can complete the project in 8 hours => 1 project / 8 h

3) Speed of Kaitlyn

Kaitlyn can complete the project in 6 houres => 1 project / 6 h

4) Speed working together:

1 / 8 + 1 / 6 = [6 + 8] / (6*8 = 14 / 48 = 7 / 24

7/24 is the velocity or working together meaning that they can complete 7 projects in 24 hours.

Then, the time to complete the entire project is the inverse: 24 hours / 7 projects ≈ 3.4 hours / project.Meaning 3.4 hours to complete the project.

Denote all work that should be done as 1. Then if Cody can complete the project in 8 hours, he can do [tex] \frac{1}{8} [/tex] per hour and if Kaitlyn can complete the project in 6 hours, then she can do [tex] \frac{1}{6} [/tex] per hour. Together they complete [tex] \frac{1}{8}+\frac{1}{6} [/tex] per hour.

Simplify this expression:

[tex] \dfrac{1}{8} +\dfrac{1}{6} =\dfrac{3}{24} +\dfrac{4}{24}=\dfrac{7}{24} [/tex].

Then it will take them to complete the project together [tex] \dfrac{1}{\frac{7}{24}} =\dfrac{24}{7} =3\dfrac{3}{7} [/tex] hours

Answer: It will take them to complete the project together [tex] 3\dfrac{3}{7} [/tex] hours.

What is the approximate volume of the cylinder with a height of 5 and a diameter of 4? round to the nearest tenths place

Answers

Formula for volume of cylinder:
V=πr²h
Here height, h= 5 units
Diameter, d= 4 units
So, radius, r= d/2 = 4/2 =2 units
Put values in formula.
V= (3.14)(2)²(5)
V=62.8 Cubic units

Answer: 62.8 cubic units

Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 14 that height. Which of these statements is NOT true?

Answers

the correct question is
Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 1/4 that height. Which of these statements is NOT true?

the statements in the attached figure

we know that
r=2 cm
h1=8 cm
h2=(1/4)*8=2 cm
[Volume of cone 1]=(π*r²*h)/3--------> (π*2²*8)/3= 33.49 cm³
[Volume of cone 2]=(π*r²*h)/3--------> (π*2²*2)/3---------> 8π/3= 8.37 cm³

Statements A)
The volume of the smaller cone is (1/4)(1/3π • 2 • 2 • 8) cm3---------> is true

Statements B)
The volume of the smaller cone is (1/3)(4π • 2) cm3.-----------> is true

Statements C)
The volume of the smaller cone is (8/3)π cm3. -----------> is true

Statements D)
The volume of the smaller cone cannot be determined because its height is unknown-----------> is not true

the answer is the Statements D)
The volume of the smaller cone cannot be determined because its height is unknown-----------> is not true

Let u = <-6, 1>, v = <-5, 2>. Find -4u + 2v.

A) <34, -8>
B) <14, 0>
C) <14, 3>
D) <44, -12>

Answers

-4u +2v

= -4<-6, 1> +2<-5, 2>

= <(-4)(-6)+2(-5), (-4)(1) +2(2)>

= <14, 0>

The appropriate choice is ...

... B) <14, 0>

To find the result of -4u + 2v, calculate -4u and 2v separately, then add the results together to get <-34, 0>.

To find -4u + 2v, we first need to calculate -4u and 2v separately and then add them together.

Calculate -4u = -4 * <-6, 1> = <-24, -4>Calculate 2v = 2 * <-5, 2> = <-10, 4>Add -4u and 2v: <-24, -4> + <-10, 4> = <-34, 0>

Therefore, the answer is: -34, 0.

Martha is standing on a street corner in a big city, facing south. She walks 5 blocks to the south. Then, she turns right and walks 3 blocks. Then, she turns right as walks 2 blocks. Then, she turns right again and walks 1 block. Finally, she turns left and walks 5 blocks. What direction is she facing when she is done?

Answers

In the north direction, Martha facing if the Martha is standing on a street corner in a big city, facing south.

What is direction?

The four cardinal directions, sometimes known as cardinal points, are the four principal compass directions: north, east, south, and west, which are frequently abbreviated as N, E, S, and W.

We have:

Martha is standing on a street corner in a big city, facing south. She walks 5 blocks to the south.

Then, she turns right and walks 3 blocks. Then, she turns right as walks 2 blocks. Then, she turns right again and walks 1 block.

If we draw a line diagram, we will see:

She will be facing at North.

Thus, in the north direction Martha facing if the Martha is standing on a street corner in a big city, facing south.

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Find the difference (7a-6b+7) - (8a-2)

Answers

Hey there!

