if the infinite series s=∑n=1[infinity](−1)n 12n is approxiately by pk=∑n=1k(−1)n 12n, what is the least value of k for which the alternating series error bound guarantees that |s−pk|<3100?

Answer:

use connects Q&A... they answer better nd quick

When the residual is negative it represents the predicted value is very much high.

Therefore, the negative residual value on the regression line represents the predicted value is very much high.

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The functions f1(t) = 4t-3, f2(t) = t2 + 1, and f3(t) = 6t2 - t are linearly independent.

To determine whether the functions are linearly dependent or independent, we need to check if there exist constants c1, c2, and c3, not all zero, such that c1f1(t) + c2f2(t) + c3f3(t) = 0 for all t.

Assume that there exist such constants. Then, we have:

c1(4t-3) + c2(t2 + 1) + c3(6t2 - t) = 0

Simplifying this equation, we get:

(6c3)t2 + (c2)t + (4c1 - c3) = 3c1 - c2

This is a polynomial equation in t, and it must hold for all t. Therefore, the coefficients of the polynomial must be equal to zero. This gives us the following system of equations:

6c3 = 0

c2 = 0

4c1 - c3 = 0

From the first equation, we have c3 = 0. Substituting this in the third equation gives us c1 = 0. But then, the second equation implies that c2 = 0 as well. Therefore, the only solution to the system of equations is c1 = c2 = c3 = 0. This means that the functions are linearly independent.

Therefore, we conclude that the functions f1(t) = 4t-3, f2(t) = t2 + 1, and f3(t) = 6t2 - t are linearly independent.

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Coating the seed typically improves seed quality and germination rates, so the same seeding rate can be maintained even with coated seed.

To convert mass-based seeding rates to population-based establishment rates, we need to consider the area conversion factors provided:

a. Given a seeding rate of 60 lbs/acre for cereal rye, we can convert it to seeds per square foot by using the conversion factor of 1 acre = 43,560 square feet.

b. Given a seeding rate of 15 kg/ha for crimson clover, we can convert it to seeds per square meter using the conversion factor of 1 hectare = 10,000 square meters.

To convert population-based seeding rates to mass-based seeding rates, we can use the given area conversion factors:

a. Given a seeding rate of 30 plants/square foot for oats, we can convert it to pounds of seed per acre.

b. Given a seeding rate of 20 plants/square meter for hairy vetch, we can convert it to kilograms of seed per hectare.

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Answer:

I think the answer is A

1,2

The projected value for the car after 10 years is equal to $10,503.42.

In Mathematics and Statistics, a population or physical asset such as a car that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or physical asset that decreases by r percent per unit of time is an exponential equation of this form:

\(P(t) = I(1 - r)^t\)

Where:

By substituting given parameters, we have the following:

\(P(t) = I(1 - r)^t\\\\P(10) = 28500(1 - 0.095)^{10}\\\\P(10) = 28500(0.905)^{10}\)

P(10) = $10,503.42

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We can Long Division method to solve quotients step by step

What is long division method and its steps ?

When splitting huge numbers, the task is divided into several sequential parts using the long division approach. The dividend is divided by the divisor, just as in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.

We need to comprehend a few stages in order to divide. A vinculum or right parenthesis separates the dividend from the quotient, while a vertical bar separates the divisor from the dividend. Let's now go through the long division stages listed below to comprehend the procedure.

1. Take the dividend's first digit starting from the left . Verify if this digit exceeds or is equal to the divisor.

2. Next, divide it by the divisor, and write the result as the quotient on top.

3. Subtract the outcome from the digit, and then put the difference below.

Step 4: Decrease the dividend's subsequent digit (if present).

Step 5: Carry out Step 4 again.

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Answer:

6:00

Step-by-step explanation:

The time taken by the skateboarder and cyclist to ride by at the same time is given by A = 18 minutes

The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF

Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers

Product of HCF x LCM = product of two numbers

Given data ,

Let the skateboarder rides by the office every 9 minutes

And , a cyclist rides by every 6 minutes

Now , time taken by the skateboarder and cyclist to ride by at the same time be A

where A = LCM of the two numbers

So , the smallest time interval at which both events occur. In other words, we need to find the least common multiple (LCM) of 9 and 6.

