Calculate the Taylor polynomials T2(x) and T3(x) centered at x=π/6 for f(x)=sin(x).
T2(x) must be of the form
A+B(x−π/6)+C(x−π/6)^2
T3(x) must be of the form
D+E(x−π/6)+F(x−π/6)2+G(x−π/6)^3

Answer:

14 pounds per hour

Step-by-step explanation:

\( \frac{490}{7\times 5} = \frac{490}{35} = 14\)

Given:

Initial value = 400

Interest rate = 5% compounded quarterly.

To find:

The function that gives you the amount of money in dollars, J(t) in t years after the initial deposit.

Solution:

The formula for amount is:

\(A=P\left(1+\dfrac{r}{n}\right)^{nt}\)

Where, P is principal, r is the rate of interest in decimals, n is the number of times interest compounded in an year and t is the number of years.

The interest rate is 5% compounded quarterly. So, r=0.05 and n=4.

Substituting \(P=400,\ r=0.05,\ n=4\) in the above formula, we get

\(A=400\left(1+\dfrac{0.05}{4}\right)^{4t}\)

\(A=400\left(1+0.0125\right)^{4t}\)

\(A=400\left(1.0125\right)^{4t}\)

The required function notation is:

\(J(t)=400\left(1.0125\right)^{4t}\)

Therefore, the amount of money in dollars, J(t) in t years after the initial deposit is \(J(t)=400\left(1.0125\right)^{4t}\).

The correct answer is D, you are right.

Answer:

The answer is D.

Step-by-step explanation:

The answer is b. (√10)/3 when The area of the triangle below is 5/6 square meters.

Let the base of the triangle be denoted by "b" and the height be denoted by "h". Then the area of the triangle is given by:

Area = (1/2)bh

We are given that the area is 5/6 square meters, so we can write:

5/6 = (1/2)bh

Multiplying both sides by 2 gives:

10/6 = bh

Simplifying this expression, we get:

5/3 = bh

Since the height of the triangle is not given, we cannot determine the value of "b" exactly. However, we can express "b" in terms of "h" as follows:

b = (2/3)h

Substituting this expression for "b" into the equation 5/3 = bh, we get:

5/3 = (2/3)h × h

Multiplying both sides by 3/2 gives:

5/2 = h²

Taking the square root of both sides gives:

h = √(5/2)

Therefore, the length of the base is:

b = (2/3)h = (2/3)√(5/2) = (2√10)/6 = (√10)/3

So the answer is b (√10)/3.

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Answer:

\(f'(x) = 4x^2 - 3\) for \(x \le -3\)

Step-by-step explanation:

See attachment for proper question

Given

\(f(x) = -\frac{1}{2}\sqrt{x + 3}\)

For

\(x \ge -3\)

Required

Determine the inverse function

\(f(x) = -\frac{1}{2}\sqrt{x + 3}\)

Replace f(x) with y

\(y = -\frac{1}{2}\sqrt{x + 3}\)

Swap the positions of x and y

\(x = -\frac{1}{2}\sqrt{y + 3}\)

Multiply both sides by -2

\(-2 * x =-2 * -\frac{1}{2}\sqrt{y + 3}\)

\(-2x =\sqrt{y + 3}\)

Square both sides

\((-2x)^2 =(\sqrt{y + 3})^2\)

\(4x^2 =y + 3\)

Make y the subject

\(y = 4x^2 - 3\)

The inverse has been solved. So, we need to replace y with f'(x)

\(f'(x) = 4x^2 - 3\)

Next, is to determine the interval

\(x \ge -3\)

Change inequality to \(\le\)

\(x \le -3\)

Hence, the inverse function is:

\(f'(x) = 4x^2 - 3\) for \(x \le -3\)

Answer:

I told my parents and x= 18

Step-by-step explanation:

Answer:

The probability that the two cards drawn form a pair is approximately 0.045.

Explanation:

There are 52 cards in an ordinary deck, and each card has a unique rank (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, or king) and suit (spades, hearts, diamonds, or clubs). There are 13 ranks and 4 suits, so there are 13*4 = 52 possible cards in the deck.

