Find the 66th derivative of the function f(x) = 4 sin (x)…..

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

Step-by-step explanation:

To find the temperature corresponding to the 67th percentile, we need to find the z-score that has an area of 0.67 to the left of it in the standard normal distribution. We can use a table or a calculator to find this z-score.

Using a standard normal distribution table, we can look up the value that corresponds to an area of 0.67 to the left of the mean, which is 0.44. This means that P(Z ≤ 0.44) = 0.67, where Z is the standard normal random variable.

Next, we can use the formula for standardizing a normal random variable to convert this z-score to the corresponding temperature on the thermometer scale:

z = (x - μ) / σ

where μ is the mean, σ is the standard deviation, and x is the temperature we want to find.

Rearranging this formula, we get:

x = μ + z * σ

Plugging in the values, we get:

x = 0 + 0.44 * 1.00

x = 0.44

Therefore, the temperature corresponding to the 67th percentile is 0.44°C.

Answer:

Step-by-step explanation:

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).

In this case, we know that P = $5500, r = 4.5% = 0.045, and we want to find t when A = $6700. We also know that the interest is compounded annually, so n = 1.

Substituting these values into the formula, we get:

$6700 = $5500(1 + 0.045/1)^(1t)

Dividing both sides by $5500, we get:

1.218181818 = (1.045)^t

Taking the natural logarithm of both sides, we get:

ln(1.218181818) = ln(1.045)^t

Using the property of logarithms that ln(a^b) = b ln(a), we can rewrite the right side as:

ln(1.218181818) = t ln(1.045)

Dividing both sides by ln(1.045), we get:

t = ln(1.218181818)/ln(1.045) ≈ 4.2

Therefore, the person must leave the money in the bank for about 4.2 years to reach $6700. To the nearest tenth of a year, the answer is 4.2 years.

The equation of the line passing through (-3, -1) with slope 3/5 is y = (3/5)x + 4/5.

What is point slope form?

The equation of a line is expressed in the point-slope form as follows: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. When we know the slope of a line and a point on the line but not the intercepts, this version of the equation is helpful. It eliminates the need to independently compute the intercepts by allowing us to state the equation of the line in terms of the given point and slope.

Given that, line passes through (-3, -1) and has a slope of 3/5.

The points slope form is given as:

y - y1 = m(x - x1)

Substituting the values we have:

y - (-1) = (3/5)(x - (-3))

y + 1 = (3/5)x + 9/5

y = (3/5)x + 4/5

Therefore, the equation of the line passing through (-3, -1) with slope 3/5 is y = (3/5)x + 4/5.

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(a) The function of price is $1600

(b) The marginal revenue is $80

(c) The revenue and marginal revenue when price is $5 is $30

Marginal revenue is the increase in revenue from selling an additional unit of product. Although marginal revenue may remain constant at a certain level of output, it follows the law of diminishing returns and eventually declines as output levels increase. In economic theory, perfectly competitive firms continue to produce until marginal revenue equals marginal cost.

Assume that a certain product has the demand function given by:

9 = 1000e -0.02p

R(x) = 80x

P(x) = -0.25x² + 40x -100

R'(x) =80

P'(x) = -0.5x + 40

Because we have refurbished x = 20 iPad this month x = 20.

Thus,

R(20) = 80(20) = $1600

P(20) = -0.5(20)² + 40(20) - 1000

         = -$300

R'(20)= $80

And, P'(20) = -0.5 (20) + 40

                   = $30

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Answer:

huh

Step-by-step explanation:

This means that we can be 95% confident that the true difference in means between Clarion and Wabash is somewhere between -3.33 and -0.88

A 95% confidence interval for the difference in means between Clarion and Wabash can be calculated using the following formula: CI95 = (μ1 - μ2) ± 1.96*√(σ1^2/n1 + σ2^2/n2),where μ1 and μ2 are the population means of Clarion and Wabash respectively, σ1 and σ2 are the population standard deviations of Clarion and Wabash respectively, and n1 and n2 are the sample sizes of Clarion and Wabash respectively. To calculate the confidence interval, we need to have access to the population means and standard deviations of Clarion and Wabash, which we do not have. In their place, we can use the sample means and standard deviations as an estimate of the population means and standard deviations. Using the sample means and standard deviations, the 95% confidence interval for the difference in means between Clarion and Wabash is (-3.33, -0.88). This means that we can be 95% confident that the true difference in means between Clarion and Wabash is somewhere between -3.33 and -0.88.

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What is the approximate 95% confidence interval for the difference in means between Clarion and Wabash?

If x and y are integer variables, then the expression that evaluates to true if x is greater than y is "x>y".

In Java, symbol of ">" is used for "greater-than" operator. So, the expression which evaluates to "true" if integer "x" is greater than integer "y" is "x > y".

This expression compares the values of x and y and returns a Boolean value of "true" if x is greater than y, and "false" otherwise.

The expression can be used in conditional statements, loops, and other constructs that require a Boolean value as a condition. It is important to note that the ">" operator only works with primitive types such as int, long, double, etc.

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Answer:

Let's start by expressing "Z increased by 16%" using algebra.

Let Z be the original value of some quantity.

To increase Z by 16%, we need to add 16% of Z to Z:

Z + 0.16Z

Simplifying this expression by factoring out Z, we get:

Z(1 + 0.16)

Combining like terms, we have:

Z(1.16)

Therefore, "Z increased by 16%" can be expressed algebraically as:

Z increased by 16% = Z(1.16)

Answer:

z(1.16)

Step-by-step explanation:

Therefore, the monthly payment for a student loan of $15,000 at a fixed APR of 12% for 20 years is $144.36.

Interest is the cost of borrowing money or the return on investing money. When you borrow money, you usually have to pay back more than you borrowed, and the additional amount you pay is the interest. The interest rate is expressed as a percentage of the borrowed amount, and it can vary depending on factors such as the borrower's credit score, the term of the loan, and the lender's policies.

Given by the question.

Assuming the loan has a fixed interest rate of 12% per annum, the amount of interest charged each year will be:

12% of $15,000 = $1,800

The total interest charged over 20 years will be:

$1,800 x 20 = $36,000

The total amount to be repaid (principal + interest) will be:

$15,000 + $36,000 = $51,000

If the loan is being repaid in equal monthly installments over the 20-year term, the monthly payment can be calculated using the following formula:

M = P * (r[tex](1+r)^{n}[/tex]) / ([tex](1+r)^{n}[/tex]- 1)

Where:

M = Monthly payment

P = Principal amount (in this case, $15,000)

r = Monthly interest rate (12% per annum / 12 months = 1% per month)

n = Total number of payments (20 years x 12 months per year = 240)

Plugging in the values:

M = $15,000 * (0.01[tex](1+0.01)^{240}[/tex]) / ([tex](1+0.01)^{240}[/tex] - 1)

M = $144.36

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The area to the right of x is 0.877.

In a normal distribution, the entire area under the curve is identical to 1. The area to the left of a specific value of x represents the possibility of observing a value largely lesser than or same tox.

However, we're capable to discover the area to the right of x with the aid of abating the left area from 1, If the place to the left of x is given.

In this case, the area to the left of x is 0.123. thus, the place to the right of x is

1-0.123 = 0.877

Thus, the area is 0.877 to the right of x.

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If Andres Michael bought a new boat. He took out a loan for $24,420 at 3.5% interest for 2 years. Andres Michael owes $18806.6 at maturity.

To calculate how much is due at maturity, we first need to determine how much of the loan remains after the two partial payments.

To do this, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest

P = Principal (original loan amount)

r = Annual interest rate

t = Time (in years)

The interest for the first two months can be calculated as:

I1 = P * r * t1

= 24420 * 0.035 * (2/12)

= 142.45

So after the first two months, the amount owing on the loan is:

P1 = P + I1 - 4330

= 24420 +142.45 - 4330

= 20,232.45

The interest for the next four months can be calculated as:

I2 = P1 * r * t2

= 20,232.45 * 0.035 * (4/12)

= 236.05

So after six months, the amount owing on the loan is:

P2 = P1 + I2 - 2600

=  20,232.45 + 236.05- 2600

= 17868.50

Now we can calculate the interest for the remaining 18 months:

I3 = P2 * r * t3

=  17868.50* 0.035 * (18/12)

= 938.10

So the total amount owing at maturity (after 2 years) is:

Total amount owing = P2 + I3

=  17868.50 + 938.10

= 18806.6

Therefore, Andres Michael owes $18806.6 at maturity.

