find a power series representation for the function. f(x) = x2 (1 − 2x)2

Answer:

-3 = x * 2

Step-by-step explanation:

-3 = x * 2

-1.5 = x * 1

-1.5 = x

x = -1.5

Chow,...!

There is a 16.7% chance or probability  of selecting three state flags without replacement, where all three flags have only two colors.

To calculate the probability of selecting three state flags with only two colors, we first need to determine how many state flags meet this criteria. Out of the 50 state flags in the United States, there are only three flags that have two colors - Maine, Maryland, and Missouri.
Now that we know there are only three possible flags to choose from, we can calculate the probability of selecting all three with only two colors.
When we randomly select the first flag, there are three possible flags to choose from. However, only one of them has only two colors. Therefore, the probability of selecting a flag with two colors on the first try is 1/3.
After the first flag is selected, there are only two flags left that meet the criteria. Therefore, the probability of selecting a second flag with two colors is 1/2.
Finally, after the second flag is selected, there is only one flag left that meets the criteria. Therefore, the probability of selecting the third flag with two colors is 1/1 (or simply 1).
To calculate the probability of all three events happening together (selecting three flags with only two colors), we need to multiply the probabilities of each event together.
Therefore, the probability of selecting three state flags without replacement, where all three flags have only two colors, is:
1/3 x 1/2 x 1/1 = 1/6 or approximately 0.167.
In simpler terms, there is a 16.7% chance of selecting three state flags without replacement, where all three flags have only two colors.

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Answer:

I think that the original price would be $30, but I'm not completely sure.

Step-by-step explanation:

Half (50%) of 40 would be 20, and half of 20 (25%) would be 10. Add 10 to 20 to get 30, because you are adding the %25 back to $20.

Hope this helps!

Answer:

$80

Step-by-step explanation:

25% = 1/4

To get original price multiply by 4:

$20 × 4 = $80

Answer:

Mac is 19 years old, Joe is 11 years old

Step-by-step explanation:

2J - 3 = M

J + M = 30

M = 30 - J

2J - 3 = 30 - J

3J = 33

J = 11

M = 30 - 11

M = 19

According to Chebyshev's theorem, at least 56% of the lifetimes lie between 724 and 1096 hours.

If a distribution is not normal or is not known to be normal, Chebyshev's theorem may be used to estimate the proportion of data that falls within k standard deviations of the mean, where k is any positive number greater than or equal to 1.

The percentage of the data falling within k standard deviations of the mean is at least as great as the percentage given by the formula 1 - 1/k².

Suppose that a random variable X has mean μ and standard deviation σ.

Let k > 0 be any number, and let a and b be real numbers such that a < μ - kσ < b.

Then Chebyshev's theorem asserts that at least 1 - 1/k² of the data values lie between a and b.

In other words, the proportion of data that falls outside the interval from a to b is no greater than 1/k².

BTG Compration produces nearly everything, but is now interested in the lifetimes of its batteries.

To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra batteries and discovers that they have an average lifespan of 910 hours and a standard deviation of 93 hours.

It is supposed that this mean and standard deviation apply to all Ultra battery populations. Let X be the random variable representing the lifespan of Ultra batteries. Then X has a normal distribution with a mean of 910 and a standard deviation of 93.  

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Answer with explanation:

hope you find this easy to understand....

Have any questions? Write in the comments.

give me brainliest if you found this answer useful

The final answers are given below

\(10.\)L

\(11.\) \(3\) (the number should be \(1,000,000\), which has six zeros)

\(00000\)

\(12\)  | |

\(00000\)

|

\(00000\)

\(15. 31 16 48 29 53 47 22 37 98 26 2025\)

A number is an arithmetic value that is used to calculate and represent a quantity.

The numbers that are more than \(20\) but less than \(30\) are \(22\) and \(26\), so they should be crossed out:

\(31 16 48 29 53 47\) X \(37 98\) X \(2025\)

Therefore the answers are given below.

