if f(x) =4x²+1 and g(x) =x²-5, find (f-g)(x)​

The series converges, and we need to add 7 terms to find the sum with an error less than 0.00005.

To test the given series for convergence or divergence, we can use the Alternating Series Test. The series is in the form:

Σ((-1)^(n+1))/(5n^4) for n=1 to infinity

1. The terms are alternating in sign, as indicated by the (-1)^(n+1) factor.
2. The sequence of absolute terms (1/(5n^4)) is positive and decreasing.

To show that the sequence is decreasing, we can show that its derivative is negative. The derivative of 1/(5n^4) with respect to n is:

d/dn (1/(5n^4)) = -20n^(-5)

Since the derivative is negative for all n ≥ 1, the sequence is decreasing.

Since both conditions for the Alternating Series Test are satisfied, the series converges.

Now, we need to use the Alternating Series Estimation Theorem to find how many terms we need to add to achieve an error less than 0.00005. The theorem states that the error is less than the first omitted term, so we have:

1/(5n^4) < 0.00005

Now, we need to solve for n:

n^4 > 1/(5 * 0.00005) = 4000

n > (4000)^(1/4) ≈ 6.3

Since n must be an integer, we round up to the nearest integer, which is 7. Therefore, we need to add 7 terms to achieve the desired error.

The series converges, and we need to add 7 terms to find the sum with an error less than 0.00005.

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The probability that a male passenger can fit through the doorway without bending is 0.9983.

To solve this problem, we need to find the probability that a randomly selected male passenger has a height less than or equal to 78 inches. We can use the standard normal distribution to do this by standardizing the height:

z = (78 - 69) / 2.8 = 3.214

Using the standard normal distribution table or calculator, we can find that the probability of a z-score less than or equal to 3.214 is approximately 0.9992.

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Answer:

-5

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

The graph of y=6(0.5)x is a decreasing exponential function.

Graph is a data structure that consists of nodes and edges. Nodes are the points which are connected by edges. Graphs are used to represent relationships between different objects, and can be used to represent real-world scenarios such as social networks, road networks, and other types of networks. Graphs are widely used in data science, machine learning, AI, and many other fields. Graphs are powerful because they can show complex relationships between data points that would otherwise be difficult to understand. With graphs, it is easier to analyze and visualize data, allowing for better decision-making.

This is because the exponent, 0.5, is a fraction less than 1, meaning that the value of y decreases at a faster rate with increasing x. This is why the graph is not a straight line, because the slope decreases with increasing x. Furthermore, the y-intercept is (0,6), meaning that the graph starts at 6 on the y-axis and decreases from there. Additionally, the x-intercept is (0.5,0), meaning that the graph crosses the x-axis at 0.5 and decreases from there. Finally, the equation of the asymptote is x=0, indicating that the graph approaches x=0 asymptotically as x approaches infinity. Thus, the graph of y=6(0.5)x is a decreasing exponential function.

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The maximum fishery biomass that can be removed yearly while still sustaining the population is known as the Maximum Sustainable Yield (MSY).

The Maximum Sustainable Yield (MSY) represents the maximum amount of fishery biomass that can be harvested from a population each year while maintaining its long-term sustainability. It is a crucial concept in fisheries management, aiming to balance resource utilization with the need for population replenishment.

By setting harvest limits below the MSY level, fish stocks can regenerate, ensuring the continuation of the fishery in the future. MSY takes into account various factors such as population growth rates, reproductive potential, and ecosystem dynamics to determine a sustainable level of extraction.

Proper adherence to MSY principles helps prevent overfishing and promotes the conservation of aquatic resources.

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Answer:

-33

Step-by-step explanation:

With the brackets in an equations, it just means you are going to be solving within there first before moving on.

For any equations such as this, you'll want to follow PEMDAS.

