Compute the exact value of the expression: sin( 7 ) cot ( 7 ) – 2 cos( 7 ) =

Answer:

59,425 square miles

Step-by-step explanation:

59,424.77 rounded to the nearest square mile would be 59,425 because the . 77 would get rounded up to a 1.

Answer:

143. Divide 91/7 = 13, then take the number of oil changes per day and times it by 11. 13 x 11 = 143.

Step-by-step explanation:

Answer:

113.75

Step-by-step explanation:

Since 11 days is only 4 days away from 11, divide 91 / 4 = 22.75. Add this number to 91 to get the answer.

Answer:

The answer is 28 more he sold it for.

Step-by-step explanation:

152+16=168. 168-140=28

I hope this helped have a good day!!

Answer:

       \(\frac{2}{7}\)

Step-by-step explanation:

3.5 = \(\frac{7}{2}\)

swap the numerator and denominator (flip the fraction):

reciprocal of \(\frac{7}{2}\) is \(\frac{2}{7}\)

Answer:

14

Step-by-step explanation:

13-6= 7(2)

7 times 2= 14

So basically 13-6= 7, and anything in parenthesis will multiply, so "7(2)" equals 7x2. If you're multiplying a number by 2, the easiest way if you don't know it, is to add it by itself, so 7+7=7x2 which also equals 14.

hope this helps

The solution of the given equation form would be 14

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given that subtract 6 from 13, them multiply by 2

13-6= 7(2)

7 x  2= 14

Thus anything in parenthesis will multiply, we get;

"7(2)" = 7x2.

If you're multiplying a number by 2,

Thus, it is equals 14.

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Answer:

Average cost per ounce is $0.65

Step-by-step explanation:

My Notes:

Monday - 12 Oz. = $7.80

Wednesday - 9 Oz. = $5.85

Find the average cost per 1 Oz. per candy.

\(\frac{12}{7.8} = 0.65\)

The AVERAGE cost per ounce is $0.65.

Step-by-step explanation:

If x and y are integers, then the even number is 2x and the odd number is 2y+1.  The product is:

2x (2y + 1)

Distribute the x:

2 (2xy + x)

This product is a multiple of 2, so the number is even.

Answer:

133

Step-by-step explanation:

180-47=133

Answer: if the shape is a triangle, 180-47=133

if it is any other shape, 360-47=313

Step-by-step explanation:

The dimensions of the rectangle with the greatest possible area are approximately:

Width = 4.389

Height = 3.259

Let's assume that the width of the rectangle is ""w"" and the height is ""h"".

Since the base of the rectangle is on the x-axis, we know that the width of the rectangle is equal to the distance between the x-coordinates of its two corners.

Let's say that the x-coordinate of the left corner is ""a"" and the x-coordinate of the right corner is ""b"". Then we have:

w = b - a

The height of the rectangle is the distance between the y-coordinate of its upper corners. Since the upper corners of the rectangle lie on the parabola y=8−x2, we can express the height in terms of ""a"" and ""b"" as follows:

h = 8 - a^2

h = 8 - b^2

The area of the rectangle is given by:

A = w * h

A = (b - a) * (8 - a^2)

To find the dimensions of the rectangle with the greatest possible area, we need to maximize the area A. We can do this by taking the derivative of A with respect to ""a"", setting it equal to zero, and solving for ""a"". Let's do that now:

dA/da = -2a^2 + 8a - b + 8

Setting this derivative equal to zero, we get:

-2a^2 + 8a - b + 8 = 0

We can solve this equation for ""b"" in terms of ""a"" as follows:

b = -2a^2 + 8a + 8

Substituting this expression for ""b"" back into the equation for the area A, we get:

A = (b - a) * (8 - a^2)

A = (-2a^2 + 8a + 8 - a) * (8 - a^2)

A = (-2a^2 + 7a + 8) * (8 - a^2)

A = -2a^4 + 15a^3 - 24a^2 + 64a

To find the value of ""a"" that maximizes this expression for A, we can take its derivative with respect to ""a"", set it equal to zero, and solve for ""a"". Let's do that now:

dA/da = -8a^3 + 45a^2 - 48a + 64

Setting this derivative equal to zero, we get:

-8a^3 + 45a^2 - 48a + 64 = 0

This equation doesn't have a nice closed-form solution, so we'll need to solve it numerically. Using a graphing calculator or a computer algebra system, we can find that one solution is:

a ≈ 2.306

To find the corresponding value of ""b"", we can use the expression we derived earlier:

b = -2a^2 + 8a + 8

b ≈ 6.695

So the width of the rectangle is:

w = b - a ≈ 6.695 - 2.306 ≈ 4.389

And the height of the rectangle is:

h = 8 - a^2 ≈ 3.259

Therefore, the dimensions of the rectangle with the greatest possible area are approximately:

Width = 4.389

Height = 3.259

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(a) The profit of the firm at the current employment levels of 25 units of labor and 50 units of capital can be calculated by subtracting the total cost from total revenue.

