The radius of a right circular cone is increasing at a rate of 4 inches per second and its height is decreasing at a rate of 3 Inches per second. At what rate is the volume of the cone changing when the radius is 40 inches and the height is 20
inches?

The surface area of the pyramid is 390.8 cm².

The surface area of the triangular pyramid is calculated as follows;

S.A = base area   +  ¹/₂ (perimeter + slant height)

The height of the pyramid is calculated by applying Pythagoras theorem;

h = √ (28²  -  14²)

h = 24.2 cm

Area of the base = ¹/₂ x 28 cm x 24.2 cm = 338.8 cm²

The surface area of the pyramid is calculated as follows;

S.A = 338.8 cm²  + ¹/₂ (76 cm + 28 cm)

S.A = 390.8 cm²

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Answer:

1,425

Step-by-step explanation:

I got this one correct

The coordinates of point j' after the rotation are (-y, x), where x and y are the original coordinates of point j

The coordinates of point j' after rotating point jkl 90° clockwise around the origin can be found by applying the following transformation:

j' = (cos(90°) * x - sin(90°) * y, sin(90°) * x + cos(90°) * y)

Since we are rotating 90° clockwise around the origin, we have cos(90°) = 0 and sin(90°) = 1, so the transformation simplifies to:

j' = (0 * x - 1 * y, 1 * x + 0 * y)

j' = (-y, x)

Therefore, the coordinates of point j' after the rotation are (-y, x), where x and y are the original coordinates of point j.

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The value of x in the given circle is 13.9.

Given that a circle D, having an inscribed angle ∠CFE = 57° and the arc opposite it arc CE = 10x-25, we need to find the measure of x,

Using the inscribed angle theorem,

It states that the angle subtended by an arc at the center of the circle is double the angle subtended by it at any other point on the circumference of the circle.

So,

m ∠CFE = arc CE / 2

57 = 10x-25 / 2

10x-25 = 114

10x = 139

x = 13.9

Hence the value of x in the given circle is 13.9.

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The probabilities are given as follows:

a) Square: 1/6.

b) Not the triangle: 43/48.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The area of the rectangle is given as follows:

A = 12 x 8 = 96.

(area of rectangle, multiply the dimensions).

The areas of each figure are given as follows:

Hence the probability of the square is given as follows:

p = 16/96 = 1/6.

(area of square divided by total area).

The probability that the region is not the triangle is given as follows:

p = (96 - 10)/96

p = 86/96

p = 43/48.

(triangle and not triangle are complementary events).

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The sculpture was worth £332.80 three years ago when it depreciates by 20% each year

To determine how much the sculpture was worth 3 years ago, we need to apply the depreciation rate of 20% per year for the past three years.

First, we need to calculate how much the sculpture would be worth after one year of depreciation:

650 - (0.20)(650) = 520

This means that after the first year, the sculpture would be worth £520.

Next, we can calculate the value of the sculpture after the second year of depreciation:

520 - (0.20)(520) = 416

After two years, the sculpture would be worth £416.

Finally, we can calculate the value of the sculpture after the third year of depreciation:

416 - (0.20)(416) = 332.8

Therefore, the sculpture was worth £332.80 three years ago.

To check this answer, we can also use another method: We can calculate the value of the sculpture using the compound interest formula, where the initial value is £x, the annual depreciation rate is 20%, and the time period is three years:

650 = x[tex](1-0.20)^{2}[/tex]

Simplifying this equation, we get:

x = 650 / [tex]0.80^{2}[/tex] = 332.80

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The volume of a trapezoidal prism is 2362.5.

The total surface area​ is 852.

We have,

The volume of a trapezoidal prism.

V = ((a + b) / 2) × h × l

where:

a and b are the lengths of the two parallel sides (the bases) of the trapezoid

h is the height of the trapezoid (the perpendicular distance between the two bases)

l is the length of the prism (the distance between the two trapezoidal faces)

Now,

a = 9

b = 12

l = 15

Height h can be calculated using the Pythagorean theorem.

15² = (12 - 9)² + h²

h² = 225 + 9

h² = 234

h = √234

h = 15

Now,

The volume of a trapezoidal prism.

