If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative ..............of f.If f(b) < f(x) in an open interval containing b, x ≠ b, then the function value f(b) is a relative ............ of f.

To estimate the average height of black spruce trees in a 1,000 ha plot with 99% confidence that the estimate is within 0.5 m, you need a sample size of at least 19. This is based on the standard deviation of tree heights in a nearby location of 1.10 m as determined in a study conducted last year.

To estimate the average height of black spruce trees in a 1,000 ha plot with 99% confidence that the estimate is within 0.5 m, we can use the formula for sample size calculation:

n = (z² × σ²) / E²

Where:

n = sample size

z = z-score for the desired confidence level (99% confidence level corresponds to a z-score of 2.576)

σ = standard deviation (1.10 m)

E = margin of error (0.5 m)

Plugging in the values into the formula, we get:

n = (2.576² × 1.10²) / 0.5²n = 18.15.

Therefore, the sample size must be at least 19 black spruce trees to have 99% confidence that the estimate is within 0.5 m.

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Answer:

Step-by-step explanation:

Im not really sure what the heck you doing because im only in 8th grade but right now im in central and i'm kind of good at math but i'll try. Lets see........ I think they would all just be $11.50, but like i said im only in 8th grade and not that good at this kind of math so before you answer it please check with someone else to see if i got it right for you, cause i don't want to give you the wrong answer and you fail it.

The total number of months he made deposits and multiply that by the monthly deposit amount.

Chase started an IRA at the age of 26 and deposited $400 each month until he retired at the age of 65. To determine the amount of money Chase deposited over the length of the investment, we need to calculate the total number of months he made deposits and multiply that by the monthly deposit amount.

Number of months = (Retirement age - Starting age) * 12
Number of months = (65 - 26) * 12
Number of months = 468

Total deposits = Number of months * Monthly deposit amount
Total deposits = 468 * 400
Total deposits = $187,200

To determine how much Chase made in interest upon retirement, we need to subtract the total deposits from the retirement savings.

Interest = Retirement savings - Total deposits
Interest = $838,879.58 - $187,200
Interest = $651,679.58

Therefore, Chase deposited a total of $187,200 over the length of the investment and made $651,679.58 in interest upon retirement.

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Answer:

x=36

y=6

system of equations

A professional golfer to make about 40.7 holes over 5 rounds of golf with the new club, while an amateur golfer would only make about 1.6.

First, let's define some variables to represent the probabilities of making a hole for a professional golfer and an amateur golfer:

Let p be the probability that a professional golfer makes a hole with the new club.

Let q be the probability that an amateur golfer makes a hole with the new club.

According to the company's claims, we know that:

p = 1.2q (since the professional golfer makes a hole 120% of the time, which is 1.2 times the probability of the amateur golfer making a hole)

Next, we need to determine the probability of each golfer making a hole during one round of golf, which consists of 18 holes. Let's assume that each hole is independent of the others, meaning that the outcome of one hole does not affect the outcome of another. In that case, the probability of making at least one hole in a round can be calculated using the complement rule:

The probability that a professional golfer makes at least one hole in a round is 1 minus the probability that the golfer misses every hole: [tex]1 - (1-p)^{18} .[/tex]

The probability that an amateur golfer makes at least one hole in a round is[tex]1 - (1-q)^{18} .[/tex]

Now, let's use these probabilities to calculate the expected number of holes each golfer will make in 5 rounds of golf:

The expected number of holes made by a professional golfer in 5 rounds is 5 times the expected number of holes made in one round, which is [tex](1 - (1-p)^{18} )\times18.[/tex]

The expected number of holes made by an amateur golfer in 5 rounds is 5 times the expected number of holes made in one round, which is [tex](1 - (1-q)^{18} )\times18.[/tex]

We can simplify these expressions using the relationship between p and q:

The expected number of holes made by a professional golfer in 5 rounds is [tex]518(1 - (1-1.2q)^{18} ).[/tex]

The expected number of holes made by an amateur golfer in 5 rounds is [tex]518(1 - (1-q)^{18} ).[/tex]

We can now evaluate these expressions using the values of p and q:

[tex]p = 1.2q, so q = p/1.2[/tex]

Substituting this into the expressions above, we get:

The expected number of holes made by a professional golfer in 5 rounds is[tex]518(1 - (1-1.2(p/1.2))^{18} ) = 518(1 - (1-p)^{18} ).[/tex]

The expected number of holes made by an amateur golfer in 5 rounds is [tex]518(1 - (1-p/1.2)^{18} ).[/tex]

Finally, we can evaluate these expressions using the given probabilities:

The expected number of holes made by a professional golfer in 5 rounds is[tex]518(1 - (1-1.2q)^{18} ) = 518(1 - (1-1.2(0.1))^{18} ) = 40.7.[/tex]

The expected number of holes made by an amateur golfer in 5 rounds is [tex]518(1 - (1-q)^{18} ) = 518(1 - (1-0.1/1.2)^{18} ) = 1.6.[/tex]

So according to these calculations, we would expect a professional golfer to make about 40.7 holes over 5 rounds of golf with the new club, while an amateur golfer would only make about 1.6

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Answer:

990 applicants

Step-by-step explanation:

We know

A university law school accepts 4 out of every 11 applicants.

If the school accepted 360 ​students, find how many applications they received.

To get from 4 to 360, we time 90

We take 11 times 90 = 990 applicants

So, they received 990 applicants.

Answer:

She earns 10 dollars per hour.

Step-by-step explanation:

They substituted h for the amount of hours, since it is unknown. And you can see 10 is multiplied with h. So that is how much she earns an hour.

Answer:

We can solve for p by isolating it on one side of the inequality symbol. First, we'll subtract 7 from both sides:

55 - 7 < -12p

48 < -12p

Next, we'll divide both sides by -12. Since we're dividing by a negative number, we'll need to flip the direction of the inequality:

48/-12 > p

-4 > p

Therefore, p is greater than -4. Written in interval notation, this solution is p ∈ (-∞, -4).

The cost of producing 2000 bagels is $796.8.

To determine the cost of producing 2000 bagels, we need to plug in the value of x into the given equation and solve for C(x).
C(x) = 300 + 0.25x - 0.4(x/1000)^3
C(2000) = 300 + 0.25(2000) - 0.4(2000/1000)^3
C(2000) = 300 + 500 - 0.4(2)^3
C(2000) = 300 + 500 - 0.4(8)
C(2000) = 300 + 500 - 3.2
C(2000) = 796.8

Therefore, the cost of producing 2000 bagels is $796.8.

In general terms, profit is nothing more than revenues minus costs. This mathematically expressed is:

Profit = Revenues - Costs

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The distance between the points C=(-7,6) and E=(-2,2) is 6.4 units.

To calculate the distance between two points, we use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the points are C=(-7,6) and E=(-2,2), so we can plug in the values into the formula:

d = √((-2 - (-7))^2 + (2 - 6)^2)

d = √((5)^2 + (-4)^2)

d = √(25 + 16)

d = √(41)

d = 6.4

Therefore, the distance between the points C=(-7,6) and E=(-2,2) is 6.4 units.

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The final expression after collecting terms is: 19zx^(2) - 3z^(2)x + 2z^(2)y

Explanation: To collect terms in an expression, we need to combine like terms. Like terms are terms that have the same variables with the same exponents. In the given expression, the like terms are 13zx^(2) and 6zx^(2). We can combine these terms by adding their coefficients:

13zx^(2) + 6zx^(2) = 19zx^(2)

The other terms, 2z^(2)y and -3z^(2)x, do not have any like terms, so we cannot combine them with any other terms. Therefore, the final expression after collecting terms is:

19zx^(2) - 3z^(2)x + 2z^(2)y

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The amount of Kingston's birth weight that was much bigger than Karmichael would be = 1 pound 4 ounces

The weight of Kingston at birth = 9 pounds 2 ounces

The weight of Karmichael at birth = 7 pounds 11 ounces.

Next, the weights are converted to ounces such as:

1 pound = 16 ounces

For 9 pounds = 16×9 = 144 ounces+ 2 ounces = 146 ounces

For 7 pounds = 16×7 = 112 ounce + 11 ounces = 123 ounce

The difference between the birth weight of Kingston and Karmichael = 146-123 = 23 ounce

Convert 23 ounce to pounds = 23/16 = 1 pound 4 ounces

Therefore, amount of Kingston's birth weight that was much bigger than Karmichael would be = 1 pound 4 ounces.

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I chose the Quadratic Formula and Graphing because they are both straightforward methods that can give us the exact solutions.

A quadratic equation in the form ax^2 + bx + c = 0 where a > 1 is 2x^2 + 5x + 3 = 0.

