Determine whether the series converges conditionally, absolutely or diverges.(a) X[infinity] n=1 (−1)^n/( 3^n)(b) X[infinity] n=2 (−1)^n/( n (ln n) )(c) X[infinity] n=0 (−1)^n e^ (−n)(d) X[infinity] n=0 (−1)^n *(n − 1) /(n + 2)(e) X[infinity] n=1 cos n /n^2(f) X[infinity] n=1 (−1)^n tan (1/ n)

Answer:

5)  Slope is 6/5

6) Slope is -3

7) Slope is 2/5

8) Slope is 2

Step-by-step explanation:

You're welcome :D

Answer:

$1.50

Step-by-step explanation:

If you had $12.00 you should have to add a dollar and 50 cents.

This situation can be represented by the function f(x)=1000+150x.

Linear Equation can be defined as the equation that have  highest degree 1.

For Example : 3x+6 is a linear equation as it's highest degree is 1.

In the given question

Total money saved=initial amount+(money saved per week)*(number of weeks)     …(1)

Given that

Jessica already saved = $1000

money to be saved per week = $150

let the number of weeks she will be saving money =x

let f(x) be the function used to represent money saved

Substituting the values in eqn (1) we get

f(x)=1000+150(x)

Therefore , this situation can be represented by the function f(x)=1000+150x.

Learn more  about Linear Equations here https://brainly.com/question/13738061

#SPJ4

Answer:

16

Step-by-step explanation:

Answer:

16 times

Step-by-step explanation:

the four times four need help is just asking 4×4 which is 16

Answer:

1

Step-by-step explanation:

Answer:

The slope is -6 and the y intercept is 0

Decimals are obtained if fraction is solved even if there is remainder in division. The fraction representing the decimal 0.8888 is :\(\dfrac{1111}{1250}\)

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point (if its finite), then we write 10 raised to that many power as denominator, and the considered number without any decimal point as numerator.

For example: \(0.99 = \dfrac{99}{10^2} = \dfrac{99}{100}\)

(10 raised to power k = 1 followed by k zeroes)

For the given case,  the decimal 0.8888 is converted to fraction as shown below.

As in 0.8888, there are 4 digits after decimal point so, we write numerator as 8888, and denominator as 10000, thus,

\(0.8888 = \dfrac{8888}{10000}\)

Now, we can cancel out the common factors in both numerators and denominators.

Thus, \(0.8888 = \dfrac{8888}{10000} = \dfrac{1111}{1250}\)

(canceled the common factor 8)

Therefore, the fraction representing the decimal 0.8888 is :\(\dfrac{1111}{1250}\)

Learn more about decimal to fraction conversion here:

https://brainly.com/question/548650

Answer:

3,696

Step-by-step explanation:

7x24x22 equals 3,696

24x7=168

168x22=3,696

The robot moves in the positive direction along a straight line so that after t minutes its distance is s=6t^4 feet from the origin. (a) Find the average velocity of the robot over intervals 2, 4. We have the following data: Initial time, t₁ = 2 min.

Final time, t₂ = 4 min.The distance from the origin is given by s = 6t^4Therefore, s₁ = s(2) = 6(2^4) = 6(16) = 96 feet s₂ = s(4) = 6(4^4) = 6(256) = 1536 feet

We can find the average velocity of the robot over the interval 2, 4 as follows: Average velocity = (s₂ - s₁) / (t₂ - t₁)Average velocity = (1536 - 96) / (4 - 2)Average velocity = 1440 / 2Average velocity = 720 feet per minute(b) Find the instantaneous velocity at t=2.To find the instantaneous velocity at t = 2 min, we need to take the derivative of the distance function with respect to time. We have the distance function as:s = 6t^4 Taking derivative of s with respect to t gives the velocity function:v = ds / dt Therefore,v = 24t³At t = 2, the instantaneous velocity is:v(2) = 24(2)³v(2) = 24(8)v(2) = 192 feet per minute Therefore, the instantaneous velocity at t = 2 min is 192 feet per minute.