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Answer:

$586.00

Step-by-step explanation:

Markup is the how much more an item or service is sold for to cover overhead fees. If the markup is 25%, then the price was increased by 25% in order to be sold for $732.50. We can set up a proportion to represent this where c is the cost.

[tex]\frac{732.5}{1.25} = \frac{c}{1.00}[/tex]

Cross-multiply.

1.25c = 732.5

c = 586

So, the cost of the item was $586.00

Answer:

36.3636364%

or 36.36

Step-by-step explanation:

Answer:

We can only see g(x) not f(x)

Step-by-step explanation:

Domain of g(x) is

[tex]( - \infty \: to \: \infty )[/tex]

Range of g(x) is

[tex](0 \: to \: \infty )[/tex]

Range lf

The t-value such that the area under the t distribution to the right of the t-value is 0.10, assuming 15 degrees of freedom (df) is 1.753050356.

We have to determine the t-value.

The area in the right tail is 0.10 with 32 degrees of freedom(df).

The t-test is a test that is used as an alternative to the z-test in statistics. If the data are normally distributed but the sample size is small and the population standard deviation is unknown, the t-test is utilized.

A value that appears on the t distribution is the critical t value. The area under the curve and the degrees of freedom can be used to determine the t statistic value.

Using Excel Formula,

The t-value = (=TINV(0.1,15))  

The t-value = 1.753050356

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The slope of this linear function is equal to: B. -2/9.

The volume of a cylinder with a height of 10 m and a radius of 5 m is equal to 785 m³.

The value of each expression is: C. a) 2, b) 1/2, c) 2/9.

In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (8 - 10)/(6 - (-3))

Slope (m) = (8 - 10)/(6 + 3)

Slope (m) =

Slope (m) = -2/9.

In Mathematics, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given parameters, we have:

Volume of cylinder, V = 3.14 × 5² × 10

Volume of cylinder, V = 785 m³

(√2)² = 2

(1/√2)² = 1/2

(√2/3)² = 2/9

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The value of height (h)  will be 6 cm.

What is Parallelogram?

A parallelogram is a four-sided polygon in which both pairs of opposite sides are parallel and equal in length. It is a special case of a quadrilateral, which means a polygon with four sides. The opposite angles in a parallelogram are also equal in measure, and the adjacent angles are supplementary, which means they add up to 180 degrees.

Given : height (H) = 5 cm

            base (B) = 12 cm

Similarly, height (h) = 5 cm

               base (h) = 12 cm

Now, we know that area of parallelogram will be same whether we use different method.

So, area of given parallelogram  =  base × height

                                         B × H    =  b × h

                                        12 × 5    =  10 × h

                                            60     =  10 h

So,   h = 60/10 = 6 cm.

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Elliptic curve cryptography (ECC) makes use of elliptic curves in which the variables and coefficients are all restricted to elements of a finite field.

ECC is a type of public-key cryptography that is based on the difficulty of solving the elliptic curve discrete logarithm problem (ECDLP), which is a variant of the discrete logarithm problem in which the group operation is performed on points on an elliptic curve.

ECC is particularly useful in settings where computational resources are limited, such as mobile devices and smart cards, as it provides the same level of security as other public-key cryptographic systems but with smaller key sizes.

ECC also offers other advantages over traditional public-key cryptography such as faster computation times, lower power consumption, and smaller message sizes.

ECC is widely used in a variety of applications, including digital signatures, encryption, and key exchange. It is implemented in many cryptographic standards, such as the Transport Layer Security (TLS) protocol used to secure internet communications, and is considered to be one of the most promising cryptographic techniques for the future.

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Complete question is:

___________ makes use of elliptic curves in which the variables and coefficients are all restricted to elements of a finite field.

The length distance of ab between the points  (-4,-6) and b (3,2) is   10.6 units.

Now to find the distance between points A(-4,6) and B(3,2), we  can use the distance formula which is :

d = sqrt((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁)=(-4,-6) and (x₂,y₂)=(3,2), now we substituting the  values into the formula  after which we get :

d = sqrt((3 - (-4))² + (2 - (-6))²) = sqrt((7)² + (8)²) = sqrt(49 + 64) = sqrt(113) ≈ 10.6

it comes out  that the distance between points A and B is approximately 10.6  units  which are rounded to the nearest tenth.

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The player should be willing to pay up to $12 to play this game and not lose money in the long run.

First we need to multiply the probability of winning by the amount won and subtract the probability of losing by the amount lost.

The probability of rolling a 1 on a 6-sided die is 1/6, and the probability of rolling any other number is 5/6.

So, the expected value of the game is:

(1/6) x $4 - (5/6) x $2

= ($4/6) - ($10/6)

= -$1/3

This means that on average, for every game played, the player can expect to lose $1/3.

To find out how much the player should be willing to pay to play this game and not lose money in the long run, we can set the expected value equal to zero:

(1/6) x $4 - (5/6) x $2 = $0

Simplifying the equation, we get:

$4/6 = $10/6

Multiplying both sides by x, we get:

(1/6) x - $2 = 0

Solving for x, we get:

x = $12

Therefore, the player should be willing to pay up to $12 to play this game and not lose money in the long run.

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Check the picture below.

so if the triangles are congruent, then CPCTC.

Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in 24 different ways.

To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations that can be made from the letters D, O, G, and Q when we choose 3 of these 4 letters.

The formula for finding the number of permutations is:

n! / (n-r)!

where n is the total number of objects and r is the number of objects we choose.

Using this formula, we can calculate the number of permutations as follows:

4! / (4-3)!

= 4! / 1!

= 4 x 3 x 2 x 1 / 1

= 24

Therefore, we can arrange the chosen 3 letters in 24 different ways.

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By answering the question the answer is standard deviation  For 0 courses: 3 students (3/55 ≈ 0.1 or 9.1%); For 1 course: 12 students (12/55 ≈ 0.2 or 21.8%)

Standard deviation is a statistic that describes the variability or variance of a group of numbers. A high standard deviation indicates that the values ​​are more dispersed, while a low standard deviation indicates that the values ​​tend to be closer to the established mean. A measure of how far the data are from the mean is the standard deviation (or ). If the standard deviation is small, the data tend to be clustered around the mean, and if the standard deviation is large, the data are more dispersed. The average variability of the dataset is measured as standard deviation. Shows the mean deviation of each score from the mean. 

To fill in the blank cells, we need to calculate the number of students who reported each course number and the relative frequency (rounded to the nearest tenth). This can be done like this:

For 0 courses:

3 students (3/55 ≈ 0.1 or 9.1%)

For 1 course:

12 students (12/55 ≈ 0.2 or 21.8%)

For 2 courses:

17 students (17/55 ≈ 0.3 or 30.9%)

For 3 courses:

9 students (9/55 ≈ 0.2 or 16.4%)

For 4 courses:

8 students (8/55 ≈ 0.1 or 14.5%)

For 5 courses:

2 students (2/55 ≈ 0.0 or 3.6%)

For 6 courses:

4 students (4/55 ≈ 0.1 or 7.3%)

The finished table looks like this:

+--------+--------+---------------------+

| Number | Number | Relative Frequency  |

|  of    | of     | (Rounded to nearest |

|Courses |Students|         tenth)      |

+--------+--------+---------------------+

|   0    |   3    |         0.1         |

|   1    |   12   |         0.2         |

|   2    |   17   |         0.3         |

|   3    |   9    |         0.2         |

|   4    |   8    |         0.1         |

|   5    |   2    |         0.0         |

|   6    |   4    |         0.1         |

+--------+--------+---------------------+

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The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.

The 30°-60°-90° Triangle Theorem states that in such a triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is the product of the length of the hypotenuse and the square root of 3 divided by 2.

Using this theorem, we can write:

y = hypotenuse

Opposite of 30° angle = 5 = hypotenuse/2

Opposite of 60° angle = x = hypotenuse × (√(3)/2)

Solving for the hypotenuse in terms of y from the first equation, we get:

hypotenuse = 5×2 = 10

Substituting this value into the third equation, we get:

x = 10 × (√(3)/2) = 5 × √(3)

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The given statement " show that there exist coefficients w0, w1, ..., wn that depend on x0, x1, ..., xn, and on a and b, such that the limit of the sum, as a approaches b, of the form summation from i=0 to n of wi*p(xi) for all polynomials p of degree <= n", is proved by the use of Lagrange form of the interpolating polynomials.

Let p(x) be a polynomial of degree at most n. Then, by the Lagrange interpolation formula from Section 4.1, we have:

p(x) = Summation from i=0 to n of p(xi) * Li(x)

where Li(x) is the ith Lagrange basis polynomial, defined by:

Li(x) = Product from j=0 to n, j != i, of (x - xj) / (xi - xj)

Now, consider the sum:

S = Summation from i=0 to n of wi * p(xi)

where wi are coefficients to be determined. We want to show that the limit of S as a approaches b exists for all polynomials p of degree at most n.

We can express S in terms of the Lagrange basis polynomials as:

S = Summation from i=0 to n of wi * p(xi)

= Summation from i=0 to n of wi * Summation from j=0 to n of p(xj) * Li(xj)

= Summation from j=0 to n of p(xj) * Summation from i=0 to n of wi * Li(xj)

Note that the summation over i is only dependent on the Lagrange basis polynomial Li(xj), and does not depend on p(xj). Therefore, we can choose the coefficients wi such that:

Summation from i=0 to n of wi * Li(xj) = 0 for j != k

Summation from i=0 to n of wi * Li(xk) = 1

for some k in {0, 1, ..., n}.

To see why this is possible, note that the Lagrange basis polynomials satisfy the property that Li(xi) = 1 and Li(xj) = 0 for j != i. Therefore, we can choose the coefficients wi to be:

wi = Li(xk) / Summation from i=0 to n of Li(xk)

which gives:

Summation from i=0 to n of wi * Li(xj) = Li(xk) / Summation from i=0 to n of Li(xk) * Summation from i=0 to n, i != k of Li(xj)

= 0 for j != k

Summation from i=0 to n of wi * Li(xk) = 1

Now, we have:

S = Summation from j=0 to n of p(xj) * Summation from i=0 to n of wi * Li(xj)

= Summation from j=0 to n of p(xj) * Li(xk)

Taking the limit as a approaches b, we get:

lim a->b S = lim a->b Summation from j=0 to n of p(xj) * Li(xk)

= Summation from j=0 to n of p(xj) * lim a->b Li(xk)

= Summation from j=0 to n of p(xj) * Integral from a to b of Li(x) dx

where we have used the fact that the limit and integral commute, and the limit of the Lagrange basis polynomial Li(xk) is equal to the integral of Li(x) over the interval [a, b], which is a constant that does not depend on k.

Therefore, we have shown that there exist coefficients w0, w1, ..., wn that depend on x0, x1, ..., xn, and on a and b, such that the limit of the sum, as a approaches b, of the form Summation from n to i=0 wi p(xi).

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_____The given question is incomplete, the complete question is given below:

Show that there exist coefficients w0,w1, . . . ,wn depending on x0, x1, . . . , xn and on a, b such that limit a to b { summation n to i=0 wi p(xi)} for all polynomials p of degree ?n.

   Hint: Use the Lagrange form of the interpolating polynomials from Section 4.1

From the given probability distribution, the probability of x being 4 in the given probability distribution is 0.15,

According to the given probability distribution in Table 1, the probability of x being 4 is 0.15. This means that out of all the possible values of x (0 to 6), there is a 15% chance that x will be equal to 4.

To understand the probability distribution better, we can visualize it using a graph. The x-axis represents the possible values of x, while the y-axis represents the probability of each value. We can plot the values from Table 1 to create a histogram or a bar graph.

From the graph, we can see that the probability distribution is skewed to the right, with the highest probability being at x=2. This means that there is a higher chance that x will be closer to 2 than to 0 or 6.

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Answer:

To find the probability that a randomly selected person is a meat-eater, we need to add up the number of meat-eaters and divide by the total number of individuals surveyed. From the given table, we can see that there are 72 meat-eaters out of a total of 190 individuals surveyed:

Total meat-eater = 72

Total surveyed = 190

So the probability of selecting a meat-eater is:

P(meat-eater) = Total meat-eater / Total surveyed

P(meat-eater) = 72 / 190

P(meat-eater) = 0.38 (rounded to the hundredths place)

Therefore, the probability that a randomly selected person is a meat-eater is 0.38 or 38%.