The daily marginal revenue function associated with selling x widgets is given by R"(x) = -21x2 + 16x + 15 where R'(x) is measured in dollars per unit per day and x denotes the number of widgets produced and sold. (a) Determine the revenue function, R(x), associated with producing and selling x widgets. R(x) = (b) Determine the demand function relating unit price, p(x), to the quantity demanded, X. P(x)

So the magnitude of the cross product between two vectors is the same regardless of the order of the vectors.

This statement is true. The magnitude of the cross product between two vectors u and v is defined as:

|u à v| = |u||v|sinθ

where θ is the angle between the two vectors. The cross product is anti-commutative, meaning that if we switch the order of the vectors, the sign of the result changes:

v à u = - (u à v)

Therefore, taking the magnitudes of both sides, we have:

|v à u| = |- (u à v)|

|v à u| = |u à v|

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If teacher is distributing sheets in a class, then the equation which is used to find number of students in class is (d) 2x+8 = 3x - 11​.

A "Linear-Equation" is a mathematical equation that represents a straight line in a coordinate plane. It is of form : y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).

Let number of students in class be denotes as "x",

If each student get 2 sheets, then 8 sheets are remaining, it is mathematically represented as : 2x + 8 ,

If each student get 3 sheets each, then there would be 11 sheets less, and this is represented as : 3x - 11,

So, the equation which is used to find number of students in class is 2x+8=3x-11,

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

If a teacher were to distribute sheets of paper so that each student got two sheets, there would be 8 sheets remaining. However, if three sheets were given to each student, the teacher would be 11 sheets short. Which equation could be used to find how many students are in the class?

(a) 2(x - 8) = 3(x + 11)

(b) 2(x + 8) = 3(x - 11)

(c) 2x-8 = 3x + 11

(d) 2x+8 = 3x - 11​

Answer:

[tex]\huge\boxed{\sf Associative\ Property\ of\ Addition}[/tex]

Step-by-step explanation:

This property is Associative Property.

(A + B) + C = A + (B + C)

Since, here the expression is being added, the given property is Associative Property of Addition.

[tex]\rule[225]{225}{2}[/tex]

Answer:

this is an associative property of addition

Answer:

165

Step-by-step explanation:

there are 165 different arrangements of 1,2,3 place possible of the 11 students

The relation that is displayed in the table can be found to be B: {(-3, -2), (-1, 1), (2, -2), (3, 3)}

The relation displayed on the table would simply refer to the points seen on the table. When writing the coordinates of a point, you should give the x value first and then give the y value.

The relations on the table are therefore { ( - 3 , - 2 ) , ( - 1 , 1 ) , ( 2 , - 2 ) , ( 3 ,  3 ) }. This represents the entire point portfolio seen on the table and therefore encompasses all the relation.

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(1) The value of x is in the inscribed chords is  110⁰.

(2) The length of PT is 7.48 cm.

(3) The length of EC is 1.93.

The value of x is calculated by applying intersecting chord theorem as shown below;

x = ¹/₂ ( 360 - ( 40⁰ +  100⁰ )

x = ¹/₂ (360 - 140 )

x = ¹/₂ (220)

x = 110⁰

2. The length of PT is calculated as follows;

The radius of the circle = length NT,  is calculated as follows;

A = πr²

r² = A/π

r = √ (A/π)

r = √ (25π/π)

r = 5 cm = NT = NM

PT is calculated by applying Pythagoras theorem as follows;

NP = NM + MP

NP = 5cm + 4 cm

NP = 9 cm

PT = √ (9² - 5²)

PT = 7.48 cm

3. The length of EC is calculated  by applying chord theorem as follows;

AE. ED = BE . EC

ED = AD - AE

ED = 12 - 3 = 9

Now, solve for EC;

AE. ED = BE . EC

3 x 9 = 14(EC)

27 = 14(EC)

EC = 27/14

EC = 1.93

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Answer:

Step-by-step explanation:

easy its 7

Answer:

Step-by-step explanation:

Both options A and B are correct, while option C is incorrect.

Option A, -6 < -4, is true because -6 is less than -4 on the number line.

Option B, 4 < 6, is also true because 4 is less than 6 on the number line.

Option C, 0 > -4, is incorrect because 0 is not greater than -4. In fact, -4 is less than 0, so the correct inequality would be -4 < 0.

Therefore, the correct options are A and

Answer:

Step-by-step explanation:

You want a formula for the volume of the given figure, which is a hemisphere of radius r atop a cylinder of the same radius and height r.

The volume of a sphere is given by ...

  V = (4/3)πr³

The volume of a cylinder is given by ...

  V =  πr²h

The given figure is composed of half a sphere, and a cylinder. The total volume will be the sum of the volumes of these parts.

  total volume = 1/2(sphere volume) + (cylinder volume)

Using a height of r for the cylinder, we can substitute the above formulas to get ...

  total volume = 1/2(4/3πr³) +(πr²·r)

  total volume = 2/3πr³ + πr³ = (2/3 +1)πr³

  total volume = (5/3)πr³

When the height is 12 inches, the radius is 6 inches, so the volume of the object is ...

  total volume ≈ (5/3)(3.14)(6 in)³ = 1130.4 in³

About 1130.4 cubic inches of glass will be needed for a paperweight that is 12 inches tall.

The probability that all three selected homes have a security system is 0.0014.

The probability that none of the three selected homes have a security system is 0.3583.

The probability that at least one of the selected homes has a security system is 0.6417.

a. The probability that the first selected home has a security system is 4/21. Since there are now only 3 homes left with security systems out of 20 total homes, the probability that the second selected home also has a security system is 3/20. Similarly, the probability that the third selected home has a security system is 2/19. Therefore, the probability that all three selected homes have a security system is:

[tex](4/21) * (3/20) * (2/19) = 0.0014[/tex]

So, the probability that all three selected homes have a security system is 0.0014.

b. The probability that the first selected home does not have a security system is 17/21. Since there are now only 16 homes left without security systems out of 20 total homes, the probability that the second selected home also does not have a security system is 16/20. Similarly, the probability that the third selected home does not have a security system is 15/19. Therefore, the probability that none of the three selected homes have a security system is:

(17/21) * (16/20) * (15/19) = 0.3583

So, the probability that none of the three selected homes have a security system is 0.3583.

c. The probability that none of the three selected homes have a security system is 0.3583 (as found in part b). Therefore, the probability that at least one of the selected homes has a security system is:

1 - 0.3583 = 0.6417

So, the probability that at least one of the selected homes has a security system is 0.6417.

d. We assumed the events to be dependent because the probability of each event is affected by the outcomes of the previous events. For example, the probability of selecting a home with a security system on the second draw is influenced by whether a home with a security system was selected on the first draw.

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For rectangular coordinates, the iterated integral would be: ∬R f(x, y) dA = ∫(from a to b) ∫(from c(x) to d(x)) f(x, y) dy dx
For polar coordinates, the iterated integral would be: ∬R f(r, θ) r dA = ∫(from α to β) ∫(from g(θ) to h(θ)) f(r, θ) r dr dθ

To decide whether to use polar coordinates or rectangular coordinates, we need to examine the shape of the region r. If r is a circular or symmetric shape, polar coordinates are often more convenient to use. If r is a rectangular or non-symmetric shape, rectangular coordinates are more appropriate.

Assuming that r is a circular or symmetric shape, we will use polar coordinates. Let's define r in terms of polar coordinates as r = {(r, θ) | 0 ≤ r ≤ a, 0 ≤ θ ≤ 2π}. We can write the double integral of f(x,y) over r in terms of polar coordinates as:

∫∫ r f(x, y) da = ∫₀^a ∫₀^2π f(r cos θ, r sin θ) r dθ dr

This is the iterated integral of f over r in terms of polar coordinates. We integrate f with respect to θ first, from 0 to 2π, and then with respect to r, from 0 to a.

Note that f is an arbitrary continuous function on r, which means that it can take on any value on the region r. We integrate f over r by multiplying f by the area element da, which is r dr dθ in polar coordinates.

To help you with this question, I need to know the specific region R you're referring to. However, I can provide you with general guidance on choosing between polar and rectangular coordinates and setting up an iterated integral.

When deciding between polar and rectangular coordinates, consider the shape and symmetry of the region R. If R has circular or radial symmetry, it's typically easier to use polar coordinates. If R has rectangular or Cartesian symmetry, use rectangular coordinates.

For rectangular coordinates, the iterated integral would be:

∬R f(x, y) dA = ∫(from a to b) ∫(from c(x) to d(x)) f(x, y) dy dx

For polar coordinates, the iterated integral would be:

∬R f(r, θ) r dA = ∫(from α to β) ∫(from g(θ) to h(θ)) f(r, θ) r dr dθ

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We're given that the difference between John's and Paul's heights is twice the difference between John's and Thom's heights.

Let's use variables to represent their heights: J for John, P for Paul, and T for Thom. The equation can be written as:

J - P = 2(J - T)

Now, we're given two pieces of information:

1) Paul is 163 centimeters tall (P = 163).
2) Thom is 173 centimeters tall (T = 173).

We'll use this information to solve for John's height and then find the average height of the three.

Step 1: Plug in the given values into the equation.
J - 163 = 2(J - 173)

Step 2: Distribute the 2 on the right side.
J - 163 = 2J - 346

Step 3: Rearrange the equation to isolate J.
J - 2J = 346 - 163

Step 4: Combine like terms.
-1J = 183

Step 5: Divide by -1 to find John's height.
J = -1(-183)
J = 183 cm

Now that we have John's height, we can find the average height of the three.

Average height = (John's height + Paul's height + Thom's height) / 3
Average height = (183 + 163 + 173) / 3
Average height = 519 / 3
Average height = 173 cm

So, the average height of John, Paul, and Thom is 173 centimeters.

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Answer:

Question 3: would equal 30.5 and Question 4: would equal 19

To find the radius of the sphere passing through points A, B, C, and D in space, we can use the fact that the sphere will be the circumsphere of triangle ABC and triangle ABD.

Since BAC = BAD = CAD = 90, we know that triangle ABC and triangle ABD are both right triangles.

Using the Pythagorean theorem, we can find the length of BC and BD:

BC^2 = AB^2 + AC^2 = 6^2 + 6^2 = 72
BD^2 = AB^2 + AD^2 = 6^2 + 6^2 = 72

Since BC = BD, we know that triangle BCD is an isosceles triangle. Therefore, the altitude from vertex C to side BD will bisect BD, and the altitude from vertex B to side CD will bisect CD. Let E be the point where the altitudes intersect.

Now we can use the Pythagorean theorem again to find the length of CE:

CE^2 = BC^2 - BE^2 = 72 - (BD/2)^2 = 72 - 36 = 36
CE = 6

Since the sphere passes through point C, its center must be equidistant from points A, B, and D. Let O be the center of the sphere. Then we have:

OA = OB = OD
OA^2 = OC^2 + AC^2 = OC^2 + 36
OB^2 = OC^2 + BC^2 = OC^2 + 72
OD^2 = OC^2 + AD^2 = OC^2 + 36

Since OA = OB = OD, we can equate the expressions for OA^2, OB^2, and OD^2:

OC^2 + 36 = OC^2 + 72 = OC^2 + 36
72 = 2(OC^2 + 36)
OC^2 = 18

Therefore, the radius of the sphere is:

r = OC = sqrt(18) = 3sqrt(2)

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the 90% confidence interval for p - um is (-0.816, 2.916), which can be rounded to (-0.82, 2.92). The closest option to this interval is (c) (-5.084, 7.284).

The point estimate for the difference in mean annual return is:

a - m = 7.3 - 6.2 = 1.1

To find the margin of error for a 90% confidence interval, we use the t-distribution with 16 degrees of freedom (conservative df) and a 5% significance level (90% confidence level):

t* = 1.745

The margin of error is then:

ME = t* * sqrt[(s1^2/n1) + (s2^2/n2)]

= 1.745 * sqrt[(0.093^2/17) + (0.124^2/17)]

= 0.916

The 90% confidence interval is:

(a - m) ± ME

1.1 ± 0.916

Thus, the 90% confidence interval for p - um is (-0.816, 2.916), which can be rounded to (-0.82, 2.92). The closest option to this interval is (c) (-5.084, 7.284).

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The sample space has 27 elements.

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is drawing one card from a well-shuffled deck of 27 cards.

To determine the number of elements in the sample space, we can count the total number of cards in the deck.

The number of red cards is 6, the number of green cards is 8, and the number of blue cards is 13. Therefore, the total number of cards in the deck is:

6 + 8 + 13 = 27

Hence, there are 27 possible outcomes when drawing one card from the deck. These outcomes consist of the 6 red cards, the 8 green cards, and the 13 blue cards in the deck.

So the sample space has 27 elements.

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The solution is:

No, this statement is not true, we know that these dimensions are not possible given the amount of fencing.

We have,

Perimeter measures the distance around a shape.

Perimeter Formula

The perimeter is 2w + 2l = P, where w is the width and l is the length. This formula is used because together, it adds together the distance of every side.

If wanted, it can be rewritten as w + w + l + l = P. This form of the formula shows all 4 sides being added together.

Inequality

We can set up an inequality to represent the situation. We know that the perimeter must be less than or equal to 150 because that is the amount of fence John has. So, we can plug the information that we know into the formula.

2(50) + 2(40) ≤ 150

Then, solve.

180 ≤ 150

Since this statement is not true, we know that these dimensions are not possible given the amount of fencing.

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complete question:

John is building a fence around his garden and has 150 feet of

fencing. The length of his garden is 40 feet and the width of

his garden is 50 feet. Does John have enough fencing to go

around the perimeter of his garden? Explain why or why not.

The perimeter and area of parallelogram WXYZ is b.) perimeter= 22cm; area= 20cm²

The formula for calculating the perimeter of a parallelogram is expressed as;

P = 2(a + b)

Such that the parameters are;

Then, we have;

Perimeter = 2(4 + 7)

Add the values

Perimeter = 22 cm

The area of a parallelogram is expressed as;

Area = bh

Where the parameters of the formula are;

Area = 5(4)

Area = 20cm²

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Answer:

382 bags of dasheen

Step-by-step explanation:

Therefore, My. Andrew packed a total of 382 bags of  dasheen

The number of cups of flour must always be 6 times the number of cups of water, under the condition Mitch made two 10-inch pizzas using a recipe that calls for 3 cups of four and cup of water.

In order to make 4 more pizzas without changing the ratio of flour to water, Mitch have to use 12 cups of flour and 2 cups of water.

To evaluate this we need to perform multiplication
Mitch used 3 cups of flour and 1 cup of water for 2 pizzas. So for each pizza, he used 1.5 cups of flour and 0.5 cups of water.
To make 4 more pizzas, he needs to use 6 cups of flour and 2 cups of water (since he needs twice as many pizzas).
Then, for each pizza, he needs to use 1.5 cups of flour and 0.5 cups of water (since he wants to keep the ratio the same).
So for 4 more pizzas, he needs to use 6 x 2 = 12 cups of flour and 2 x 2 = 4 cups of water.
Since he wants to keep the ratio the same, he needs to use 12 cups of flour and 2 cups of water.

Therefore, the number of cups of flour must always be 6 times.
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The complete question is
Mitch made two 10-inch pizzas using a recipe that calls for 3 cups of four and cup of water. Mitch wants to make 4 more pizzas without changing the ratio of flour to water. Enter a number to make the sentence about the ingredients true.
The number of cups of flour must always be___ times the number of cups of water.

Answer:

27

Step-by-step explanation:

1. 100% - 25% = 75%

2). 3/4 x 36 = 27

Answer:

27

Step-by-step explanation:

There are 2 ways we can solve this:

The first way is with percents:

100%-25%=75%

75/100=0.75 or 3/4

3/4·36

27

The second way is to use common knowledge:

We know that 25% is 1/4 of anything.  So, 1/4 of 36 is 9.

36-9=27

Hope this helps! :)

The number of moles for the first equation is 1.8 and the number of moles for the second equation is 0.0240.