To find the number of solutions based on the discriminant, we can use the formula D = b^2 - 4ac. In this case, D = (5)^2 - 4(2)(3) = 25 - 24 = 1. Since D > 0, the quadratic equation has two distinct real solutions.

Two ways to find the specific solutions or show that there is no solution are the Quadratic Formula and Graphing.

The Quadratic Formula is x = (-b ± √D)/2a. Plugging in the values from the equation, we get x = (-5 ± √1)/4 = (-5 ± 1)/4. This gives us the two solutions x = -1 and x = -2.

Graphing is another way to find the solutions. We can graph the equation y = 2x^2 + 5x + 3 and find the x-intercepts, which are the solutions to the equation. The graph shows that the x-intercepts are -1 and -2, which are the same solutions we found using the Quadratic Formula.

I chose the Quadratic Formula and Graphing because they are both straightforward methods that can give us the exact solutions. The Quadratic Formula is a formula that can be applied to any quadratic equation, and Graphing allows us to visually see the solutions. The other methods, such as Factoring, Square Root Property, and Completing the Square, may not always be applicable or may require more steps to find the solutions.

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The solution of the inequaltiy is v <= 6 or v >= 2.

To solve the compound inequality 4v+3<=27 or 2v-4>=0, we need to solve each inequality separately and then combine the solutions.

For the first inequality, 4v+3<=27, we can isolate the variable on one side of the inequality by subtracting 3 from both sides:

4v <= 24

Next, we can divide both sides by 4 to get:

v <= 6

For the second inequality, 2v-4>=0, we can isolate the variable on one side of the inequality by adding 4 to both sides:

2v >= 4

Next, we can divide both sides by 2 to get:

v >= 2

Now, we can combine the solutions to get the final solution for the compound inequality:

v <= 6 or v >= 2

This means that the solution set includes all values of v that are less than or equal to 6 or greater than or equal to 2.

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In answering the question above, the solution is If you know the lengths Pythagorean theorem of the other two sides of the right triangle, you may use these formulae to determine the length of the missing side.

The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.

[tex]a^2 + b^2 = c^2[/tex]

where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.

c = √[tex](a^2 + b^2)[/tex]

You may rewrite the formula as follows to get the length of one of the other sides:

a = √[tex](c^2 - b^2)[/tex]

b = √[tex](c^2 - a^2)[/tex]

If you know the lengths of the other two sides of the right triangle, you may use these formulae to determine the length of the missing side.

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The area of the triangular piece of property is approximately 63,121.75 square feet.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Starting at the first corner, the surveyor walks 480 ft in the direction N36°W. We can break this down into its northward and westward components:

Northward component = 480 cos(36°)

≈ 388.75 ft

Westward component = 480 sin(36°)

≈ 295.42 ft

This takes the surveyor to the second corner of the property.

From the second corner, the surveyor walks S21°W to get to the third corner. We can again break this down into its southward and westward components:

Southward component = 480 cos(21°)

≈ 435.89 ft

Westward component = 480 sin(21°)

≈ 168.75 ft

Finally, the surveyor walks N82°E to get back to the starting point.

We can break this down into its northward and eastward components:

Northward component = 388.75 ft

Eastward component = 435.89 sin(82°)

≈ 426.04 ft

Now we have the lengths of all three sides of the triangular property:

Side 1 = 480 ft

Side 2 = √[(295.42 - (-168.75))^2 + (388.75 - 435.89)^2]

≈ 421.66 ft

Side 3 = √[(426.04 - 295.42)^2 + (388.75 - 0)^2]

≈ 296.13 ft

calculate the area of the triangular property, we can use Heron's formula:

Area = √[s(s - a)(s - b)(s - c)]

where s is the semiperimeter (half the perimeter) of the triangle,

and a, b, and c are the lengths of its sides.

s = (480 + 421.66 + 296.13)/2 ≈ 598.40

Area = √[598.40(598.40 - 480)(598.40 - 421.66)(598.40 - 296.13)]

Area ≈ 63,121.75 sq ft

Therefore, the area of the triangular piece of property is approximately 63,121.75 square feet.

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The moments of a variate 'X' are defined by the expected value of the variate raised to the power of r, where r is an integer. In this case, the moments of 'X' are defined by E(X^r) = 0.6, for r = 1, 2, 3. This means that the expected value of X, X^2, and X^3 are all equal to 0.6. The probability of an event occurring is represented by P(X). In this case, P(X > 0) = 0.4, P(X = 1) = 0.6, and P(X^2 = 1) = 0.2. Convergence in probability refers to the concept that a sequence of random variables converges to a specific value with a probability of 1 as the number of trials approaches infinity.

These probabilities represent the likelihood of X being greater than 0, equal to 1, and squared equal to 1, respectively. This means that the probability of the sequence being within a certain distance of the specific value approaches 1 as the number of trials increases.

Two laws of convergence in probability are the Law of Large Numbers and the Central Limit Theorem. The Law of Large Numbers states that the average of a sequence of random variables converges to the expected value as the number of trials approaches infinity. The Central Limit Theorem states that the distribution of the sum of a sequence of random variables approaches a normal distribution as the number of trials approaches infinity.

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Answer: 50 total stamps = 30 Postcard Stamps + 20 Letter Stamps

Step-by-step explanation:

Postcard Stamp = Ps

Letter Stamp = Ls

Ps = 20c

Ls = 33c

50 total stamps = $12.60

50 total stamps = X Ps + Y Ls

12.60 = 30 Ps + 20 Ls

$12.60 = 30(20c) + 20(33c)

50 total stamps = 30 Postcard Stamps + 20 Letter Stamps

Answer:

You have 30 postcard stamps and 20 letter stamps.

Step-by-step explanation:

To solve this you'll need to set up a system of equations. Let's use P for postcard stamps and L for letter stamps

Remember, since the price is in cents, it'll be 0.2 and 0.33.

The equations can be in any order, this is just the order I chose.

0.2P + 0.33L = 12.60

P + L = 50

Your next step is to cancel out one of the variables to solve for the other. Let's cancel out P and solve for L. (You can switch these if you want, you'll still get the same answsrs.) Remember to multiply by a negative so the variable cancels out.

Here's what your work will look like:

0.2P + 0.33L = 12.60

-0.2(P + L = 50)

Here's what your new equations will look like after distributing:

0.2P + 0.33L = 12.60

-0.2P - 0.2L = -10

Now add these two equations together. When you do so, the P cancels out, and you can now solve for L.

Here's what your new equation will look like after adding the two equations:

0.13L = 2.6

Now, divide both sides by 0.13 to get what L equals. After doing so, you should get L = 20. This means that you have 20 letter stamps.

Your last step is to plug the value of L (which is 20) into either of your original equations to solve for how many postcard stamps you have. Let's use our second equation, P + L = 50. (You can use either original equation and get the same answer, but this one is more simpler to use.)

Here's what your work will look like:

P + 20 = 50

Subtract 20 from both sides:

P = 30. This means you have 30 postcard stamps.

Hope this helps!

Rounding up to the nearest integer, the sample size is approximately 803.

To find the sample size, we need to use the formula for margin of error:

The margin of error = Z * √[(p * (1 - p))/n]

Where Z is the Z-score, p is the proportion of the population with the characteristic of interest (in this case, favoring the death penalty), and n is the sample size.

We are given the margin of error (3.4 percentage points, or 0.034) and the proportion (0.52), and we need to find the Z-score and the sample size.

The Z-score corresponds to the confidence level, which is 95% in this case. Using the standard normal cumulative probabilities table, we can find that the Z-score for a 95% confidence level is 1.96

Plugging in the values we have into the formula:

0.034 = 1.96 * √[(0.52 * (1 - 0.52))/n]

Squaring both sides and rearranging:

n = (1.96^2 * 0.52 * (1 - 0.52))/(0.034^2)

n = 802.33

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Answer:

7 and 4

Step-by-step explanation:

take away 3 each time so

10-3=7

7-3=4

The answer is 0(zero)

The remainder when dividing 4x4 - 2x2 by x3 - x2 + 1 can be found using polynomial long division.

The calculation is shown below:

Therefore, the remainder when dividing.

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Answer:

Step-by-step explanation:

2-Bs:  4 x 3.8 = 15.2     2 x 15.2 = 30.4 m²

2-Cs:  11.5 x 3.8 = 43.7   2 x 43.7 = 87.4 m²

Total S.A. = 92 + 30.4 + 87.4 = 209.8 m²

Answer: 2.98m squared i think im not sure im just guessing im still not fully awake yet bro.

Step-by-step explanation:

The simplified expression is u^(3) - v^(3).

To perform the indicated operation on the algebraic expressions, we need to multiply each term in the first expression by each term in the second expression and then simplify the resulting expression.

