Can someone help me?

To determine whether the given series converges or diverges, we will use the Comparison Test.

The series we are analyzing is:

Σ(1/(n^2 + 1)^(1/2)) from n=1 to infinity.

First, we can observe that (n^2 + 1) > n^2 for all n, which means that:

1/(n^2 + 1) < 1/n^2 for all n.

Now, taking the square root of both sides:

(1/(n^2 + 1)^(1/2)) < (1/n^2)^(1/2) = 1/n.

We know that the series Σ(1/n) is a harmonic series and it diverges. Since the given series is smaller term-by-term than a divergent series, we can use the Comparison Test to conclude that the given series converges.

Your answer: The series Σ(1/(n^2+1)^(1/2)) from n=1 to infinity converges.

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Let the number be x

ATQ

\(\\ \sf\longmapsto 3x+2=18\)

\(\\ \sf\longmapsto 3x=18-2\)

\(\\ \sf\longmapsto 3x=16\)

\(\\ \sf\longmapsto x=\dfrac{16}{3}\)

\(\\ \sf\longmapsto x=5.3\)

\(\\ \sf\longmapsto x\approx 5\)

Answer:

0.68754935415

Diameter = Circumference

Pi

0.68754935415 = 2.16

Pi

Answer:

Step-by-step explanation:

The required sample size to ensure that the sample mean is within 0.014 of the population mean at a 99% confidence level is 76,166.

To determine the sample size, we use the range rule of thumb which estimates the standard deviation (σ) as one-sixth of the range (R). In this case, R is 6 - 0 = 6. Thus, σ = 1.5.

The formula for the required sample size (n) is given by:

n = (Z * σ / E)^2

Using a 99% confidence level, the corresponding Z-value is approximately 2.576.

Plugging in the values, we get:

n = (2.576 * 1.5 / 0.014)^2 ≈ 76,166

Therefore, the required sample size is 76,166, which is a fairly large number. This sample size is necessary to achieve a high level of precision and confidence in estimating the population mean.

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Answer:

Positive...

2+43

equals 45

Step-by-step explanation:

hope this helps

2 + 43 = 45

Positive is the answer.

The distance between the two towers is 30 meters, and the height of the second tower (Tower B) is 90 meters.

We have two towers. Let's call the first tower Tower A, and the second tower Tower B. The height of Tower A is given as 30 meters. The angle of elevation of the top of Tower A from the foot of Tower B is 60 degrees. The angle of elevation of the top of Tower B from the foot of Tower A is 30 degrees. Our goal is to find the distance between the two towers and the height of Tower B.

In triangle ABC, where A is the foot of Tower A, B is the top of Tower B, and C is the top of Tower A:

tan(30 degrees) = AB / BC

Since tan(30 degrees) = 1 / √3, we can rewrite the equation as:

1 / √3 = AB / BC

Cross-multiplying, we get:

BC = AB * √3

In triangle ABC:

tan(60 degrees) = AC / BC

Since tan(60 degrees) = √3, we can rewrite the equation as:

√3 = AC / BC

Substituting the value of BC from Step 3:

√3 = AC / (AB * √3)

Cross-multiplying, we get:

AC = AB * 3

We have two equations:

BC = AB * √3

AC = AB * 3

Dividing equation 2 by equation 1:

AC / BC = 3 / √3

Simplifying, we get:

√3 = 3 / √3

Cross-multiplying, we get:

3 = 3

Since 3 = 3 is a true statement, we can conclude that the two towers are at the same distance as their heights. Therefore, the distance between the two towers is 30 meters.

Using the value of the distance between the towers (30 meters), we can substitute this value into one of the previous equations to find the height of Tower B. Let's use equation 2:

AC = AB * 3

Substituting AB with the distance (30 meters):

AC = 30 * 3

Simplifying, we find:

AC = 90 meters

Therefore, the height of Tower B is 90 meters.

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Alex can paint 4.5 dollhouses with one can of paint.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

The total number of dollhouses paint by Alex in 2 cans = 9

To find number dollhouses paint by 1 cans, use ratio property,

2 cans = 9 dollhouses

1 can = 9/2 dollhouses

1 can = 4.5 dollhouses

4.5 dollhouses can be paint with each can of paint.

