Find the First five terms of the power series and the interval
and center of convergence for ((1)/(1+16x))

Answer:

106.81mm or 34 pi

Step-by-step explanation:

C=2πr=2·π·17≈106.81415

Answer:

Answer: Olivia and Danny have each filled 16 baskets in 1 hour

Step-by-step explanation:

We can solve this using simultaneous equations.

Let h be the number of hours of picking apples when both have the same number of baskets

Danny already has 11 baskets. If he picks apples for 1 hour and fills them at the rate of 5 baskets per hour he will have filled a total of
11 + 5h baskets after h hours

Olivia has 12 baskets filled and is filling baskets at 4 baskets per hour

After h hours the number of filled baskets she has

= 12 + 4h

Equate the two

11 + 5h = 12 + 4h

Subtract 11 from both sides

11 - 11 + 5h = 12 - 11 + 4h

5h = 1 + 4h

Subtract 4h from both sides:

5h - 4h = 1

h = 1

Number of baskets filled after 1 hour (including the original baskets filled) = 11 + 5(1) = 16 = 12 + 4(1)

Answer: Olivia and Danny have each filled 16 baskets in 1 hour

Answer: y = 30 + 40x

Step-by-step explanation: 30 inches is the initial height of the sunflower, 40 inches is the rate of change the sunflower grows each month.

No, there is not a significant difference between these two values at the 95% confidence level.

The difference between the mean and literature values is 0.011 g/ml, which is less than the standard error of the mean (0.00387 g/ml). Therefore, the difference is not statistically significant. To reach a 95% confidence level, the difference must be greater than two standard errors of the mean. This would mean that the difference must be greater than 0.00773 g/ml, which it is not. Therefore, there is no significant difference between these two values at the 95% confidence level.

To know more about confidence level refer to the link brainly.com/question/22851322

#SPJ4

Answer:

Next to 6 is 9, next to 15 is 27, and next to 3 is 5

Step-by-step explanation:

If you imagine 6 photos for every 2 minutes as a fraction and simplify it, the answer to this would be 3 photos for every 1 minute (basically 3/1). By using this unit fraction, you'll see that you're supposed multiply the amount of minutes by 3, or you can divide the # of photos by 3.

For 3 mins, you multiply that by 3 to get 9 photos.

For 9 mins, you multiply that by 3 to get 27 photos

For 15 photos, you divide that by 3 to get 5 photos.

Ok, have a Spooky Halloween!

The manufacturer of allay pain reliever offered a free sample of the product to visitors who registered at its website. in this case, the communications objective of the website was to increase awareness of Allay Pain Reliever and generate customer leads.

Communication objectives are the aims and principles that guide how a person or company interacts with customers, staff, or other stakeholders. Workplaces can establish and uphold uniform standards for every contact by adopting communication strategies.

In order to achieve marketing goals with an increase in the rate of purchases or information requests, the communication objectives must first develop a good consumer attitude.

To know more about  communication objectives visit:

https://brainly.com/question/28263316

#SPJ4

Microliters (µL) and liters (L) are both units of volume measurement. A microliter is a very small unit of volume, equivalent to one millionth of a liter. To convert microliters to liters, we can use a simple conversion factor.

The conversion factor is based on the fact that one liter is equivalent to one million microliters. Therefore, to convert microliters to liters, we divide the number of microliters by one million. This can be expressed as:

L = µL / 1,000,000

For example, if we have a volume of 500 µL that we want to convert to liters, we can use the formula above as follows:

L = 500 µL / 1,000,000

L = 0.0005 L

Therefore, 500 µL is equivalent to 0.0005 liters.

It is important to keep track of the units when making conversions and to use appropriate significant figures. Additionally, it is worth noting that microliters are often used in situations where very small volumes are involved, such as in medical or laboratory settings, whereas liters are used for larger volumes such as in the context of cooking or liquid measurements.

To know more about microliters to liters, click here:

brainly.com/question/17204784

#SPJ4

Answer:

A:   -1 + 2 log4^x

C: log4 (1/4) + log4 x^2

Step-by-step explanation:

Apply logarithm properties:

log4 (1/4x^2)  =  log4 (1/4) + log4 x^2

Evaluate: log4 (1/4)

log4 (1/4) = -1

Substitute the value back:

-1 + lg4 x^2

Apply logarithm properties:

-1 + 2 log4 ^x

Draw a conclusion:

The expressions equivalent to: log4 (1/4x^2) are:

Answer Choices: A, and C

A= -1 + 2 log4^x

C=  log4 (1/4) + log4 x^2

Hope this helps!

a)  The volume of paint left in the can is:

.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

b)  the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

(a) To convert gallons to cubic meters, we need to know the conversion factor between the two units. One U.S. gallon is equal to 0.00378541 cubic meters. Therefore, the volume of paint left in the can is:

0.878 gallons * 0.00378541 m^3/gallon = 0.003321 m^3

(b) We can use the formula for the volume of a rectangular solid to find the volume of wet paint needed to coat the wall evenly:

Volume = area * thickness

We want to solve for the thickness, so we rearrange the formula to get:

Thickness = Volume / area

The volume of wet paint needed is equal to the volume of dry paint needed since they both occupy the same space when the paint dries. Therefore, the volume of wet paint needed is:

0.003321 m^3

The area of the wall is given as:

13.7 m^2

So the thickness of the layer of wet paint is:

0.003321 m^3 / 13.7 m^2 = 0.000242 m

Therefore, the thickness of the layer of wet paint is 0.000242 meters or 0.242 millimeters (since there are 1000 millimeters in a meter).

