A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the container will be made of syrofoam costing 0.02 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production cost.
Helpful information:
h : height of cylinder, r : radius of cylinder
Volume of a cylinder: V=πr2h
Area of the sides: A=2πrh
Area of the top/bottom: A=πr2
To minimize the cost of the package:
Radius: cm
Height: cm
Minimum cost: cents

The area and circumference of the circle are 16π cm² and 8π cm respectively.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

The circumference of a circle is expressed mathematically as;

C = 2πr

Where r is radius and π is constant pi.

Given the diameter of the circle as 8 cm, we can find the radius by dividing the diameter by 2:

r = 1/2 × diameter

r = 1/2 × 8cm

r = 4cm

Using the radius, we can now calculate the area and circumference of the circle:

Area of circle = πr²

A = π(4 cm)²

A = 16π cm²

Circumference of circle = 2πr

C = 2π(4 cm)

C = 8π cm

Therefore, the circumference of the circle is 8π cm.

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The mean, median, mode and range of the data set after you perform the given operation on each data value include the following: C. Mean: 13.8, Median: 14, Mode: 14, Range 15.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data, we have;

Total, F(x) = 9 + 7 + 12 + 13 + 9 + 3

Total, F(x) = 53

Mean = 53/6

Mean = 8.8.

By adding 5 to the mean, we have the following:

Mean = 8.8 + 5 = 13.8

Mode = 9 + 5 = 14

Median = (9 + 9)/2 + 5 = 14.

Range = (13 - 3) + 5 = 15

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The amount of water Sharon needs in liters is given by A = 12 liters

Given data ,

Sharon is making a huge batch of lemonade for her lemonade stand

Now , recipe calls for 26 pints of water

And , 6.5 pints = 3 liters

So , 1 pint = ( 3/6.5 ) liters

On simplifying the equation , we get

The amount of water in liters A = 26 pints

26 pints = 26 ( 3/6.5 ) Liters

26 pints = 12 liters

Hence , the equation is A = 12 liters

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Answer: its 7 i took the quiz

So the vector  form of the equation is: y = -1(x - 2)² + 3.

To convert from standard form to vertex form, we complete the square by following these steps:

Factor out the coefficient of the x-squared term:

y = -x² + 4x - 1

= -1(x² - 4x) - 1

To complete the square inside the parentheses, add and subtract the square of half of the coefficient of the x-term (-4/2)^2 = 4:

y = -1(x² - 4x + 4 - 4) - 1

Simplify the expression inside the parentheses by factoring a perfect square:

y = -1((x - 2)² - 4) - 1

Distribute the -1 and simplify:

y = -1(x - 2)² + 3

Therefore, the vertex of the parabola is at (2, 3), and the negative coefficient of the x-squared term means that the parabola opens downwards.

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The largest three-digit positive integer n for which the sum of the first n positive integers is not a divisor of the product of the first n positive integers is 995.

We have,

To solve this problem, let's consider the sum and the product of the first n positive integers separately.

The sum of the first n positive integers can be expressed as:

S = 1 + 2 + 3 + ... + n = (n(n+1))/2.

The product of the first n positive integers can be expressed as:

P = 1 x 2 x 3 x ... x n = n!.

We want to find the largest three-digit positive integer n for which S is not a divisor of P.

Since P = n! grows faster than S = (n(n+1))/2, we need to find a value of n where P is not divisible by S.

By observing the answer choices, we can start from the largest answer choice and work our way down until we find a value where P is not divisible by S.

Let's test the values of n given in the answer choices:

For n = 999:

P = 999! and S = (999(999+1))/2 = 499500.

In this case, S is not a divisor of P.

For n = 998:

P = 998! and S = (998(998+1))/2 = 498501.

In this case, S is not a divisor of P.

For n = 997:

P = 997! and S = (997(997+1))/2 = 497503.

In this case, S is not a divisor of P.

For n = 996:

P = 996! and S = (996(996+1))/2 = 496506.

In this case, S is not a divisor of P.

For n = 995:

P = 995! and S = (995(995+1))/2 = 495510.

In this case, S is not a divisor of P.

Therefore,

The largest three-digit positive integer n for which the sum of the first n positive integers is not a divisor of the product of the first n positive integers is 995.

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The sine of the angle θ is given as follows:

sin(θ) = -16/65.

The trigonometric identity relating the cosine of an angle, along with the sine of the same angle, is given as follows:

sin²(θ) + cos²(θ) = 1.

In this problem, we have that cos(θ) = 63/65, hence the sine of θ is obtained as follows:

sin²(θ) + (63/65)² = 1

sin²(θ) = 1 - (63/65)²

sin(θ) = +/- sqrt(1 - (63/65)²)

sin(θ) = -16/65.

The sine has a negative sign as on the fourth quadrant, the sine is negative.

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The equation of the parabola is

The equation of the parabola is solved using the equation

y = a(x - r1) (x - r2)

where r1 and r2 are the roots or x-intercept

The roots of the equation is given as -2 and 4.

hence we have that

y = a(x + 2) (x - 4)

Using (-1, -3) we solve for a

-3 = a(-1 + 2) (-1 - 4)

-3 = a(1) (-5)

-3 = -5a

a = 3/5

Plugging this figure back into the original equation,

y = 5/3(x + 2) (x - 4)

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So there are 6 permutations possible with the letters "ABC". These are: ABC, ACB, BAC, BCA, CAB, CBA.

Permutations are a way of arranging objects in a specific order. The number of permutations of a set of n distinct objects is given by n!, where n! denotes the factorial of n.

In the case of the letters "ABC", there are three distinct objects: A, B, and C. Therefore, the number of permutations possible with these letters is:

3! = 3 x 2 x 1 = 6

This means that there are 6 possible ways of arranging the letters "ABC" in a specific order. These permutations are:

ABC

ACB

BAC

BCA

CAB

CBA

To see why there are 6 possible permutations, consider the first position. There are three letters to choose from, so there are three possible choices for the first position. Once the first letter is chosen, there are two letters left to choose from for the second position. Finally, there is only one letter left to choose from for the third position. Therefore, the total number of permutations is:

3 x 2 x 1 = 6

In summary, the number of permutations of a set of n distinct objects is given by n!, and in the case of the letters "ABC", there are 3! = 6 possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA.

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Answer:

Step-by-step explanation:

o.10

Answer: $7,200 So, Jenna pays a total of $7,200 in interest.

Step-by-step explanation:

we can multiply the yearly interest by the number of years: Total Interest = Yearly Interest × Number of Years Total Interest = $480 × 15 Total Interest = $7,200 So, Jenna pays a total of $7,200 in interest.

Answer:

Step-by-step explanation:

the interest she pays is $7,000

the total amount she pays is $15,200

the interest caclucuation:

= 6/100 × 8,000

= 0.06 × 8000

= 480

= 480 × 15

= $7200

the total amount she pays:

= $7200 +$8000

= $15,200

Answer: To find the surface area of a cylinder, we need to add the areas of the top and bottom circles to the lateral surface area (the curved surface that connects the circles).

1.) Given that the diameter (d) of the cylinder is 10m and the height (h) is 8m.

First, let's find the radius of the cylinder (r):

r = d/2 = 10m/2 = 5m

Then, we can find the surface area of the cylinder:

The area of each circle is given by A = πr^2

A(top and bottom circles) = 2π(5m)^2 = 2π(25m^2) = 50πm^2

The lateral surface area is given by A = 2πrh

A(lateral) = 2π(5m)(8m) = 80πm^2

The total surface area is the sum of the areas of the top and bottom circles and the lateral surface area:

A(total) = A(top and bottom circles) + A(lateral)

A(total) = 50πm^2 + 80πm^2

A(total) = 130πm^2

Therefore, the surface area of the cylinder is 130π square meters (or approximately 408.4 square meters if you round to one decimal place).

Answer:

Greg borrowed $10 from his friend.

Step-by-step explanation:

[tex]38.32+12.25+12.75 = 63.32 \\ 63.32 - 60 = 3.32 \\ 3.32 + 6.68 = 10[/tex]

The solution of the given equation; tan 23 = 22 / x for the variable x as required is; 52.07.

It follows from the task content that the value of x in the given equation is to be determined.

Since the given equation is; tan (23) = 22 / x;

By multiplying both sides by; x / tan (23); we have that;

x = 22 / tan (23)

x = 22 / 0.4225

x = 52.07.

Ultimately, the solution of the equation for x is; 52.07.

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Answer:

The carrying capacity of a population refers to the maximum number of individuals that a particular ecosystem can sustainably support over the long-term. It is affected by factors such as the availability of resources like food, water, and shelter, as well as disease, predation, and other environmental factors.

The carrying capacity of a population can vary over time and depends on many different variables, including the species in question, the environment it lives in, and the management practices that are in place. Therefore, it is not possible to determine the approximate carrying capacity of a population without specific details about the particular species and ecosystem in question.

Similarly, it is impossible to determine when a population reached its carrying capacity or how long it stayed there without specific information about the population and its environment. Population data over time can help to estimate changes in population size and to understand how it may have been impacted by different factors, but a detailed analysis of the specific ecosystem and species is required to make accurate predictions about carrying capacity and population dynamics.

Step-by-step explanation:

The requried cost of the item is $2392, and the sale tax is 4.5% of the cost of the item.

As given in the question,
Total spent = $2500
Total sale's tax paid = $108
Sale's tax % = 108/[2500-108]×100%
Sale's tax % = 4.5%

The cost of the item is given as:

= $2500 - $108
= $2392

Thus, the requried cost of the item is $2392, and the sale tax is 4.5% of the cost of the item.

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The question seems to be incomplete,
The question must be,
What is the sale tax for a purchase of $2,500 and what is the cost of an item with a sales tax of $108?

Based on the information you provided, it seems that a simple linear regression model was used to analyze the relationship between the size of a house (in square feet) and its selling price (in 1,000 dollars).

The dependent variable in this model was the price, while the independent variable was the size. The sample size used for this analysis was 8.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient would indicate how closely the selling price of a house is related to its size. The value of r can range from -1 to 1, with values closer to -1 or 1 indicating a stronger relationship, while values closer to 0 indicate a weaker relationship.

Without knowing the specific value of r, it is difficult to draw conclusions about the strength of the relationship between the size of a house and its selling price. However, in general, it is reasonable to assume that there is a positive correlation between these two variables - that is, as the size of a house increases, its selling price is likely to increase as well.

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Based on the nutritional facts provided, there are 4.8 grams of unsaturated fat in 240 g of these crisps.

Based on the nutritional facts provided, 2/35 of fat are unsaturated fats.

The percentage of unsaturated fat in 35% of fats is calculated below:

The percentage of unsaturated fat in 35% fats = 2/35 * 35/100

The percentage of unsaturated fat in 35% fats = 2.00%

The mass in grams of unsaturated fat in 240 g of crisps, is calculated below as follows:

mass in grams of unsaturated fat = 2% * 240 g

mass in grams of unsaturated fat = 4.8 g

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The volume of the given solid enclosed by the paraboloids y = x2 + z2andy = 72 − x2 − z2 is 10368 cubic units.

Using a triple integral, we will integrate over the region of the xz-plane that is enclosed by the paraboloids.

The limits of integration for x and z can be found by solving the two equations for x^2 + z^2:

$x^2 + z^2 = y = x^2 + z^2 + 72 - x^2 - z^2$

$x^2 + z^2 = 36$

Therefore, the limits of integration for x and z are from -6 to 6.

The limits of integration for y are from the equation of the lower paraboloid $y = x^2 + z^2$ to the equation of the upper paraboloid $y = 72 - x^2 - z^2$.

Therefore, the limits of integration for y are from $x^2 + z^2$ to $72 - x^2 - z^2$.

The triple integral for the volume of the solid is:

$\iiint_V dV = \int_{-6}^{6} \int_{-6}^{6} \int_{x^2+z^2}^{72-x^2-z^2} dy dz dx$

Integrating with respect to y:

$\int_{x^2+z^2}^{72-x^2-z^2} dy = 72 - 2(x^2 + z^2)$

Substituting this into the triple integral gives:

$\iiint_V dV = \int_{-6}^{6} \int_{-6}^{6} (72 - 2(x^2 + z^2)) dz dx$

Integrate with respect to z:

$\int_{-6}^{6} (72 - 2(x^2 + z^2)) dz = 72(12) - 4x^2(6) = 864 - 24x^2$

Integrate with respect to x:

$\int_{-6}^{6} (864 - 24x^2) dx = 2(864)(6) - 2\int_{0}^{6} (24x^2) dx = 10368$

Therefore, the volume of the solid enclosed by the paraboloids $y = x^2 + z^2$ and $y = 72 - x^2 - z^2$ is 10368 cubic units.

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The value of "x" in the expression 5ˣ⁻² = 8; by using the change of base formula is approximately 3.2920.

We have to find the value of "x" in the "logarithmic-expression" : 5ˣ⁻² = 8; for which we have to use the change-of-base formula, which is [tex]log_{b} (y) = \frac{log(y)}{log(b)}[/tex].

we take "log" on both sides of 5ˣ⁻² = 8;

We get,

⇒ (x-2)log(5) = log(8),

⇒ x-2 = log(8)/log(5),

By using the "change of base formula",

We get,

⇒ x-2 = log₅(8),

⇒ x-2 = 1.2920

⇒ x = 1.2920 + 2;

⇒ x ≈ 3.290,

Therefore, the value of x is approximately 3.2920.

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The given question is incomplete, the complete question is

Find the value of "x" in the expression 5ˣ⁻² = 8 . Using the change of base formula [tex]log_{b} (y) = \frac{log(y)}{log(b)}[/tex].

The correct answer is Prediction intervals make sense since they account for both the vulnerability in evaluating the mean and the inconstancy of personal perceptions.

A confidence interval is an estimate of the range of values ​​over which the true population mean is likely to fall within the specified confidence level.

It is based on the sample mean and sample size and assumes that the variability of observations is constant across the range of predictor variables.

A prediction interval, on the other hand, is an estimate of the range of values ​​to which a single observation is likely at a given confidence level.

This accounts for both the uncertainty in estimating the mean and the variability of individual observations.

It is therefore wider than a confidence interval that only accounts for the uncertainty in estimating the mean.

Therefore, it makes sense that the prediction interval for y is wider than the confidence interval.  

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Answer:

(-3,3)

Step-by-step explanation:

left 1 = (-5,3)

right 2 = (-3,3)

Answer:

-3,3

Step-by-step explanation:

The points of intersection of the line and of the circle are given as follows:

(0.94, -4.06) and (17.06, 12.06).

The equations are given as follows:

Replacing y = x - 5 into the equation of the circle, we obtain the x-coordinates of the points of intersection, as follows:

(x - 5)² + (x - 5 + 1)² = 25

(x - 5)² + (x - 4)² = 25

x² - 10x + 25 + x² - 8x + 16 = 25

x² - 18x + 16 = 0.

The coefficients of the quadratic equation are given as follows:

a = 1, b = -18, c = 16.

Using a calculator, the solutions are:

x = 0.94 and x = 17.06.

Hence the y-coordinates are:

Hence the points are:

(0.94, -4.06) and (17.06, 12.06).

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Note that the system of graphs has two y-intersects hence the two solutions. Note tht in the graph there ar etwo parabolas.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation meets the coordinate system's y-axis. This is done in analytic geometry using the usual convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points fulfill x = 0 because of this.

Replace x in the equation with 0 and then solve for y, keeping in mind that the y-intercept always has an associated x-value of 0. Finding the value of y at x=0 on a graph will reveal the y-intercept. The graph's intersection with the y-axis occurs at this location.

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The larger of the two expressions is maxvalue(r, n - k - r, k).

The expression with -1 as the second parameter to maxvalue is maxvalue(n-k-r, -1, k).

To see why this is the case, let's consider the definition of maxvalue(r, a, b). This function returns the maximum value among r, a, and b.

Now, suppose that k < n - r. Then, we have:

n - k - r > n - (n - r) - r = r

This means that n - k - r is greater than r, so maxvalue(r, n - k - r, k) will return either n - k - r or k, whichever is greater.

On the other hand, since -1 is less than any non-negative integer, we have:

-1 < 0 <= r

Therefore, maxvalue(r, -1, k) will return either r or k, whichever is greater.

Since r is non-negative, we have:

maxvalue(r, -1, k) = max(r, -1, k) = max(r, k)

So, the larger of the two expressions is maxvalue(r, n - k - r, k).

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If Nasim invests money in an account paying a simple interest of 1. 3% per year and he invests $70 and no money will be added or removed from the investment, the amount he will have in one year is 70 dollars and 91 cents

Simple interest refers to the interest that is calculated on the original amount or the principal. Simple interest is calculated by:

Interest = P * r * t

where P is the principal

r is the rate of interest (in decimal)

t is the time

Given in the question,

P = $70

r = 1.3% = 0.013

t = 1 year

Interest = 70 * 0.013 * 1

= $0.91

Amount = P + i

where P is principal

i is interest

A = 70 + 0.91

A = $70.91

The amount that Nasim has after 1 year is $70.91.

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Answer:  B.  5.6 mi

Step-by-step explanation:

The want you to convert 9km to mi

you can multiply by conversion factors to convert

[tex]9km*\frac{1 mi}{1.61 km}[/tex]      >The conversion factor is equivalent measurements.  The

                         >measurement you want to cancel out goes on the bottom.

=5.6 mi

Answer:

Step-by-step explanation: what would halve of 5 be?

The exact value of sin 4π/3 using both double and half angle identities is:  -¹/₂√3

Trigonometric Identities are defined as the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.

Using the trigonometric identity: sin 2A = 2sin A cos A

Thus:

sin 2(2π/3) = 2 sin (2π/3) cos (2π/3)

From trigonometric tables, we have:

= 2((√3)/2 * -1/2)

= -¹/₂√3

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Therefore, the vertex form of the equation is y = -2(x - 3)² - 3.

To change the standard form of a quadratic equation to vertex form, we need to complete the square.

First, we factor out the leading coefficient -2 from the quadratic terms:

y = -2(x² - 6x) - 21

Next, we need to add and subtract a constant term inside the parenthesis to make the quadratic term a perfect square trinomial:

y = -2(x² - 6x + 9 - 9) - 21

y = -2((x - 3)² - 9) - 21

y = -2(x - 3)² + 18 - 21

y = -2(x - 3)² - 3

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