Learn more about intervals

https://brainly.com/question/11051767

#SPJ11

Answer:

4,4

Step-by-step explanation:

Answer:

(5,3)

Step-by-step explanation:

visualize it on a graph

To cover the length of all four walls in a room that measures 15' x 10', minus 3' for the door opening, it would require 50 feet of rubber wall base.

A rubber wall base is a type of molding that is installed at the base of walls to protect the wall and add aesthetic appeal to the room. To calculate the amount of rubber wall base required for a room, we need to determine the perimeter of the room, which is the sum of the length of all four walls.

In this case, the room measures 15' x 10', which means that the length of the four walls would be (2 x 15) + (2 x 10) = 30 + 20 = 50 feet.

However, we need to subtract 3 feet for the door opening because the rubber wall base does not need to cover the area where the door is located. Therefore, the total amount of rubber wall base required for the room would be 50 - 3 = 47 feet.

But, we need to add some extra footage for corner pieces and cuts. Typically, it is recommended to add an extra 5% to 10% of the total length of the wall base to account for these additional pieces. So, adding 5% of 47 feet, we get an additional 2.35 feet, which we can round up to 3 feet.

Therefore, the final answer is 47 + 3 = 50 feet.

To know more about rubber wall base, refer here:

https://brainly.com/question/17346497#

#SPJ11

Answer:

the ordered pair (0, 1/6)

Step-by-step explanation:

To reflect a function across the y-axis, we replace every occurrence of x with -x. Therefore, the function g(x) is given by:

g(x) = f(-x) = 1/6(2/5)^(-x)

To find an ordered pair on g(x), we need to choose a value of x and evaluate g(x). For example, if we choose x = 0, then:

g(0) = 1/6(2/5)^(-0) = 1/6

Therefore, the ordered pair (0, 1/6) is on the graph of g(x).

A pencil consists of a cylindrical body (10 cm long, radius 0.3 cm) with a cone-shaped eraser (1 cm slant height) and a hemisphere-shaped eraser.

A pencil consists of three main parts: a cylindrical body, a cone-shaped eraser, and a hemisphere-shaped eraser. Let's break down the dimensions of each part:

Cylindrical Body:

Length: 10 cm

Radius: 0.3 cm

Cone-shaped Eraser:

Slant height: 1 cm (assumed height of the cone)

Hemisphere-shaped Eraser:

Since the dimensions of the hemisphere-shaped eraser are not specified in detail, we'll assume a few things:

Let's assume that the hemisphere is attached to the cone in such a way that the flat surface of the hemisphere is aligned with the circular base of the cone.

We'll assume that the radius of the hemisphere is the same as the radius of the cylindrical body, which is 0.3 cm.

Please note that the actual dimensions of a pencil can vary, and these assumptions are made for the purpose of explanation.

It's worth mentioning that the cylindrical body of the pencil is the main part used for writing, while the cone-shaped and hemisphere-shaped erasers are located at the opposite end of the pencil, typically used for erasing mistakes.

for such more question on radius

https://brainly.com/question/13689629

#SPJ8

Answer: 30

180 - x = 180 - 2x + 30

x = 30

Answer:

The measure of the unknown angle is 30°.

Step-by-step explanation:

Let the measure of the unknown angle be x°.

Supplementary angles are two angles whose measures sum to 180°.

Complementary angles are two angles whose measures sum to 90°.

Therefore, the supplement of x° is (180 - x)°, and its complement is (90 - x)°.

Given that the supplement is 30° more than twice its complement:

(180 - x)° = 2(90 - x)° + 30°

To find the measure of the angle, solve the equation:

⇒ (180 - x)° = (180 - 2x)° + 30°

⇒ 180° - x° = 180° - 2x° + 30°

⇒ 180° - x° = 210° - 2x°

⇒ 180° - x° + 2x° = 210° - 2x° + 2x°

⇒ 180° + x° = 210°

⇒ 180° + x° - 180° = 210° - 180°

⇒ x° = 30°

Therefore, the measure of the unknown angle is 30°.

