The x values of a function is the output true or false

By using power series the approximate value of the given definite integral is 0.000397.

A power series is a numerical portrayal of a capability as a boundless amount of terms, where each term is a steady increased by a variable raised to a particular power.

Based on the information provided:

To approximate the definite integral ∫[0.2 to 0] (x^4/(1+x^5)) dx using a power series, we can use the technique of Taylor series expansion.

First, we need to find a power series representation for the integrand \((x^4/(1+x^5))\). We can start by expressing the denominator as a power of \((1+x^5)\) using the binomial theorem:

\((1+x^5)^{-1}= 1 - x^5 + x^{10} - x^{15} + ...\)

Now we can multiply the numerator x^4 with the power series for (1+x^5)^(-1) to get the power series representation for the integrand:

\(x^4/(1+x^5) = x^4(1 - x^5 + x^{10} - x^{15} + ...)\)

The power series can then be integrated term by term within the specified interval, from 0.2 to 0. We can integrate the integrand's power series representation from 0 to 0.2 because power series can be integrated term by term within their convergence interval.

\(\int\limits^{0.2}_ 0 \,(x^4/(1+x^5)) dx = \int\limits^{0.2}_0} \, (x^4(1 - x^5 + x^{10} - x^{15} + ...)) dx\)

After a certain number of terms, we can now approximate the integral by truncating the power series. To get a good estimate, let's truncate the power series after the x-10 term:

\(\int\limits^{0.2}_0 \, (x^4/(1+x^5)) dx\)     ≈ \(\int\limits^{0.2}_0 (x^4(1 - x^5 + x^{10}) dx\)

Now we can integrate the truncated power series term by term within the interval [0 to 0.2]:

\(\int\limits^{0.2}_0 \, x^4(1 - x^5 + x^{10} )dx\)\(= \int\limits^{0.2}_0 \, (x^4 - x^9 + x^{14}) dx\)

We can integrate each term separately:

\(\int\limits^{0.2}_0 \, x^4 dx - \int\limits^{0.2}_0 \, x^9 dx + \int\limits^{0.2}_0 \, x^{14} dx\)

Using the power rule for integration, we can find the antiderivatives of each term:

\((x^5/5) - (x^{10}/10) + (x^{15}/15)\)

Now we can evaluate the antiderivatives at the upper and lower limits of integration and subtract the results:

\([(0.2^5)/5 - (0.2^{10})/10 + (0.2^{15})/15] - [(0^5)/5 - (0^{10})/10 + (0^{15})/15]\)

Plugging in the values and rounding to six decimal places, we get the approximate value of the definite integral:

0.000397 - 0 + 0 ≈ 0.000397

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Using a power series to approximate the given definite integral to six decimal places, we get:

∫ 0.2 0 (x⁴/1+x⁵) dx ≈ -0.000023

A power series is a numerical portrayal of a capability as a boundless amount of terms, where each term is a steady increased by a variable raised to a particular power.

We can use a power series to approximate the given definite integral:

∫ 0.2 0 (x⁴/1+x⁵) dx = ∫ 0.2 0 (x⁴)(1 - x⁵ + x¹⁰ - x¹⁵ + ...) dx

The series representation of (1/(1-x)) is 1 + x + x² + x³ + ..., so we can substitute (-x⁵) for x in this series and get:

1 + (-x⁵) + (-x⁵)² + (-x⁵)³ + ... = 1 - x⁵ + x¹⁰ - x¹⁵ + ...

Substituting this series in the original integral, we get:

∫ 0.2 0 (x⁴/1+x⁵) dx = ∫ 0.2 0 (x⁴)(1 - x⁵ + x¹⁰ - x¹⁵ + ...) dx

= ∫ 0.2 0 (x⁴)(1 + (-x⁵) + (-x⁵)² + (-x⁵)³ + ...) dx

= ∫ 0.2 0 (x⁴)∑((-1)^n)\((x^{(5n)}) dx\)

= ∑((-1)ⁿ)∫ 0.2 0 \((x^{(5n+4)}) dx\)

= ∑((-1)ⁿ)\((0.2^{(5n+5)})/(5n+5)\)

We can truncate this series after a few terms to get an approximate value for the integral. Let's use the first six terms:

∫ 0.2 0 (x⁴/1+x⁵) dx ≈ (-0.2⁵)/5 - (0.2¹⁰)/10 + (0.2¹⁵)/15 - (0.2²⁰)/20 + (0.2²⁵)/25 - (0.2³⁰)/30

≈ -0.0000226667

Therefore, using a power series to approximate the given definite integral to six decimal places, we get:

∫ 0.2 0 (x⁴/1+x⁵) dx ≈ -0.000023

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Yes, this sample provides a likely estimate of the population parameter. To calculate the sample proportion, we need to divide the sample size by the number of successes.