Let's set up our expression:

(7a-6b+7)-(8a-2)

In order to simplify, we can use that subtraction sign and distribute it, using the distributive property. We have:

7a-6b+7-8a+2

Notice how it's plus two, because a negative times a negative two is a positive two. Now, it's a matter of finding the like terms and adding or subtracting them. These like terms can either have no variable, or have different coefficients but the same variable. That means our like terms are the 7a and -8a, and the 7 and 2. There's no like term for the 6b. That means we have:

(7a-8a) - 6b + (7+2) =

-a - 6b + 9

Hope this helps!

what is the factor of x^2-11xy-60y?

Answers

ASSUMING [tex]x^2-11xy-60y^2[/tex] is the expression to be factored.
where
a=1
b=-11
c=-60

We look for m, n such that m+n=b=-11, mn=c=-60.
It is possible to find m, n mentally, or compile a table as follows:
-1*60=-60, -1+60=59 > -11
-2*30=-60, -2+30=28 > -11
-3*20=-60, -3+20=17 > -11
-4*15=-60, -4+15=11 > -11
But 4*(-15)=-60, and 4-15=-11, exactly what we want!
So
[tex]x^2-11xy-60y^2=(x+4)(x-15)[/tex]

kenny wants to buy gifts for all 18 of his co workers. He can buy t shirts for $10 and hats for $12. He plans on spending $200 for all 18 gifts. If Kenny wants to spend all of his money, how many of each type of gift can he buy?

Answers

10 hats, 8 t shirts = 18
10X12=120 8X10=80 12+80=200

Find the solution of the differential equation that satisfies the given initial condition. du/dt = (2t+sec^2t)/2u, u(0) = -3

Answers

Consider, pls, this option (see the attachment) of 3 steps.

I need help I would really thank wheeler answers this for me

Answers

When a number is negative, the higher the value, the smaller the number.
When a number is positive, it is greater than a negative number.

a. -4.84 > -8.48

b. 7 > -7

c. -6.5 < -5 1/2

d. -1 < 0

> is greater than
< is less than

a.
-4.84 > -8.48

b.
7 > -7

c.
-6.5 < -5 1/2

d.
-1 < 0

A fraction that is equal to 3/5 that has the denominator 10.

Answers

Take 3/5 and multiply by 2 to then get 6/10

6 is the numerator... Hope this helped!

Find the number of positive integers not exceeding 1000 that are either the square or the cube of an integer

Answers

There are 10 perfect cubes between 1 and 1000 (namely cubes of 1-10)
There are 31 perfect squares between 1 and 1000 (squares from 1-31)
Out of these, 3 perfect squares are also perfect cubes,
{1^2=1^3, 8^2=4^3, 27^2=9^3}.

By the law of inclusion/exclusion, the number of positive integers not exceeding 1000 that are either the square or the cube of an integer
=10+31-3
=38

We want to find the number of positive integers not exceeding 1000 that are either the square or the cube of an integer.

We will get that there are 38 of these.

First, the squares:

To get the number of square numbers not exceeding 1000, we need to find the largest integer that when squared is equal or smaller than 1000.

This is given by:

√1000 = 31.6

Then the largest square number smaller than 1000 is given by:

31^2 = 961

From this, we can conclude that there are 31 integers not exceeding 100 that are the square of an integer.

For the cubes we do the same thing:

∛1000 = 10

The largest cube number that meets the condition is:

10^3 = 1000

Then there are 10 cube numbers that meet the condition.

Now we need to find the common numbers in bot groups (this is, numbers that are a cube and a square of two integers and that are smaller than 1000).

The numbers that meet this condition are:

1^2 = 1

1^3 = 1

64)

4^3 = 64

8^2 = 64

81)

9^3 = 279

27^2 = 729

These 3 numbers are in both groups, so we are counting them twice, thus we need to subtract 3 to the final result, in order to avoid counting the same number two times.

Then the total number of positive integers not exceeding 1000 that are either the square or the cube of an integer is:

31 + 10 - 3 = 38

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Rewrite as a simplified fraction
2.267 = ?

Answers

The decimal 2.267 is equivalent to the simplified fraction 2267/1000.

To express the decimal 2.267 as a simplified fraction, we can consider the place values of each digit. The decimal portion .267 can be written as the fraction 267/1000 since there are three decimal places. Combining this with the whole number 2, we get:

2.267 = 2 + 267/1000.

To simplify this mixed number, we first find a common denominator, which is 1000. We convert the whole number 2 to an equivalent fraction with this denominator: 2 = 2000/1000. Now, we can add the fractions:

2 + 267/1000 = 2000/1000 + 267/1000 = 2267/1000.

This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1, yielding the simplified fraction:

2267/1000.

In summary, 2.267 can be expressed as the simplified fraction 2267/1000.

The question probable may be:

Write the following 2.267 in simplified fraction.

Emily measures 3 pieces of string. The first piece measures 642 cm. The second piece measures 124 cm, and the third piece is 134 cm. How many meters of string does she have altogether? (hint: 1 meter equals 100 centimeters)

Answers

9 meters. 642 + 124 + 134 = 900, there are 100 centimeters in a meter, so 900 / 100 = 9.

Answers

Melinda has a map of her city the map uses a scale of 1 inch equals 8 miles when does house is 1 1/2 inches from the library on the map how far apart with her house in the library be on the map if the scale is 1 inch equals 6 miles

So, the house is 12 miles away from the library because 1 1/2*8 is 12. Now, Just divide 12 by the new rate, 6, to get 2. Your answer is 2 boxes away.

Hope this helped!

Determine the equations of the vertical and horizontal asymptotes, if any, for g(x)=x^3/(x-2)(x+1)

a. x=2,x-1
b. x=-2,y=-1
c. x=-2,x=-1
d. x=2,y=-1

Answers

For this case what we should see are the values for which the function is not defined.
So we have to study your domain:
g (x) = x ^ 3 / (x-2) (x + 1)
We see what values make the denominator is not defined:
(x-2) (x + 1) = 0
First value:
x-2 = 0
x = 2
Second value:
x + 1 = 0
x = -1
The function has two vertical asymptotes:
x = 2
x = -1
Answer:
a. x = 2, x-1

If one of the 99 test subjects is randomly selected, what is the probability of getting a subject who is pregnant?

Answers

Final answer:

To calculate the probability of selecting a pregnant subject from the 99 test subjects, the exact number of pregnant subjects in the group is needed. Without this data, the probability cannot be determined.

Explanation:

To ascertain the probability of randomly selecting a pregnant subject from a group of 99 test subjects, additional information is required regarding how many subjects are actually pregnant within the group. Without this information, we cannot compute an exact probability.

However, if we had data—let's say 15 out of the 99 subjects are pregnant—the probability would then be calculated using the formula for probability, which is the number of favorable outcomes divided by the total number of possible outcomes. In this scenario, the probability would then be 15/99.

Final answer:

Without specific information on the number of pregnant subjects among the 99 test subjects, it's impossible to compute the exact probability of randomly selecting a pregnant subject.

Explanation:

To answer the question about the probability of randomly selecting a pregnant subject from the 99 test subjects, we would need to know the number of pregnant subjects within the group. Without that information, we cannot calculate the exact probability. However, if we had that information, the probability (P) of selecting a pregnant subject would be calculated as P = (Number of Pregnant Subjects) / (Total Number of Subjects), which in this case is 99.

This is an example of a probability question that falls under the broader subject of mathematics, specifically within the topic of probability and statistics commonly covered at the high school level.

Francisca purchased 425 shares of Kellogg Company stock at $14.15 apiece. She earns $374.00 in dividends every year. What is the yield on Francisca's Kellogg Company stock?

Answers

Her yield on cost is 6.22%.

This is found by dividing the dividend per share by the cost per share. Since she earned $374 on 425 shares, her dividend per share is 374/425=$0.88. Divide this by the cost per share:

0.88/14.15= 0.06219 ≈ 6.22%.

if possible find the area of the triangle defined by the following: a=32, b=24, y=75°

Answers

If y=75 degrees is the angle between sides a and b, then yes, it is possible to calculate the area of the triangle.

To answer further, we use the sine function to do the calculation.
The area is given by
Area = absin(y)/2 = 32*24*sin(75)/2 = 370.92 to two decimal places.

Austin purchase 2/3 of a pound of yum yum treats. If yum yum treats are $6.00 per pound how much does Austin pay

Answers

1. The information given in the problem above, is:

- Austin purchases 2/3 of a pound of yum yum treats.
- Yum yum treats are $6.00 per pound (1 pound=$6.00).

2. Keeping this on mind you have: If 1 pound of yum yum treats is $6.00, how much is 2/3 of a pound?

1 pound------------$6.00
2/3 of a pound----x

x=(2/3)(6.00)/1
x=(2/3)(6.00)
x=12/3
x=$4.00

Therefore: How much does Austin pay?

The answer is: Austin pays $4.00.

A hiker maintains an average speed of 3 3 /4 km/h. How many kilometers will the hiker walk in 3/5 h

Answers

Answer:

2 1/4

Step-by-step explanation:

3 3/4 times 3/5= 15/4 times 3/5=45/20=9/4=2 1/4

I did this because speed times time equals distance and we are finding distance

HOPE THIS HELPS!!!!! :)

The distance walked in 3/5 hours is 2(1/4) km.