The total revenue is given by the output multiplied by the market price, which is $2. The total cost is the sum of the wage cost (W) and the rental cost of capital (R), multiplied by their respective quantities.

Profit = Total Revenue - Total Cost

Profit = (Output * Price) - (Wage * Labor + Rental * Capital)

Given that the output is determined by the production function Y = 100K^(1/2) + 40L^(1/2), the profit can be calculated as follows:

Profit = (100K^(1/2) + 40L^(1/2)) * $2 - ($8 * 25 + $10 * 50)

(b) The profit-maximizing quantity of capital for this firm can be determined by setting the marginal revenue product of capital (MRPK) equal to the rental cost of capital (R). MRPK represents the additional revenue generated by employing an additional unit of capital.

MRPK = R

The marginal revenue product of capital can be calculated as the partial derivative of the production function with respect to capital (K), multiplied by the market price (P):

MRPK = (∂Y/∂K) * P

Using the production function Y = 100K^(1/2) + 40L^(1/2), we can calculate the marginal revenue product of capital as follows:

MRPK = (∂Y/∂K) * P = (50K^(-1/2)) * $2

Setting this equal to the rental cost of capital (R) of $10, we have:

(50K^(-1/2)) * $2 = $10

Simplifying the equation, we find:

K^(-1/2) = 1/5

Squaring both sides of the equation, we get:

K = 25

Therefore, the profit-maximizing quantity of capital for this firm is 25 units.

(c) To raise profits, the firm should decrease its capital employment from 50 to 25 units. This is because the profit-maximizing quantity of capital is determined to be 25 units, as calculated in part (b). By employing fewer units of capital, the firm can reduce its rental cost while still maintaining the optimal level of capital for production. As a result, the firm can lower its total cost and increase its profit. Employing more capital beyond the profit-maximizing level would lead to diminishing returns, where the additional costs outweigh the additional revenue generated. Therefore, reducing capital employment to the optimal level of 25 units would be the most favorable decision for the firm to maximize its profits.

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The compass needle always points north because it is magnetic north pole.

Earth has magnetic field due to magnetic elements present in Earth's core in molten form. They are assumed to be in the form of giant bar to ease the calculations concerning magnetic field and polarity. The assumptions are geographic south pole harbours magnetic north pole and vice versa for the opposite pole.

So, we know that like poles attract each other and unlike poles repel each other. The north end of magnetic needle will point towards the magnetic south pole which is geographic north pole. Thus, we see compass needle directed to North pole.

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The required indefinite integral is equal to -1/8 (3x^2 - 4x + 3)^-4 + C.

Evaluation of the indefinite integral of the function of the form: ∫ f (x) dx, is the inverse operation of differentiation. It is finding a function F(x) such that F'(x) = f(x). It is also known as an antiderivative. Now, we need to evaluate the indefinite integral. ∫ (3x-2) /(3x^2−4x+3)^5  dx

By using the substitution method, we take u = 3x^2 - 4x + 3, and then du/dx = 6x - 4dx = du/6.

Rearranging, we get 3/2 dx = du/(2x - 3)

Next, we can simplify the integral by using the substitution with

u.∫ (3x - 2)/(3x^2 - 4x + 3)^5 dx = ∫ 1/2 * [(2x - 3)/(3x^2 - 4x + 3)^5] * (3/2) dx

We substitute u in the integral.

∫ 1/2 * u^-5 * du = 1/2 (-u^-4/4) + C = -1/8 (3x^2 - 4x + 3)^-4 + C

Finally, we have the solution as:

∫ (3x-2) /(3x^2−4x+3)^5  dx = -1/8 (3x^2 - 4x + 3)^-4 + C.

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Blake has 5 dimes and 10 nickels.

Let x represent the number of dimes and y represent the number of nickels.

Each dime is worth 10 cent ($0.1) and each nickel is worth 5 cents ($0.05).

Since he has a minimum of 13 coins, hence:

x + y ≥ 13     (1)

It is worth at most $1 combined, hence:

0.1x + 0.05y ≤ 1     (2)

From the graph, a possible solution is (5, 10).