Factors of 9 : 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

Factors of 6 : 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

So , common multiple and the LCM is 18

Hence , the time taken is 18 minutes

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Answer:

7.2 feet

Step-by-step explanation:

Torque is calculated by T=Frsin(theta). Betty's total torque is 9 x 1000 (mg) = 9000. Since ginger weighs 125 pounds, 9000 = (125 x 10) x r. Solve for r and get 7.2 feet.

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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Step-by-step explanation:

Since they do not replace it the total amount of marbles are the same

Answer:

B, C

Step-by-step explanation:

7 - x = 18

A.

7 - 2x = 18 - x

126 - 14x = 324 - 18x

We are nowhere near the solution.

B.

-x = 11

x = -11

This works.

C.

7 = x + 18

-11 = x

This works.

D.

25 - x = 36

-25 + x = -36

This does not help.

E.

7 = x + 18

0 = x + 11

We still do not have a solution.

Answer: B, C

Answer:

36

Step-by-step explanation:

Since 4x6=24 you'll have to find out 6x6 wich is 36!

Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

Answer: 400 units

Step-by-step explanation:

Volume=1/3a^2h

=1/3(10)^2(12)

=400

The correct answer is 400. I had the same question on a test I took not to long ago.

Answer:

\(12x\leq 24\); \(x\leq 2\)

Step-by-step explanation:

So you have 12 math problems that each take x amount of minutes, and have 24 minutes to finish them. Remember, you can't exceed the 24 minutes (but you are allowed to equal that time). So:

\(12x\leq 24\)

Then you can simplify by dividing both sides by 2:

\(x\leq 2\)

The point on the hyperbola closest to (0, -3) is (√2, -3√2).

The distance formula is a formula used to calculate the distance between two points in a coordinate plane or in a three-dimensional space.

For two points in a two-dimensional coordinate plane, \((x_1, y_1) and (x_2, y_2)\), the distance formula is:

d = \(\sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\)

To find the point on the hyperbola closest to the point (0, -3), we need to find the point on the hyperbola where the distance to (0, -3) is minimized.

We can use the distance formula to find the distance between any point on the hyperbola (x, y) and (0, -3):

d = √[(x - 0)² + (y - (-3))²]= √[x² + (y + 3)²]

We want to minimize this distance, subject to the constraint that (x, y) lies on the hyperbola 6x² - 5y² = 10.

To solve this problem, we can use Lagrange multipliers. Let L(x, y, λ) = d² - λ(6x² - 5y² - 10), where λ is the Lagrange multiplier. We square the distance to avoid dealing with the square root. We also subtract λ times the constraint function, since we want to maximize the distance subject to the constraint.

Taking partial derivatives with respect to x, y, and λ, we get:

∂L/∂x = 2x - 12λx = 0

∂L/∂y = 2(y + 3) + 10λy = 0

∂L/∂λ = 6x² - 5y² + 10 = 0

Solving the first equation for λ and substituting into the second equation, we get:

λ = 1/2x

2(y + 3) + 5yx = 0

Solving for y in terms of x, we get:

y = -6/(5x)

Substituting into the equation for the hyperbola, we get:

6x² - 5(-6)²/(5x)² = 10

Multiplying both sides by (5x)², we get:

\(30x^4 + 180 = 25x^2\)

Rearranging and factoring, we get:

30(x² - 2)(x² + 3) = 0

The only positive value of x that satisfies this equation is x = √2. Substituting into y = -6/(5x), we get y = -3√2. Therefore, the point on the hyperbola closest to (0, -3) is (√2, -3√2).

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Answer:

y = 5/6x+11/12

Step-by-step explanation:

divide by -1 on both sides to get 10x+11=12y

divide by 12 on both sides

Answer:

Answer:

this and that, I ain't even gonna cap I don't know the answer  

Step-by-step explanation:

Answer: X=8 Y=138

Step-by-step explanation:

Answer: x=2 and y=12

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

por que el le dio 5 manzanas a jose y le quedaron 2

Answer:

t = -0.9

Step-by-step explanation:

-1(t+8) = -7.1

(t+8) = 7.1

t = -0.9

Swimmers jump from a railroad bridge to river. Using equations of motion, the height of the bridge is calculated to be 17.8m, their speed when hitting the water is 18.6m/s. If the bridge were twice as high, the drop time would be 4.18s.

We can use the equations of motion to solve this problem. Let h be the height of the bridge, g be the acceleration due to gravity, and t be the time taken by the swimmers to fall from the bridge to the water. We can assume that the swimmers start from rest.

(a) Using the equation h = (1/2)gt^2, we can find the height of the bridge:

h = (1/2)gt^2 = (1/2)(9.81 m/s^2)(1.9 s)^2

h = 17.8 m

Therefore, the height of the bridge is 17.8 meters.

(b) Using the equation v = gt, we can find the speed of the swimmers just as they hit the water:

v = gt = (9.81 m/s^2)(1.9 s)

v = 18.6 m/s

Therefore, the swimmers were moving at a speed of 18.6 m/s when they hit the water.

(c) If the bridge were twice as high, the time taken by the swimmers to fall would be:

t' = sqrt(2h/g) = sqrt(2(2h)/g) = sqrt(4h/g) = 2sqrt(h/g)

Using this equation, we can find the new drop time:

t' = 2sqrt(h/g) = 2sqrt(17.8 m / 9.81 m/s^2)

t' = 4.18 s

Therefore, if the bridge were twice as high, the swimmers would take 4.18 seconds to fall from the bridge to the water.

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Answer:

Your profit would be 32.10$

Step-by-step explanation:

You spent 20.40$ on string, then you spent 7.50$ on beads too. That adds up to 27.90$ in total, so once you make your 30 necklaces you sell them for 2.00$ let's say you sell them all in one day your coming come with 32.10$ profit. Because you put 27.90$ into making the necklaces.

Answer:

i think about $3.80

Step-by-step explanation:

Answer:

the answer is C

you have to use horner Division because its so easily to use

just search horner divission in polonium and you will find it

The expression f(x)/g(x) defines function h(x)=3x^2+12x.The answer is C.

We have given that,

\(f(x)=3x^2+9x^2-12x\)

\(g(x)=x-1\)

and,    \(h(x)=3x^2+12x\)

Suppose f(x) and g(x) are function,

\((\frac{f}{g}) (x)=\frac{f(x)}{g(x)}\)

So we have given function us

\(f(x)=3x^2+9x^2-12x\)

\(g(x)=x-1\)

We have divide f(x) by g(x)

\(=\frac{3x^3+9x^2-12x}{x-1}\)

\(=3x\left(x+4\right)\)

\(=3x^2+12x\)

Therefore we get the expression f(x)/g(x) defines function h.

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Answer:

Option A

Step-by-step explanation:

\(D=3ef^2\\\)

we need to make e the subject of the formula so here goes,

On the right side 3 is being multiplied by ef^2 so when it moves to the left side it will divide

\(\frac{D}{3}=ef^2\)

now f^2 is also being multiplied by e on the right side so when it moves to the left side it will divide

\(\frac{D}{3f^2}=e\\\\\)

The  values of x will f(x) > 0 for x < 0, and f(x) < 0 for -6 < x < 0 and x > -6.

To determine the values of x for which f(x) > 0, we need to find the intervals where the function is positive. Let's analyze the function f(x) = x*-x³-6x².

First, let's factor out an x from the expression to simplify it: f(x) = x(-x² - 6x).

Now, we can observe that if x = 0, the entire expression becomes 0, so f(x) = 0.

Next, we analyze the signs of the factors:

1. For x < 0, both x and (-x² - 6x) are negative, resulting in a positive product. Hence, f(x) > 0 in this range.

2. For -6 < x < 0, x is negative, but (-x² - 6x) is positive, resulting in a negative product. Therefore, f(x) < 0 in this range.

3. For x > -6, both x and (-x² - 6x) are positive, resulting in a negative product. Thus, f(x) < 0 in this range.  

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