V = ((a + b) / 2) × h × l
V = ((9 + 12) / 2) x 15 x 15

V = 2362.5

And,

The surface area (A) of a trapezoidal prism can be calculated using the formula:

A = ph + 2B

where p is the perimeter of the trapezoidal base, h is the height of the prism, and B is the area of one of the bases.

So,

p = 12 + 8 + 12 + 8 = 44

h = 15

B = 12 x 8 = 96

Now,

Total surface area​.
= 44 x 15 + 2 x 96

= 660 + 192

= 852

Thus,

The volume of a trapezoidal prism is 2362.5.

The total surface area​ is 852.

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The values of the combination expressions are ¹²C₁₁ = 12, ¹²C₁₀ = 66, ¹²C₅ = 792, ¹²C₁ = 12, ¹²C₁₂ = 1, ⁵C₄ + ⁵C₃ = 15, ⁵C₃/⁵C₂ = 1 and 4⁷C₂ = 84

Also, the number of ways is 30045015

From the question, we have the following parameters that can be used in our computation:

¹²C₁₁

The formula for combination is

ⁿCₓ = n!/[(n - x)! * x!]

So, we have

¹²C₁₁ = 12!/[(12 - 11)! * 11!]

Evaluate

¹²C₁₁ = 12

Using the above as a guide, we have the following:

¹²C₁₀ = 12!/[(12 - 10)! * 10!]

¹²C₁₀ = 66

¹²C₅ = 12!/[(12 - 5)! * 5!]

¹²C₅ = 792

¹²C₁ = 12!/[(12 - 1)! * 1!]

¹²C₁ = 12

¹²C₁₂ = 12!/[(12 - 12)! * 12!]

¹²C₁₂ = 1

⁵C₄ + ⁵C₃ = 5!/[(5 - 4)! * 4!] + 5!/[(5 - 3)! * 3!]

⁵C₄ + ⁵C₃ = 15

⁵C₃/⁵C₂ = 5!/[(5 - 3)! * 3!] / 5!/[(5 - 2)! * 2!]

⁵C₃/⁵C₂ = 1

4⁷C₂ = 4 * 7!/[(7 - 2)! * 2!]

4⁷C₂ = 84

For the number of ways to get people hired, we have

n = 30

x = 10

So, we have

³⁰C₁₀ = 30!/[(30 - 10)! * 10!]

³⁰C₁₀ = 30045015

Hence, the number of ways to get them hired is 30045015 ways

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The average temperature from month 1 to month 6 is approximately 58.3 degrees Fahrenheit.

The temperature of a town t months after January can be estimated by the function f(t) = –20 cos(64t) + 66. To find the average temperature from month 1 to month 6, we need to evaluate the integral of f(t) from t=1 to t=6 and divide by the number of months:

Average temperature = (1/6 - 1) ∫[1,6] f(t) dt

= (1/6 - 1) ∫[1,6] (-20 cos(64t) + 66) dt

= (1/6 - 1) [-5 sin(64t) + 66t] [1,6]

= (1/6 - 1) [-5 sin(646) + 666 - (-5 sin(641) + 661)]

= (1/6 - 1) [-5 sin(384) + 395]

≈ 58.3 degrees Fahrenheit

Therefore, the average temperature from month 1 to month 6 is approximately 58.3 degrees Fahrenheit.

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The area of ΔRST, to the nearest square inch is,

Area = 29,17,735.54 square inches

We have,

In ΔRST, s = 990 inches, ∠S=8° and ∠T=60°.

Apply sine rule formula,

sin S / s = sin T / t

sin 8° / 990 = sin 60° / t

0.14 / 990 = 0.87 / t

0.14t = 990 x 0.87

0.14t = 861.3

t = 6,152 inches

Here, ∠R = 180° - (8 + 60)°

∠R = 180 - 68

∠R = 112°

sin S / s = sin R / r

sin 8° / 990 = sin 112° / r

0.14 / 990 = 0.92 / r

0.14r = 0.92 x 990

0.14r = 910.8

r = 910.8 / 0.14

r = 6505 inches

We use the formula

Heron's formula = √s(s - a)(s - b)(s - c)

Where s = a + b + c/2

Solving for s

s = 990 + 6505 + 6,152 /2

s = 6823.5

Solving for the area of the triangle

= √6823.5 × (6823.5 - 990) × (6823.5 - 6,152) × (6823.5 - 6505)

= √6823.5 x 5833.5 x 671.5 x 318.5

= 29,17,735.54 square inches

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The answer would be D

Since Lucy's number has a digit of 5 which is 10x greater than Ethan's number, 5 x 10 = 50; so 50 would be in the tenth place, and option d is the only one with 5 in the tenth place.

The value of a number moves one decimal place to the left for each position it moves to the right. So, the number that Lucy could have written where the number 5 has a value 10 times larger than Ethan's number is 4974.65.

In order for the value of the digit 5 to be 10 times larger in Lucy's number than it is in Ethan's, the '5' in Lucy's number should reside one place left compared to Ethan's. This means the 5 should be in the tens place, hundreds place, or beyond. So, we should look for a number having digit 5 at those places.

Let's examine the given options:

Therefore, the correct answer is C. 4974.65.

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Answer:

The answer is 9

Step-by-step explanation:

When x = 2,

f(2) = 3×2^2-3

f(2) = 3×4-3

f(2) = 12-3

f(2)= 9

62% of the dancers did not get into the show.

To find the percentage of dancers who did not get into the show.

First, identify the total number of dancers auditioning and the number of dancers who did not get into the show.

In this case, there are 150 dancers in total, and 93 of them did not get in.
Next, divide the number of dancers who did not get into the show by the total number of dancers auditioning.

This will give us the proportion of dancers who did not get in.
  Proportion = (Number of dancers who did not get in) / (Total number of dancers)
  Proportion = 93 / 150
Finally, to find the percentage, multiply the proportion by 100:
  Percentage = Proportion * 100
  Percentage = (93 / 150) * 100.

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The measure of angle m<BEC is 80 degrees

From the information shown, we have that;

m< AD = 120 degrees

m< BC = 80 degrees

To determine the value of m<BEC, we need to know that it is a minor arc in the circle.

Also, a minor arc is described as the shorter arc that connects two endpoints on a circle.

The measure of a minor arc is less than 180° , and  is equal to the measure of the arc's central angle.

We can see than the angle measure of m<BC = m<BEC

Then,

m<BEC = 80 degrees

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Relevant parameter is the difference between actual and scheduled arrival time. Also the difference in sample means is -1.70 minutes. We get a p-value of 0.017 and the conclusion is that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.

a. Relevant parameter: the difference between actual and scheduled arrival time.

Null hypothesis: The average difference between actual and scheduled arrival time is the same for Delta Air Lines and United Air Lines.

Alternative hypothesis: The average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.

b. Sample mean for Delta Air Lines: -2.31 minutes

Sample mean for United Air Lines: -4.01 minutes

Difference in sample means: -1.70 minutes

c. To create a randomization distribution, we can pool the data from both airlines and randomly assign them to two groups with the same sample sizes as Delta Air Lines and United Air Lines. We then calculate the difference in sample means for each random assignment. Repeating this process many times gives us a randomization distribution. Using StatKey with 10,000 iterations, we get a p-value of 0.017, which is less than 0.01.

d. At a significance level of 0.01, we reject the null hypothesis and conclude that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines. Specifically, the average difference for United Air Lines is greater than that of Delta Air Lines. This could have implications for travelers who prioritize arriving on time, as they may wish to consider

Delta over United.

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When the price of the new product is $9.25, the demand for the product is 200 units.

The quantity of a specific commodity or service that consumers are willing and able to buy at a specific price and time is referred to as demand. It stands for consumers' willingness and capacity to pay for a good or service.

The demand for a new product at a price of x dollars is denoted by the notation D(x). So, the notation D(9.25) represents the demand for the new product when the price is $9.25. According to the given information, D(9.25) = 200.

Therefore, we can interpret this as: when the price of the new product is $9.25, the demand for the product is 200 units.

D(9.25) = 200

where D(x) represents the demand for the new product when the price is x dollars. We substitute x = 9.25 into the equation to find the demand when the price is $9.25, which is 200 units.

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The detail that adds tension to the rising action of the story is when Mother Wolf tells Mowgli that some day he will have to kill Shere Khan.

This statement introduces a sense of conflict and foreshadows a significant challenge that Mowgli must face in the future. The idea of Mowgli, a young boy raised by wolves, confronting and defeating the powerful and dangerous Shere Khan adds suspense to the story, as readers anticipate the eventual showdown between these two characters.

Other details, such as Mowgli growing stronger and learning life lessons, or Mowgli forgetting his mother's advice, are relevant to his character development, but do not contribute as directly to the story's tension. Similarly, Mowgli considering himself a wolf and lacking the ability to speak like a human reflects his unique upbringing, but does not add tension in the same way as the impending confrontation with Shere Khan.

In conclusion, Mother Wolf's warning about Mowgli's future encounter with Shere Khan adds tension to the rising action of the story, as it sets up an exciting and challenging conflict for the protagonist to face, capturing the reader's interest and anticipation.

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John threw the javelin 3 standard deviations below the mean

An equation is an expression that shows how numbers and variables using mathematical operators.

The z score shows by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given that John threw 106 feet. The average throw was 130 ft. The standard deviation was 8 feet. Hence:

z = (106 - 130) / 8

z = -3

John threw 3 standard deviations below the mean

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If boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water, the distance from point A to point B is approximately 973 feet.

To find the distance from point A to point B, we can use trigonometry and the fact that the angles of elevation from both points are known.

Let x be the distance from point A to the lighthouse, and y be the distance from point B to the lighthouse. We can set up two equations using tangent function:

tan(5) = 119/x

tan(18) = 119/y

We can solve for x and y by isolating them in each equation:

x = 119/tan(5) ≈ 1343.44 feet

y = 119/tan(18) ≈ 370.79 feet

Therefore, the distance from point A to point B is approximately 1343.44 - 370.79 = 972.65 feet.

We rounded the final answer to the nearest foot, which is 973 feet.

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The length of one side of the square is x - 6 units

The formula for calculating the area of a square is expressed as;

A = a²

Such that the a is the length of its side

From the information given, we have that;

Area = x^ 2 − 12 x + 36

solve the quadratic expression, we have that;

x² - 6x - 6x + 36

group in pairs

(x²- 6x) - (6x + 36)

factorize the terms

x(x - 6) - 8(x - 6)

Then, we have;

(x - 6) and (x - 6) units

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The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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The sine function for the graph is given as follows:

y = sin(3x).

(a one should be placed on the green blank).

The standard definition of the sine function is given as follows:

y = Asin(Bx).

For which the parameters are given as follows:

The function oscillates between y = -1 and y = 1, for a difference of 2, hence the amplitude is obtained as follows:

2A = 2

A = 1.

The period is of 2π/3 units, hence the coefficient B is given as follows:

B = 3.

Then the equation is:

y = sin(3x).

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Answer:

C. An obtuse triangle has two angles less than 90 degrees and one angle greater than 90 degrees.

There is a 95.52% chance that there are no customers in the system, a 9.93% chance that a customer has to wait in line, and a 31.20% chance that the server is busy.

λ = 2.6  guests per hour( Poisson  appearance rate)  μ =  1/ 12 hours per  client( exponential service rate)  c =  1 garçon( design adviser )  Using Little's Law, we can find the average number of  guests in the  staying line   L =  λ * W  

where W is the average time a  client spends in the system(  staying and being served). To find W, we can use the formula  

W =  1/( μ- λ)   Using these formulas, we get  

W =  1/(1/12-2.6) = 0.1154

hours = 6.92  twinkles

L = 2.6 *0.1154 = 0.3000  guests

 So on average, there will be0.3  guests  staying in line and each  client will  stay for6.92  twinkles before being served.

 We can also  cipher the probability that there are no  guests in the system(P_0), the probability that a  client has to  stay(P_w), and the probability that the garçon is busy

(P_b)   =  1- λ/ μ

= 0.9552  

 λ/ μ2 *( 1/( 1- λ/ μ)) = 0.0993  =  λ/ μ = 0.3120

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Answer:

pls mrk me brainliest (⁠・⁠(⁠ｪ⁠)⁠・⁠）

The outcome with a frequency closest to its expected frequency is C (3).