The balanced chemical equation is 4Al + 3O² → 2Al₂O₃. The molar ratio of Al to O₂ is 4:3. Therefore, if 1.35 moles of O₂

4 moles Al/₃ moles O₂ = x moles Al/1.35 moles O₂

x = 1.8 moles of Al

The balanced chemical equation is N + 2H₂O → NaOH + H₂. The molar ratio of N to H₂ is 1:1. Therefore, if 0.0240 moles of N is used, then the number of moles of H₂ produced would be:

1 mole N/1 mole H₂ = 0.0240 moles N/x moles H₂

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The equation of the tangent to the curve at the point corresponding to t=1 is y = x - 2.

To find the equation of the tangent to the curve at the point corresponding to t=1:

We first need to find the corresponding values of x and y. Substituting t=1 into the given equations, we get:

[tex]x = 1^4 + 3 = 4[/tex]
[tex]y = 1^3 + 1(1) = 2[/tex]

So the point on the curve corresponding to t=1 is (4,2).

To find the equation of the tangent at this point,

we need to find the slope of the curve at this point. We can do this by taking the derivative of y(x) with respect to x:

[tex]dy/dx = (dy/dt)/(dx/dt) = (3t^2+t)/(4t^3)[/tex]

Substituting t=1, we get:

dy/dx = (3+1)/(4) = 1

So the slope of the curve at the point (4,2) is 1.

Now we can use the point-slope form of the equation of a line to find the equation of the tangent:

y - 2 = 1(x - 4)

Simplifying, we get:

y = x - 2

So the equation of the tangent to the curve at the point corresponding to t=1 is y = x - 2.

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Answer:

Unclear, but assuming it takes 2 minutes to cut one piece, your answer would be 10 minutes to cut 5 pieces.

Step-by-step explanation:

We have 5 pieces, each takes 2 minutes, so:

5×2=10

If it takes more or less than 2 minutes per piece, replace the "2" with another value. (EXAMPLE: 5 minutes per piece would be 5×5=25)
Other:
If this is wrong, I apologize, as there was not enough information given to your question.

The dimensions of the actual painting are 32 inches by 40 inches. So, the answer is option B: 32 inches by 40 inches.

To find the dimensions of the actual painting, we need to use the scale factor and the dimensions of the scaled painting. Since the scale factor is 4:1, this means that the actual painting is four times larger than the scaled painting.

Let the dimensions of the actual painting be x and y. Then, we can set up the following proportion:

Scaled painting dimensions: actual painting dimensions = 1 : 4

This can also be written as:

8: x = 1: 4 (for the width)

10: y = 1: 4 (for the length)

Solving for x and y, we get:

x = 8 x 4 = 32 inches

y = 10 x 4 = 40 inches

Therefore, the dimensions of the actual painting are 32 inches by 40 inches. So, the answer is option B: 32 inches by 40 inches.

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Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that union efforts to organize have increased union membership.

We can use a one-sample proportion test to determine if the proportion of union members in the sample is significantly different from the population proportion of 11.3%.

The null hypothesis is that the population proportion is equal to 11.3%:

H0: p = 0.113

The alternative hypothesis is that the population proportion is greater than 11.3%:

Ha: p > 0.113

The sample proportion is P = 58/400

= 0.145

The standard error of the sample proportion is:

SE = √(p*(1-p)/n)

= √(0.113*(1-0.113)/400)

= 0.0197

The test statistic is:

z = (P - p) / SE

= (0.145 - 0.113) / 0.0197

= 1.6244

The p-value for this test is the probability of getting a z-score of 1.6244 or greater, assuming the null hypothesis is true:

p-value = P(Z > 1.6244)

= 0.0515 (using a standard normal distribution table)

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There are 19,958,400 different ways Grace can select the batting order for her club baseball team.

Using permutation formula: P(n,r) = n! / (n - r)!

where n is the total number of players on the team (12) and r is the number of batters in the batting order (10).

So, we have:

P(12,10) = 12! / (12 - 10)!

P(12,10) = 12! / 2!

P(12,10) = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3

P(12,10) = 19,958,400

Therefore, there are 19,958,400 different ways Grace can select the batting order for her club baseball team.

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