Parenthesis (x)
Exponents \(x^{2}\)
Multiplication x * y
Division x/y or x÷y or \(\frac{x}{y}\)
Addition x+y
Subtraction x-y

To start, we're just going to take the bracket equations 2+4 x 2 + (10 - 5)

\(2+4*2+5/5\)

Moving down PEMDAS we have no exponents, but multipication and division, whichever comes first in the equation.

4*2 = 8

5/5 = 1

2+8+1 = 11

-3[11] = (You use multiplication here) -33

-39

Step-by-step explanation:

\({ \blue{ \sf{ - 3{[2 + 4 \times 2 + (10 - 5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[6 \times 2 + (10 - 5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[12 + (10 - 5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[12 + (5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[12 + 1]}}}}\)

\( { \blue{ \sf{ - 3[13]}}}\)

\({ \red{ \sf{ - 39}}}\)

nevermind im wrong. ;(((((((((((((

Answer:

Go 6 units to the right and then 8 units up.

Answer:

so Go 6 units to the right and then 8 units up. and then you should get your point on the graph id apreciate brainliest

Step-by-step explanation:

Answer:

- x - y

-(-12) -(2)

12-2

10 the answer is D

Answer:

[See Below]

Step-by-step explanation:

\(Hey~There!\)

________________________

➜ Solve:

________________________

So based on our work above we can conclude that the equation is equal because when solve it equals \(1\), making \(1=1\).

________________________

\(Hope~this~helps~Mate!\\-Your~Friendly~Answerer,~Shane\) ヅ

Answer:

(x + 5)² + (y + 2)² = 120

Step-by-step explanation:

You need two pieces of information to write the equation of a circle, the center and the radius. This was given in the question so you can just use the following fill-in-the-blank formula to write the equation.

If the center is (h, k) and the radius is r, fill them in here:

(x - h)² + (y - k)² = r²

For your question the center is (-5, -2) and r is√120.

You do need to already know that "minus-a-negative" IS the same as "plus-a-positive" (that's why the final answer has + inside the parentheses) ALSO, you need to know that square and squareroot un-do each other. So if you square sqrt120, you just get "plain" 120. That is, (sqrt120)² is 120.

Fill in the center and radius:

(x - h)² + (y - k)² = r²

(x - -5)² + (y - -2)² = (√120)²

Simplify.

(x + 5)² + (y + 2)² = 120

Taaa-daaa! that's it! Don't you think more people would hate formulas less if they were sold as "fill-in-the-blank" and "shortcuts" !?!  I think so!

So the total surface area of the composite figure is 138 square inches.

To find the surface area of the composite figure, we need to add the areas of all the faces of the figure.

The square has an area of 6 * 6 = 36 square inches.

The green rectangular prism has a base with an area of 6 * 3 = 18 square inches. It also has four lateral faces, each with an area of 3 * 7 = 21 square inches. The total area of the lateral faces is 4 * 21 = 84 square inches.

So the total surface area of the composite figure is 36 + 18 + 84 = 138 square inches.

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For a function, f(x) = 1 + 3x , the computed value of lim h→0 [f(5 + h) − f(5)]/h is equals to the three.

In Mathematics, the limit of a function is a value of the function as the input of the function tries approaches some number. Function limits are used to define continuity, integrals, and derivatives. Mathematically, let f(x) be a function and L be limit of function, f(x) at x a exist if and only if lim f(x) = lim f(x) = L

x→a⁻ x→a⁺

We have, f(x) = 1+3x and will compute lim h→0 [f(5 + h) − f(5)]/h . Firstly, determine the value of function at x = 5 , x = 5+h.

So, f(5) = 1+ 3×5 = 16 and f(5+ h) = 1+3(5+h)

= 16+ 3h

Now, lim [ f(5 + h) − f(5)]/ h

h→0

= lim [(16 + 3h) − (16) ]/ h

h→0

= lim [ 16 + 3h - 16 ]/ h

h→0

= lim [ 3h/ h ] = lim [ 3h¹h⁻¹ ]

h→0 h→0

= lim [ 3h¹⁻¹ ] = lim [ 3h⁰ ]

h→0 h→0

= lim 3 (1) = 3 ( since, x⁰ = 1 )

h→0

Hence, the required limit value is 3.

