Find the sum of the series3,7,15,31,.....for the first 110 terms?

there are 1000 milligrams in 1 gram

Hope this helps

Given that three charges (-25 nC, 79.1nC, and −55.9nC) are placed at three of the four corners of a square with sides of length 22.2 cm. We need to determine the value of the electric potential (in V) at the empty comer if the positive charge is placed in the opposite corner.

The formula for the electric potential at a point in space is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) + ….. ]where;k = Coulomb's constant (8.99 × 10^9 Nm²/C²)q1, q2, q3,…. are the charges at the cornersr1, r2, r3,…. are the distances from the corner to the point whose potential is being calculated Now we can calculate the electric potential at the empty corner as follows;The three charges can be represented as shown below:Charges at corners of a square

The distance from any corner to the opposite corner (where the positive charge is placed) is given by d = √[ (22.2 cm)² + (22.2 cm)² ] = 31.4 cmTherefore, the electric potential at the empty corner is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) ]Here, q1 = -25 nC, q2 = -55.9 nC, q3 = 79.1 nC, r1 = r2 = r3 = d = 31.4 cm = 0.314 mPlugging in the values we get;V = 8.99 × 10^9 [ (-25 × 10^-9 / 0.314) + (-55.9 × 10^-9 / 0.314) + (79.1 × 10^-9 / 0.314) ]= 8.99 × 10^9 [ -0.0795 - 0.1783 + 0.252 ]= 8.99 × 10^9 × 0.0052= 46.8 VTherefore, the value of the electric potential at the empty comer if the positive charge is placed in the opposite comer is 46.8 V.

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Answer:

Step-by-step explanation:

yeah hope its was helpful

Answer:

A,C,E

Step-by-step explanation:

group:children

4x6=24 good

12x2=24 but has to have more than 2 children in each group

8x3=24 good

4x9=36 36>24

2x12=24 good

The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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Step-by-step explanation:

The following system answer is no solution. Change one number to make the system an infinite solution and explain why it is now an infinite solution.

12y = 17 - 9x

-4y - 3x = 31

In a function, there is only one value of y for a given value of x. In this case, we are told that for each radio frequency (x) there is exactly one radio station (y), then this relation of x and y is a function

The LHS and the RHS of the given expression do not match 240.469= -215 and so the given expression is FALSE.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra.

Here, we refer to these letters as variables.

So, we have the expression:

(−18−−−√3)3+334=(−183)3 + 334

Now, check it as follows:

(−18√3)3+334=(−183)3 + 334

-93.531+334=-549+334

240.469= -215

Ans: FALSE

Therefore, the LHS and the RHS of the given expression do not match 240.469= -215 and so the given expression is FALSE.

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Correct question:

Evaluate the expression: (−18−−−√3)3+334=(−183)3 + 334=?

Answer:

18(x + 2)

Step-by-step explanation:

-4/5 ( 30x -  40) + (42x + 4) = -24x + 32 + 42x + 4 = 18x + 36 = 18(x + 2)

Answer:

18x+36

Step-by-step explanation:

1. Simplify  \frac{4}{5}(30x-40)54(30x−40)  to  \frac{4(30x-40)}{5}54(30x−40).

-\frac{4(30x-40)}{5}+42x+4−54(30x−40)+42x+4

2. Factor out the common term 1010.

-\frac{4\times 10(3x-4)}{5}+42x+4−54×10(3x−4)+42x+4

3. Simplify  4\times 10(3x-4)4×10(3x−4)  to  40(3x-4)40(3x−4).

-\frac{40(3x-4)}{5}+42x+4−540(3x−4)+42x+4

4. Simplify  \frac{40(3x-4)}{5}540(3x−4)  to  8(3x-4)8(3x−4).

-8(3x-4)+42x+4−8(3x−4)+42x+4

5. Expand by distributing terms.

-(24x-32)+42x+4−(24x−32)+42x+4

6. Remove parentheses.

-24x+32+42x+4−24x+32+42x+4

7. Collect like terms.

(-24x+42x)+(32+4)(−24x+42x)+(32+4)

8. Simplify.

18x+3618x+36

hope this helps

The volume of empty space left inside the cylindrical container is 2153.64 \(cm^{3}\).