Blake has 5 dimes and 10 nickels.

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The mean of the total withdrawals in 8 hours is $2400 and the standard deviation is approximately $178.89.

To find the mean of the total withdrawals in 8 hours, we first need to find the mean of withdrawals per hour. Since the rate of customers arriving at the ATM is 10 per hour, we can assume that there are also 10 withdrawals per hour. Therefore, the mean of withdrawals per hour is 10 x $30 = $300.

To find the mean of total withdrawals in 8 hours, we can multiply the mean of withdrawals per hour by the number of hours: $300 x 8 = $2400.

To find the standard deviation of total withdrawals in 8 hours, we need to use the formula: standard deviation = square root of (variance x n), where variance is the square of standard deviation and n is the number of observations.

The variance of withdrawals per hour can be calculated as follows:

Variance = (standard deviation)^2 = $20^2 = $400

Therefore, the variance of total withdrawals in 8 hours is:

Variance = $400 x 8 = $3200

And the standard deviation of total withdrawals in 8 hours is:

Standard deviation = square root of ($3200 x 1) = $56.57

So, the mean of total withdrawals in 8 hours is $2400 and the standard deviation is $56.57.
Hello! I'd be happy to help you with this question. To find the mean and standard deviation of the total withdrawals in 8 hours, we'll first determine the expected number of customers and then use the given information about the mean and standard deviation of the withdrawals.

1. Determine the expected number of customers in 8 hours: Since customers arrive at a rate of 10 per hour, in 8 hours we can expect 10 * 8 = 80 customers.

2. Calculate the mean of total withdrawals: Multiply the mean withdrawal per transaction by the expected number of customers. The mean withdrawal is $30, so the mean of total withdrawals in 8 hours is 80 * $30 = $2400.

3. Calculate the variance of total withdrawals: Since the withdrawals are independent, we can multiply the variance of individual withdrawals by the expected number of customers. The variance is the square of the standard deviation, which is $20^2 = $400. The variance of total withdrawals in 8 hours is 80 * $400 = $32,000.

4. Calculate the standard deviation of total withdrawals: Take the square root of the variance. The standard deviation is √$32,000 ≈ $178.89.

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(a) The standard deviation is 2.582

(b) No, because the standard deviations of these two distributions are not too different from one another.

a) In this question we have been given

The given information is:

First Digit      1     2    3    4    5    6      7     8      9

Probability   1/9 1/9 1/9 1/9 1/9  1/9   1/9  1/9  1/9

Now we find the standard deviation.

The mean for given data is:

μ = ∑xP(X = x)

μ = (1*1/9) +(2*1/9)+(3*1/9)+(4*1/9)+(5*1/9)+(6*1/9)+(7*1/9)+(8*1/9)+(9*1/9)

μ = 5

The standard deviation is:

σ² = ∑(x - μ)²P(X)

σ² = (1 - 5)² *1/9 +(2 - 5)²*1/9+(3 - 5)²*1/9+(4 - 5)²*1/9 + (5 - 5)²*1/9+(6 - 5)²*1/9+(7-5)²*1/9+(8-5)²*1/9)+(9-5)²*1/9

σ² = 2.582

(b) The uniform distribution's standard deviation is 2.582, while Benford's law's standard deviation is 2.46

Using the standard deviation to detect fraud is not a good idea because the two distributions have about the same standard deviation

Therefore, (a) The standard deviation is 2.582

(b) using standard deviations would not be a good way to detect fraud.

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The complete question is:

Benford’s law and fraud

(a) Using the graph from Exercise 21, calculate the standard deviation σY. This gives us an idea of how much variation we’d expect in the employee’s expense records if he assumed that first digits from 1 to 9 were equally likely.

(b) The standard deviation of the first digits of randomly selected expense amounts that follow Benford’s law is . Would using standard deviations be a good way to detect fraud? Explain your answer.

Answer:

A.

Step-by-step explanation:

A way to find the equation of the graph is to find the solutions.

On the graph, the solutions are where the function intersects the x-axis. That would be where x = -2, x = 1, and x = 3.

In the equations, you will need to find factors when the x is inputted, the factor equals 0. For example, one of the factors is (x + 2). This is because x + 2 = 0, so x = 0 - 2, so x = -2. So, the three factors are (x + 2), (x - 1), and (x - 3).

The correct equation is A.

Hope this helps!

Answer:

x = -5

Step-by-step explanation:

f(x) = \(\frac{x+5}{4}\)

Okay, so in order to find the zeroes of the equation, we need to find the values of x for which f(x) = 0.