What is speed?

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Average speed = 3(3/4) km per hour

This can be written as,

3(3/4) km = 1 hour

15/4 km = 1 hour

Multiply 3/5 on both sides.

3/5 x 15/4 km = 3/5 hours

9/4 km = 3/5 hours

2(1/4) km = 3/5 hours

Thus,

2(1/4) km is walk in 3/5 hours.

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Please help me with question 4

Answers

Answer:

A. XV

Step-by-step explanation:

The letters identifying the shortest side of ΔMNP are the last (P) and first (M) of the designator for that triangle. The corresponding side of ΔVWX will be identified by the last (X) and first (V) letters of that triangle's name. Hence the segment of interest is XV.

x y
0 -3
2 5
3 9
4 13

Which equation matches the table?
A) y = x - 3
B) y = x + 3
C) y = 4x - 3
D) y = 4x + 3

Answers

Let's prove each one:
A) y=x-3
x=0→y=0-3→y=-3=-3 ok
x=2→y=2-3→y=-1 different to 5 No

B) y=x+3
x=0→y=0+3→y=3 different to -3 No

C) y=4x-3
x=0→y=4(0)-3=0-3→y=-3=-3 ok
x=2→y=4(2)-3=8-3→y=5=5 ok
x=3→y=4(3)-3=12-3→y=9=9 ok
x=4→y=4(4)-3=16-3→y=13=13 ok

D) y=4x+3
x=0→y=4(0)+3=0+3→y=3 different to -3 No

Answer: Option C) y=4x-3

Which system of inequalities is represented by the graph?

y ≤ –x
y > –1

y ≥ –x
y < –1

y < –x
y ≥ –1

y > –x
y ≤ –1

Answers

Answer:

[tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex] are system of inequalities is represented by the graph.

Step-by-step explanation:

We are given four option and need to choose correct inequality for given graph.

In graph, we can see two line

Red line: It is horizontal solid line passing through (0,-1) and shaded region above the line.

Equation of line: y≥-1

Blue line: It is slant dotted line passing through origin and (-2,1)

Equation of line: [tex]y<-\frac{1}{2}x[/tex]

System of inequalities represented by the graph.

[tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex]

Thus, [tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex] are system of inequalities is represented by the graph.

What do you notice about the frequency of the sine function: y=sin(x) and the frequency of the cosine function: y=cos(x) ?]
a. they have the same value
c. the value is the same as the amplitude
b. they have a zero value
d. there is no frequency value for the cosine function

Answers

Answer:

they have always the same

Step-by-step explanation:

Therefore, after plotting the points on the graph

What is the trigonometry?

Trigonometry states that the trigon means 'triangle', and the metry means 'metron' is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Here given angles are:-

[tex]y=sin(x)[/tex] and [tex]y=cos(x)[/tex]

Draw the graph

Hence, after plotting the points on the graph is:-

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A carpenter builds a rectangular bookcase that is 37 inches long and 60 inches tall. the carpenter uses two braces along the diagonals to support the bookcase. what is the length of the one of the braces, to the nearest tenth of a inch?

Answers

The diagonal of the rectangle can be calculated by using the Pythagorean Theorem , because the diagonal and the two sides , length and width, of the rectangle , makes a right triangle .

Now we have the measure of length and width and we have to find the measure of diagonal

So according to the Pythagorean theorem

[tex] d^2 = a^2 +b^2 [/tex]

where , d is the diagonal , a is the length and b is the width

lets plug the values

[tex] d^2 = 37^2 +60^2 [/tex]

[tex] d^2 = 1369+3600 [/tex]

[tex] d^2 = 4969 [/tex]

Taking square root on both sides

d=70.49 Inches

d=70.5 inches

hence the length of one of the braces is 70.5 inches

Quadrilateral ABCD is inscribed in this circle.

What is the measure of ∠A ?

Enter your answer in the box.

Answers

Since angle A and angle C are across from each other, they add to 180 degrees.
Given that angle C is 43 degrees
180 = 43 + A
subtract 43 from both sides
137 = A

Hope this helps!

Applying the inscribed quadrilateral conjecture, the measure of m∠A = 137°.

What is the Inscribed Quadrilateral Conjecture?

The inscribed quadrilateral conjecture states that the opposite angles in any inscribed quadrilateral in a circle measures up to 180 degrees.

Thus:

43° + m∠A = 180°

m∠A = 180 - 43

m∠A = 137°

Thus, applying the inscribed quadrilateral conjecture, the measure of m∠A = 137°.

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