A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A , is A=2πr2+2πrh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides).


A round cylinder with a circle top and base with radius r and a height of h




Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r , so we can write that as A(r)=2πr2+16πr. What is the domain of A(r) ? In other words, for which values of r is A(r) defined?




Part b: Continue to assume that the height of your cylinder is 8 inches. Write the radius r as a function of A. This is the inverse function to A(r) , i. E. , to turn A as a function of r into r as a function of A.




r(A)=

Preview Change entry mode

Hints:


To calculate an inverse function, you need to solve for r. Here, you would start with A=2πr2+16πr. This equation is the same as 2πr2+16πr−A=0 which is a quadratic equation in the variable r , and you can solve that using the quadratic formula. You will want to keep A as a variable when you plug the values into the quadratic formula.

If you want to type in 3π+1x+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.



Part c: If the surface area is 100 square inches, then what is the radius r ? In other words, evaluate r(100). Round your answer to 2 decimal places.


Hint: To compute a numeric square root such as 17. 3−−−−√ , you could


Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17. 3)

Use a browser to connect to the Internet and type in sqrt(17. 3) into a search field

Use a calculator



The radius is

inches if the surface area is 100 square inch

a) We would expect approximately 0.2325 × 200 = 46.5 vehicles

to fail in their first 2 years. Since we cannot have a fraction of a vehicle

failing, we would expect around 46 or 47 vehicles to fail in their first 2

years.

b) The approximate probability that 50 or more vehicles fail in

the first 2 years is 0.0004.

c) The approximate probability that no more than 10 of the remaining

vehicles fail in their first 2 years, given that 30 have already failed, is 0.0002.

a) The average lifespan of the vehicle is 8 years, and it follows an

exponential distribution, which has a probability density function of

\(f(x) = (1/θ) \times e^(-x/θ)\),

where θ is the mean of the distribution. Thus, θ = 8.

The probability that a vehicle fails in the first 2 years can be found by

integrating the exponential probability density function from 0 to 2:

P(X ≤ 2) = ∫[0,2] f(x) dx = ∫[0,2] (1/8) × e^(-x/8) dx

Using a calculator or a table of integrals, we can find this probability to

be approximately 0.2325.

b) The number of vehicles that fail in the first 2 years follows a Poisson

distribution with parameter λ = 200 × P(X ≤ 2) = 200 × 0.2325 = 46.5.

The probability that 50 or more vehicles fail in the first 2 years can be

found using the Poisson distribution with parameter λ = 46.5:

P(X ≥ 50) = 1 - P(X < 50)

Using a Poisson distribution table or a calculator, we can find that P(X <

50) is approximately 0.9996.

Thus, P(X ≥ 50) = 1 - 0.9996 = 0.0004 (approximately).

c) Given that 30 vehicles have already failed in under 2 years, we need

to find the probability that no more than 10 of the remaining 170 vehicles

fail in their first 2 years.

The number of vehicles that fail in the first 2 years follows a Poisson

distribution with parameter λ = 170 × P(X ≤ 2) = 170 × 0.2325 = 39.525

(rounded to 40).

Thus, we need to find P(Y ≤ 10), where Y is a Poisson random variable

with parameter λ = 40.

Using a Poisson distribution table or a calculator, we can find that P(Y ≤

10) is approximately 0.0002.

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The solution that we have here is a combination question not a permutation.

You can order pizza with:  1, 2, 3, 4 toppings for $10.

The ways to do the ordering are

In total there would be  3060+816+153+18=4047 ways of ordering for the pizza.

3. Given 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 and there are no restrictions, we would have

2¹⁸ ways of ordering = 262144 ways

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The F-ratio is a measure used in statistical tests, specifically in ANOVA (Analysis of Variance) to test for differences between means of multiple groups.

a) On average, what value is expected for the F-ratio if the null hypothesis is true?

The answer is a. 1. If the null hypothesis is true, it means that there is no significant difference between the means of the groups being compared. Under this assumption, the F-ratio is expected to have a value close to 1, as the variance between the groups is not significantly different from the variance within the groups.

b) On average, what value is expected for the F-ratio if the null hypothesis is false?

The answer is d. Much greater than 1.00. If the null hypothesis is false, it means that there is a significant difference between the means of the groups being compared. Under this assumption, the F-ratio is expected to have a value much greater than 1, as the variance between the groups is significantly larger than the variance within the groups.

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Answer:

c = $130

Step-by-step explanation:

Given:

c = 100 + 0.30m

Where,

c = cost of renting a car (in dollars)

m = number of miles driven (in miles)

If m = 100 miles

c = 100 + 0.30m

= 100 + 0.30(100)

= 100 + 30

= 130

c = $130

Answer:

34.

Step-by-step explanation:

All angles of a triangle combined equal 180, so if 1 angle measures 146, subtract 146 from 180. 180-146=34

Therefore, the solution of the problem of the function ƒ"(2) come out to be 200.

For some time now, you've been experimenting with equations of the "y=" variety. You've also noticed that the "pleasant" equations are the ones you can solve for "y=" and then input into your graphing calculator, such as straight lines as opposed to ellipses. They are functions, these "y=" equations.

Here,

Given ƒ(2) = 10

and_ƒ'(x) = \(x^{2}\)ƒ(x)

thus we differentiate  it with respect to x

then ƒ'(2) = 22ƒ(2) = 4×10=40

then we again differentiate it with respect to x

ƒ"(x) = \(x^{2}\)ƒ'(x)+2xf(x)

ƒ"(2) = 22ƒ (2)+2×2ƒ(2)=4×40+4x10=160+40

ƒ"(2) = 200

Therefore, the solution of the problem of the function ƒ"(2) come out to be 200.

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Answer:

It's 120 different ways I think

Step-by-step explanation:

The mean μ=9 is the setting so that an 8 ounce cup will overflow when only 0.5% of the time.

A Z-score indicates how far a given value is from a standard deviation. A Z-score (standard value) is the number of standard deviations that a particular data point is above or below the mean. Standard deviation essentially reflects the amount of variability within a given data set.

The average is calculated as: From the Z-score formula:

z=(x-μ)/σ

Z-score associated with 0.5% is 0

(8μ)/0.4=0

Solving for x gives:

μ=9

For μ=9, an intermediate setting such that the 8 ounce cup overflows 0.5% of the time.

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2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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Answer:

Step-by-step explanation:

Answer:

Option (A)

Step-by-step explanation:

Option A

Each small segment on the number line measure (0.5) unit.

Red point on the number line is 5 small segment distant from center 0.

So, the position of the point = 0.5 × 5 = 2.5

Since, the point is on the negative side position will be → -2.5

Option B

Position of the point = 0.5 ×3 = 1.5

Option C

Position of the point = 0.5 × 1 = -0.5 (negative sign shows the position of the point on the negative side of the number line)

Option D

Position of the point = 5 × 0.5 = 2.5

Answer the answer is A

Step-by-step explanation:

what do you need answered the opp length?

Answer:

6^2-3^2=36-9=27

squareroot of 27= 3\(\sqrt{3}\)

Step-by-step explanation:

Answer:

A quadratic function has the formula y equals a x squared right and once you have a square.

Answer:

It's actually worth 15 points

Answer:

She should of used quotient rule since the beginning but if not its step 2

Step-by-step explanation:

The required order for the three according to the turn of the audition is Heather, Jen, and bob.

Given that,
Jen, Heather, and Bob are auditioning for the same role. Jen auditions 10 minutes before four, Heather auditions 30 minutes before Jen, and Bob auditions 5 minutes before four. Order the three by who will audition first.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let's order the timeline,

Jen's audition was 10 minutes before the 4, so the time is 3:50
Heather's audition was 30 minutes before so the time would be 3:20
Bob's audition was 5 minutes before the 4 so the time would be 3:55
So from the above calculation. the order of the audition is Heather, Jen, and bob.

Thus, the required order for the three according to the turn of the audition is Heather, Jen, and bob.

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Let the total number of goats that McDonald had be x. After evenly dividing them between Lilly and Hawk, each of them would have received x/2 goats. However, Lilly lost 35 goats, so she was left with (x/2 - 35) goats. Similarly, Hawk lost 40 goats and was left with (x/2 - 40) goats.

When Lilly sold each goat for $80, she earned (x/2 - 35) * $80 = 80x/2 - 35*80 = 40x - 2800 dollars. When Hawk sold each goat for $60, he earned (x/2 - 40) * $60 = 60x/2 - 40*60 = 30x - 2400 dollars.

Given that Lilly earned $1100 more than Hawk, we can set up the equation:

40x - 2800 = 30x - 2400 + 1100

Solving for x, we get x = 400. Therefore, McDonald had a total of 400 goats.

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Answer:

The area of the trapezoid:

A = (base1 + base2) x height/2

  = (6 + 12) x 8/2

  = 18 x 4

  = 72

Hope this helps!

:)

Answer:

The answer is 0.55

Step-by-step explanation:

Because 55% = \(\frac{55}{100}\) = 0.55

If a between-subjects design uses random assignment, the design will be called an independent groups design.

This means that participants are randomly assigned to either the experimental or control group, ensuring that the groups are equivalent at the start of the study. This type of design allows for a comparison of the effects of the independent variable on the dependent variable between the groups. I

t is important to note that an independent groups design is different from a matched groups design, in which participants are paired based on certain characteristics before being assigned to different groups. The use of random assignment in an independent groups design helps to control for extraneous variables and increase the internal validity of the study.

If a between-subjects design uses random assignment, the design will be called a(n) c. independent groups design. This design involves assigning participants to different experimental groups or conditions using random allocation. This ensures that each participant has an equal chance of being assigned to any group, reducing potential confounds and increasing the validity of the results. The independent groups design allows for comparison between the groups and the examination of the effects of the independent variable on the dependent variable.

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The angle of elevation from where Jack is standing to the top of the stairs is approximately 26.6 degrees.

To determine the angle of elevation, we can use trigonometry. The tangent function relates the angle of elevation to the ratio of the height opposite the angle (2 feet) to the distance adjacent to the angle (4 feet). In this case, we want to find the angle, so we can rearrange the equation as follows:

\(tan(angle) = height / distance\)

Plugging in the values, we have:

\(tan(angle) = 2 feet / 4 feet\)

Simplifying, we get:

\(tan(angle) = 0.5\)

To find the angle, we need to take the inverse tangent (arctan) of both sides of the equation:

\(angle = arctan(0.5)\)

Using a calculator, we find that the angle is approximately 26.6 degrees.

Therefore, the angle of elevation from where Jack is standing to the top of the stairs is approximately 26.6 degrees.

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Volume of a figure is measure of the space it occupies. The volume of the larger rectangular prism is given as: Option C: 1620 cm³

If a rectangular prism has dimensions a unit, b unit, and c units, then its volume is given as

\(V = a \times b \times c \: \rm unit^3\)

They are scaled. It means, if two figures are similar, then we can get one figure from another by multiplying some constant value(same for one pair of similar figure) to its dimensions.

For example,

if for given case, one rectangular prism has got dimensions a, b, and c centimetres, then

the second rectangular prism, which is similar, let the scale factor is 'd',t then second prism's dimensions will be a x d units, b x d units, and  c x d units.

For first prism(smaller), its one side is given to be 5 cm, let its other two sides be 'b' cm, and 'c' cm, then,

\(60 \: \rm cm^3 = 5\times b\times c \\\\b\times c = \dfrac{60}{5} = 12\)

Now, the larger prism has 15 cm corresponding side, thus, scale factor was 3 (since 15 is 3 times 5).

Thus, its dimensions would be 15, 3 x b, 3 x c

Thus, its volume would be

\(15 \times 3 \times b \times 3 \times c = 135 \times b\times c = 135 \times 12 = 1620 \: \rm cm^3\)

Thus,

The volume of the larger rectangular prism is given as: Option C: 1620 cm³

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Answer:

I can confirm that the answer is 1620 because I just finished my test

Step-by-step explanation:

Social scientists gather data from samples instead of populations because c. populations are often too large to test.

Social scientists often cannot test an entire population due to its size, so they gather data from a smaller group or sample that is representative of the larger population. This allows them to make inferences about the larger population based on the data collected from the sample. The sample size must be large enough to accurately represent the population, but it is not necessarily larger or more complete than the population itself. Trustworthiness, meaning, and interest are subjective and do not necessarily determine why social scientists choose to gather data from samples.

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The point of concurrency which is not always inside a triangle is circumcenter and orthocenter.

We are given that;

The four options

Now,

A point of concurrency is a single point shared by three or more lines1. In a triangle, there are four points of concurrency that are associated with different types of line segments: centroid, incenter, circumcenter and orthocenter.

The centroid is the point of concurrency of the medians of a triangle, which are the line segments that connect the midpoints of the sides to the opposite vertices. The centroid is always inside the triangle.

The incenter is the point of concurrency of the angle bisectors of the triangle, which are the line segments that divide the angles into two equal parts. The incenter is also always inside the triangle.

The circumcenter is the point of concurrency of the perpendicular bisectors of the sides of the triangle, which are the line segments that are perpendicular to the sides and pass through their midpoints.

The circumcenter can be inside or outside the triangle, depending on the type of triangle. For an acute triangle, it is inside; for a right triangle, it is at the midpoint of the hypotenuse; for an obtuse triangle, it is outside

Therefore, by triangle the answer will be circumcenter and orthocenter.

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Answer:

Fourteen fourteen fourteenth fourteenth fourteenth fourteenth

Therefore, the slope of the tangent line to the graph of the polar equation r = cos(θ/3) at the point specified by θ = π is -sqrt(3)/6.

To find the slope of the tangent line to the graph of the polar equation r = cos(θ/3) at the point specified by θ = π, we need to find the derivative of r with respect to θ and then evaluate it at θ = π.

Using the chain rule, we have:

dr/dθ = dr/d(u) * d(u)/dθ, where u = θ/3

dr/dθ = -sin(u)/3

Substituting u = θ/3, we get:

dr/dθ = -sin(θ/3)/3

To find the slope of the tangent line at θ = π, we evaluate dr/dθ at θ = π:

dr/dθ = -sin(π/3)/3 = -sqrt(3)/6

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Answer:

y=1/-4x+4

Step-by-step explanation:

hey

Step-by-step explanation:

Slope (x) is rise/run. From one intersecting point to the next, we find it is moving 4 y down and 1 x over. Using this we conclude the slope is -4/1x (or -4x)

The second number in the system is b, or y-intercept. The line intercepts at 4y. If we combine these together, the outcome is y = -4x + 4

The best way is to use the Ratio Test to see that the series = ∑∞ₙ₋₁ n/5ⁿ converges.

In mathematics, convergence definition is the property (some described by myriad series and functions) that it approaches its limit more and more distinctly as the arguments (variables) of the function increase or decrease, or as the number of terms in the series increases.

For example, the function y = 1/x converges to zero as x increases. Even in this case, the final value of x doesn't affect the value of y to actually be zero, and the marginal value of y is zero, since y can be made arbitrarily small by choosing a large enough "x". The line y = 0 (x-axis) is known as the asymptote of the function.

According to the Question:

Let aₙ= n/5ⁿ. If  lim(n→∞)

|an+1|/ |an| <1, the Ratio Test will imply that  

∑∞ₙ₋₁ aₙ = ∑∞ₙ₋₁ n/5ⁿ converges.

Now,

aₙ₊₁ = n + 1/ 5ⁿ⁺¹

    = n + 1 /5.5ⁿ.

Therefore,

since these terms are positive,

    |aₙ₊₁|/|aₙ| = n + 1 /5⋅5ⁿ

⇒ n +1/ 5ⁿ → 1/5 as n→∞

Hence,

∑∞ₙ aₙ = ∑∞ₙ₋₁ n/5ⁿ converges.

Full Question:

How do you test the series (n/5ⁿ ) from n = 1 to infinity for convergence? Determine the values of all positive, for which the series. Determine the values of all positive k for which the series. Express your answer in interval notation will converge. Express your answer in interval notation.

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Answer:

54°

Step-by-step explanation:

∠A = 2x + 10, ∠C = 3x - 14

∠E + 266 = 360 (sum of angles around a point)

∠E = 360 - 266

∠E = 94°

AB is parallel to line BD. Lets draw a line cuts line AB and line BD to form ∠B and ∠D. Hence:

∠B + ∠D = 180° (sum of interior angles on the same side)

∠A + ∠B + ∠C + ∠D + ∠E = 540° (sum of angles in a pentagon)

2x + 10 + 3x - 14 + 94 + 180 = 540

5x + 270 = 540

5x = 540 - 270

5x = 270

x = 54°