In this case, the sample proportion is the number of teenagers that received the MMR vaccination (116) divided by the total sample size (400). This produces a sample proportion of 0.29 or 29%. This is close to the population parameter of 33%, so it provides a likely estimate of the population parameter. This can also be demonstrated by calculating the 95% confidence interval of the sample proportion. Using the formula (P ± 1.96√((P)(1-P)/n)), where P is the sample proportion (29%), and n is the sample size (400), the 95% confidence interval is (25.2%, 32.8%). Since the population parameter (33%) falls within this interval, it provides a likely estimate of the population parameter.

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The quadratic expression cannot be factorized, because the discriminant is less than 0

The expression is given as:

x²+12x+180

Calculate the discriminant of the expresison using:

D = B² - 4AC

So, we have:

D = 12² - 4* 1 * 180

Evaluate

D = -576

Because the discriminant is less than 0, then the expression cannot be factorized

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Answer:

2

Step-by-step explanation:

look above

hope it helps:)

Answer:

The final answer would be 2.

400

Explanation:

1/3 of 600 is 200. That represents the boys.

Subtract 200 from 600, you get 400. That represents everybody else in the sample size (in this case, girls).

Answer:

Step-by-step explanation:

Let base be b, height be h

h = 7+b or we can say that b = h -7

A = 15 cm²

General formula for area of a triangle

A = b · h

Substitute what we know to find the height h

15 = (h-7) · h

15 = h² -7h

0 = h²-7h -15

h = (7 ±√49 + 4·1·15)/2

h = (7 ±√109)/2

h ≈ -1.72 reject this solution because height cannot be negative

h ≈ 8.72 cm

Answer:

9 \(\frac{1}{3}\)

Step-by-step explanation:

\(\frac{4}{1}\) x \(\frac{7}{3}\) = \(\frac{28}{3}\) = 9 \(\frac{1}{3}\)

Answer:

x=2

Step-by-step explanation:

-2(1-4x)=3x+8

-2*1 and -2*-4x

-2+8x=3x+8

+2  -3  -3 +2

5x=10

/5.  /5

x=2

Answer:

$103.08

Step-by-step explanation:

The total cost of the scooter including tax to the nearest cent will be $103.08.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

Olive is going to buy a scooter that costs $95. The sales tax rate is 8.5%.

The amount of the sales tax will be

Sale tax = 8.5% of $95

Sale tax = 0.085 × $95

Sale tax = $8.075

The total cost of the scooter including tax to the nearest cent will be

Total cost = $95 + $8.075

Total cost = $103.075 ≈ $103.08

The total cost of the scooter including tax to the nearest cent will be $103.08.

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Answer:

-17+9= -8-9+9

-17+9= -8+0

Step-by-step explanation:

The nines cancel each other then we are left with -8+0

Answer:

Step-by-step explanation:

A line of best fit is a straight line that shows the appropriate correlation among scatter plots of a given data. It is majorly used when the plotted points are not linear, it can be used to express the relationship between dependent and independent variables.

The sum of the residuals should be close to zero because it shows that the line of best fit is accurately drawn. Thus, it implies that there is a linear relationship between the two variables. Since he residual is close to zero, the graph could be said to be a linear graph.

Answer:

82 because 102.50/1.25=82

please mark as brainliest and have a good day

Step-by-step explanation:

Bobby spent $20 out of $75 of his monthly allowance on paintbrushes.

What is monthly allowance?

Giving someone money on a regular basis to help them pay for the things they need is known as giving them an allowance.

Main Body:

total monthly allowance = $75

Now Bobby spent 40% on his art supplies,

which means we need to calculate 40% of 75.

⇒(40/100)*75

⇒30

so Bobby spent $30 on art supplies.

now according to question,

Bobby spent 2/3 on paintbrushes

⇒2/3 of art supplies

⇒(2/3 )*30

⇒$20

Hence Bobby spent $20 on his paintbrushes.

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Step-by-step explanation:

y = 200  - 3 *x  has slope = -3   this is downward sloping from L to R

Answer:downward sloping

Step-by-step explanation:

negative slope

Combine like terms.

6x + 5z + 4

Answer:

x<6

Step-by-step explanation:

7x-3<3+6x

add the 3 to both sides

7x<6+6x

subtract the 6x from both sides

x<6

Answer:

x=-3

Step-by-step explanation:

Let's solve your equation step-by-step.

−7+2(−4x−3)=11

Step 1: Simplify both sides of the equation.

−7+2(−4x−3)=11

−7+(2)(−4x)+(2)(−3)=11(Distribute)

−7+−8x+−6=11

(−8x)+(−7+−6)=11(Combine Like Terms)

−8x+−13=11

−8x−13=11

Step 2: Add 13 to both sides.

−8x−13+13=11+13

−8x=24

Step 3: Divide both sides by -8.

−8x

−8

=

24

−8

x=−3

Answer:

-17/5

Step-by-step explanation:

Multiply ten to everything to get

6x-1= x+2-20

Simplify to 5x= -17

Solve to get x = -17/5

The lateral surface area of the rectangular prism is 72 square inches.

All of the sides of the object are the lateral surface of an object, except its base and top (when they exist). The lateral surface area is the lateral surface zone. This is to be distinguished from the overall surface area, which, along with the base and top areas, is the lateral surface area.

Given that, length =7 inches, breadth =5 inches and height =3 inches.

We know that, the lateral surface area of the rectangular prism is 2(l+b)h

Now, the lateral surface area = 2(7+5)×3

= 2×12×3

= 72 square inches

Therefore, the lateral surface area of the rectangular prism is 72 square inches.

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Among the provided answer options, the closest value to -0.555 is -0.55, which is option c. Therefore, option c (-0.55) is the value of c that satisfies P(Z ? c) = 0.71.

The notation P(Z ? c) represents the probability that a standard normal random variable Z is less than or equal to c. To find the value of c that corresponds to P(Z ? c) = 0.71, we need to determine the Z-score associated with this probability.

Using a standard normal distribution table or a calculator, we can find that a Z-score of approximately 0.555 corresponds to a cumulative probability of 0.71. However, since we are looking for the value of c in P(Z ? c), we need to consider the opposite inequality.

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Answer:

prolly like 689

Step-by-step explanation:

As per the given data, approximately 499 of the 1,000 students obtained a score from 70 to 95.

A standardized score is an example of a z-score. A z-score is a measure of how far a data point is from the mean in a distribution.

To solve this problem, we need to calculate the number of students who obtained a score from 70 to 95.

First, we need to calculate the z-scores for these two scores using the formula:

z = (score - mean) / standard deviation

For a score of 70:

z = (70 - 70) / 5 = 0

For a score of 95:

z = (95 - 70) / 5 = 5

Next, we need to find the area under the standard normal distribution curve between these two z-scores using a standard normal distribution table or calculator.

The area between z = 0 and z = 5 is approximately 0.499, or 49.9%.

Finally, we can calculate the number of students who obtained a score from 70 to 95 by multiplying this proportion by the total number of students:

Number of students = proportion x total number of students

Number of students = 0.499 x 1000

Number of students ≈ 499

Therefore, approximately 499 of the 1,000 students obtained a score from 70 to 95.

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Answer:

x-intercept: (2,0)

y-intercept: (0,-4/3)

vertical asymptote: x = -3

Step-by-step explanation:

To find the x-intercepts, we can set f(x) to 0, which is y=0:

2x-4/x+3 = 0

2x-4 = 0

2x = 4

x = 2

To find the y-intercepts, we can set x to 0:

2(0)-4/(0)+3 = y

y = -4/3

To find the vertical asymptote, we can set the denominator equal to 0:

x+3 = 0

x = -3

The relation R is not reflexive, but it is symmetric and transitive.

A homogeneous relation R over the set A, which comprises the elements x, y, and z, is known as a transitive relation. If R relates x to y and y to z, then R likewise relates x to z.

For x, y ∈ Z, xRy if and only if (x+y)² ≡ ±1.

(a) Reflexivity: For x ∈ Z, we have (x + x)² = 4x² ≡ 0 (mod 1), which is not equal to ±1. Therefore, xRx does not hold for any x ∈ Z, and R is not reflexive.

(b) Symmetry: For x, y ∈ Z, if xRy, then (x + y)² ≡ ±1. This implies that (y + x)^2 ≡ (x + y)² ≡ ±1. Therefore, yRx also holds, and R is symmetric.

(c) Transitivity: For x, y, z ∈ Z, if xRy and yRz, then (x + y)² ≡ ±1 and (y + z)² ≡ ±1. Expanding these expressions, we get:

(x + y)² ≡ ±1  =>  x² + 2xy + y² ≡ ±1

(y + z)² ≡ ±1  =>  y² + 2yz + z² ≡ ±1

Adding these two equations, we get:

x² + 2xy + y² + y² + 2yz + z² ≡ ±2

Simplifying, we get:

x² + 2xy + 2yz + z² ≡ ±2 - 2y²

Now, we need to show that (x + z)² ≡ ±1. Expanding (x + z)², we get:

(x + z)² = x² + 2xz + z²

Substituting x² + 2xy + 2yz + z² ≡ ±2 - 2y², we get:

(x + z)² ≡ 2 - 2y² + 2xz

To complete the proof, we need to show that there exists some integer k such that 2 - 2y² + 2xz - k² ≡ ±1. We can rewrite this expression as:

2xz - k² ≡ 2y² - 3 (mod 4)

Since the left-hand side is even, the right-hand side must also be even. Therefore, y² ≡ 1 (mod 4), which implies that y is odd.

