If you have $75 and then lose $25, what is the percent change?

(a) At time t=c, the rate of change of the volume is -9π cubic inches per minute.

(b) The rate at which the height of the clay is increasing with respect to time is 8/3 inches per minute.

(c) The rate of change of the radius of the clay with respect to the height of the clay can be expressed as dr/dh = -V/(2πh²).

Given that,

A sculptor is using modeling clay to form a cylinder.

The clay has a constant volume.

The height of the clay increases as the radius decreases, but it retains its cylindrical shape.

At time t=c:

The height of the clay is 8 inches.

The radius of the clay is 3 inches.

The radius of the clay is decreasing at a rate of 1/2 inch per minute.

We know that the volume of the clay remains constant.

So, using the formula V = πr²h,

Where V represents the volume,

r is the radius, and

h is the height,

We can express the volume as a constant:

V = π(3²)(8)

= 72π cubic inches.

(a) To find the rate of change of the volume with respect to time.

Since the radius is decreasing at a rate of 1/2 inch per minute,

Express the rate of change of the volume as dV/dt = πr²(dh/dt),

Where dV/dt is the rate of change of volume with respect to time,

dh/dt is the rate of change of height with respect to time.

Given that dh/dt = -1/2 (since the height is decreasing),

dV/dt = π(3²)(-1/2)

= -9π cubic inches per minute.

So, at time t=c, the rate of change of the volume is -9π cubic inches per minute.

(b) To find the rate at which the height of the clay is increasing with respect to time,

Differentiate the volume equation with respect to time (t).

dV/dt = π(2r)(dr/dt)(h) + π(r²)(dh/dt).          [By chain rule]

Since the volume (V) is constant,

dV/dt is equal to zero.

Simplify the equation as follows:

0 = π(2r)(dr/dt)(h) + π(r²)(dh/dt).

We are given that dr/dt = -1/2 inch per minute, r = 3 inches, and h = 8 inches.

Plugging in these values,

Solve for dh/dt, the rate at which the height is increasing.

0 = π(2)(3)(-1/2)(8) + π(3²)(dh/dt).

0 = -24π + 9π(dh/dt).

Simplifying further:

24π = 9π(dh/dt).

Dividing both sides by 9π:

⇒24/9 = dh/dt.

⇒ dh/dt = 8/3

Thus, the rate at which the height of the clay is increasing with respect to time is dh/dt = 8/3 inches per minute.

(c) For the last part of the question, to find the rate of change of the radius of the clay with respect to the height of the clay,

Rearrange the volume formula: V = πr²h to solve for r.

r = √(V/(πh)).

Differentiating this equation with respect to height (h), we get:

dr/dh = (-1/2)(V/(πh²)).

Therefore,

The expression for the rate of change of the radius of the clay with respect to the height of the clay is dr/dh = -V/(2πh²).

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Answer:

C. 50 degrees

Step-by-step explanation:

Angle EDG is 90 degrees

x = 10

5 multiplied by 10 is 50

4 multiplied by 10 is 40

40+50=90

Answer:

50 = EDH

Step-by-step explanation:

We know that angle EDG is a right triangle (measures 90°). We also know that angle EDH and angle HDG make up angle EDG which is 90°. So ultimately we can state that;

EDH + HDG = EDG

 5x  +   4x  =   90

      9x = 90

        x = 90/9

        x = 10

Now that we know that value of x, we can say that;

EDH = 5x

since x = 10

EDH = 5(10)

EDH = 50

Hope this helps!

Answer:

Maybe 143 degrees i dont know

Step-by-step explanation:

thought that cause 180 - 37 is 143

if not sorry

The given statement is true

What is a rational number?

In contrast to irrational numbers, which cannot be stated as fractions, rational numbers can be expressed as the ratio of two integers with the condition that the denominator not be equal to zero. Irrational numbers don't have ending or recurring decimals, but rational numbers do.

p/q where q is not equal to 0 is the form of a rational number, which is a sort of real number in mathematics. Any fraction with a non-zero denominator is considered rational. Half, one fifth, three quarters, and so on are a few examples of rational numbers.

So, the given statement is true

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By running at least 100 simulations and calculating the variance of the project duration, you can estimate the variance of the project based on the uniformly distributed time intervals for each activity.

