Find a power series representation for the function. (Give your power series representation centered at x = 0.)
f(x) = x2 x 4 + 81
f(x) = [infinity] n = 0.

Answer:

-1020

Step-by-step explanation:

-17 x - 5 x - 12 =

- 17 x 60 =

- 1020

Answer:

$150

Step-by-step explanation:

so you can divvy this up into 3 parts

$150 each

now put 2 parts into one, and one into the other. The cost of the washer is $150

cost of the dryer is$ 300

Answer:

137.24 mm²

Step-by-step explanation:

Big square = 9x9=81

Small rectangle at bottom = 2x3=6

Quarter Circle = 1/4(3.14)(8)(8)=50.24

81+6+50.24=137.24

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:1/6

Step-by-step explanation: divide both sides by 3 as 3 itself and 18 can be divided by 3

The correct piece of aluminum with correct length and width in cm., that

makes the volume of the cylinder maximum.

Reasons:

When the perimeter of the rectangle is 21 cm., we have;

2·l  +  2·w = 21 cm

Where, represents the length of the rectangle and w represents the width of the rectangle.

Which gives;

\(\displaystyle l = \frac{21 - 2\cdot w}{2} = \mathbf{10.5 -w}\)

The volume of the cylinder = π·r²·w

Where;

2·π·r = l

\(\displaystyle r = \frac{l}{2 \cdot \pi} = \mathbf{\frac{10.5 - w}{2 \cdot \pi}}\)

Which gives;

\(\displaystyle V = \pi \cdot r^2 \cdot w = \pi \times \left(\frac{10.5 - w}{2 \cdot \pi}\right)^2 \times w = \mathbf{ \frac{w^3-21 \cdot w^2 + 110.25 \cdot w}{4 \cdot \pi}}\)

At maximum volume, we have;

\(\displaystyle V' = \frac{d}{dw} \left( \displaystyle \frac{w^3-21 \cdot w^2 + 110.25 \cdot w}{4 \cdot \pi} \right) = \mathbf{\frac{0.75 \cdot w^2- 10.5 \cdot w + 27.5625}{\pi}} = 0\)

Which, by using a graphing calculator, gives;

(w - 3.5)·(w - 10.5)·0.75 = 0

w = 3.5 or 10.5

At w = 10.5, we have, l = 10.5 - w = 10.5 - 10.5 = 0

Therefore, the possible width is; w = 3.5

∴ The length, l = 10.5 - 3.5 = 7

The correct option is;

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Answer:

I think this is the answer for the second question.

The simplification form of the expression is 3x²/2 + 2x or three-halves x squared + 2 x option second is correct.

It is defined as the combination of constants and variables with mathematical operators.

We have:

A community garden with raised beds is being redesigned. The area of the new rectangular beds can be expressed as one-half x (3 x + 4).

The expression:

\(\rm = \dfrac{1}{2}(3x+4)\)

By using the distributive property:

\(\rm = \dfrac{1}{2}\times3x^2+\dfrac{1}{2}\times4x\)

\(\rm = \dfrac{3}{2}x^2+2x\)

Thus, the simplification form of the expression is 3x²/2 + 2x or three-halves x squared + 2 x option second is correct.

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Step-by-step explanation:

the equation of a circle centered at the origin is

x² + y² = r²

r being the radius (the distance of the center to every point on the circle's arc).

so, we get a point on the arc : (0, -5).

what is its distance to the origin ?

the origin is (0, 0).

we see, both points have the same x coordinates. they are therefore on the same vertical line going through x=0.

that means there is no distance between them in x direction.

the only distance is in y direction : 0 to -5.

a distance is always positive (no matter in what direction).

so, the distance from 0 to -5 is : 5 units.

that means r = 5.

and our equation is

x² + y² = 5² = 25

Answer: If each person who receives the email sends it to five other people, the number of people who receive it multiplies by five each time the email is forwarded. Therefore, the number of people who receive the email after n iterations are given by:

5^n

Initially, the email is sent to five people, so after the first iteration, 5^1 = 5 people have received the email. After the second iteration, 5^2 = 25 people have received the email. After the third iteration, 5^3 = 125 people have received the email. And so on.