Now, we can substitute y = 2m + 1 for some integer m, and simplify:

2xz - k² ≡ 8m² + 8m - 1 (mod 4)

We can rewrite the right-hand side as 4(2m² + 2m) - 1, which is congruent to -1 (mod 4). Therefore, there exists some integer k such that 2xz - k² ≡ ±1, which implies that (x + z)² ≡ ±1. Hence, xRz holds, and R is transitive.

In summary, the relation R is not reflexive, but it is symmetric and transitive.

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Using Substitution method ,

the solution of expression is either

x =( -5 +√21 )/2 or x = ( -5-√21 )/2.

Substitution method : In mathematics, the substitution method is generally used to solve a system of equations.

In this method, first solve the equation for one variable and substitute the value of the variable into the second equation.

Finally, solve the equation to find the value of the second variable.

We have given expression,

(x + 4)² – 3(x + 4) – 3 = 0

use substituion, a = (x+4)

then we get , a² - 3a - 3 = 0

the above equation is quadrtic equation.

we solve it by using the formula of finding roots of a quadratic equation.

formula for px² + qx + c = 0 quadratic equation is x =( -q +- √q²- 4qc )/2p

so, we have p= 1 , q = - 3 , c = -3

putting the values in above formula we get,

a ={ -(-3) +- √9 - 4×1(-3)}/2×1

=> a = { 3 +/- √21}/2

substitute, a= x+ 4 => x = a-4

=> x = (3 +- √21)/2 - 4 = 1/2 ( 3 +- √21 - 8)

=> x = 1/2( -5 +- √21)

either x = 1/2( -5+√21) or। x = 1/2(-5 -√21)

Hence, the solution for given equation are

x = (-5+√21)/2 or (-5-√21)/2

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The poll conducted among 1755 internet users indicates that a portion of them have posted a photo or video online. However, it is not possible to definitively conclude whether more than half of internet users have done so based solely on this survey.

The poll results show that a specific percentage of the surveyed internet users have posted a photo or video online. However, it is important to note that the sample size of 1755 users might not represent the entire population of internet users accurately. The survey participants might not be a diverse and representative sample, which can introduce biases. Additionally, there may be various reasons why some internet users choose not to share photos or videos online, such as privacy concerns, lack of interest, or limited access to technology. Therefore, while the poll provides insights into the habits of the surveyed individuals, it is not sufficient to draw a conclusive statement about the behavior of all internet users. To make a more accurate conclusion about the overall proportion of internet users who post photos or videos online, a larger and more diverse study encompassing a broader population would be needed.

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Answer:

Sides = 8 each and base = 6

Step-by-step explanation:

Let congruent legs = x, then the base is x - 2 so,

P = x + x + (x - 2)

22 = 3x - 2

24 = 3x

8 = x (sides)

base = 8 - 2 = 6

Answer:(3^3 * 2^(1/2))^1/2 = 3^(3/2) * 2^(1/4) = 3* 3^(1/2) * 2^(1/4)

Step-by-step explanation:

Check the picture below.

well, ∡CED is the same as ∡CEA and those are right-angles so those are pretty much given, now

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{29}\\ a=\stackrel{adjacent}{20}\\ o=\stackrel{opposite}{CE} \end{cases} \\\\\\ CE=\sqrt{ 29^2 - 20^2}\implies CE=\sqrt{ 841 - 400 } \implies CE=\sqrt{ 441 }\implies \boxed{CE=21} \\\\\\ \stackrel{\textit{since we know the radius CB=29}}{CB-CE = EB\implies }\boxed{EB=8}\)

Answer:

angle CED 90°. CE = 21. EB = 8.

Step-by-step explanation:

angle CED = 90° (right angle).

the radius (centre to edge) is the same right around the circle.

so that means that distance CD = 29.

draw a line from C to D. notice how that has just become an hypotenuse?

we know that DE = 20.

we have a right-angled triangle.

CE² = hypot² - DE²

       = 29² - 20²

       = 841 - 400

       = 441

CE = √441 = 21.

EB must be radius subtract CE. that is, 29 - 21 = 8.

Answer: A, C, 57

Step-by-step explanation:

I multiply by 0.40 for the first one, and then multiply by 1.0625. 0.40 = 40% and multiplying by 1.0625 is the same as adding 6.25%. For the second, I multiply by 0.70 because that is 70%. For the last, I multiply by 0.95 for the same reason.