\(10.\)L

\(11.\) \(3\) (the number should be \(1,000,000\), which has six zeros)

\(00000\)

\(12\)  | |

\(00000\)

|

\(00000\)

\(15. 31 16 48 29 53 47 22 37 98 26 2025\)

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t = 14.31 days

The formula for calculating the interest is given as:

where:

P is the principal

R is the rate

T is the time

Given the following parameters

P = $6800

I = $20

rate = 7.5% = 0.075

Substitute the given parameters into the formula

Convert to days

Since there are 365days in a year, hence;

Hence the time of the loan is about 14.31 days

Answer:

If you multiple 1050 by 20 you will get 21,000.

Answer:

The line should look like: y=5x+4

Step-by-step explanation:

The equation for slope-intercept form is y=mx+b, where m is your slope and b is your y-intercept.

Therefore, if we plug in the given values, our equation should look like the following:

y=5x+4

Answer:

y=5x+4

y=mx+b

The calculated value of the side length in the triangle is 144

From the question, we have the following parameters that can be used in our computation:

The simiar triangles

Using the theorem of corresponding sides, we hav

GH = 2JK

So, we have

10x - 36 = 2 * 4x

Multiply

So, we have

10x - 36 = 8x

Evaluate

2x = 36

So, we have

x = 18

This means that

GK = 4 * 18

GK = 144

Hence, the indicated side length in the triangle is 144

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2 nickles, 6 dimes. Not 100% sure but I think it's right

Answer:

a: -3x+1

Step-by-step explanation:

-3x+1

hope it helps <3

Work Shown:

r = 6 = radius

V = volume of a sphere of radius r

V = (4/3)*pi*r^3

V = (4/3)*pi*6^3

V = 904.77868423386

V = 904.8

I used my calculator's stored version of pi (instead of something like pi = 3.14)

The units "cubic meters" can be abbreviated to m^3 or \(m^3\)

The volume of the given sphere is 904.8 cubic meters. Thus, option B is the answer.

         The volume of a sphere can be calculated using the formula:

V = \(4/3 * \pi * r^3\),

Where V is the volume and r is the radius of the sphere.

\(\pi\) = 3.14

The radius of the sphere (r) = 6m

Plugging in the given radius of 6m into the formula, we get:

V = (4/3) * \(\pi\) * (6^3)

V = 1.333 * \(\pi\) * 216

V = 1.333 * 3.14 * 216

V = 4.1866 * 216

V = 904.8 cubic meters

Therefore, when the radius of the sphere is 6m, the volume of the sphere is 904.8  cubic meters.

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Answer:

Last one

A student‘s test score is likely to increase about 20 points for each hour of studying

Step-by-step explanation:

We can see that the indepedent value is hours spent studying and dependent value is test scores.

As the hours of studying get greater, so does the test scores. So it has to be either the second to last or last one.

If you pay attention to the numbers, you’d see that the last one would be the answer.

Answer:

last one

Step-by-step explanation:

each hour spent studying increases the by around 20 points. the slope of the line is 20.

btw there's nothing on the intercept in the question

Without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

To calculate a 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B, we can use the least squares means estimates provided in the JMP output.

According to the JMP output, the estimate for the mean time required to stabilize emergency condition 4 using display panel B is 10.375000.

To calculate the confidence interval, we need to find the margin of error. The margin of error can be calculated using the formula:

Margin of Error = Critical Value * Standard Error

In this case, we need to find the critical value for a 95 percent confidence interval. Since we have a sample size of 24 (as mentioned in the question), we can use the t-distribution with (24-1) degrees of freedom to find the critical value.

Looking up the critical value in the t-distribution table, with (24-1) degrees of freedom and a confidence level of 95 percent, we find that the critical value is approximately 2.064.

The standard error can be calculated using the formula:

Standard Error = Standard Deviation / √(sample size)

The standard deviation is not provided in the given information. Therefore, we cannot calculate the standard error or the confidence interval without this information.

In summary, without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

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The sequence {an} = {\(8n^4 + n + 1\)} is not convergent. It diverges to infinity as n approaches infinity.

To determine whether the sequence {an} = {\(8n^4 + n + 1\)} is convergent, we need to examine the behavior of the terms as n approaches infinity.

