The profit in dollars from the sale of x expensive watches is P(x) = 0.08x² - 5x + 6x0.2 - 5200 Find the marginal profit when (a) x = 300. (b) x = 2000, (c) X = 5000, and (d) x = 12,000.

The probability that a seal properly fits a valve is approximately 0.9332 or 93.32%.

To determine the probability that a seal properly fits a valve, we need to calculate the probability that the difference in diameter between the seal and valve is less than or equal to 2 mm.

Let X be the diameter of the valve and Y be the diameter of the seal. Then, the difference in diameter between the seal and valve can be expressed as Z = Y - X. We want to find P(Z ≤ 2).

We know that X ~ N(50, 0.3²) and Y ~ N(51, 0.4²), and since Z = Y - X, we have:

Z ~ N(51 - 50,  √(0.3² + 0.4²)²) = N(1, 0.5²)

To find P(Z ≤ 2), we standardize Z by subtracting the mean and dividing by the standard deviation:

(Z - 1)/0.5 ~ N(0, 1)

P(Z ≤ 2) = P((Z - 1)/0.5 ≤ (2 - 1)/0.5) = P(Z ≤ 1.5)

Using a standard normal table or calculator, we find that P(Z ≤ 1.5) ≈ 0.9332.

Therefore, the probability that a seal properly fits a valve is approximately 0.9332 or 93.32%.

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To build a house in 96 days, more workers are required such that the total number of workers becomes 24.

Let W be the number of workers required to build the house in 96 days. Using the work formula, we can write:

(16 workers) x (144 days) = (W workers) x (96 days)

Simplifying the equation, we get:

W = (16 workers x 144 days) / 96 days = 24 workers

Therefore, to build the house in 96 days, 24 workers are required, which is 8 more workers than the original 16. This is because, to complete the work in a shorter time, more workers are needed to contribute their efforts to the work.

The total work done by all the workers remains constant, so if we decrease the time taken to complete the work, we need to increase the number of workers to maintain the same work rate.

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The best step when constructing a tangent to the circle is to strike an arc on bq with a center of b that has a length the same as the radius of circle q. The correct answer is option a.

When constructing a tangent to a circle with a center point of Q that passes through point B, and having already connected points Q and B to form line segment BQ, the best next step is to: A) Strike an arc on BQ with a center of B that has a length the same as the radius of circle Q.

This will help you find the point where the tangent line intersects the circle, allowing you to complete the tangent construction. The tangent line will be perpendicular to the radius at the point of tangency.

Therefore option a is correct.

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it's not possible to sell at least $675 worth of tickets while also staying within the seating limit of 150 tickets. The theater may need to consider raising ticket prices or finding a larger venue to accommodate more audience members.

Let's denote the number of adult tickets sold as "A" and the number of child tickets sold as "C". Then we can set up the following system of equations to represent the given information:

A + C ≤ 150    (limit on seating)

12A + 7.5C ≥ 675   (minimum revenue required)

We want to find the possible values of A and C that satisfy these equations.

One way to solve this system is to graph the inequalities and find the region of overlap. However, since there are only two variables, we can also use substitution or elimination to solve for one variable in terms of the other.

Let's solve for A in terms of C using the first equation:

A ≤ 150 - C

Substitute this expression for A in the second equation:

12(150 - C) + 7.5C ≥ 675

Expand and simplify:

1800 - 12C + 7.5C ≥ 675

-4.5C ≥ -1125

C ≤ 250

So the number of child tickets sold must be less than or equal to 250.

Now we can substitute this inequality into the first equation to find the maximum number of adult tickets sold:

A + 250 ≤ 150

A ≤ -100

This doesn't make sense, since we can't sell negative tickets. Therefore, there is no solution that satisfies the given conditions.

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The value of the simplified expression is -15.

The simplification of the expression is determined by substituting the appropriate values of the variables into the equation.

The given expression; = 54/g - 8h

The value of g = 6 and the value of h = 3,

The value of the expression is calculated as follows;

= 54/g - 8h

= 54/6 - 8(3)

= 9 - 24

= - 15

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The complete question is below:

54/g - 8h, when g = 6 and h=3

Answer:

[tex]A = 68.75 \text{ square inches}[/tex]

Step-by-step explanation:

First, we need to identify the trapezoid's dimensions:

base 1 = 16

base 2 = 11.5

height = 5

Then, we can plug these values into the trapezoid area formula:

[tex]A = \dfrac{b_1+b_2}{2} \cdot h[/tex]

[tex]A = \dfrac{16 + 11.5}{2} \cdot 5[/tex]

[tex]A = \dfrac{27.5}{2} \cdot 5[/tex]

[tex]A = \dfrac{137.5}{2}[/tex]

[tex]\boxed{A = 68.75 \text{ square inches}}[/tex]

The expansion of (1+root 2)(3-root 2) is 1 +2√2.

What is distributive property?

The distributive Property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.

Apply the distributive property

1(3-√2) + √2(3-√2)

Apply distributive property

1.4+ 1(-√2) +√2 (3-√2)

Apply the distributive property

1.3 + 1(-√2) + √2. 3+√2 (-√2)

3+1(−√2)+√2⋅3+ √2(-√2)

Multiply − √2 by 1

3−√2+ √2⋅3+√2(−√2)

Move 3 to the left of √2.3−√2+3⋅√2+√2(−√2)

Multiply √2(−√2)

3−√2+3√2−√2²

Rewrite

√2² as 2.

3−√2+3√2− 1⋅2

Multiply − 1 by 2.

3−√2+3√2−2

Subtract 2 from 3.

1−√2+3√2

Add  −√2 and 3√2.

1+2√2

Exact Form:

1 +2√2

Decimal Form:

3.82842712

Therefore, the expansion of (1+root 2)(3-root 2) is 1 +2√2.

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The length of the hypotenuse of the right triangle is 15 cm.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Using this formula, we can calculate the length of the hypotenuse of a right triangle.

Given that the longer sides of the right triangle are 9 cm and 12 cm long, we can assume that one of these sides is the shorter side and the other is the longer side. Let's assume that the shorter side is 9 cm long and the longer side is 12 cm long.

Using the Pythagorean Theorem, we can calculate the length of the hypotenuse as follows:

Hypotenuse² = Shorter side² + Longer side²

Hypotenuse² = 9² + 12²

Hypotenuse² = 81 + 144

Hypotenuse² = 225

Taking the square root of both sides, we get:

Hypotenuse = √225

Hypotenuse = 15

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Step-by-step explanation:

I had to add some assumed portions to your posted picture. See image.

 The yellow boxed angle is 84 degrees (upper LEFT) due to alternate interior angles of parallel lines transected by another line.

  then, since the triangle is isosceles ....the other (lower LEFT)  angle is 84 degrees also....

      that means that k= 12 degrees    for the triangle interior angles to sum to  180 degrees .

The rule for the reflection shown above is (x, y) → (x, -y).

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

Conversely, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

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The probability that a student took AP Chemistry given they did not get into their first-choice college is 0.0566.

The probability that a student took AP Chemistry given they did not get into their first-choice college is calculated using the formula below:

P(Not 1st | Chem) =0.1375

P(Chem) = 0.25

P(Not 1st) = P(Chem and Not 1st) + P(Phys and Not 1st) + P(ES and Not 1st) + P(Bio and Not 1st)

P(Not 1st)= 0.1375 + 0.1575 + 0.2400 + 0.0700

P(Not 1st)= 0.6050

Substituting the values in the formula above:

P(Chem | Not 1st) = 0.1375 * 0.25 / 0.6050

P(Chem | Not 1st) = 0.0566

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David's net worth: 86,329.95

To calculate David's new net worth, we need to add the increase in assets and subtract the decrease in liabilities from his current net worth.

New assets value = 62,784.24 + 2,784.89 = 65,569.13

New liabilities value = David's current net worth - his current assets value

New liabilities value = 45,765.78 - 62,784.24 = -17,018.46

Since his liabilities have decreased by 3,742.36, we need to subtract this value from the new liabilities value:

New liabilities value = -17,018.46 - 3,742.36 = -20,760.82

Now we can calculate his new net worth by subtracting his new liabilities value from his new assets value:

New net worth = 65,569.13 - (-20,760.82) = 86,329.95

Therefore, David's new net worth is 86,329.95.

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(a) WAT is not true for the open interval (0,1) with function f(x) = 1/x.

(b) WAT holds for the closed set [a,∞) with any continuous function f(x).

(a) The Weierstrass Approximation Theorem (WAT) is not true if we replace the closed interval [a,b] with the open interval (a,b). A counterexample is the function f(x) = 1/x on the open interval (0,1). This function is continuous on (0,1) but it is not uniformly continuous, so it cannot be uniformly approximated by a polynomial.

(b) The Weierstrass Approximation Theorem holds if we replace [a,b] with the closed set [a,∞). That is, if f(x) is a continuous function on [a,∞), then for any ε > 0, there exists a polynomial p(x) such that |f(x) - p(x)| < ε for all x in [a,∞). The proof is similar to the proof of the original theorem using the Bernstein polynomials.

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A. proj_v(u) = (586 / 68) * (8i + 2j) = (293 / 34) * (8i + 2j) ≈ 8.62i + 2.15j

B. u_orthogonal = (71 + 9j) - (8.62i + 2.15j) ≈ 62.38i + 6.85j

(a) To find the projection of vector u onto vector v, we use the formula:

proj_v(u) = (u·v / ||v||^2) * v

where u = 71 + 9j, v = 8i + 2j, "·" represents the dot product, and ||v|| represents the magnitude of v.

First, let's find the dot product u·v:

u·v = (71)(8) + (9)(2) = 568 + 18 = 586

Next, we find the magnitude of v:

||v|| = √((8)^2 + (2)^2) = √(64 + 4) = √68

Now, we find ||v||^2:

||v||^2 = 68

Finally, we can find the projection of u onto v:

proj_v(u) = (586 / 68) * (8i + 2j) = (293 / 34) * (8i + 2j) ≈ 8.62i + 2.15j

(b) To find the vector component of u orthogonal to v, we subtract the projection of u onto v from u:

u_orthogonal = u - proj_v(u)

u_orthogonal = (71 + 9j) - (8.62i + 2.15j) ≈ 62.38i + 6.85j

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I must have left home at 4:54 PM in order to arrive at the park at 4:30 PM after 24 minutes of travel time.

Given the parameters in the question: if i went to park at 4:30 and it took me 24 minutes

Arrival time = 4 : 30PM

Travel time = 24 minutes

I can determine when i left home by simply subtracting the travel time from the time I arrived.

Hence,

Add the travel time to the time you arrived at the park.

4:30 PM (arrival time) + 24 minutes (travel time) = 4:54 PM

Therefore, I must have left home at 4:54 PM.

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Answer:

3595.5

Step-by-step explanation:

Answer: C. 1/24 and that's is your answer to your question

we can say with 99% confidence that the true proportion of times the number cube would land with a six facing up is between 0.05 and 0.49.

To find the 99% confidence interval for the true proportion of times the number cube would land with a six facing up, we can use the formula:

CI = p ± zsqrt(p(1-p)/n)

where:

CI is the confidence interval

p is the sample proportion (number of times the cube landed with a six facing up divided by the total number of rolls)

z is the z-score corresponding to the desired confidence level (99% in this case)

n is the sample size (45 in this case)

First, let's calculate the sample proportion:

p = 12/45 = 0.27

Next, we need to find the z-score corresponding to a 99% confidence level. Using a standard normal distribution table or calculator, we find that the z-score is 2.58.

Now we can plug in the values and calculate the confidence interval:

CI = 0.27 ± 2.58sqrt(0.27(1-0.27)/45)

CI = 0.27 ± 0.22

CI = (0.05, 0.49)

The number cube would land with a six facing up between 0.05 and 0.49.

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19.29 cubic feet  is the volume of the composite figure if both the height and the diameter of the cylinder are 2. 5 feet

Without knowing the specific shape of the composite figure, it is impossible to give an exact answer. However, we can provide a general formula for the volume of a cylinder with height h and diameter d, and assume that the composite figure consists of a cylinder and some other shape.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder. The diameter of the cylinder is given as 2.5 feet, which means the radius is 1.25 feet.

If the height of the cylinder is also 2.5 feet, then the volume of the cylinder is:

V_cylinder = π(1.25)^2(2.5) = 6.15π cubic feet (exact)

To approximate to two decimal places, we can use the approximation π ≈ 3.14:

V_cylinder ≈ 6.15(3.14) = 19.29 cubic feet (approximate to two decimal places)

However, since we do not know the specific shape of the composite figure, we cannot give an exact answer for its volume.

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Jerome will need approximately 138.72 square meters of grass seed to cover his lawn.

To find the area that the grass seed needs to cover, we first need to find the area of the entire lawn. Let's assume that the lawn is rectangular in shape.

Jerome hasn't given us the dimensions of the lawn, so let's say that it measures 10 meters by 15 meters. Therefore, the area of the entire lawn would be:

10 meters x 15 meters = 150 square meters

Now we need to subtract the area of the pool from the area of the entire lawn.

The pool measures 4 5/6 meters by 2 1/3 meters, which we can convert to improper fractions:

4 5/6 = (4 x 6 + 5) / 6 = 29 / 6
2 1/3 = (2 x 3 + 1) / 3 = 7 / 3

So the area of the pool would be:

29/6 meters x 7/3 meters = 203/18 square meters

To find the area that the grass seed needs to cover, we subtract the area of the pool from the area of the entire lawn:

150 square meters - 203/18 square meters

To subtract these two values, we need to get a common denominator:

150 square meters = (150 x 18) / 18 = 2700/18 square meters
203/18 square meters = 203/18 square meters

So the area that the grass seed needs to cover would be:

2700/18 square meters - 203/18 square meters = 2497/18 square meters

We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 1:

2497/18 square meters ≈ 138.72 square meters

Therefore, Jerome will need approximately 138.72 square meters of grass seed to cover his lawn, excluding the area around the pool.

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The ounces of filler will the factory need in order to make meatballs out of this shipment of beef is  56.7 oz of filler.

A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which remains almost unmodified. The avoirdupois ounce, also known as the US customary and British imperial ounce, is equal to one-sixteenth of an avoirdupois pound.

One factory obtained 90 kg of beef from overseas.

They want to add 1.4oz of filler for each pound of beef.

Given is:

0.45 kg = 1 pound

So,  90 kg = 90 x 0.45 = 40.5 pounds

The company want to add 1.4 oz of filler for each pound of beef.

So for 1 pound we have 1.4 oz of filler

So, for 40.5 pounds they will need = x oz of filler.

x = 1.4 x 40.5 = 56.7

Therefore, the company needs 56.7 oz of filler.

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Complete question;

Factories often add filler when making meatballs sold by the bag. One factory obtained 90kg of beef from overseas. They want to add 1.4oz of filler for each pound of beef. How many ounces of filler will the factory need in order to make meatballs out of this shipment of beef?

Null Hypothesis (H0): The proportion of adults who feel their children will have a better life is equal to 0.5.

Alternative Hypothesis (HA): The proportion of adults who feel their children will have a better life is not equal to 0.5.

The sign test is a non-parametric statistical test used to test the hypothesis that the median of a population is equal to a specified value.

The critical value is 1.96.

The absolute value of the test statistic is greater than 1.96. Therefore, we reject the null hypothesis and conclude that there is a significant difference between the number of adults who feel their children will have a better life compared to a worse life.

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The measure of the trade places with any opponent region is 30°

Let the measure of the trade places with any opponent = x

Move two space is twice the angle as trade places with any opponent

Move two space = 2x

Move one space is three times the angle as moving two spaces

Move one space = 3(2x)

Move one space = 6x

Lose your turn is a quarter

Lose your turn = 90°

The sum of a complete angle = 360°

90 + x + 2x + 6x = 360°

9x = 360 - 90

9x = 270

x = 30

The measure of the trade places with any opponent region is 30°

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Answer:

-9

Step-by-step explanation:

Recall the following relationships about the sum of cubes and a square binomial:

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

[tex](a+b)^2=a^2+2ab+b^2[/tex]

The second factor on the right hand side of equation 1 looks similar to the right hand side of equation 2, but differs slightly.

Carefully choosing to subtract 3ab from both sides of the equation 2, and Combining like terms  yields...