We want to know how many iterations it will take for the email to reach everyone in Australia. According to the Australian Bureau of Statistics, the population of Australia was approximately 25.7 million people in 2021. Therefore, we need to solve the equation:

5^n >= 25,700,000

Taking the logarithm of both sides, we get:

n*log(5) >= log(25,700,000)

n >= log(25,700,000) / log(5)

n >= 7.9

Therefore, it will take at least 8 iterations for the email to reach everyone in Australia. Since each iteration takes 5 minutes, the total time it will take for everyone in Australia to read the email is:

8 iterations x 5 minutes per iteration = 40 minutes.

So, it will take 40 minutes for everyone in Australia to read the email, assuming every person who receives the email forwards it to five new people who have not yet received it.

Step-by-step explanation:

Assuming that everyone who receives the email forwards it to exactly five other people who have not yet received it, we can use a simple exponential growth formula to estimate how long it would take for the entire population of Australia to receive the email:

N = 5^x

where N is the total number of people who have received the email after x rounds of forwarding. Initially, the email is sent to 5 people, so N = 5 when x = 0.

We want to find the value of x when N is equal to the population of Australia, which was approximately 25.7 million people in 2021. So we can set up the following equation:

25.7 million = 5^x

Taking the logarithm of both sides, we get:

x log(5) = log(25.7 million)

Solving for x, we get:

x = log(25.7 million) / log(5)

x ≈ 8.56

Therefore, it would take approximately 8.56 rounds of forwarding for the email to reach every person in Australia. Since each round of forwarding takes 5 minutes, the total time it would take for everyone in Australia to receive the email would be:

8.56 rounds x 5 minutes per round = 42.8 minutes

So it would take about 42.8 minutes for the email to reach every person in Australia, assuming everyone who receives the email forwards it to exactly five other people who have not yet received it.

The surface area of the prism is 70.44 yd²

A prism is a solid shape that is bound on all its sides by plane faces. There are different types of prism, triangular prism, rectangular prism e.t.c

The surface area of a prism is expressed as;

SA = 2B +pH

where B is the base area and p is the perimeter of the base and h is the height of the prism

Base area = 1/2 bh

= 1/2 × 3 × 3 = 4.5 yd²

The hypotenuse of the triangle = √3²+3²

= √9+9 = √18 = 4.24

perimeter of the base = 4.24+3+3 = 10.24yds

Therefore,

SA = 2×4.5 + 10.24 × 6

SA = 9 + 61.44

SA = 70.44 yd²

therefore the surface area of the prism is 70.44yd²

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Answer:

calculator gave me 6.5732

Step-by-step explanation:

Answer:

Ninety thousand, four hundred and three.

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

5.4 hope this help

Answer: 12,800

Step-by-step explanation:

           To find 20% of 64,000, we will turn 20% into a decimal and then multiply. In math, the term "of" usually means multiplication.

20% / 100 = 0.2

64,000 * 0.2 = 12,800

                    20% of 64,000 is 12,800.

Answer:

No se me puedes ayudar por fa

Answer:

6 snack bags

Step-by-step explanation:

This is found by finding the greatest common factor which in this case is 6.  To do this, list our all factors of each and find the one they share that is the greatest.

Hope this helps

Step-by-step explanation:

The way you can think about volume is that we have some cross sectional area times the height of the solid.

27.

The volume of a square based pyramid is

\(v = {s}^{2} ( \frac{h}{3} )\)

where h is the height of the pyramid

s is the side length of the square base.

S=7

h=12

\(v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196\)

28. The volume of a rectangular prism

\(v = l \times w \times h\)

where l is length

w is width

h is height

\(v = 11 \times 11 \times 8 = 968\)

29.

Use the same formula in 27

\(v = 100(3) = 300\)

30.

Volume of a Cylinder is

\(v = \pi {r}^{2} h\)

where r is the radius of the circle

where h is the height

r is half of the diameter

The diameter is 22, thus the radius is 11.

\(v = {11}^{2} (8)(\pi)\)

\(v = 968\pi\)

pi is approximately 3.14

\(v = 3041.06\)

31. Volume of A Sphere

\( \frac{4}{3} \pi {r}^{3} = v\)

The radius is half of diamter, thus r=7

\( \frac{4}{3} \pi( {7}^{3} ) = 1436.76\)

Answer:

Step-by-step explanation:

Construction speed

Time

Road length

We are going to need to multiply to find the total length of road they built.

3 5/6 * 8

23/6 * 8/1

184/6

30.66.. or 30 2/3

Therefore, they built 30 2/3km of road.

Best of Luck!

Answer:

just 2 outcomes

Step-by-step explanation:

no matter how often you throw it, there are only two sides available

The following elements were included in the response: labeling x-axis as age, labeling y-axis as texting speed, plotting points according to age and texting speed, and identifying a relationship between texting speed and age.

In the response, the following elements were included:

1. Labeling the x-axis as the input variable, age: This is important to indicate the independent variable being plotted.

2. Labeling the y-axis as the output variable, texting speed: This is crucial to indicate the dependent variable being represented.

3  Plotting the points according to age and texting speed: This involves placing the ordered pairs (age, texting speed) on the coordinate plane, with age values on the x-axis and texting speed values on the y-axis.

4. Identifying a relationship between the change in texting speed as age increases: By analyzing the plotted points and examining the pattern or trend, one can determine if there is a relationship between age and texting speed. For example, if the texting speed generally increases as age increases or if there is a linear or nonlinear relationship between the two variables.

Including all of these elements allows for a comprehensive analysis of the relationship between age and texting speed, providing a visual representation and enabling the identification of any patterns or trends.

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A) Cube

the two squares will form the top and one side.

Each square right, top and bottom of the square will form the sides

The correlation coefficient of the health research institute data measures the relationship between the age and the years of the smokers

The correlation coefficient is 0.53

The correlation coefficient (r) is calculated as:

\(r = \frac{n(\sum xy) - \sum x \sum y}{\sqrt{[n \sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2}}\)

Using the given parameters, we have:

\(r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1257^2][20 * 836 - 116^2}}\)

Evaluate the exponents

\(r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1580049][20 * 836 - 13456}}\)

Evaluate the products

\(r = \frac{164980 - 145812}{\sqrt{[1976460 - 1580049][16720 - 13456}}\)

Evaluate the differences

\(r = \frac{19168}{\sqrt{[396411*3264}}\)

Evaluate the product

\(r = \frac{19168}{\sqrt{1293885504}}\)

Evaluate the root

\(r = \frac{19168}{35970.6}\)

Evaluate the quotient

\(r = 0.53\)

Hence, the correlation coefficient is 0.53

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With the help of percentage increase information, we conclude that,  Americans spent approximately $1,141.31 on summer vacation in 2014.

What is percenatge increase?

Percentage increase is a measure of how much a value has increased in comparison to the original value, expressed as a percentage.

To find what Americans spent in 2014, we need to use the percentage increase and the 2015 amount.

Let X be the amount spent in 2014.

We know that the increase from 2014 to 2015 is 3.4%, which can be expressed as:

3.4% = 0.034 (as a decimal)

We also know that the amount spent in 2015 is $1,180.

Using this information, we can set up an equation:

X + 0.034X = 1180

Simplifying the left side:

1.034X = 1180

Dividing both sides by 1.034:

X = 1141.31

So Americans spent approximately $1,141.31 on summer vacation in 2014.

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The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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The required change in the percentage is 20%.

Given that,
clarissa's division test was 60% in the first six weeks and 72% in the second six weeks. To determine the percent change.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
According to the question,
The change in the percentage  = (72 - 60) / 60 × 100
The change in the percentage = 20%

Thus, the required change in the percentage is 20%.

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