The sequence {an} is said to be convergent if there exists a real number L such that the terms of the sequence get arbitrarily close to L as n approaches infinity.

To investigate convergence, we can calculate the limit of the sequence as n approaches infinity.

lim(n→∞) \((8n^4 + n + 1)\)

To evaluate this limit, we can look at the highest power of n in the sequence, which is \(n^4.\) As n approaches infinity, the other terms (n and 1) become insignificant compared to n^4.

Taking the limit as n approaches infinity:

lim(n→∞) \(8n^4 + n + 1\)

= lim(n→∞) \(8n^4\)

Here, we can clearly see that the limit goes to infinity as n approaches infinity.

Therefore, the sequence {an} = {\(8n^4 + n + 1\)} is not convergent. It diverges to infinity as n approaches infinity.

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Answer:

A. 1.20x; individuals signing up the day of the activity get charged 20% more

Step-by-step explanation:

Amount charged before the day of activity = x

Amount charged on any individual who decides to sign up on the day of activity would be the normal price, x dollars, plus an additional price of 0.20x dollars.

0.20x = 20% of x.

That is, the additional fee added to the normal price is 20% of the normal price.

Therefore, amount paid on the day of the activity is x + 0.20x = 1.20x dollars.

What this fee means is that those who decide to sign up on the day of the activity are charged 20% more.

The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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To determine when the ball strikes the ground, we need to find the value of t when the height h(t) is 0.

The equation for the ball's height h at time t seconds after launch is:

h(t) = -4.9t^2 + 9.31t + 239.12

Setting h(t) to 0, we get:

0 = -4.9t^2 + 9.31t + 239.12

We can solve this quadratic equation using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -4.9, b = 9.31, and c = 239.12.

Answer: 6.12 seconds

Step-by-step explanation:

To find when the object strikes the ground, we need to find the time t when the height h(t) is equal to 0 (since the ground is at height 0). We have the equation:

h(t) = -4.9t² + 9.31t + 239.12

To find the time when the object strikes the ground, we need to find the value of t when h(t) = 0:

0 = -4.9t² + 9.31t + 239.12

This is a quadratic equation of the form at² + bt + c = 0, where a = -4.9, b = 9.31, and c = 239.12. We can solve this equation for t using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

Plugging the values of a, b, and c into the formula, we get:

t = (-(9.31) ± √((9.31)² - 4(-4.9)(239.12))) / (2(-4.9))

t = (-9.31 ± √(86.6161 + 4694.336)) / (-9.8)

t = (-9.31 ± √(4780.9521)) / (-9.8)

t ≈ (-9.31 ± 69.14) / (-9.8)

We will have two possible values for t:

t₁ ≈ (-9.31 + 69.14) / (-9.8) ≈ 6.12 (rounded to two decimal places)

t₂ ≈ (-9.31 - 69.14) / (-9.8) ≈ 8.00 (rounded to two decimal places)

Since the height function describes the motion of the ball from a platform, we can discard the negative solution as it represents an invalid time before the ball is launched. Thus, the object strikes the ground at approximately t ≈ 6.12 seconds.

Answer:

the equation is 9.75c=20.75

then the amount is 2.13

Step-by-step explanation:

Answer: c - 9.75 = 20.75

  flip it   20.75 - 9.75 = c

             -  9.75

        ____________

                11.00

C = 11.00

Step-by-step explanation:

Application of Formulas in Geometry By textbook tactics

99,096 views•May 25, 2012

This Video should help you solve your equation

Hope it Helps :)

The net pay of  Alisha Gregory  is $30606.4

Since we are given the weekly gross  pay of her  is $640

The annual gross pay will  be  52 *  640 =33280.

Here the local income tax is  1.5% of the gross, which is  1.5/100 * 33280  = 499.2 and  it is also specifically said that the state tax is the 3.0% of taxable income.

So we have:

3/100 * 33280= 998.4

The medical insurance is $1,940 for a year from where the company  pays 60 %

For which we have:

60/100 *1940

= 1164

At the last he pays  $4.50  for union dues and $7.50 for others.