When we draw two cards without replacement, there are 52 ways to draw the first card and 51 ways to draw the second card, for a total of 5251 = 2652 possible outcomes. Of these, there are 4 ways to draw a pair of cards with the same rank (for example, 2 of spades and 2 of hearts) and 13 ranks to choose from, so there are 413 = 52 pairs in the deck. Therefore, the probability of drawing a pair is 52/2652 = 1/51, or approximately 0.0196.

Alternatively, we can calculate the probability by considering the complement of the event (that is, the probability of not drawing a pair). There are 48 non-pair cards in the deck (since there are 52 total cards and 4 pairs), and there are 48*47 = 2256 ways to draw two non-pair cards. Therefore, the probability of not drawing a pair is 2256/2652 = 48/51, or approximately 0.931. The probability of drawing a pair is then 1 - 0.931 = 0.069, or approximately 0.045.

Either way, we can see that the probability of drawing a pair is relatively low, at about 4.5%.

The Law of Sines says that for a given triangle, the ratio between the sine of an angle and the length of the opposite side is the same for all three angles in a triangle. the sine values of all three internal angles will be the samethe sine values of all three internal angles will be proportional to each otherthe ratio between the sine of the angle and the opposite side will match for all three internal anglesthe sine values of all three angles will be different

In a triangle, we have three angles and three sides. The Law of Sines says that for any triangle, the ratio between the sine of an angle and the length of the opposite side will be the same for all three angles. In other words, the sine values of each angle are proportional to the length of the opposite side.

To put this in mathematical terms, let's consider a triangle with angles A, B, and C, and sides a, b, and c respectively. The Law of Sines can be written as:

sin(A)/a = sin(B)/b = sin(C)/c

This means that if we know the length of any two sides and the measure of the angle opposite one of those sides, we can use the Law of Sines to find the measure of the other angles and sides.

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The correct option is \(\(b.\)  \(f(x) = -\frac{{(x - 4)^2}}{5}\).\) The function that has a range of \(\(\{y | y \leq 5\}\)\) is option \(\(b.\)  \(f(x) = -\frac{{(x - 4)^2}}{5}\).\)

To determine this, let's analyze the options:

\(\(a.\)  \(f(x) = \frac{{(x - 4)^2}}{5}\)\): This function will have a range of  \(\(y\)\)-values greater

than or equal to 0, so it does not have a range of \(\(\{y | y \leq 5\}\).\)

\(\(b.\)  \(f(x) = -\frac{{(x - 4)^2}}{5}\)\) : This function is a downward-opening parabola, and when we substitute various values of \(\(x\)\) , we get \(\(y\)\)-values less than or equal to 5. Therefore, this function has a range of \(\(\{y | y \leq 5\}\).\)

\(\(c.\)   \(f(x) = \frac{{(x - 5)^2}}{4}\)\): This function is an upward-opening parabola, and its

range will be  \(\(y\)\)-values greater than or equal to 0, so it does not have a

range of \(\(\{y | y \leq 5\}\).\)

\(\(d.\)   \(f(x) = -\frac{{(x - 5)^2}}{4}\)\): This function is a downward-opening parabola, and its range will be \(\(y\)\)-values less than or equal to 0, so it

does not have a range of \(\(\{y | y \leq 5\}\).\)

Therefore, the correct option is \(\(b. f(x) = -\frac{{(x - 4)^2}}{5}\).\)

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Answer:

16.28

Step-by-step explanation:

A. the exponential rate of change, k, is approximately -0.74688.

B. the temperature of the water at 4:30 pm is approximately 66.14 degrees.

C. the cup of water will become frozen around 9:49 pm

A. We are given that after 1 hour, the temperature of the water is 80 degrees. We can use this information to find the exponential rate of change, k.