\(\frac{x+5}{4}\) = 0

We can start by multiplying both sides by 4.  Anything multiplied by 0 equals 0, so we have the following:

x + 5 = 0

Now, subtracting 5 from both sides in order to isolate x, we have:

x = -5

To check our work, let's substitute -5 into our equation:

f(-5) = \(\frac{-5+5}{4}\) = \(\frac{0}{4}\)

0 divided by anything equals 0, so f(-5) = 0.

The probability that Luke will hit the inner ring fewer than 3 times is  0.069.

To calculate the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X, we need to know the distribution of X.

Assuming that each shot is independent and has the same probability p of hitting the inner ring, X follows a binomial distribution with parameters n=5 and p.

The mean of a binomial distribution is given by μ = np, so in this case, the mean of X is 5p.

To find the probability that X is less than 5p, we can use the cumulative distribution function (CDF) of the binomial distribution. Let F(k) denote the CDF of the binomial distribution with parameters n=5 and p, evaluated at k.

Then the probability that X is less than 5p is:

P(X < 5p) = F(4p)

Note that we use 4p instead of 5p in the argument of F, since we want the probability that X is strictly less than 5p, not less than or equal to 5p.

Using a binomial table or calculator, we can look up or compute the value of F(4p) for a given value of p.

For example, if p=0.6 (which corresponds to Luke hitting the inner ring 60% of the time), we get:

P(X < 5p) = F(2.4) ≈ 0.069

So the probability that Luke will hit the inner ring fewer than 3 times (which is less than 5p=3) out of the 5 attempts is about 0.069, assuming he hits the inner ring with a probability of 0.6 on each shot.

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Answer:

B

Step-by-step explanation:

a fraction is equal to 0 when the numerator is 0

x - 4 = 0

x = 4

The correct answer is x=4.

Step-by-step explanation:

When the numerator is 0, a fraction is equal to 0.

x - 4 = 0

x = 4

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Answer:(3x+2)(x+4)

Step-by-step explanation: First you combine like terms to get 3x^2+10x+8

Then you use the cross method to get (3x+2)(x+4)

Answer:

3.142 and 22/7

Step-by-step explanation:

thats its

The minimum area of the square box built with a volume of 6912 in³ is 1728 inches².

It is a measure of a three-dimensional space. The length is related to volume. By knowing the length and breadth of an item, we can easily calculate volume. It is used to measure the capacity of a solid shape.

Vₙ=Aₙ×h

Aₙ=x²

Vₙ=x²y

y=Vₙ/x²

y=6912/x²

We have to find the optimization function.

Aₓ=Aₙ+A₁

Aₓ(x, y) =x²+4xy

Aₓ(x)=x²+4x(6912/x²)

Aₓ(x)=x²+(27648/x)

Now, we have to have to find the optimization function for the critical point.

Aₓ(x)=x²+(27648/x)

A'ₓ(x)=2x-(27648/x²)

A'ₓ(x)=0

2x-(27648/x²)=0

2x= (27648/x²)

x³=13824

x=24

x=24∈D

A'ₓ(x)=2x-(27648/x²)

A"ₓ(x)=2+(55296/x³)

A"ₓ(24)=6>0

A"ₓ(x)=>0

x=24

Aₓ(x, y) =x²+4xy

Aₓ(24,12)=(24)²+4(24)(12)

Aₓ(24,12)=1728

The dimensions of the box are length=24 inches, height= 12inches

And the minimum area of the square box with a given volume is 1728 inches².

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Answer:

the answers are -4 and 4 i hope this helps you or anyone else who visits this question :3

Step-by-step explanation:

Answer:

No!

Step-by-step explanation:

3/4 does NOT go into 80/100 because say if you had 3 shiny quarters out of 4 quarters total that is equal to 75 cents of shiny quarters but if you were to have 100 pennies and 80 of them were shiny that is 80 cents worth of shiny pennies.

Hope that helped :)

Answer:

15.9

Step-by-step explanation:

6^2 + x^2 = 17^2

36 + x2 = 289

x2 = 253

x= √ 253 = 15.9

The solution to the equation 58p - 34 = 4 is p = 38/58

An equation is an expression used to show the relationship between two or more variables and numbers.

From the question, given the equation:

58p - 34 = 4

Add 34 to both sides of the equation:

58p - 34 + 34 = 4 + 34

58p = 38

To make p the subject of the equation, divide through by 58:

58p/58 = 38/58

p = 38/58

The solution to the equation 58p - 34 = 4 is p = 38/58

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