Since we know that the net pay is nothing but the amount we get after subtracting the deductions from the annual gross pay

So the net pay = 33280- (499.2+998.4+1164+4.50+7.50)

                         =  33280  -(2673.6)

                         =  30606.4

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So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

Given

r= 2cost and theta = 9t

To Find

the velocity and acceleration vector

Solution

We can start by expressing the position vector r in terms of the Cartesian coordinates x and y:

x = r cos(theta) = 2cos(t)

y = r sin(theta) = 2sin(t)

To find the velocity vector, we can take the time derivative of the position vector:

v = (dx/dt) i + (dy/dt) j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the derivatives:

dx/dt = -2sin(t)

dy/dt = 2cos(t)

Substituting these back into the velocity vector equation:

v = (-2sin(t)) i + (2cos(t)) j

To find the acceleration vector, we can take the time derivative of the velocity vector:

a = (d^2x/dt^2) i + (d^2y/dt^2) j

Taking the derivatives:

d^2x/dt^2 = -2cos(t)

d^2y/dt^2 = -2sin(t)

Substituting these back into the acceleration vector equation:

a = (-2cos(t)) i + (-2sin(t)) j

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

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Answer:

13.994 grams

Step-by-step explanation:

Using the given balanced equation: 2Na + 2H2O → 2NaOH + H2

Calculate the molar mass of NaOH:

Na: atomic mass = 22.99 g/mol

O: atomic mass = 16.00 g/mol

H: atomic mass = 1.01 g/mol

Molar mass of NaOH = (1 * Na) + (1 * O) + (1 * H) = 22.99 + 16.00 + 1.01 = 40.00 g/mol

Determine the number of moles of Na:

Given mass of Na = 8.0465 g

Number of moles of Na = mass / molar mass = 8.0465 g / 22.99 g/mol = 0.35015 mol

Use stoichiometry to convert moles of Na to moles of NaOH:

According to the balanced equation, 2 moles of Na produce 2 moles of NaOH.

Number of moles of NaOH = 0.35015 mol * (2 mol NaOH / 2 mol Na) = 0.35015 mol

Convert moles of NaOH to grams:

Mass of NaOH = number of moles of NaOH * molar mass of NaOH = 0.35015 mol * 40.00 g/mol = 13.994 g

Using 5 significant figures, the mass of NaOH that can be produced from 8.0465 g of Na is approximately 13.994 g.

986.58 cubic meters  of water needs to be pumped into the chamber for one lift

To find the amount of water that needs to be pumped into the chamber for one lift, we need to find the volume of the chamber. the volume of the chamber can be calculated using the formula for volume which is

Volume = length × width × height

where

length = 42 m

width = 8.1 m and

height = 2.9 m.

Volume = 42 m × 8.1 m × 2.9 m

Volume = 986.58 cubic meters

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Positive curve graphs will be upward-sloping.

Negative curve graphs will be downward-sloping.

Both graphs in the first image attached below, show curves sloping upward from left to right. As with upward-sloping straight lines, we can say that generally the slope of the curve is positive. While the slope will differ at each point on the curve, it will always be positive.

In the graphs in the second image attached, both of the curves are downward sloping. Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.

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Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.

Answer:

\(\mathrm{Slope } = \dfrac{2}{3}\)

Step-by-step explanation:

To find the slope take any two convenient x, y value combo.

Find the difference between the two y-values(we call it rise).

Find the difference in the corresponding x-values (we call this the run)

\(\dfrac{rise}{run} = slope\)

Take points (3, 1) and (6,3). I could choose any two points but working with positive numbers makes it easier

Rise = 3- 1 = 2

Run = 6 - 3 = 3

\(\mathrm{Slope } = \dfrac{2}{3}\)

Just for the heck of it let's take two other points to make sure we haven't goofed

Take points (-1, - 5/3) and (1, -1/3)

rise = -1/3 - (-5/3) = -1/3 + 5/3 = 4/3

run = 1 - (-1) = 2

rise over run = 4/3 ÷ 2 = 4/3 x 1/2 = 2/3