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The number of blueberries sold is B = 171 blueberries

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of blueberries sold be B

Now , the total number of muffins = 380 muffins

The total percentage of chocolate chunk = 15 % of the total

So , the number of muffins that were chocolate chunk = ( 15/100 ) x 380

The number of muffins that were chocolate chunk = 57 chocolate chunk

The number of muffins that were banana nut = ( 2/5 ) of the total

The number of muffins that were banana nut = 152 banana nuts

And , the remaining trees were blueberry

So , on simplifying the equation , we get

The number of blueberries = 380 - number of muffins that were banana nut - number of muffins that were chocolate chunk

The number of blueberries = 380 - 152 - 57

The number of blueberries = 171 blueberries

Hence , the number of blueberries is 171

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The given matrix is an elementary matrix that represents an elementary row operation of multiplying the second row by 4k. The determinant of this matrix is determinant of the original matrix, which is 4k.

Therefore, the determinant of the given elementary matrix is 4k.

To verify this result, we can also compute the determinant using the formula for a 3x3 matrix. The matrix obtained by applying the elementary row operation to the identity matrix is:

\(\left[\begin{array}{ccc}1&0&0\\0&4k&0\\0&0&1\end{array}\right]\)

The determinant of this matrix is calculated as: det(A) = 1 * (4k) * 1 - 0 * 0 * 0 - 0 * (4k) * 0 = 4k. So, the determinant of the given elementary matrix is indeed 4k, which matches our previous result.

In summary, the determinant of the elementary matrix is 4k, and this can be verified by calculating the determinant using the formula for a 3x3 matrix.

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Answer:

Determine the type of elasticity of demand

Answer:

121 mocha cupcakes

Step-by-step explanation:

\( \frac{45}{100} \times 220 = 99 \\ 99of \: the \: cupcakes \: were \: chocolate \\ mocha \: cupcakes = 220 - 99 \\ = 121\)

the value of the successive terms of the given series will be a₃ = 3, a₄ = -13, and a₅ = 7.

The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the sequence. The nth term of an arithmetic sequence is given by a  = a + (n – 1)d

Given, a sequence, such that

a₁ = -4

a₂ = 5

aₙ = -aₙ₋₁ - 2aₙ₋₂

To find a₃, we need to use the recursive formula:

a₃ = -a₂ - 2a₁

a₃  = -5 - 2(-4)

a₃ = 3

To find a₄, we need to use the recursive formula again:

a₄ = -a₃ - 2a₂

a₄ = -3 - 2(5)

a₄ = -13

To find a₅, we once again use the recursive formula:

a₅ = -a₄ - 2a₃

a₅ = 13 - 2(3)

a₅ = 7

Therefore, a₃ = 3, a₄ = -13, and a₅ = 7.

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Answer:

17.0 meters

Step-by-step explanation:

The diagonal of a square is calculated as sqrt(2) x a, where a is the side

= sqrt (2) x 12 = approx. 16.97 (round to 17.0)

Hope this helps :)

12cm2 or 24 because if u do b and h and subtract half u will 12

\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

Answer: 75

Step-by-step explanation:

In algebra, we do operations to both sides to work out what a letter is.

In this case, s-70=5, so we add 70 to both sides

5+70=75

Therefore, x=75

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The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.

Given that,

For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290

We have to find the data of IQR.

We know that,

IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.

IQR Formula is Q₃ - Q₁

So,

Q₃ = 290

Q₁ = 200

Then ,

IQR = Q₃ - Q₁

IQR = 290 - 200

IQR = 90

Therefore, The value of IQR is 90.

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The area of the given circle is 25π square meter.

Given that, the circumference of a circle is 10π m.

We know that, the formula to find the circumference of a circle is 2πr.

Here, the circumference of a circle = 2πr = 10π

r = 5 m

As we know, area of a circle is πr².

= π×5²

= 25π square meter.

Therefore, the area of the given circle is 25π square meter.

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Answer:

x=12

Step-by-step explanation:

Answer:

the answer its 12 hope this helps

By solving for the density of the two metal cubes, we can determine that the two metal cubes are not made from the same material.