[tex](a+b)^2-3ab=a^2-ab+b^2[/tex]

This now matches the second factor on the right hand side of the first equation.  So, with substitution, the first equation becomes:

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

[tex]a^3+b^3=(a+b)((a+b)^2-3ab)[/tex]

Note that all of the parts on the right hand side of the equation are given in the question:

a+b=3 and ab=4

With some substitution and simplification

[tex]a^3+b^3=(a+b)((a+b)^2-3ab)[/tex]

[tex]=(3)((3)^2-3(4))[/tex]

[tex]=(3)(9-3(4))[/tex]

[tex]=(3)(9-12)[/tex]

[tex]=(3)(-3)[/tex]

[tex]=-9[/tex]

The correct inequality to describe the problem is A. 10 + x > 15, which means that the total time Farid spends on the level (10 + x) must be greater than 15 minutes in order for him to lose a life.

To solve the inequality, we can start by isolating x on one side of the inequality:

10 + x > 15

Subtracting 10 from both sides, we get:

x > 5

This means that Farid can play for up to 5 more minutes on the level without losing a life, since spending a total of 10 + 5 = 15 minutes on the level would cause him to lose a life.

Therefore, the solution to the inequality is "Farid can play less than 5 more minutes on that level without losing a life."

Overall, the correct option is A. 10 + x > 15.

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Points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.

Every triangle has inner angles that add up to 180 degrees. A right angle and a right triangle are both formed when one of their internal angles is 90 degrees.

Given coordinates :

a(5,2) , b(2,-3) and c(-8,3).

Find the distance between the points using the distance formula:

d = √[(x2 - x1)² + (y2 - y1)²]

ab = √[(2 - 5)² + (- 3 - 2)²]

ab = √[(-3)² + (- 5)²]

ab = √[9 + 25]

ab = √34

ab² = 34

bc = √[(2 + 8)² + (- 3 - 3)²]

bc  = √[(10)² + (- 6)²]

bc  = √[100 + 36]

bc  = √136

bc²  = 136

ac = √[(-8 - 5)² + (3 - 2)²]

ac = √[(-13)² + (1)²]

ac = √[169 + 1]

ac = √170

ac² = 170

Now,

(ac)² = (bc)² + (ab)²

170 = 136 + 24

170 = 170

This, points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.

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Answer:no image

Step-by-step explanation:

Formula for the volume of a cylinder = pi x r^2 x h

---r = radius

---h = height

This problem gives us the diameter. To find the radius from a given diameter, all we need to do is divide the diameter by 2.

radius = 3

height = 22

volume = 3.14 x 3^2 x 22

volume = 3.14 x 9 x 22

volume = 621.72

volume (rounded) = 622

Answer: 622 m^3

Hope this helps!

In a case whereby Natalie saves money in her piggy bank. Maria saves money in a savings account at a bank the statement about the savings plans that is true is B.Maria's way of saving money allows her to earn interest and make her money grow.

An efficient approach to keep your money safe and earning interest is in a savings account. You can keep your savings in a liquid state with a savings account, which allows you to access your money anytime you need to, while also creating some breathing room between your savings and your daily spending requirements.

Because of their safety, liquidity, and potential for collecting interest, savings accounts are a suitable way to put money set aside for future use. These accounts are perfect for saving for short-term objectives like a trip or home repair or for your emergency fund.

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The recursive sequence are: 17, 13, 9, 5, 1.

The recursive rule for the sequence  [tex]a_{n}[/tex] = 17 - 4n is

[tex]a_{1[/tex] = 17

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 4 for n ≥ 2

Using this rule, we can find the first few terms of the sequence

[tex]a_{1[/tex] = 17

[tex]a_{2}[/tex] = [tex]a_{1[/tex]  - 4 = 17 - 4 = 13

[tex]a_{3}[/tex] = [tex]a_{2}[/tex] - 4 = 13 - 4 = 9

[tex]a_{4}[/tex] = [tex]a_{3}[/tex] - 4 = 9 - 4 = 5

[tex]a_{5}[/tex] = [tex]a_{4}[/tex]  - 4 = 5 - 4 = 1

and so on.

Therefore, the recursive sequence are: 17, 13, 9, 5, 1.

The question is incorrect and correct question is '' Write a recursive sequence that represents the sequence defined by the following explicit formula  [tex]a_{n}[/tex] = 17 - 4n and find [tex]a_{1[/tex] and   [tex]a_{n}[/tex] ''.

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