The cubic capacity refers to the volume of a cylinder between the upper point inside the cylinder head to the bottom dead center of the piston.

We must first determine the volume of the cylinder containing the three spheres and then deduct the sum of the volumes of the three balls to determine the volume of the remaining space inside the container.

The cylinder has a height equivalent to one ball's diameter, or 14 cm, and a radius of 7 cm. As a result, the cylinder's capacity is:

\(= \pi r^{2} h\\= 3.148 * 7^{2} *14\)

= 2156.64 \(cm^{3}\)

Since the radius of each ball is 7 centimeters, the volume is:

The volume of a ball is Vball is = \(\frac{4}{3} \pi r^{3}\)

= \(\frac{4}{3} \ * 3.148 * (7)^{3}\)

= 1436.76 cm³

The three spheres' combined volume is equal to Vtotal = 3Vball

= 3 * 1436.76 cm³

= 4310.28 cm³

The container's remaining interior area has the following volume:

Vcylinder = Vtotal - Vempty

                = 2156.64 \(cm3\) - 4310.28\(cm3\\\)  

                = -2153.64 \(cm3\)

We round the result to the closest hundredth and calculate the absolute value because we cannot have a negative volume:

|Vempty| = 2153.64 \(cm3\)

As a result, there is roughly 2153.64 \(cm3\) of empty space inside the container.

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By analyzing the graph, we will see that the inequality is:

y > 2x + 1

From a first look, we can see two things.

From that we can conclude that the inequality is something like:

y > line.

To find the equation of the line, we can look at the graph.

We can see that it intercepts the y-axis at y = 1, and for each increase of one unit in the x-axis increases 2 units on the y-axis, so the line is:

2x + 1

Then the inequality is:

y > 2x + 1.

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Answer and Step-by-step explanation:

Essentially, the figure FEHG got scaled by a factor of 1.5, and turned into BADC

So 2.4 times 1.5 is 3.6

3.6 = x

Hope this helps! #teamtrees #WAP (Water And Plant)

Answer:

The x would be 3.6

Step-by-step explanation:

If you see the relation or ration between the ABCD triangle and the EFGH then we can see that the side 2 is multiplied by 1.5 to get to 3. so you do the same thing to 2.4 and multiple that by 1.5 and 3.6.

Using Double-Angle Formulas, 2 sin(16°) cos(16°)= sin(32°), 2 sin(40°) cos(40°) = sin(80°)., tan(0) = 0.

To simplify the expressions using Double-Angle Formulas and solve the equation.

(a) 2 sin(16°) cos(16°)

Using the Double-Angle Formula for sine: sin(2x) = 2sin(x)cos(x), we can rewrite the expression as:

sin(2 * 16°) = sin(32°)

So, the simplified expression is sin(32°).

(b) 2 sin(40°) cos(40°)

Using the same Double-Angle Formula for sine: sin(2x) = 2sin(x)cos(x), we can rewrite the expression as:

sin(2 * 40°) = sin(80°)

So, the simplified expression is sin(80°).

Now, let's solve the given equation:

tan(0) = 0

There is no need to provide a comma-separated list of answers because tan(0) is always equal to 0.

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Answer:

D.

Step-by-step explanation:

f(x) = \(\sqrt[3]{4x}\)

g(x) = 2x + 3

\(\frac{f}{g}\) (x)  = 'f' divided by 'g'

\(\frac{\sqrt[3]{4x} }{2x+3}\)    Substitute.

x cannot be -\(\frac{3}{2}\) because that would create a zero in the denominator.

That's a no-no.

It makes it 'undefined'

Answer:

C

Step-by-step explanation:

To solve the initial value problem y" + 4y = 4u_n(t), where y(0) = 0 and y'(0) = 1, we will follow these steps:

a. Find the Laplace transform of the solution y(t).

The Laplace transform of the given differential equation can be obtained using the properties of the Laplace transform. Taking the Laplace transform of both sides, we get:

s^2Y(s) - sy(0) - y'(0) + 4Y(s) = 4U_n(s),

where Y(s) represents the Laplace transform of y(t) and U_n(s) is the Laplace transform of the unit step function u_n(t).

Since y(0) = 0 and y'(0) = 1, the equation becomes:

s^2Y(s) - s(0) - 1 + 4Y(s) = 4U_n(s),

s^2Y(s) + 4Y(s) - 1 = 4U_n(s).

Taking the inverse Laplace transform of both sides, we obtain the solution in the time domain:

y''(t) + 4y(t) = 4u_n(t).

b. Find the solution y(t) by inverting the transform.

To find the solution y(t) in the time domain, we need to solve the differential equation y''(t) + 4y(t) = 4u_n(t) with the initial conditions y(0) = 0 and y'(0) = 1.

The homogeneous solution to the differential equation is obtained by setting the right-hand side to zero:

y''(t) + 4y(t) = 0.

The characteristic equation is r^2 + 4 = 0, which has complex roots: r = ±2i.

The homogeneous solution is given by:

y_h(t) = c1cos(2t) + c2sin(2t),

where c1 and c2 are constants to be determined.

Next, we find the particular solution for the given right-hand side:

For t < n, u_n(t) = 0, and for t ≥ n, u_n(t) = 1.

For t < n, the particular solution is zero: y_p(t) = 0.

For t ≥ n, we need to find the particular solution satisfying y''(t) + 4y(t) = 4.

Since the right-hand side is a constant, we assume a constant particular solution: y_p(t) = A.

Plugging this into the differential equation, we get:

0 + 4A = 4,

A = 1.

Therefore, for t ≥ n, the particular solution is: y_p(t) = 1.

The general solution for t ≥ n is given by the sum of the homogeneous and particular solutions:

y(t) = y_h(t) + y_p(t)

y(t) = c1cos(2t) + c2sin(2t) + 1.

Using the initial conditions y(0) = 0 and y'(0) = 1, we can determine the values of c1 and c2:

y(0) = c1cos(0) + c2sin(0) + 1 = c1 + 1 = 0,

c1 = -1.

y'(t) = -2c1sin(2t) + 2c2cos(2t),

y'(0) = -2c1sin(0) + 2c2cos(0) = 2c2 = 1,

c2 = 1/2.

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Answer:-6

Step-by-step explanation:maybe

To make the function f(x) = {mx - 8 if x < -4, \(x^{2}\) + 4x - 4 if x ≥ -4} continuous for all values of x, the constant m must be equal to 6.

To ensure continuity of the function, we need to find the value of m that makes the two parts of the function meet at x = -4 without any abrupt changes. At x = -4, both expressions should yield the same value.

First, let's find the value of f(x) for x < -4. We substitute x = -4 into the expression mx - 8:

f(-4) = m(-4) - 8 = -4m - 8

Next, we find the value of f(x) for x ≥ -4. We substitute x = -4 into the expression \(x^{2}\) + 4x - 4:

f(-4) = \((-4)^{2}\) + 4(-4) - 4 = 16 - 16 - 4 = -4

For the function to be continuous at x = -4, the values of f(x) from both expressions should be equal. Therefore, we have the equation:

-4m - 8 = -4

Solving this equation, we find:

-4m = 4

m = -1

Thus, the constant m should be equal to -1 for the function to be continuous. However, this contradicts the original question, which states that m must be positive. Therefore, there is no value of m that makes the function continuous.

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For each of the given confidence intervals for β, we can determine whether there is a linear relationship between the two variables and, if there is, whether y is increasing or decreasing as x increases.

(a) Confidence interval (-3.24, -1.23):

(i) Based on the confidence interval, there is evidence of a linear relationship between the two variables because the interval does not include zero.

(ii) Since the interval is negative, we can infer that as x increases, y is expected to decrease.

(b) Confidence interval (-5, 2):

(i) In this case, the confidence interval includes zero, which indicates that there may not be a linear relationship between the two variables.

(ii) Without a linear relationship, we cannot determine whether y is increasing or decreasing as x increases.

(c) Confidence interval (2.86, 5.92):

(i) Similar to the first case, the confidence interval does not include zero, suggesting the presence of a linear relationship between the variables.

(ii) Since the interval is positive, we can infer that as x increases, y is expected to increase.