Using the formula T(x) = 10 + \(170e^{kx}\), we substitute x = 1 and T(x) = 80:

80 = 10 + \(170e^{k*1\)

Simplifying the equation:

70 = 170\(e^k\)

Dividing both sides by 170:

\(e^k\) = 70/170

Taking the natural logarithm (ln) of both sides:

ln(\(e^k\)) = ln(70/170)

k = ln(70/170)

Using a calculator, we can find the value of k rounded to 5 decimal places:

k ≈ -0.74688

Therefore, the exponential rate of change, k, is approximately -0.74688.

B. We need to find the temperature of the water at 4:30 pm, which is 1.5 hours after 3 pm. Using the formula T(x) = 10 + \(170e^{kx\), we substitute x = 1.5:

T(1.5) = 10 + \(170e^{-0.74688*1.5\)

Calculating the value using a calculator:

T(1.5) ≈ 10 + \(170e^{-1.12032\)

T(1.5) ≈ 10 + 170(0.32594)

T(1.5) ≈ 10 + 56.14098

T(1.5) ≈ 66.14098

Therefore, the temperature of the water at 4:30 pm is approximately 66.14 degrees.

C. We need to find the time at which the cup of water becomes frozen, which occurs when the temperature reaches 32 degrees. Using the formula T(x) = 10 + \(170e^{kx\), we set T(x) = 32 and solve for x:

32 = 10 + \(170e^{-0.74688x\)

Subtracting 10 from both sides:

22 = \(170e^{-0.74688x\)

Dividing both sides by 170:

\(e^{-0.74688x\) = 22/170

Taking the natural logarithm (ln) of both sides:

\(ln(e^{-0.74688x})\) = ln(22/170)

-0.74688x = ln(22/170)

Solving for x by dividing both sides by -0.74688:

x ≈ ln(22/170) / -0.74688

Using a calculator, we can find the value of x:

x ≈ 6.8201

Therefore, the cup of water will become frozen approximately 6.8201 hours after it is put in the freezer.

To convert this to the time of day, we add 6.8201 hours to 3 pm:

3 pm + 6.8201 hours = 9:49 pm

Therefore, the cup of water will become frozen around 9:49 pm (rounded to the nearest minute).

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Answer:

d = -29

Step-by-step explanation:

-(1/8)d -4 = -(3/8)

Multiply everything by 8 to get rid of the fractions

8*-(1/8)d -4*8 = -(3/8)*8

-d -32 = -3

Add 32 to each side

-d+32 -32 = -3+32

-d = 29

Multiply everything by -1

d = -29

Reduced sample size is a result of a fall in predicted rate, an increase in the tolerated rate, and a rise in the allowable risk of estimating control risk too low.

Given that,

We have to find what impact does a larger acceptable risk of estimating control risk too low have on sample size in characteristics sampling.

The term "risk of over-reliance" refers to the "risk of estimating control risk too low" in characteristics sampling, and it relates with the so-called 

Reduced sample size is a result of a fall in predicted rate, an increase in the tolerated rate, and a rise in the allowable risk of estimating control risk too low.

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Answer:

To calculate how many packages Marcella has wrapped, you need to first calculate how many packages each roll of wrapping paper can be used for. Since Marcella uses 1/2 of a roll of wrapping paper for every 3 packages, it follows that she can wrap 3 packages for every 1/2 roll of wrapping paper. Therefore, 2 1/2 rolls of wrapping paper can be used to wrap 15 packages.

Answer:

Step-by-step explanation:

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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Answer:

its 155

Step-by-step explanation:

125 + 10 + 10 + 10 i had answered before but it got deleted

Answer:

\(\\x \quad\quad \;\;\;f(x)\\\\-3 \quad\quad f(-3) -= - f(3) = -(-11) = \boxed{11}\\\\-1\quad\quad f(-1) = -f(1) = \boxed{-19}\\\\2\quad\quad\:\:\: f(2) = - f(-2) = \boxed{- 5}\\\\4\quad\quad\:\:\:f(4) = - f(-4) = - (-3) = \boxed{3}\)

Step-by-step explanation:

A function is "even" when:

\(f(- x) = f(x) \textrm{\;for\;all\;x}\)