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The probability that the dispensers dispense less than 9.95gl is 0.0013.

Given that,The sample size (n) = 80 Mean (μ) = 9.8 Standard deviation (σ) = 0.1

We need to find the probability that the dispensers dispense less than 9.95gl, i.e., P(X < 9.95).

Let X be the amount of gasoline dispensed when a 10gl tank was filled.

A 10gl tank can be filled with X gl with a mean of μ = 9.8 and standard deviation of σ = 0.1.gl.

So, X ~ N(9.8, 0.1).

Using the standard normal distribution, we can write;

Z = (X - μ)/σZ = (9.95 - 9.8)/0.1Z

= 1.5P(X < 9.95) = P(Z < 1.5).

From the standard normal distribution table, the probability that Z is less than 1.5 is 0.9332.

Hence,P(X < 9.95) = P(Z < 1.5) = 0.9332.

Therefore, the probability that the dispensers dispense less than 9.95gl is 0.0013.

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Answer:

That's great to hear that Pete, the skateboarding penguin, is practicing on a ramp!

Based on the information provided, we have a right triangular prism with a height of 8 meters and a hypotenuse of 17 meters.

The ramp is in the shape of a right triangular prism, which means it has a triangular base and extends upward in a perpendicular direction to form a prism.

The height of the ramp is the vertical distance from the base to the top of the ramp, which is given as 8 meters.

The hypotenuse of the triangular base is the slant height of the ramp, and it is given as 17 meters.

It's important to note that in a right triangle, the hypotenuse is always the longest side and is opposite the right angle.

In this case, the hypotenuse of the triangular base is 17 meters, and it is opposite the right angle of the triangular base.

Knowing the height and hypotenuse of the ramp, we can use the Pythagorean Theorem to find the length of the base of the triangular ramp. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

In this case, the height (a) is 8 meters, the hypotenuse (c) is 17 meters, and the length of the base (b) is what we need to find.

We can use the Pythagorean Theorem to solve for

b:a^2 + b^2 = c^2

8^2 + b^2 = 17^2

64 + b^2 = 289

b^2 = 289 - 64

b^2 = 225

b = sqrt(225)

b = 15

So, the length of the base of the triangular ramp is 15 meters.

Step-by-step explanation:

The nullspace of A is the set of all scalar multiples of the vector [1;-2;1].

As a language model, I do not have access to the specific exercises you are referring to. However, I can provide a general explanation of how to find the nullspace of a matrix.

The nullspace of a matrix A is the set of all solutions to the equation Ax = 0. In other words, it is the set of all vectors x that satisfy the equation Ax = 0.

To find the nullspace of a matrix, we need to solve the equation Ax = 0. This can be done by reducing the matrix A to its reduced row echelon form (RREF) using row operations. The RREF will have a certain structure that makes it easy to identify the solutions to the equation Ax = 0.

The RREF of a matrix A will have one or more leading 1's in each row, with all other entries in the row equal to 0. The columns containing the leading 1's are called pivot columns, and the columns without leading 1's are called free columns.

If a column is a pivot column, then the corresponding variable is a basic variable and can be expressed in terms of the free variables. If a column is a free column, then the corresponding variable is a free variable and can take on any value.

Using this information, we can express the solutions to the equation Ax = 0 in terms of the free variables. The nullspace of A is then the set of all linear combinations of the free variables that satisfy the equation Ax = 0.

For example, consider the matrix A = [1 2 3; 4 5 6; 7 8 9]. To find its nullspace, we first find its RREF:

[1 0 -1; 0 1 2; 0 0 0]

The RREF has two pivot columns (columns 1 and 2) and one free column (column 3). The corresponding variables are x1 and x2 (basic variables) and x3 (free variable). Expressing the solutions in terms of the free variable, we get:

x1 = x3

x2 = -2x3

The nullspace of A is then the set of all linear combinations of the free variable x3:

null(A) = {t[1;-2;1] : t is a scalar}

So, the nullspace of A is the set of all scalar multiples of the vector [1;-2;1].

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The numerical length of PQ is 20

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that the line segments are: -

OQ=11  O P = 9

The numerical value of PQ will be calculated as below.

OP+OQ=PQ

11+9=PQ=11+9=PQ

Therefore PQ=20=PQ

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Answer:

A

Step-by-step explanation:

Answer:

f(a+2)=3a+11/a+2

Step-by-step explanation:

Answer: -8

Step-by-step explanation: 2.25x-20 = 6.5x +14

Subtract 14 on both sides and rearrange, 6.5x= 2.25x -34

then subtract 2.25x from both sides, 4.25x= -34

Finally divide both sides by 4.25 to get x = -8

Hope this helped!

Answer:

Step-by-step explanation:

6.5x + 14 = 2.25x - 20

4.25x + 14 = -20

4.25x = -34

x= -8

The odds in favor of obtaining a number divisible by 3 or 4 in a single roll of a die are 7:5 or 7/5.

The probability of obtaining a number divisible by 3 or 4 in a single roll of a die can be found by adding the probabilities of rolling 3, 4, 6, 8, 9, or 12, which are the numbers divisible by 3 or 4.

There are six equally likely outcomes when rolling a die, so the probability of obtaining a number divisible by 3 or 4 is:

P(divisible by 3 or 4) = P(3) + P(4) + P(6) + P(8) + P(9) + P(12)

P(divisible by 3 or 4) = 2/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

P(divisible by 3 or 4) = 7/12

The odds in favor of an event is the ratio of the probability of the event occurring to the probability of the event not occurring. Therefore, the odds in favor of obtaining a number divisible by 3 or 4 in a single roll of a die are:

Odds in favor = P(divisible by 3 or 4) / P(not divisible by 3 or 4)

Odds in favor = P(divisible by 3 or 4) / (1 - P(divisible by 3 or 4))

Odds in favor = 7/5

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The measure of RS to the nearest hundredth is 23.09 m

From the given figure, we have the following parameters

Adjacent to <R = RS

hypotenuse = 20cm

Using the theorem;

cos theta = opp/hyp

cos<R = RS/20
cos 30 = RS/20
RS = 20/cos30

RS =23.094 m

Hence the measure of RS to the nearest hundredth is 23.09 m

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A confidence interval cannot instantly lead to rejecting the null hypothesis in a hypothesis test. In the given case the null hypothesis is either rejected or rejected based on test statistics.

α = 0.05

μ = 2

If the confidence interval is 1.0 or 2.0, then the null hypothesis value of 2 drops exceeds the interval, this makes the data contradict the null hypothesis and may reject the null hypothesis.

This alone would not be good to decline the null theory - the conclusion to reject or not reject the null hypothesis is determined by the test statistic and the alternate p-value.

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Answer:

-72

Step-by-step explanation:

first replace x with -12 so 5(-12)-12

then simplify which makes it -60-12

finally solve that which gives you -72

hope this helps :)

Answer:

\(\frac{5}{12}\)

Step-by-step explanation:

Make both fractions have a common denominator

\(\frac{5}{12}=\frac{50}{120}\)

\(\frac{6}{10}=\frac{72}{120}\)

Therefore, \(\frac{5}{12}<\frac{6}{10}\) since \(\frac{50}{120}<\frac{72}{120}\)

We used the induction hypothesis to write U₁ + U₂ + ... + Uₘ₋₁ as a direct sum of subspaces, and then applied the formula for the dimension of the sum of two subspaces to U₁ + U₂ + ... + Uₘ₋₁ and Um. The result followed by simplification.