In summary, for confidence interval (a), there is a linear relationship with y decreasing as x increases. For confidence interval (b), the presence of a linear relationship cannot be determined. For confidence interval (c), there is a linear relationship with y increasing as x increases.

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Answer:

To find 2/3 of an hour first we will divide 1 hour that is 60 minutes into 3 parts. So we will get 20 minutes. So we 2parts out of 3 parts of an hour so we get 20X2=40minutes

Step-by-step explanation:

Answer:

220 inches

Step-by-step explanation:

Formula for the circumference of circle is

2πr

Replacing it with the given values

2 x 3.14 × 35 = 219.8 inches

or 220 inches rounded

According to the discount, the price of the tablet computer after the markup is $610.30.

In this problem, a store offered a 30% discount on a tablet computer that originally sold for $670. We can calculate the discounted price of the tablet computer by finding 30% of its original price and subtracting it from the original price.

Discounted price = Original price - Discount

Discounted price = $670 - 30% of $670

Discounted price = $670 - $201

Discounted price = $469

So, the discounted price of the tablet computer is $469.

The problem then asks us to find the price of the tablet computer after it is marked up by 30%. To do this, we need to add 30% of the discounted price to the discounted price.

Markup price = Discounted price + Markup

Markup price = $469 + 30% of $469

Markup price = $469 + $141.30

Markup price = $610.30

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Answer:

Use the formula  

a n  =  a 1  +  d  (  n  −  1  )

to identify the arithmetic sequence.

a n  =  2 n  +  10

Step-by-step explanation:

Answer:

12+2=14  14+2 16+2   18+2

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The verticle line in the box is the median

Answer:

-7/(x-5) - 3

Step-by-step explanation:

First off, to reflect an equation in the y axis, just multiply by -1. Now that it is reflected, to stretch an equation by a factor of 7, multiply it by 7. Now we have -7/x.

Then, to move an equation down by 3 units, simply subtract it by 3. Now we have -7/x - 3.

Lastly, since you want to translate it 5 units to the left, you want the equation to be undefined at x = 5 (because originally it is undefined at x = 0). To do that, set the denominator to x - 5. We arrive at our answer: -7/(x-5) - 3.

Using translation concepts, it is found that the new definition for the function is:

\(g(x) = -\frac{7}{x - 5} - 3\)

----------------------------

The parent function is:

\(f(x) = \frac{1}{x}\)

\(g(x) = 7 \times \frac{1}{x} = \frac{7}{x}\)

\(g(-x) = \frac{7}{-x} = -\frac{7}{x}\)

\(g(x) = -\frac{7}{x - 5}\)

\(g(x) = -\frac{7}{x - 5} - 3\)

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Answer:

The bill before tax and tip was $11.60. Then, a sales tax of 7.5% was added, which is $0.87. So, the total cost of the meal before tip was $11.60 + $0.87 = $12.47. Rajani tipped 12% on the amount after the added sales tax, 12% of $0.87 = $0.10. Therefore, the total cost of the meal, including tax, tip, and the original bill, was $12.47 + $0.10 = $12.57.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Thenks you.

The sample size of N=120 and significance level of α=0.01 would be the most likely to lead to the highest power.

To maximize statistical power, we want to select the sample size and importance degree in order to maximize the likelihood of detecting a real effect if one exists. Better pattern size and a decreased importance degree each tend to increase statistical energy.

Assuming a -tailed test and equal variances, we will use a power analysis to determine the sample size needed to acquire a favored degree of power. Based totally on the impact size we count on to examine, we will estimate the minimum sample size required for the take look to have 80% energy (that is regularly considered acceptable).

For instance, if we count on a small impact length (d=0. 2) and an importance level of α=0. 05, we might need a pattern size of about n=128 to reap 80% power. Growing the sample length in addition would retain increased strength, however, the marginal returns could diminish.

As for significance level, lower alpha degrees tend to cause higher strength due to the fact they lessen the possibility of a type I error (false wonderful), which frees up extra of the kind I error rate for detecting genuine outcomes. However, excessively low alpha tiers can boom the chance of kind ii errors (fake negatives), which decreases strength.

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Answer:

you will need to save 80 each month to get the tires

Answer:

8.6 × 10-9

Step-by-step explanation: