Find the taylor series for f(x)=x-3 centered at c=1. And please
explain when it would be sufficient to stop taking the derivative.
Thank you.

Recall the definition of each concept to check if it fits the figure.

A) Square: A square is a quadrilateral whose sides all have the same length.

B) Polygon: A polygon is a 2D shape formed by non-intersecting straight segments.

C) Triangle: A triangle is a polygon with exactly 3 sides.

D) Polyhedron: A polyhedron is a 3D shape formed by flat polygonal shapes.

E) Pyramid: A pyramid is a polyhedron formed by a simple polygon whose lateral faces are triangles that converge in a common vertex.

F) Prism: A prism is a polyhedron formed by two parallel and equal polygonal faces, whose lateral faces are parallelograms.

The given object is a 3D shape formed by flat polygonal shapes, with a base that is a quadrilateral and whose lateral faces are triangles that converge in a common vertex.

Therefore, the only two terms that correcty describe the given object are:

D) Polyhedron

E) Pyramid

Answer:

(3, 0)

Step-by-step explanation:

So with the 2 equations you can either choose which to start with but you need to make the X or Y the opposite from the other equation.

1.

3x + y = 9 (keep as is)
x + 2y = 3 --> -3( x + 2y = 3) In this case I chose to make the X the opposite of each other

--

3x - 3x = 0 (forced to get rid of)

y - 6y = -5y (Get the -6 by -3 x 2)

9 - 9 (Get the -9 by -3 x 3)

Left with:

-5y = 0 (Divide both sides by -5 to get X alone)

y = 0

----------------------------------------------------------

(Choose any ORIGINAL equation)

x + 2y = 3

x + 2(0) = 3 (substitute)

Left with:

x = 3  (x + 0 = 3)

-------------------------------------------------------------

Optional:

Chose the other equation (the opposite from above)

Substitute X and Y in 3x + y = 9

3(3) + (0) = 9

Left with: 9 = 9 (check)

Hope this helps!

Lowes Depot uses a (Q, R) policy to manage its stock levels for a popular mini drill with a replacement lead time of 14 weeks. Historical demand during the replacement lead time is normally distributed with a mean of 90.4616 and a standard deviation of 14.3795. Each drill costs $6, and backorders result in a loss of goodwill of $10. The supplier charges $15 per order, and holding costs are based on a 30% annual interest rate.

To determine the optimal order quantity Q and reorder point R, we need to use the (Q, R) policy. The policy specifies that when the inventory level reaches the reorder point R, an order of size Q is placed. We need to determine Q and R such that the total annual cost is minimized.

The total annual cost consists of three components: ordering costs, holding costs, and shortage costs. Ordering costs are the costs associated with placing an order, which is given by (number of orders per year) x (ordering cost per order). The number of orders per year is the annual demand divided by the order quantity, which is Q. The ordering cost per order is $15. Therefore, the ordering cost is 15 X (Demand rate/Q).

Holding costs are the costs associated with holding inventory, which is given by (inventory level) x (holding cost per unit per year). The holding cost per unit per year is 30% of the unit cost, which is 0.3 x $6 = $1.8.

Shortage costs are the costs associated with backordering, which is given by (expected shortage per year) x (shortage cost per unit). The expected shortage per year is the probability of a stockout during the lead time multiplied by the expected demand

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Answer:

B

Step-by-step explanation:

A=1/2bh=1/2(8)(6)=24

4 × 24 = 96 sq cm

There is 60 total number of marbles in the bag for the probability of selecting a red marble is 7/10.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

let the total possible outcome = x

probability of selecting a red marble = P(R) = 7/10

Given that there are 42 red marbles tgen:

42/x = 7/10

x = (42 × 10)/7 {cross multiplication}

x = 420/7

x = 60

Therefore, given the probability of selecting a red marble to be 7/10, the total number of marbles in the bag is derived to be 60

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Answer:

4

Step-by-step explanation:

x=3

x2 means 3 square (+3)

3×3+3

=9+3

12÷3

4

Answer:

B

Step-by-step explanation:

The value of x to the nearest tenth for the given set of triangles is 5.6 units.

A triangle is a three-sided polygon that has three angles and three vertices. It is a basic geometric shape that is often used in mathematics, science, and engineering. The sum of the angles in a triangle is always 180 degrees. This property is known as the Triangle Sum Theorem. Triangles have several important properties and formulas that are used in various mathematical applications. For example, the Pythagorean theorem relates the sides of a right triangle, and the law of cosines and law of sines can be used to relate the sides and angles of any triangle.

Here,

Using the concept of similar triangle, the ratio of sides of triangle is equal.

4.3/x=4.1/5.3

4.3*5.3/4.1=x

x=5.56 units

x≈5.6 units

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Answer:

4

Step-by-step explanation:

Function 1 is moving at a constant rate meaning it has the rate of change of 0/1 or 0.

Function 2 says y is 4x meaning that the rate of change is 4/1 or 4.

0 - 4= I-4I or 4

1600 + 30m is the expression indicates the amount of water, in gallons, in the swimming pool after m minutes.

An expression is combination of variables, numbers and operators.

Given that there are already 1,600 gallons of water in a swimming pool.

water is filling the pool at a rate of 30 gallons per minute,

We need to find the expression indicates the amount of water, in gallons, in the swimming pool after m minutes

Let m = number of minutes

The expression will be:

1600 + (30 × m)

1600 + 30m

Hence, 1600 + 30m is the expression indicates the amount of water, in gallons, in the swimming pool after m minutes.

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The expression is equivalent is 6x/4 + 24y/12

Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.

These expressions also consisting of mathematical operations, such as;

Given the expression;

1/4(3x+4y) + 3(1/4x+ 2/3y)

expand the bracket

3x/4 + 4y/4 + 3/4x + 3/3y

collect like terms

3x/4 + 3/4x + 4y/4 + 3/3y

add like terms

3x + 3x/4 +  12y + 12y /12

add the numerators

6x/4 + 24y/12

Hence, the expression is 6x/4 + 24y/12

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The range for the average age of all site visitors is found to be between 21.15 and 23.55.

For the given question;

Confidence interval  CI = 90% = 0.9

Sample size n = 56 users

Mean (x) = 22.5 years years

Standard deviation (s) = 5 years

Then formula for the CI is given as,

CI = x + z.s/√n

The steps included are-

1. Subtract 1 from sample size to get the degree of freedom df:

df = 56 - 1 = 55

2. To get teh alpha level.

α = (1 - 0.9)/2 = 0.05

3: check df and α in t-distribution to get z score.

z = 2.003

4: To get sample size,

S = s/√n

S = 5/√56

S = 0.66

z x S = 0.66 x 2.033 = 1.35

5: To get the lower range subtract 1.35 from sample mean

22.5  -  1.35 = 21.15

6:n  To get the upper range, add t 1.35 from sample mean.

22.5 + 1.35 = 23.55

Thus, the confidence interval is 21.15 and 23.55.

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Answer:

B. x = -7, y = -8

Step-by-step explanation:

Equation 1 : -7x + 6y = 1

Equation 2 : -4x + 3y = 4

Multiply Equation 2 by 2.

Subtract Equation 3 from Equation 1.

Substitute x in Equation 1.

Solution

Answer:

The answer is 9.0909

Step-by-step explanation:

n=1  p=.11

mean = 1/0.11 = 9.0909

The mean of X, the number of patients seen until an injection-site reaction occurs is 9.0909.

The mean refers to "the average set of values".

According to the question,

The percentage of patients experiencing injection- site reactions with the current needle is 11%.

Mean = \(\frac{sum of the all values}{Total number of values}\)

Total number of values = 11% = 0.11 and  n = 1.

Mean = \(\frac{1}{0.11}\)

=9.0909.

Hence, the mean of X, the number of patients seen until an injection-site reaction occurs is 9.0909.

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After using the unitary method we will get, Required number of boxes is 9

What is unitary method?

The unitary method, in its most basic form, is used to calculate the value of a single unit from the a given multiple. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary method can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is primarily applied using this method. The unitary method involves first determining the value of a single unit, followed by the value of the necessary number of units.

Here, one box contains 46 programs.

Number of box required for 383 programs = \(\frac{383}{46} = 8.326\)

Number of box cannot be in decimal.

So, required number of boxes = 9

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The derivative dz/dt can be found by applying the chain rule. Let's first substitute the given expressions for x and y into the equation for z:

z = (x + y)e^y

z = (3t + 1 - t^2)e^(1 - t^2)

Now, we can differentiate z with respect to t using the chain rule. The chain rule states that if u = f(g(t)), then du/dt = f'(g(t)) * g'(t).

Applying the chain rule to the given equation, we have:

dz/dt = d((3t + 1 - t^2)e^(1 - t^2))/dt

To differentiate this expression, we need to consider the derivative of each term. Let's break it down:

1. The derivative of 3t with respect to t is simply 3.

2. The derivative of 1 with respect to t is 0 since it is a constant.

3. The derivative of -t^2 with respect to t is -2t.

4. The derivative of e^(1 - t^2) with respect to t can be found using the chain rule again.

For the fourth term, let's define u = 1 - t^2. The derivative of u with respect to t is du/dt = -2t. Now, we have:

dz/dt = (3 + 0 - 2t)e^(1 - t^2) + (3t + 1 - t^2)d(e^(1 - t^2))/dt

Using the chain rule once more, we differentiate e^(1 - t^2) with respect to u:

d(e^(1 - t^2))/du = e^(1 - t^2) * d(1 - t^2)/dt

The derivative of 1 - t^2 with respect to t is -2t. Substituting this back into our expression, we get:

dz/dt = (3 + 0 - 2t)e^(1 - t^2) + (3t + 1 - t^2)(-2t)e^(1 - t^2)

Simplifying the expression, we have:

dz/dt = (3 - 2t)e^(1 - t^2) - 2t(3t + 1 - t^2)e^(1 - t^2)

Therefore, the derivative dz/dt is given by (3 - 2t)e^(1 - t^2) - 2t(3t + 1 - t^2)e^(1 - t^2), where e represents the exponential function.

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The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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Answer:

20%

Step-by-step explanation:

An easy and simple way to solve this problem would be to divide 60 by 300, keep going threw the decimals until you have no remainder, which gives you .2,

60/300 = .2

then you multiply .2 x 100 for your % answer, you could also count by 60s until you reach 300,

60 x 5 = 300

100/5 = 20%

hope this helps a lil!

Answer:

70 is what percent of 280?

Step-by-step explanation:

Percent means per 100. So the example question asks 70 out of 280 is what percent. You can do this problem a couple of different ways.

1. Set up a proportion (two fractions equal to each other,) and solve.

70/280 = x/100

reduce the left side.

7/28 = x/100

reduce further.

1/4 = x/100

cross-multiply.

1(100) = 4x

100 = 4x

divide by 4

100/4 = 4x/4

25 = x

70 is 25% of 280.

OR

you could divide directly and move the decimal two places to the right to find the percent.

70/280

= .25

move the decimal two places to the right.

.25 becomes 25%

I can edit if you actually wanted to see 60 and 300. Hope this helps!

Answer:

508.8 seconds

Step-by-step explanation:

The most accurate determination mathematically is to assume that Lola will maintain an average of 5.3 seconds per signature as she signs all 96 invitations.

Therefore, multiply the time it takes her to sign each invitation (5.3 seconds) by the total number of invitations there are (96 invitations) to get the projected total amount of time that it will take Lola to sign all 96 invitations:\(96\cdot 5.3=\boxed{508.8\text{ seconds}}\)

Answer:

508.8 seconds (8.48 minutes)

Step-by-step explanation:

96 × 5.3 = 508.8

Option B: The probability distribution of all x values calculated from all possible samples of size n is the correct answer.

What is probability?

Probability is a fundamental concept in statistics and mathematics that helps to measure the likelihood or chance of an event occurring. It provides a way to quantify uncertain events or situations and make informed decisions based on that information. The probability of an event can range from 0 to 1, with 0 indicating impossibility and 1 representing certainty.

When dealing with a sample mean, the sampling distribution refers to the probability distribution of all possible sample means of a given sample size taken from a population.

It is a theoretical distribution that shows all possible sample means that could be obtained from the population, and is a crucial tool in statistical analysis and inference.

Therefore, the correct answer is -

Option B: the probability distribution of all x values calculated from all possible samples of size n.

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Function y=cosx

For the given function:

Phase shift: how fat the function is shifted horizontally from the ussual position: In y=cosx the first wave goes to minimum in π and in the given graph in π/2.

Midline: In y=cosx the midline is y=0.

Period: Measure from one peak to next.