Step 1: Multiply each term in the first expression by each term in the second expression:

(u)(u^(2)) + (u)(uv) + (u)(v^(2)) - (v)(u^(2)) - (v)(uv) - (v)(v^(2))

Step 2: Simplify the resulting expression by combining like terms:

u^(3) + u^(2)v + uv^(2) - u^(2)v - uv^(2) - v^(3)

Step 3: Simplify further by canceling out terms that are equal but opposite in sign:

u^(3) - v^(3)

Therefore, the simplified expression is u^(3) - v^(3).

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Mengxi invested $4,200 in the term deposit paying 5% /year and $5,800 in Canada Savings Bonds paying 3.5% /year. The total interest earned is $413.

Let's assume that Mengxi invests x dollars in the term deposit paying 5% /year, and the remaining (10000 - x) dollars in Canada Savings Bonds paying 3.5% /year.

At the end of the year, Mengxi earns a total of $413 in simple interest. The interest earned from the investment in the term deposit is calculated as 0.05x, while the interest earned from the investment in Canada Savings Bonds is 0.035(10000 - x).

Thus, we can write the following equation to represent the total interest earned:

0.05x + 0.035(10000 - x) = 413

Simplifying the equation, we get:

0.015x + 350 = 413

0.015x = 63

x = 4200

Therefore, Mengxi invested $4,200 in the term deposit paying 5% /year, and $5,800 (10000 - 4200) in Canada Savings Bonds paying 3.5% /year.

To check the answer, we can calculate the interest earned from each investment and add them up:

0.05(4200) + 0.035(5800) = 210 + 203 = 413

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The two linearly independent solutions are y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + … and y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...

We can use the power series method to find the two solutions of the given differential equation:

Let y = ∑anxn be a power series solution. Then, we have:

y' = ∑nanxn-1

y'' = ∑nan(n-1)xn-2

Substituting these into the differential equation and equating coefficients of like powers of x, we get:

3x∑nan(n-1)xn-1 + ∑anxn = 0

Simplifying, we obtain:

∑[3nan(n-1) + an-1]xn = 0

Since x ≠ 0, the coefficients of like powers of x must be zero. This gives us the recurrence relation:

an = -an-1/(3n(n-1)), n ≥ 1

Using this recurrence relation and the initial condition y(0) = 1, we can find the power series solution:

y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + ...

To find a second linearly independent solution, we can use the method of reduction of order. Let y₂(x) = v(x)y₁(x). Then, we have:

y₂' = v'y₁ + vy₁'

y₂'' = v''y₁ + 2v'y₁' + vy₁''

Substituting these into the differential equation and simplifying, we get:

v''y1x + (2v'y1' + vy1'')x + 3vy1 = 0

Since y₁(x) is a solution, we have:

y₁'' + (1/3x)y₁ = 0

Multiplying by y1 and integrating, we obtain:

(y₁')² + y₁²/3 = C

where C is a constant of integration. Using the initial condition y₂(0) = 0, we can find the second solution:

y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...

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Kim Chung owes $176 in federal income taxes.

What is the interest?

In finance, interest refers to the fee that a borrower pays to a lender for the use of money or assets. It is a cost of borrowing money, usually expressed as a percentage of the principal amount borrowed (or invested).

To calculate the federal income tax owed by Kim Chung, we need to first determine his taxable income.

Kim Chung's taxable income is calculated as follows:

Total Income = $2,897 (wages) + $57 (interest) = $2,954

Adjustments = $0

Adjusted Gross Income (AGI) = Total Income - Adjustments = $2,954 - $0 = $2,954

Since Kim Chung's parents claim him as a dependent, his standard deduction for tax year 2022 is $1,150.

Taxable Income = AGI - Standard Deduction = $2,954 - $1,150 = $1,804

To determine the federal income tax owed, we need to use the tax tables provided by the IRS for tax year 2022.

According to the tax tables, the tax on $1,804 of taxable income is $176.

Therefore, Kim Chung owes $176 in federal income taxes.

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1. a) The price is 5 dollars. b) The rate of change of demand with respect to price, p, when x = 4 is 5/6 thousands of units per dollar. c) The elasticity of demand when x = 4 is 25/24.

2. a) The price is 2*sqrt(3) dollars. b) The rate of change of demand with respect to price, p, when x = 10 is - (3 * sqrt(3))/(7) thousands of units per dollar. c) The elasticity of demand when x = 10 is -6/7.

3. Demand is increasing at -23.30 thousands of units per week.

4. If the daily production is 800 cases, then revenue is decreasing at a rate of -1200 dollars per day.

5. Supply is rising at a rate of 150.90 thousands of styluses per week.

1)
(a) Compute the price, p, when x = 4.
Price, p = −3(4)^2 − 4(4) + 69 = -48 -16 + 69 = 5 dollars
(b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 4.
Rate of change of demand, x' = - (2 * -3 * x + 4)/(-3 * 2 * x) = -(-24 + 4)/(-24) = 20/24 = 5/6 thousands of units per dollar
(c) Compute the elasticity of demand when x = 4.
The elasticity of Demand = (x'/x) * (p) = (5/6)/(4) * (5) = 25/24

2)
(a) Compute the price, p, when x = 10.
Price, p = sqrt((216 - 10^2 - 8*10)/3) = sqrt((216 - 100 - 80)/3) = sqrt(12) = 2*sqrt(3) dollars
(b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 10.
Rate of change of demand, x' = - (2 * 3 * p)/(2 * x + 8) = - (6 * 2 * sqrt(3))/(20 + 8) = - (12 * sqrt(3))/(28) = - (3 * sqrt(3))/(7) thousands of units per dollar
(c) Compute the elasticity of demand when x = 10.
Elasticity of Demand = (x'/x) * (p) = (- (3 * sqrt(3))/(7))/(10) * (2*sqrt(3)) = -6/7

3)
The weekly demand equation is given by p + x + 3xp = 53,
where x is the number of thousands of units demanded weekly and p is in dollars. If the price p is decreasing at a rate of 70 cents per week when the level of demand is 5000 units, then demand is increasing at a rate of (53 - 5000 - 70)/(3*70 + 1) = -4917/211 = -23.30 thousands of units per week.

4)
A company is decreasing production of math-brain protein bars at a rate of 100 cases per day. All cases produced can be sold. The daily demand function is given by p(x) = 20 − x/200,
where x is the number of cases produced and sold, and p is in dollars.
If the daily production is 800 cases, then revenue is decreasing at a rate of (20 - 800/200) * (-100) + (800) * (-1/200) * (-100) = (20 - 4) * (-100) + (800) * (1/2) = -1600 + 400 = -1200 dollars per day.

5)
The wholesale price p of e-tablet writing styluses in dollars is related to the supply x in thousands of units by 400p^2 − x^2 = 14375,
If 5,000 styluses are available at the beginning of a week, and the price is falling at 30 cents per week, then supply is rising at a rate of (2 * 400 * p * (-0.30) - 2 * x * x')/(2 * -1 * x) = (800 * p * (-0.30) - 0)/(2 * -5000) = (800 * sqrt(14375 + 5000^2)/400 * (-0.30) - 0)/(2 * -5000) = (800 * sqrt(14375 + 25000000)/400 * (-0.30))/(2 * -5000) = (2 * sqrt(14375 + 25000000) * (-0.30))/(-5000) = 0.012 * sqrt(14375 + 25000000) = 150.90 thousands of styluses per week.

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According to the information, the expressions that would match the descriptions would be both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.

To find the correct descriptions that match the expressions we must look at the graph. In this case q and n represent two numbers on the number line. In this case, to relate them to a description we must find the number to which they refer:

In accordance with the above, we could say that the descriptions would look like this:

In this case, both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.

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Answer: 10,210$

Step-by-step explanation:
Its simple really. The formula is 800 x 2.65 x 1. 10,210.

Use this next time, good luck :)

Answer: $879.50

Step-by-step explanation:

The simple interest formula is I = prt

Plug values in:

(Percent move decimal over 2 and time has to be in years, so 3 years and 9 months is 3.75 years)

I = (800)(0.0265)(3.75)

I = (21.2)(3.75)

I = 79.5

Add the interest to the principle:

800 + 79.5 = $879.50

Hope this helps!

The value that best approximates the radius of the circle is 25.38 inches.

The measure of the central angle in degrees is related to the length of the arc intercepted by the central angle and the radius of the circle by the formula:

Arc length = (Central angle measure / 360°) x (2πr)

where r denotes the circle's radius.

Substituting the given values, we have:

16 inches = (37° / 360°) x (2πr)

Simplifying and solving for r, we get:

r = 16 inches / [(37/360) x (2π)]

r ≈ 25.38 inches (rounded to two decimal places)

Therefore, the value that best approximates the radius of the circle is 25.38 inches.

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