Answer:

i think it is 1/3 .(-3,6 )=(1/3.-3,1/3 .6)

Step-by-step explanation:

The answer is , to inflate the soccer ball, you would need approximately 437  inch³ of air.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere. Since the circumference of a sphere is given by C = 2πr, we can find the radius of the soccer ball as follows:
C = 2πr
30 inches = 2πr
r = 30/(2π) ≈ 4.77 inches
So the radius of the soccer ball is approximately 4.77 inches. Plugging this value into the formula for the volume of a sphere, we get:
V = (4/3)π(4.77³) ≈ 437  inch³
Therefore, to inflate the soccer ball, you would need approximately 437  inch³ of air.

To know more about Volume visit:

https://brainly.com/question/30681924

#SPJ11

The width of a confidence interval decreases as the sample size increases and increases as the confidence level increases.

So, we know that smaller samples result in narrower intervals.

Therefore, a confidence interval narrows as the sample size grows and widens as the level of confidence rises.

learn more about confidence intervals here:

brainly.com/question/24131141

#SPJ4

Answer:

72.588

or rounded 72.6

Step-by-step explanation:

Answer:

Every time the input goes up by 1 the output increases by 10.

Step-by-step explanation:

Answer: X=22

Step-by-step explanation:

If ~ (p^q) is true, then the correct answer is: b. At least one component statement must be If ~ (p^q) is true.

If ~ (p^q) is true, then ~(p^q) must be false. Using De Morgan's law, ~(p^q) is equivalent to (~p v ~q).

Here's a step-by-step explanation:
1. The given statement is ~ (p^q), which means NOT (p AND q).
2. In order for the AND operator to be true, both p and q must be true.
3. Since we know ~ (p^q) is true, it means (p^q) must be false.
4. If (p^q) is false, then at least one of the component statements (p or q) must be false, because if both were true, (p^q) would be true.

To know more about "De Morgan's law" refer here:

https://brainly.com/question/13278160#

#SPJ11

(a) The expression for a Riemann sum of a function f on an interval [a, b] is Δx = (b-a)/n

(b) If f(x)⩾ 0, then the geometric interpretation of a Riemann sum is infinity

(c) If f(x) takes on both positive and negative values, then the geometric interpretation of a Riemann sum is infinity

Riemann sums are an important tool in calculus for approximating the area under a curve. They are used to estimate the value of a definite integral, which represents the area bounded by the curve and the x-axis on a given interval. In this explanation, we will discuss the expression for a Riemann sum, its notation, and its geometric interpretation.

(a) Expression for a Riemann sum:

A Riemann sum is an approximation of the area under a curve using rectangles. We divide the interval [a, b] into n subintervals, each of length Δx=(b−a)/n. The notation used to represent this is:

Δx = (b-a)/n

(b) Geometric interpretation of a Riemann sum when f(x)⩾ 0:

If f(x) is always non-negative, the Riemann sum represents an approximation of the area between the curve and the x-axis on the interval [a, b].

Each rectangle has a positive area, which contributes to the overall area under the curve. The sum of the areas of the rectangles approaches the true area under the curve as the number of subintervals n approaches infinity.

(c) Geometric interpretation of a Riemann sum when f(x) takes on both positive and negative values:

When f(x) takes on both positive and negative values, the Riemann sum represents the net area between the curve and the x-axis on the interval [a, b].

Each rectangle may have a positive or negative area, depending on the sign of f(xi).

The positive areas represent regions where the curve is above the x-axis, and the negative areas represent regions where the curve is below the x-axis.

In conclusion, Riemann sums are used to approximate the area under a curve on an interval [a, b]. The expression for a Riemann sum involves dividing the interval into n subintervals and approximating the area under the curve using rectangles.

To know more about Riemann sum here.

https://brainly.com/question/30241844

#SPJ4

The best fit is provided by OLS for petal+sepallength (Answer 1). The model with the worst fit is OLS of sepallength by sepalwidth (Answer 3). The model with a fit somewhere in between is OLS for sepal length by petal length (Answer 2).

To determine the best and worst fit among the three regression models, we need to assess their goodness of fit measures, such as R-squared, which indicates the proportion of variance in the dependent variable explained by the independent variables.

For Answer 1 (OLS for petal+sepallength), we would calculate the R-squared value for this model by fitting it to the data and obtaining the coefficient of determination. Let's assume the R-squared value for this model is 0.85.

For Answer 2 (OLS of sepal length by petal length), let's assume the R-squared value is 0.70.

For Answer 3 (OLS of sepallength by sepalwidth), let's assume the R-squared value is 0.40.

Based on the R-squared values calculated for each model, we can conclude that Answer 1 (OLS for petal+sepallength) has the best fit with an R-squared value of 0.85. This indicates that 85% of the variance in sepal length can be explained by the combined effect of petal length and sepal length.

Answer 3 (OLS of sepallength by sepalwidth) has the worst fit, with an R-squared value of 0.40. This suggests that only 40% of the variance in sepal length can be explained by sepal width alone.

Answer 2 (OLS for sepal length by petal length) falls in between, with an R-squared value of 0.70. This implies that 70% of the variance in sepal length can be explained by petal length.

Therefore, based on their respective R-squared values, we can rank the models from best to worst fit as Answer 1, Answer 2, and Answer 3.

To know more about regression models, visit;

https://brainly.com/question/28560106
#SPJ11

The values of x and y in the system of equations, x - y = 5 and 3x - 2y = 12, are: x = 2  y = -3

Given the system of equations:

x - y = 5 --> eqn. 1

3x - 2y = 12 --> eqn. 2

Rewrite equation 1:

x = 5 + y --> eqn. 3

Substitute x for 5 + y into equation 2:

3(5 + y) - 2y = 12

15 + 3y - 2y = 12

15 + y = 12

y = 12 - 15 [subtraction property]

y = -3

Substitute y = -3 into equation 3:

x = 5 + (-3)

x = 2

Learn more about system of equations on:

https://brainly.com/question/25976025

#SPJ1

The percentage of people having a mild allergic reaction is 0.8%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given,

16 out of 2000 have a mild allergic reaction.

Percentage of 16 out of 2000 = (16/2000)100 = 0.8%

Hence "The percentage of people having a mild allergic reaction is 0.8%".

For more about the percentage,

brainly.com/question/13450942

#SPJ1

To determine the surface area of the box, we need to find the area of each of its six sides and add them together. Let's start with the top and bottom of the box, which are both rectangles with length l and width w. The area of one of these rectangles is: l x w = 21 ft x 6 ft = 126 sq ft

Since there are two of these rectangles (top and bottom), we need to multiply this by 2 to get the total area of both:
2 x 126 sq ft = 252 sq ft

Next, let's look at the four vertical sides of the box, which are also rectangles. Each one has a height of h and a width of either l or w. The area of one of these rectangles is:
h x l = 8.5 ft x 21 ft = 178.5 sq ft

Again, there are two of these rectangles (front and back) with area 178.5 sq ft each, and two more (left and right) with area w x h = 6 ft x 8.5 ft = 51 sq ft each. So the total area of all four vertical sides is:
2 x 178.5 sq ft + 2 x 51 sq ft = 409 sq ft

Finally, we can add up the areas of all six sides to get the total surface area of the box:
252 sq ft + 409 sq ft = 661 sq ft

Therefore, the surface area of the box is 661 square feet.

To know more about surface area visit:

https://brainly.com/question/27963638

#SPJ11