Answer:

y = -1/3x + 2

Step-by-step explanation:

The gradient of the given line is 3 because (y = mx +c where m is the gradient)

Therefore, to find the gradient of the perpendicular line (at 90 degrees), you need to find the negative reciprocal.

The negative reciprocal of 3 is -1/3 because imagine if 3 = 3/1, to get the reciprocal, you flip it, and to get the negative, you just flip the sign.

Now we know that Line M is y = -1/3x + c, we need to find the y-intercept.

To do this, just input the point (3,1) into y = -1/3x + c, to get c. This is because we know (3,1) is on the line from the question.

So it would be 1 = (-1/3 x 3) +c

Which would be 1 = -1 +c

And so c = 2

Put everything together and you get y = -1/3x + 2

Answer:

the highest common factor of 12 , 15 and 60 is 3

Step-by-step explanation:

So thus 3 is the HCF that is why i underlined it

The numbers of bars that the team have to get from each company in order for the total cost to be equal is 40.

Since n = numbers of bars purchase.

y= total cost in dollars

Company A = 0.75n

Company B = 10 + 0.50n

Therefore, to find the numbers of bars that the team would need to purchase from each company in order for the total cost to be equal =

0.75n = 10 + 0.50n

0.2n = 10

n = 40

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Since 80 out of 100 free throws were successful, the standard deviation of the success rate would be 8, and the standard deviation of a binomial distribution is the square root of (p*q)/n, where p is the probability of success, q is the probability of failure (1-p), and n is the total number of trials.

Standard deviation is calculated as follows:

p*q/n = 0.8*0.2/100 = 0.0016 = 0.04 = 8

Since 80% of 100 equals 80 successful free throws, the standard deviation of the successes from 100 free throws would be 8. The dispersion in a set of data is measured by standard deviation. A binomial distribution's standard deviation is equal to the square root of (p*q)/n, where p is the success probability, q is the failure probability (1-p), and n is the number of trials. Since the success rate in this instance is 80%, p = 0.8, q = 0.2, and n = 100. The standard deviation is then equal to the square root of (p*q/n): (0.8*0.2/100) = (0.0016) = (0.04), which equals 8. Therefore, the standard deviation of the successes from 100 free throws for a basketball player who makes 80% of them would be 8.

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The indefinite integral is: (t^2)i + (t)j + (3t)k + C

To find the indefinite integral of the given vector function (2ti + j + 3k) with respect to t, we need to integrate each component separately.

Step 1: Integrate the i-component with respect to t:
∫(2t) dt = t^2 + C1

Step 2: Integrate the j-component with respect to t:
∫(1) dt = t + C2

Step 3: Integrate the k-component with respect to t:
∫(3) dt = 3t + C3

Now, combine the integrated components and the constants of integration (C1, C2, C3) to form the final result:

Your answer: (t^2)i + (t)j + (3t)k + C

Here, C = (C1)i + (C2)j + (C3)k is the constant of integration in vector form.

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Given:

The leading coefficient of a polynomial is 8.

Polynomial roots are 1 and 2.

The graph passes through the point (4,5).

To find:

The 3rd root and the equation of the polynomial.

Solution:

The factor form of a polynomial is:

\(y=a(x-c_1)(x-c_2)...(x-c_n)\)

Where, a is a constant and \(c_1,c_2,...,c_n\) are the roots of the polynomial.

Polynomial roots are 1 and 2. So, \((x-1)\) and \((x-2)\) are the factors of the polynomial.

Let the third root of the polynomial by c, then \((x-c)\) is a factor of the polynomial.

The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:

\(y=8(x-1)(x-2)(x-c)\)

The graph passes through the point (4,5). Putting \(x=4,y=5\), we get

\(5=8(4-1)(4-2)(4-c)\)

\(5=8(3)(2)(4-c)\)

\(5=48(4-c)\)

Divide both sides by 48.

\(\dfrac{5}{48}=4-c\)

\(c=4-\dfrac{5}{48}\)

\(c=\dfrac{192-5}{48}\)

\(c=\dfrac{187}{48}\)

Therefore, the 3rd root on the polynomial is \(\dfrac{187}{48}\).

Answer:

55 MOVIES???!!               ok here's the answer: 33 is 60 percent of 55 = 60

Step-by-step explanation:

Answer:

2 : 3

Step-by-step explanation:

24 : 36 ( divide both parts by 12 )

= 2 : 3 ← in simplest form