Density, denoted by ρ, is a property of any substance that is defined as the ratio between the mass and volume of the substance.

ρ = m/v

where ρ = density

m = mass

v =  volume

Solving the density of each cube.

Cube 1 :

ρ = m/v

ρ = m/e^3

ρ = 43. 63 g/(3. 2 cm)^3

ρ = 1.3315 g/cm^3

Cube 2 :

ρ = m/v

ρ = m/e^3

ρ = 683. 5 g/(8. 34 cm)^3

ρ = 1.1783 g/cm^3

If two objects have the same density, then they are made from the same material. Since the density of the two cubes are not equal, then they are not made form the same material.

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Answer:

when X =2/3

Step-by-step explanation

y=2-9*2/3

2-6

-4

The unit rate of the table is 2. The table and the equation has the same unit rates.

According to the question,

We have the following information:

We have a table where the values of X and Y are given in two vertical columns.

Now, we know that unit rate means that for any question (including measurements of physical quantities) the denominator should be 1.

In this case, the unit rate of table can be found by taking any two rows.

Let's take the first two rows to find the unit rate of the table:

(6-4)/(3-2)

2/1

2

So, the unit rate of the table is 2.

The unit rate of the equation is y = 2x or y/x = 2.

Hence, the unit rate of the table and the equation is 2.

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Answer:

A. 140

Step-by-step explanation:

width times height times length

5·7·4=140

Answer:

Step-by-step explanation:

P=8/13≈0.62

Answer:

pencils=$4

pen=$1.5

Step-by-step explanation:

Step one:

given data

let pencils be x and pens be y

Mara bought 8 boxes of pencils and 3 packages of pens for $24

8x+3y=24------------1

Elaine bought 4 boxes of pencils and 6 packages of pens for $30

4x+6y=30------------2

solve 1 and 2 simulteneoulsy

8x+3y=24---------X1

4x+6y=30----------X2

subtract the answer bellow

8x+3y=24

8x+12y=60

0-9y=-36

divide both sides by- 9

y=36/9

y=$4

put y= 4 in 1

8x+3*4=24

8x+12=24

8x=24-12

8x=12

divide both side by 8

x= 12/8

x=3/2

x= $1.5

The equation of the perpendicular bisector of the line AB when A(1 ,0) and B is (-3 ,-4) is; y = -x-3

It follows from the task.comtent that the two lines share the midpoint of.tge line AB.

On this note, it follows that the point shared by the two lines is; (-1, -2)

The slope of the line AB is; 1 from evaluation.

On this note, the equation of the perpendicular bisector with slope -1 is;

-1 = (y - (-2))/(x -(-1))

-1 = y +2/x+1

y = -x-3

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Answer:

18, 20, 20, 22, 24, 26, 30

Step-by-step explanation:

We know that the largest number of the list is 30 and the smallest number is 12 less than that, which is 30 - 12 = 18.

This is our list so far: 18, __ , __ , __ , __ , __ , 30

The median of a set is the middle number of the set. In this case, since there are 7 terms in the set, the median, which the problem states is 22, must be the 4th number, since the 4th number is in the middle.

This is our list now: 18, __ , __ , 22, __ , __ , 30

Now, let's deal with the mode. The mode of a set is the term that shows up the most. Since the set is in ascending order and 20 < 22, we know that the two numbers in between 18 and 22 must be 20 and 20. This means that no term can show up more than once, with the exception of 20 because it is the mode.

This is our list now: 18, 20, 20, 22, __ , __ , 30

Finally, we'll deal with the last two numbers. We know that they must be even and that they both must be in between 22 and 30 (since the set is in ascending order). We also know that the two numbers must be different (see last paragraph) and that they sum to 50. The only two numbers that satisfy all of these conditions are 24 and 26, so they must be our last two numbers.

Therefore, the answer is 18, 20, 20, 22, 24, 26, 30. Hope this helps!

The area of the parallelogram  will be equal to 60 in²

Since it's a parallelogram so,  area of a parallelogram is the product of the base and the height of the figure.

area of a parallelogram = Base x Height

We are given that area of a parallelogram = Base x Height

A = bh

A =  6×1 0

A = 60 in²

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