In a spinner game where the pointer spins on a wheel with six equal-sized sections, the expected frequency of each section is 1/6 or 16.67%. Based on the given spinner, section A has an expected frequency of 1/6, section B has an expected frequency of 4/6, section C has an expected frequency of 4/6, section D has an expected frequency of 1/6, section E has an expected frequency of 2/6, and section F has an expected frequency of 4/6.

To determine the outcome with a frequency closest to its expected frequency, we need to compare the expected frequency to the actual frequency for each section.

Based on the given spinner, section A has an actual frequency of 1/18, section B has an actual frequency of 4/18, section C has an actual frequency of 4/18, section D has an actual frequency of 1/18, section E has an actual frequency of 2/18, and section F has an actual frequency of 4/18.

Calculating the difference between the expected and actual frequency for each section, we find that section C has the smallest difference, making it the outcome with a frequency closest to its expected frequency.

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Answer:

------------------------------------------------

A linear equation is an equation of a straight line.

It describes the straight-line graph of a set of ordered pairs (x, y) that are solutions to the equation.

There are different forms of linear equations.

The slope-intercept form of a linear equation is y = mx + b.

The equation y = -2x + 10 is in slope-intercept form. Its graph is a line with slope -2 and y-intercept 10. It shows the set of all solutions to the equation.

As per description above, the correct answer choice is B, all the other options are false.

The value of (f + g)(−3) given the functions f(x) = x² − 6x − 4 and g(x) = 5x + 3 is 11.

To find (f + g)(-3), we first need to add the functions f(x) and g(x) together, and then evaluate the resulting function at x = -3.

f(x) = x² - 6x - 4
g(x) = 5x + 3

Now, let's add f(x) and g(x):

(f + g)(x) = (x² - 6x - 4) + (5x + 3) = x² - x - 1

Now that we have the combined function, we can evaluate it at x = -3:

(f + g)(-3) = (-3)² - (-3) - 1 = 9 + 3 - 1 = 11

So, (f + g)(-3) = 11.

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The statements true of the two-dimensional plane sections that could result from one of these slices made by Misha are B, C, D, E, and F.

A. False. The only two-dimensional plane sections that could result from slicing a cube with a plane are squares or rectangles, but not triangles.

B. True. A plane section that is square could result from one of these slices through the cube.

C. True. A plane section that is rectangular but not square could result from one of these slices through the cube.

D. True. A plane section that is triangular could result from one of these slices through the pyramid.

E. True. A plane section that is square could result from one of these slices through the pyramid.

F. True. A plane section that is rectangular but not square could result from one of these slices through the pyramid.

Therefore, the correct statements are B, C, D, E, and F.

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The first derivative of f(x) is f'(x) = -12(-2x + 1)2.  The second derivative is f''(x) =48(-2x + 1), and all higher derivatives have the form f^(n)(x) = (-1)n * 6 * n! * (-2x + 1)^(3-n).

To calculate the derivatives of all orders for f(x) = (-2x + 1)3, we first need to find the first derivative:

f(x) = (-2x + 1)³

f'(x) = 3(-2x + 1)²(-2)
f'(x) = 3(-2x + 1)²(-2)

f'(x) = -12(-2x + 1)2

Next, we find the second derivative:

f''(x) = d/dx(-12(-2x + 1)²)

f''(x) = 2(-2)(-12)(-2x + 1)
f''(x) = -12[2(-2x + 1)(-2)]

f''(x)= 48(-2x + 1)

We can continue this process to find the third and fourth derivatives:

f'''(x) = d/dx(96(-2x + 1))

f'''(x) = -384

f''''(x) = d/dx(-384)

f''''(x) = 0
Notice that the fourth derivative is 0, meaning that all higher derivatives will also be 0.

This is because the original function is a polynomial of degree 3, so its fourth derivative will be the derivative of a constant, which is 0.

Therefore, we can conclude that:

f(4)(x) = 0
f(n)(x) = 0 for all n ≥ 4.

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Answer:  In order least to greatest, our answer would be-

2.704 ,  2.74  ,  4.2  , 4.27  ,  4.72

.70 is less than .74. In the second set of numbers .2 is less than .27, while they are all less than .72, which gives us the number arrangement above.

I hope this helped & Good Luck!!!

Answer: The answer is 2.704, 2.74, 4.2, 4.27, 4.72

Step-by-step explanation: