Write the formula that shows the dependence of the edge length a on the volume V of a cube.

To minimize the cost of the package, we need to find the dimensions that minimize the cost function.

The cost function is the sum of the cost of the side and bottom (made of syrofoam) and the cost of the top (made of paper). Let r be the radius and h be the height of the cylinder. Then the cost function is:

C(r, h) = 0.02(2πrh + πr^2) + 0.05(πr^2)

We need to find the values of r and h that minimize this function subject to the constraint that the volume of the cylinder is 600 cubic centimeters. That is:

V = πr^2h = 600

We can solve for h in terms of r from the volume equation:

h = 600/(πr^2)

Substituting this expression for h in the cost function, we get:

C(r) = 0.02(2πr(600/(πr^2)) + πr^2) + 0.05(πr^2)

= 0.04(600/r) + 0.05πr^2

To minimize C(r), we take the derivative with respect to r and set it equal to zero:

dC/dr = -0.04(600/r^2) + 0.1πr = 0

Solving for r, we get:

r = (300/π)^(1/3) ≈ 5.17 cm

Substituting this value of r into the volume equation, we get:

h = 600/(πr^2) ≈ 2.17 cm

Therefore, the dimensions of the cylinder that minimize the production cost are r ≈ 5.17 cm and h ≈ 2.17 cm, and the minimum cost is:

C(r, h) ≈ $1.24

So, the minimum cost of producing a microwaveable cup-of-soup package in the shape of a cylinder with a volume of 600 cubic centimeters is about $1.24, with a radius of about 5.17 cm and a height of about 2.17 cm.

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Answer:

Step-by-step explanation:

The equation of the absolute value function y = |x| is a V-shaped graph centered at the origin. To translate this graph left 4 units, we need to replace x with (x + 4) in the equation. Also, since the question asks for y = -|x|, we need to reflect the graph across the x-axis by multiplying the entire equation by -1. Therefore, the equation of the translated absolute value function is:

y = -|x + 4|

This equation represents a V-shaped graph that is centered at x = -4 and opens downward (since it is multiplied by -1), with the vertex at (-4,0).

Answer: y = -|x+4|

Step-by-step explanation:

the formula for absolute value is

y = a|x-h| +k    

(h, k), is your vertex

h, is your shift left or right

k, is your shift up or down

a, is your stretch and negative in front indicates a reflections.

if you want to shift he function left for that's -4 so substitut in your  equations for h -4

y= -|x-(-4)|

y = -|x+4|

The total number of five-digit odd numbers is 864 + 216 = 1080

The units digit must be one of 7 or 9 to make a five-digit odd number. The last four digits can be any of the six provided digits, and they can be repeated.

So we have two scenarios:

Case 1: The first digit of the units is 7.

In this scenario, we have four options for the initial digit (2, 4, 6, or 8) and six options for the following digits. As a result, the total number of five-digit odd numbers is:

4 x 6 x 6 x 6 = 864

Case 2: The unit digit is nine.

In this scenario, we only have one option for the initial digit (7) and six options for the other digits.

As a result, the total number of five-digit odd numbers is 864 + 216 = 1080

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Cosx, -sinx, -cosx + C, sinx + C are the derivative answers to the question.

The derivative of sin x with respect to x is cos x.
The derivative of cos x with respect to x is -sin x.
The antiderivative of sin x with respect to x is -cos x + C, where C is the constant of integration.
The antiderivative of cos x with respect to x is sin x + C, where C is the constant of integration.

1. The derivative of sin(x) with respect to x is cos(x).
2. The derivative of cos(x) with respect to x is -sin(x).
3. The antiderivative of sin(x) with respect to x is -cos(x) + C, where C is the constant of integration.
4. The antiderivative of cos(x) with respect to x is sin(x) + C, where C is the constant of integration.

A derivative in mathematics is a measurement of how much a function alters as its input alters. It refers to how quickly a function alters in relation to its input variable. The slope of the tangent line to the function at a certain point is what it is, in other words.

The limit of the ratio of the change in the output to the change in the input, as the change in the input approaches zero, is known as the derivative of a function, indicated by the symbols f'(x) or [tex]dy/dx[/tex].

The opposite of differentiation is an antiderivative, usually referred to as an indeterminate integral. It is a function that yields the original function when differentiated. In other words, f(x) follows if [tex]f'(x) = g(x)[/tex].

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The number of white marbles in the bag is w = 7

Given data ,

Let's write "w" for the quantity of white marbles in the bag. Four of the twelve marbles in the bag are blue, as shown by the information provided. This indicates that "12 - 4 = 8" applies to the remaining white marbles.

Now , when a marble is randomly selected and returned to the bag, the probability of selecting a white marble is w/12, where "w" is the number of white marbles and 12 is the total number of marbles in the bag.

Similarly, when a second marble is randomly selected (with replacement), the probability of selecting a blue marble is 4/12, since there are 4 blue marbles out of 12 marbles in total.

So , the probability is given by

(w/12) x (4/12) = 7/36

On simplifying , we get

4w/144 = 7/36

Cross-multiplying:

144 x (4w/144) = 144 x (7/36)

4w = 28

Dividing both sides by 4:

w = 28/4

w = 7

Hence , the number of white marbles in the bag is 7

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There is a fraction of 0.525 liters of vinegar in the container for a container that holds 0.7 liters of oil and vinegar and 3/4 of the mixture is vinegar.

First, find out how much of the mixture is vinegar:

3/4 of the mixture = 3/4 × 0.7 = 0.525 liters

Therefore, there are 0.525 liters of vinegar in the container.

To express this as a fraction, we can write 0.525 as 525/1000 and simplify it to 21/40.

So, the answer in both fraction and decimal forms are:

0.525 liters = 21/40 liters

To check our answer in decimal form, we can add the amount of oil and vinegar to make sure it equals the total volume of the container:

0.525 + (1 - 0.75) × 0.7 = 0.525 + 0.175 = 0.7

As expected, the sum is equal to the total volume of the container, which is 0.7 liters.

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The question is -

A container holds 0.7 liters of oil and vinegar. 3/4 of the mixture is vinegar. how many liters of vinegar is in the container?

Answer:

The answer for x is 20

Step-by-step explanation:

a=1

b=10

<C=60°

cos 60=b/hyp

let hyp be x

cos 60=10/x

x=10/cos 60

x=10/0.5

x=20

Answer:its b

Step-by-step explanation:

The probability of event B given event A has occurred is 0.5.

By using the conditional probability formula, we have:

P r(B | A) = P r(A ∩ B) / P r(A)

We are given that P r(A) = 0.4 and P r(A ∩ B) = 0.2.

Substituting these values, we get:

P r(B | A) = 0.2 / 0.4

By simplifying;

P r(B | A) = 0.5

Therefore, the probability of event B given event A has occurred is 0.5.

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The probability that the cycle time exceeds 65 minutes given that it exceeds 55 minutes is 1/3.

To solve this problem, we can use conditional probability. We know that the cycle time for trucks hauling concrete is uniformly distributed between 50 to 70 minutes. Let X be the cycle time in minutes.

So, P(X > 65 | X > 55) = P(X > 65 and X > 55) / P(X > 55)

We can simplify the numerator as P(X > 65 and X > 55) = P(X > 65) since if X is greater than 65, it is also greater than 55. Using the formula for the uniform distribution, we get:

P(X > 65) = (70 - 65) / (70 - 50) = 1/4

Similarly, we can calculate the probability of X being greater than 55:

P(X > 55) = (70 - 55) / (70 - 50) = 3/4

Putting these values in the conditional probability formula, we get:

P(X > 65 | X > 55) = (1/4) / (3/4) = 1/3

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The scientific notation of mass 6,200,000 is 6.2 × 10⁶kg and 6.2 × 10⁹g

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an unusually long string of digits.

It can be referred to as scientific form or standard index.

A mass of 6,200,00 kg can be written to index form by putting it to base of 10.

6200000/1000000

= 6.2 × 1000000 = 6.2 × 10⁶kg

1 kg = 10³ g

therefore;

6.2 × 10⁶kg = 6.2 × 10⁶kg × 10³

= 6.2 × 10⁹g

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Based on the given information, we can conclude that f(2) is an analytic function in a deleted neighborhood of infinity. This means that f(z) has a Laurent expansion in the form of

[tex]f(z) = ..._c-2/z^2 + _c-1/z + c0 + c1z + ... + cnz^n + ...,[/tex]

where the coefficients

[tex]_c-2, _c-1, c0, c1, ...,[/tex]

cn are constants.

The point morc is a singular point of f(z) that can be either removable, a pole of order m, or an essential singular point. The type of singular point depends on the behavior of the Laurent expansion of f(z).

If the Laurent expansion of f(z) contains no positive powers of z, then the point morc is a removable singular point. This means that the singularity can be "filled in" or removed, and the function can be defined at that point.

If the Laurent expansion of f(z) contains only a finite number of positive powers of z, with the highest positive power being m, then the point morc is a pole of order m. This means that the singularity is a simple pole, double pole, triple pole, or higher order pole, depending on the value of m.

If the Laurent expansion of f(z) contains infinitely many positive powers of z, then the point morc is an essential singular point. This means that the singularity cannot be removed or "filled in", and the behavior of the function at that point is very complex.

In summary, the type of singular point at the point morc depends on the behavior of the Laurent expansion of f(z) at that point.

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We need a sample size of at least 62 to detect the alternative hypothesis with power of at least 0.80 at a 5% significance level.

To answer this question, we need to use power analysis. Power is the probability of rejecting the null hypothesis when it is false. In this case, the null hypothesis is m = 0 and the alternative hypothesis is m > 0. We want to detect the alternative hypothesis with power of at least 0.80 at a 5% significance level.

Assuming that s is 20 and we want to detect the alternative m > 4, we can use the following formula to calculate the sample size:

n = (Zα/2 + Zβ)² * σ² / δ²

where:
- Zα/2 is the critical value for the significance level α/2 (α = 0.05, so Zα/2 = 1.96)
- Zβ is the critical value for the power (power = 0.80, so Zβ = 0.84)
- σ is the standard deviation (σ = 20)
- δ is the difference between the null hypothesis and the alternative hypothesis (δ = 4)

Substituting these values into the formula, we get:

n = (1.96 + 0.84)² * 20² / 4²
n = 61.61

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The value of the fraction -5/7 and -4/7 added and subtracted from the fraction -21/2 added to 1/22 is 64/77.

The sum of 1/2 and -21/22 can be found by finding a common denominator,

1/2 = 11/22 (since 11 x 2 = 22)

-21/22 = -21/22

Therefore, the sum of 1/2 and -21/22 is,

= 11/22 - 21/22

= -10/22 = -5/11

The sum of -4/7 and -5/7 is,

-4/7 - 5/7 = -9/7

Now, subtracting as asked in the question.

= (-5/11)-(-9/7)

= (-5/11)+(9/7)

Finding common denominator to add the fractions,

7 x 11 = 77

(-5x7)/(11x7)+(9x11)/(7x11)

= -35/77 + 99/77

Now, we can combine the numerators,

-35/77 + 99/77 = 64/77

Therefore, the final answer is 64/77.

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Based on the information, the most appropriate graph for this situation would be option A.

To identify the most appropriate graph for this situation we must analyze the data. In this case we have the relationship of the toppings with the number of customers who prefer each variety.

Now, We get;

Due to the above, we could affirm that the best option is A because it shows the number of people who prefer each topping in the order in which the table organizes them.

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Answer:

look the picture for the representation

thank you

240 wooden cubes can fit in box.

We have,

Volume of wooden cube= 1/2 cubic foot

Dimension of box = 5ft x 8 ft x 3 ft

So, the Volume of Box

= l w h

= 5 x 8 x 3

= 120 ft³

Now, the number of wooden cubes fit in box

= 120/ 0.5

= 240

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The measure of the shorter base is approximately 28.85.

To solve this problem, we need to use the fact that the line segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases and has a length equal to half the sum of the bases. Let's call the shorter base "x".

We know that the longer base is 97, so the sum of the bases is x + 97.

We also know that the line segment joining the midpoints of the diagonals has a length of 3. Since this line segment is parallel to the bases, it divides the trapezoid into two smaller trapezoids that are similar to the original trapezoid.

Using the similar triangles, we can set up the following equation:

3/x = (x + 97)/97

Cross-multiplying and simplifying, we get:

3*97 = x^2 + 97x

Multiplying out the right side and rearranging, we get:

x^2 + 97x - 291 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac))/2a

Plugging in a=1, b=97, and c=-291, we get:

x = (-97 ± sqrt(97^2 - 4(1)(-291)))/2(1)

x = (-97 ± sqrt(9429))/2

x = (-97 ± 97)/2 or x = (-97 ± sqrt(9429))/2

Since we're looking for the shorter base, we can discard the negative solution:

x = (-97 + sqrt(9429))/2

x ≈ 28.85

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The volume of the box is given as follows:

V = 199.5 in³.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem, in inches, are given as follows:

10.5, 9.5 and 2.

Hence the volume of the box is given as follows:

V = 10.5 x 9.5 x 2

V = 199.5 in³.

The problem asks for the volume of the box.

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Answer:

Step-by-step explanation:

1 plus 2 equals 3

3 plus 3 equals 6

6 plus 4 equals 10

10 plus 5 equals 15.       did this help?

The probability that Kelsi will eat a custard filled donut and then a chocolate donut is approximately 0.1455.

To calculate the probability of Kelsi eating a custard filled donut and then a chocolate donut, we need to use the concept of conditional probability.

The probability of Kelsi eating a custard filled donut first is 4/12 (since there are 4 custard filled donuts out of a total of 12 donuts).

After Kelsi eats a custard filled donut, there are only 11 donuts left, and 6 of them are chocolate donuts. So the probability of Kelsi eating a chocolate donut second, given that she already ate a custard filled donut, is 6/11.

To find the probability of both events happening together (Kelsi eating a custard filled donut first and a chocolate donut second), we multiply the probabilities:

P(custard first and chocolate second) = P(custard first) * P(chocolate second | custard first)

P(custard first and chocolate second) = (4/12) * (6/11)

P(custard first and chocolate second) = 0.1455

Rounding to 4 decimal places, we get:

P(custard first and chocolate second) ≈ 0.1455

Therefore, the probability that Kelsi will eat a custard filled donut and then a chocolate donut is approximately 0.1455.

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The conclusion about p using an absolute value inequality would be that |p - 72| ≤ 4. This means that the difference between the true proportion p and the estimated proportion 72% is no more than 4%.

In other words, p is most likely to fall within the range of 68% to 76%, as determined by the margin of error in the statistical polling calculation. This emphasizes the importance of recognizing and accounting for the potential for error and uncertainty in estimating percentages and proportions in various fields, including politics and marketing.
To describe the conclusion about the percentage (p) in statistical polling using an absolute value inequality, you can use the margin of error (4% in this example) as a way to create the inequality.
In this case, we have a poll result of 72% and a margin of error of 4%. So, the absolute value inequality would be:
|p - 72%| ≤ 4%
This inequality shows that the difference between the true percentage (p) and the poll result (72%) should be less than or equal to the margin of error (4%). In other words, the true percentage (p) is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).

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Answer:5/14

Step-by-step explanation:

you have 5 red and 14 total so your probability is 5/14 and 5/14 is the simplest terms

The slope and y-intercept are 4.5 and 25 respectively.

A graph of the equation for the total shipping charges is shown below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about this freight company, the total shipping charges are given by;

C = 4.5n + 25

By comparison, we have the following:

Slope, m = 4.5.

y-intercept = 25.

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The radius of a sphere with volume 288π cm³ is equal to 6 centimeter.

In Mathematics and Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):

Volume of a sphere = 4/3 × πr³

Where:

r represents the radius.

By substituting the given parameters into the formula for the volume of a sphere, we have the following;

288π = 4/3 × π × r³

r³ = 864/4

Radius, r = ∛216

Radius, r = 6 centimeter.

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Answer:

$4853

Step-by-step explanation:

Since there are 12 months in 1 year, the monthly salary is 1/12 of the yearly salary. We divide the annual salary by 12 to calculate the monthly salary.

$58236/12 = $4853

Answer: 512 feet^3

Step-by-step explanation:

The volume of a cube is x^3, where x is the sidelength.  8^3 is equal to 512 and since its in the 3rd dimension it's feet^3 or feet cubed.

Answer:

Approximately 243.917

Step-by-step explanation:

The cube has a volume of 8³ = 512.

The sphere has a volume of   [tex]\frac{4}{3}\pi r^3[/tex].

The volume inside the cube but outside the sphere is:

[tex]512-\frac{4}{3}\pi r^3[/tex] (1)

The radius of the sphere is equal to the sidelengths of the cube divided by 2 as seen by the picture.

So r = 8/2 = 4.

Substituting r into (1):

[tex]512-\frac{4}{3}\pi 4^3=512-\frac{256\pi }{3}=243.917[/tex]