In the first problem, we were asked to find a number t such that the set of vectors {(3,1,4), (2,-3,5), (5,9,t)} is not linearly independent in R³. We can determine the value of t by calculating the determinant of the matrix formed by these vectors, and setting it equal to zero. Solving for t, we get t = -182. This means that the vector (5,9,-182) can be expressed as a linear combination of the other two vectors, and therefore the given set is linearly dependent.

In problem 12, we were asked to find a basis of the subspace U defined by U = {(x₁, x₂, 2x₁, x₄, x₅) ∈ R⁵ : 2x₁ = x₂ and x₄ = x₅}, and a subspace W of R⁵ such that R⁵ = U ⊕ W. We found that a basis for U is {(1,2,2,0,0), (0,1,0,1,1)}, which are linearly independent and span U. To find a subspace W, we chose the subspace spanned by {(0,0,1,0,0), (0,0,0,1,0), (0,0,0,0,1)}, which is also linearly independent and has dimension 3. Since dim(U) + dim(W) = 2 + 3 = 5, and U ∩ W = {0}, we have shown that R⁵ = U ⊕ W.

In problem 13, we were asked to show that if V₁, V₂, ..., Vₘ is a linearly independent list of vectors in V, then the list lV₁, V₂, ..., Vₘr is also linearly independent for any scalar l ≠ 0. To prove this, we assumed that there exists a nontrivial linear combination of the vectors lV₁, V₂, ..., Vₘ that equals zero, and showed that this implies the existence of a nontrivial linear combination of the vectors V₁, V₂, ..., Vₘ that also equals zero. This contradicts the assumption that V₁, V₂, ..., Vₘ is a linearly independent list, and therefore we proved that lV₁, V₂, ..., Vₘr is linearly independent.

In problem 14, we were asked to prove that if U₁, U₂, ..., Uₘ are finite-dimensional subspaces of V, then the sum U₁ + U₂ + ... + Uₘ is also finite-dimensional, and its dimension is given by dim(U₁ + U₂ + ... + Uₘ) = dim(U₁) + dim(U₂) + ... + dim(Uₘ) - dim(U₁ ∩ U₂) - dim(U₁ ∩ U₃) - ... - dim(Uₘ₋₁ ∩ Uₘ). To prove this, we used induction on m, the number of subspaces. For the base case m = 2, we used the fact that the intersection of two subspaces is also a subspace, and applied the formula for the dimension of the sum of two subspaces.

For the general case, we used the induction hypothesis to write U₁ + U₂ + ... + Uₘ₋₁ as a direct sum of subspaces, and then applied the formula for the dimension of the sum of two subspaces to U₁ + U₂ + ... + Uₘ₋₁ and Um. The result followed by simplification.

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To find the volume of a triangular-based pyramid, you can use the following formula:

\(V = (1/3) * A_{base} * h\)

\(V = (1/3) * A_{base} * h\)

where:

- V represents the volume of the pyramid

- \(A_{base\) represents the area of the triangular base

- h represents the height of the pyramid

1. Determine the measurements: Measure the length of the base of the triangle (b) and the height of the triangle (\(h_{base\)). If the triangle is not right-angled, use trigonometric calculations to determine the height.

2. Calculate the area of the base: Use the formula for the area of a triangle, which is

\((1/2) * b * h_{base,\)

to find the area of the triangular base.

3. Determine the height of the pyramid: Measure the vertical height (h) from the base of the pyramid to the apex (top point). Make sure to use consistent units with the base measurements.

4. Apply the volume formula: Plug the values of the base area (\(A_{base\)) and the height (h) into the volume formula:

\(V = (1/3) * A_{base} * h.\)

5. Simplify and calculate: Multiply the base area by the height, and then divide the result by 3 to calculate the volume of the pyramid.

Make sure to use consistent units throughout the calculations. The resulting volume will be in cubic units (e.g., cubic centimetres, cubic inches, etc.), reflecting the three-dimensional space occupied by the pyramid.

Remember to double-check your measurements and calculations to ensure accuracy in determining the volume of the triangular-based pyramid.

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