To estimate the variance of the project duration using simulation in Excel, you can follow these steps:

1. Create a new Excel worksheet and label columns for activities A, B, and C.

2. In the cells under each activity, use the "RANDBETWEEN" function to generate random numbers within the given intervals. For example, for activity A, the formula would be "=RANDBETWEEN(1,5)".

3. In a separate cell, calculate the total duration of the project by summing the durations of activities A, B, and C. For example, if the durations are in cells A1, B1, and C1, the formula would be "=A1 + B1 + C1".

4. Repeat steps 2 and 3 at least 100 times to generate multiple random durations for the project.

5. Calculate the average duration of the project using the "AVERAGE" function. For example, if the durations are in cells D1:D100, the formula would be "=AVERAGE(D1:D100)".

6. Calculate the variance of the project duration using the "VAR.P" function. For example, if the durations are in cells D1:D100, the formula would be "=VAR.P(D1:D100)".

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\(\bold{3(n - 1) < 21 }\\\\\bold{ 3n - 3 < 21 }\\\\\bold{ 3n < 21 + 3} \\\\\bold{ 3n < 24} \\\\\bold{ n < \cancel\frac{24}{3}} \\\\ \bold{n < 8}\)

hope helpful~

Hello.

The first step is to use the Distributive Property and distribute 3:

3(n-1)<21

3n-3<21

Now, add 3 to both sides:

3n-3+3<21+3

3n<24

Divide both sides by 3:

n<8

Therefore, the answer is

n<8

I hope it helps.

Have a nice day.

\(\boxed{imperturbability}\)

Answer:0.7

Step-by-step explanation:trust me

Answer: The answer is  58.6

Step-by-step explanation:

After figuring out this equation by the nearest 10th I've come up with the answer  58.6

Answer:

-6, -5, -4, -3, -2

or

-5, -4, -3, -2, -1

depending on if N starts at 0 or 1

Step-by-step explanation:

If n starts at 0 then the first 5 terms are the following,

-6, -5, -4, -3, -2

If n starts at 1 then the first 5 terms are these,

-5, -4, -3, -2, -1

question says.

answer is

0.21

Answer:

7

Step-by-step explanation:

42/6=7

Answer:

10.95

Step-by-step explanation:

15/1.75=8.57

10/.75=13.33

13.33+8.57=21.9

21.9/2=

10.95

Answer:

miles

Step-by-step explanation:

the amount of miles a car travels DEPENDs on the amount of gas is left in the car

Answer:

1.7, 3.2, 1.6

Step-by-step explanation:

if you add any 2 numbers from the 3 it has to be greater than the last number so

1.7+3.2>1.6

1.6+1.7>3.2

3.2+1.6>1.7

In a 4 x 4 x 4 design, there are three main effects, three 2-way interactions, and one 3-way interaction.

In a factorial design, the number of main effects and interactions can be determined by examining the number of factors and their levels. In a 4 x 4 x 4 design, there are three factors, each with four levels.

For each factor, there is one main effect. Since there are three factors in the design, there are three main effects.

To determine the number of possible interactions, we consider the possible combinations of factors. In a 4 x 4 x 4 design, we can have 2-way interactions, 3-way interactions, and a 4-way interaction.

2-way interactions: There are three pairs of factors (A-B, A-C, B-C), resulting in three 2-way interactions.

3-way interactions: There is only one combination of three factors (A-B-C), resulting in one 3-way interaction.

4-way interaction: Since there are no additional factors beyond the three factors, there is no 4-way interaction.

Therefore, in a 4 x 4 x 4 design, there are three main effects, three 2-way interactions, and one 3-way interaction.

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Answer:

113.04cm

............

Answer:

27 -3= 24

24 /6= 4

Tickets were $4 each

Step-by-step explanation:

Answer:

$374

Step-by-step explanation:

561-187=374

Answer

Step-by-step explanation:

Answer:

determinant formula looks like  ad - bc in a 2 x2 matrix when it's in the from of

a b

c d

as the one is here

Step-by-step explanation:

5*2 - (-4*8)

=10 - (-32)

=10 + 32

= 42

The expression is simplified to  - 2( 2m + 1)

Algebraic expressions are defined as expressions that consists of arithmetic operations, such as;

These expressions are also known to be composed of terms, coefficients, variables, factors and constants.