Learn more about meters here:

https://brainly.com/question/29367164

#SPJ11

The following statements are true:

The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)

Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;

For the lines, the lines that are parallel to each other are:

For skew lines, they are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC

Learn more about parallel and skew lines here: https://brainly.com/question/18013592

a machine can pack a 3 ft by 3 ft by 1 ft carton with packing material in 3 seconds Then it would take 32 seconds to fill a carton that measures 4 ft by 4 ft by 6 ft

1) we calculate the volume of the first carton:

volume=length x width x height

volume=3 ft * 3 ft * 1 ft=9 ft³

Therefore:

A machine can fill 9 ft³ in 3 seconds.

2) we calculate the volume of the second carton.

volume=length x width x heigth

volume=4 ft * 4 ft * 6 ft=96 ft³

3) we calculate the time that the machine needs for fill the second carton with packing material by the rule of three.

9 ft³---------------------3 seconds

96 ft³--------------------      x

x=(96 ft³ * 3 seconds) / 9 ft³=32 seconds.

Hence , a machine can pack a 3 ft by 3 ft by 1 ft carton with packing material in 3 seconds Then it would take 32 seconds to fill a carton that measures 4 ft by 4 ft by 6 ft

learn more about of measurement here

https://brainly.com/question/1243504

#SPJ4

Answer: Wheres the table

Step-by-step explanation:

Answer:

Step-by-step explanation:

40

Answer:  A

Step-by-step explanation:

A for 1 gram it is $1.00

B for 1 gram it is $1.25

C for 1 gram it is $1.66

D for 1 gram it is $1.25

Answer:

(- 3, 2 )

Step-by-step explanation:

Given the 2 equations

x + 3y = 3 → (1)

- 2x + 3y = 12 → (2)

Subtract (1 ) from (2) term by term to eliminate y

- 2x - x + (3y - 3y) = 12 - 3

- 3x = 9 ( divide both sides by - 3 )

x = - 3

Substitute x = - 3 into either of the 2 equations and solve for y

Substituting into (1)

- 3 + 3y = 3 ( add 3 to both sides )

3y = 6 ( divide both sides by 3 )

y = 2

solution is (- 3, 2 )

Plug the points into y2-y1/x2-x1

(-10) - (-4)/(-12) - (-20)

you will get A. -3/4

hope this helps !! :)

Answer:

the quotient

Step-by-step explanation:

H should equal 96

because 10 - 6 equals 4

96 divided by 4 equals 24

Answer:

85

Step-by-step explanation:

2x+192=180

2x= -12

x= -6

-6+91= 85

Given that the advertising company had a setup fee of $80, this would mean that

Next, since it is stated that they add $4 for every advertisment, we let x as the number of advertisement, and this would mean that we add 4x to the equation that we initially had

Now, to write ordered pairs for the fees for 10, 20, 30, and 40 advertisements, we just have to substitute these values to the equation

x = 10

( 10, 120 )

x = 20

( 20, 160 )

x = 30

Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

Answer:

F

Step-by-step explanation:

Answer:

The point of intersection is F as that is the point where both lines cross each other, and since that is the only point where both lines go through it, it is the point of intersection.

Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

Answer: ( . = multiplication sign)

1. 24

2.  4 questions

3.  3 questions

Step-by-step explanation:

1. You first need to find how many points each part was worth. To do this, you need to find the lowest common multiple for 6 and 8. The lowest common multiple is 24.

2.  Part A has questions that were each worth 6 points so, you need to find the value of  X in this equation: X . 6 = 24 .

The value of X is 4.

3. Part B had questions that were 8 points each so you need to find the value of X in this equation: X . 8 = 24  .

X = 3

Answer:

Ali ran 25.13 m more than bily

Step-by-step explanation:

From the diagram, we can see that bully runs with the inner track line while Ali runs with the outer track line.

Thus;

Diameter of inner semi circle = 20 m

Diameter of outer semi circle = 20 + 4 + 4 = 28 m

Perimeter of inner semi circle = πD/2 = 10π

Perimeter of outer semi circle = πD/2 = 14π

Now, perimeter of Billy = 80 + 80 + 10π + 10π = 222.83 m

Perimeter of Ali = 80 + 80 + 14π + 14π = 247.96 m

Thus, in one lap, difference in distance between Ali and billy = 247.96 - 222.83 = 25.13 m

The histogram for the frequency table is illustrated below.

To create the frequency table, we need to count how many times each time appears in the data set. The time 9:23 appears twice, so we would put a frequency of 2 in the row corresponding to 9:23. We do this for each time in the data set.

Here is the completed frequency table:

Time Frequency

6:10 1

6:21 1

6:55 1

7:12 1

7:20 1

7:34 1

8:15 1

9:01 1

9:14 1

9:15 1

9:18 1

9:23 2

As you can see, each time appears only once or twice in the data set. This tells us that there is no dominant time that most students ran the mile in.

To create the histogram, we'll draw a bar above each time on the x-axis with a height equal to the frequency of that time. For example, there are two times of 9:23, so we'll draw a bar above 9:23 with a height of 2.

As you can see, the histogram shows a relatively even distribution of times. The most common times are around 9 minutes, but there are also several times below 8 minutes and one time below 7 minutes.

To know more about histogram here

https://brainly.com/question/30354484

#SPJ4