In other words there is symmetry about the y-axis (like a reflection):

A function is "odd" when
\(f(-x) = -f(x) \textrm{ for all x}\)
The symmetry is around the origin

Looking at the table and using the property of an odd function we can solve for the missing values

\(\\x \quad\quad \;\;\;f(x)\\\\-3 \quad\quad f(-3) -= - f(3) = -(-11) = \boxed{11}\\\\-1\quad\quad f(-1) = -f(1) = \boxed{-19}\\\\2\quad\quad\:\:\: f(2) = - f(-2) = \boxed{- 5}\\\\4\quad\quad\:\:\:f(4) = - f(-4) = - (-3) = \boxed{3}\)

The length of the support wire is approximately 54 feet. To find the length of the support wire, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the telephone pole forms the height of a right triangle, and the distance from the base to the anchor point forms the base.

We can find the length of the support wire, which is the hypotenuse.

Using the Pythagorean theorem, we have:
Length of support wire = √(30^2 + 45^2)
Length of support wire = √(900 + 2025)
Length of support wire = √2925
Length of support wire ≈ 54 feet

Therefore, the length of the support wire is approximately 54 feet.

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False , the variance and standard deviation are not measures of central location

Given data ,

The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset

Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset

The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.

In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.

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The exponential function f, whose graph is given below, can be written as f(x)=4.7ˣ.

In mathematics, a function is a rule that maps each element (or input) of a set, called the domain, to a unique element (or output) of another set, called the range. Functions are often represented using function notation, such as f(x), where "f" is the name of the function and "x" is the input variable. The value of f(x) is the output or image of x under the function f.

Here,

If the exponential function f can be written as f(x) = a ⋅ b^x, where a and b are constants, then the graph of f will have the following characteristics:

The y-intercept of the graph will be a, which is the value of f(0).

The base of the exponential function, b, determines the rate of growth or decay of the function. If b > 1, the function grows as x increases. If 0 < b < 1, the function decays as x increases. If b = 1, the function is constant.

The graph of f will be increasing if b > 1 and decreasing if 0 < b < 1. The rate of increase or decrease will be determined by the magnitude of b.

The graph of f will never cross the x-axis, but it will approach the x-axis as x becomes very negative (if b > 1) or very positive (if 0 < b < 1).

Note that the graph of an exponential function can also be characterized by its asymptote, which is a horizontal line that the function approaches but never crosses. The asymptote is the line y = 0 if 0 < b < 1, and the line y = a if b > 1.

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All lower bounds of 12 and 18 there are four lower bounds in total.

In the poset (d36, |), we have the partial order relation a | b, if a divides b, for all a, b ∈ d36.

To find the lower bounds of 12 and 18, we need to find all the elements in d36 that divide both 12 and 18.

The divisors of 12 are {1, 2, 3, 4, 6, 12}.

The divisors of 18 are {1, 2, 3, 6, 9, 18}.

The common divisors of 12 and 18 are {1, 2, 3, 6}.

Therefore, the lower bounds of 12 and 18 are 1, 2, 3, and 6.

There are four lower bounds in total.

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In the poset (d36, |), where d36 = {1, 2, 3, 4, 6, 9, 12, 18, 36}, we are asked to find all lower bounds of 12 and 18. A lower bound of a set is an element that is less than or equal to all the elements in the set. In this poset, the partial order is defined as | (divisibility), meaning a is less than or equal to b if a divides b.

Thus, a lower bound of 12 and 18 is any number that divides both 12 and 18. The only such number is 1. Therefore, 1 is the only lower bound of 12 and 18. In conclusion, there is only one lower bound for both 12 and 18 in this poset.
In the poset (d36, |), "d36" represents the divisors of 36 and "|" means "divides." The divisors are {1, 2, 3, 4, 6, 9, 12, 18, 36}. To find the lower bounds of 12 and 18, we look for the common divisors of both numbers. The common divisors are {1, 2, 3, 6}, meaning these elements are the lower bounds of 12 and 18 in this poset. There are 4 lower bounds in total.

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Answer: The range is 1731

Step-by-step explanation: lowest number 4572- 2841 highest

The expected value of a distribution is the weighted average of all possible values that a random variable can take on.

The expected value of a distribution is calculated by multiplying each possible value by its probability and then summing all of these products.

In other words, the expected value is the mean of the distribution.

To calculate the expected value of a distribution, you can use the following formula:

E(X) = ∑xP(x) , where

E(X) = the expected value,

x = possible value of the random variable,

P(x) = the probability of that value occurring.

For example, let's say we have a distribution with the following values and probabilities:

   x:   1       2       3       4        5
P(x): 0.1    0.2    0.3    0.2    0.2

To calculate the expected value, we would multiply each value by its probability and then sum the products:

E(X) = ∑xP(x)

       = (1)(0.1) + (2)(0.2) + (3)(0.3) + (4)(0.2) + (5)(0.2)

       = 0.1 + 0.4 + 0.9 + 0.8 + 1.0

       = 3.2

So, the expected value of this distribution is 3.2.

It is important to note that the expected value is a theoretical value and may not necessarily be observed in actual data. However, it is a useful measure for understanding the central tendency of a distribution.

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Answer:

\(given \: that \: it \: is \: issoscless \: triangl e \\ so \: the \: third \: side \: must \: be \: 2 \\ thank \: you\)

The decimal numbers with benchmark numbers have been correctly placed on the number line shown below.

The correct arrangement of the decimal numbers from least to greatest is 2.02, 2.19, 2.46, 2.53, and 2.85.

In Mathematics, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Therefore, a number line primarily decreases in numerical value towards the left from zero (0) and increases in numerical value towards the right from zero (0).

By critically observing the number line (see attachment), we can logically deduce that all of the decimal numbers are located to the right of 2 and left of 3.

In conclusion, the decimal numbers should be arranged or sorted in ascending order as follows;

2.02, 2.19, 2.46, 2.53, 2.85.

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To find the volume of the given solid using polar coordinates, we integrate the function over the appropriate range of values for the radial coordinate and the angle.

The given solid consists of a cone and a ring in the xy-plane. The cone is defined by the equation z = √(x² + y²), which represents a right circular cone with its vertex at the origin and opening upwards. The ring is defined by the inequality 1 ≤ x² + y² ≤ 64, which represents a circular region centered at the origin with an inner radius of 1 unit and an outer radius of 8 units.

To evaluate the volume using polar coordinates, we can express the equations in terms of the radial coordinate (r) and the angle (θ). In polar coordinates, the cone equation becomes z = r, and the ring equation becomes 1 ≤ r² ≤ 64. To set up the integral, we need to determine the range of values for r and θ. For the radial coordinate, r ranges from 1 to 8, as that corresponds to the region defined by the ring. For the angle θ, we can integrate from 0 to 2π, covering a full revolution around the origin.

The volume integral is then given by V = ∫∫∫ r dz dr dθ over the region defined by 1 ≤ r² ≤ 64 and 0 ≤ θ ≤ 2π. By evaluating this triple integral, we can find the volume of the solid.

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The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

You failed to make the minimum payment by the due date. This is an action that can result in a message that "you've triggered the Penalty APR so that it has now climbed to 28.99%."

A charge APR is a charge that can be applied if you don't pay your bills on time. It may be set up so that future transactions may be subject to a penalty APR that is higher than the card's standard rate.

If the minimum payment was not made by the due date, Penalty APR would be applied.

But if the card also has a penalty APR and you trigger it, you will likely lose that promotional offer. Federal consumer protections that limit penalty APRs don't apply to small-business credit cards. That means issuers can be more punitive, such as applying penalty APRs sooner than 60 days after not making payments.

Therefore,

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

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Answer:

−24= 12

Step-by-step explanation:

Answer:

-2=1

Step-by-step explanation:

-24=(-6)-(-18)

-24=(-6)+18

-24=12

-24/12 = 12/12

-2=1

(2 negatives make a positive)