From the information, we have the expression;

4m−2+(−8m)

Let's take the following steps to simply the expression

expand the bracket

4m - 2 - 8m

Now, collect like terms

4m - 8m - 2

subtract like terms

- 4m - 2

factor the common terms

- 2( 2m + 1)

Hence, the expression is - 2( 2m + 1)

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Answer:

a and b

Step-by-step explanation:

t was done this before

Answer:

A. p is the independent variable, and s is the dependent variable.

Step-by-step explanation:

In this scenario, the number of people attending the potluck is the independent variable because it is the variable that is being controlled or determined before the brownies are cut. The number of squares the brownies are cut into, on the other hand, depends on the number of people attending the potluck. Therefore, the number of squares is the dependent variable in this scenario.

The side lengths of the real object will be 50 inches and 60 inches.

The scale factor is the ratio of the actual size of the image to the new size of the image. It is used to Map the objects like if you want to increase or decrease the size without changing the original shape of the image it is done by the scale factor.

The given scale factor is 5:1, which means that the dimensions of the scale drawing are 1/5 of the dimensions of the real object.

To find the side lengths of the real object, we can use the ratio of the dimensions in the scale drawing and the real object.

For example, the length of the real object can be found by multiplying the length of the scale drawing by the scale factor:

Real object length = Scale drawing length x Scale factor

Real object length = 10 in x 5

Real object length = 50 in

Similarly, the width of the real object can be found using the same method:

Real object width = Scale drawing width x Scale factor

Real object width = 12 in x 5

Real object width = 60 in

Therefore, the side lengths of the real object are 50 inches and 60 inches.

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Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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Answer:

\(P(5)=\frac{1}{6}\)

Step-by-step explanation:

Since the number 5 appears once on a 6-sided die, then \(P(5)=\frac{1}{6}\)

Answer:

Step-by-step explanation: Hope this helps

Answer:

x<-1

Step-by-step explanation:

-5(x-1)>10, distribute the -5

-5x+5>10, subtract 5 from both sides

-5x>5, divide by -5

x<-1

(When you divide an inequality by a negative, the sign flips)

Answer:

yeah you're right! Its G

Step-by-step explanation:

Multiply 26 hours by 38 weeks and you get 988 hours!

Answer:

283.5 cm squared

Step-by-step explanation:

The surface area of a solid is basically just the sum of the areas of all the exterior sides. In this figure, we have 3 congruent triangles at the top, 3 congruent rectangles on the sides, and 1 triangle at the base. We need to find all these areas.

3 congruent triangles:

The area of a triangle is denoted by: A = (1/2) * b * h, where b is the base and h is the height.

Here, the base of one triangle is 10 and the height is 4. So:

A = (1/2) * b * h

A = (1/2) * 10 * 4 = 20

Since there are 3 such triangles, multiply 20 by 3:

20 * 3 = 60 cm squared

3 congruent rectangles:

The area of a rectangle is denoted by: A = lw, where l is the length and w is the width.

Here, the length is 6 and the width is 10, so:

A = lw

A = 6 * 10 = 60

There are 3 such rectangles, so multiply 60 by 3:

60 * 3 = 180 cm squared

1 base triangle:

Again we use the formula A = (1/2) * b * h for this area.

Here, the base is 10 and the height is 8.7, so:

A = (1/2) * b * h

A = (1/2) * 10 * 8.7 = 43.5 cm squared

Add all these together:

60 + 180 + 43.5 = 283.5 cm squared

The answer is thus 283.5 cm squared.

Answer:

283.5 cm²

Step-by-step explanation:

3 rectangles + 3 triangles on top + triangular base

3(10×6) + 3(½×10×4) + (½×10×8.7)

180 + 60 × 43.5

283.5 cm²

Answer:

2992 or 2112

Step-by-step explanation:

$1,000 times 10% (0.1) = $100

$1,200 in a year.

$2,400 in a year + $1,000 originally = $3,400.

$3,400 * 0.12 = $408

#3,400 = $408 = $2,992.

Or..

$2,400 * 0.12 = $288

$2,400 - $288 = $2,112.

Use the rise/run strategy to draw the line. Start at the y-intercept (0, 12), and count 8 up and 1 to the right to the point (1, 20). Then, draw a line through the points. Test the point (3,36) in the equation y = 8x + 12 to verify that the line is correct.

Answer:

the answer and work if you needed work shown.

Step-by-step explanation: