9. [-/2 points) DETAILS LARCALC11 3.7.030. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 141 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
Radius = ___in
Length = ___in

Answer:

24

Step-by-step explanation:

Answer:

Angie is thinking of the number 24.

Explanation:

24 can be divided into 8 three times & can be divided by 12 only two times.

Answer: we would need 7 bags of fertilizer to cover the area of the triangle.

Step-by-step explanation:

To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle can be found by taking the square root of the semi-perimeter multiplied by the difference of the semi-perimeter and each side length.

The semi-perimeter of the triangle is (2.1+1.8+2.7)/2 = 2.7

The area of the triangle is sqrt(2.7*(2.7-2.1)(2.7-1.8)(2.7-2.7)) = sqrt(2.70.60.9*0) = 1.35

Each bag of fertilizer covers 0.2 square miles, so we need to divide the area of the triangle by the area covered by each bag to find how many bags are needed: 1.35 / 0.2 = 6.75

Rounding up to the nearest whole number, we would need 7 bags of fertilizer to cover the area of the triangle.

Answer:

She earned $288 this week

Step-by-step explanation:

x = 12

Work = 2(12) + 8

24 + 8 = 32 hours

Earned = (12) - 3 = 9 per hour

32 × 9 = $288

I hope this helps!

To prove the congruence between two triangles there are several postulates, that can be applied depending on the congruent parts of the triangles.

The postulates are:

SAS (Side-Angle-Side): This postulate states that if two triangles have two corresponding sides congruent and one corresponding angle congruent, we can conclude that those triangles are completely congruent.

ASA (Angle-Side-Angle): This postulate states that if two triangles have two corresponding angles congruent and one corresponding side congruent, then those triangles are congruent.

SSS (Side-Side-Side): This postulate states that if two triangles have all three corresponding sides congruent, then triangles are congruent.

AAS (Angle-Angle-Side): If two pairs of corresponding angles are congruent and one pair of corresponding sides is congruent, then both triangle are congruent each other.

HL (Hypothenuse-Leg): this postulate is applied when we have right angles. It states that two right triangles are congruent if they have one pair of corresponding leg congruent, and the hypothenuses are also congruent. We could conclude that those right triangles are congruent.

From these postulate, we can demonstrate the congruence between two triangles. Then, from that congruence, we deduct the congruence between each corresponding parts of those triangles. For example, if we demonstrate the congruence by AAS, we deduct that the third angle is also congruent, and the other two sides are also congruent.

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In order for the exponential function and the tangent line to be equivalent at a certain point, their function values and their first derivatives must be equal at that point.

At a given point, if the function values of an exponential function and its tangent line are equal, it means that they have the same value and slope at that point.

This requires that their first derivatives at that point are equal. The first derivative of an exponential function is also an exponential function, so the derivative of the tangent line must also be an exponential function with the same slope as the original function.

Therefore, the two functions must have the same first derivative at that point. This condition is necessary for the two functions to be equivalent at that point.

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Answer:

185

Step-by-step explanation:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,2021.22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40

I give up

The 185th digit in the pattern is 5.

It is a sequence where the difference between each consecutive term is the same.

We have,

To find the 185th digit in the pattern, we can first calculate the total number of digits in the pattern up to and including the 16th number.

We can do this by noticing that the first nine numbers each have one digit, the next 90 numbers each have two digits, and the final 7 numbers each have three digits.

So, the total number of digits in the pattern is:

9 x 1 + 90 x 2 + 7 x 3

= 9 + 180 + 21

= 210

Since 210 is greater than 185, we know that the 185th digit must be one of the first 16 numbers.

To figure out which number it is, we can subtract the total number of digits in the first 15 numbers from 185, which gives us:

185 - (9 x 1 + 90 x 2 + 6 x 3)

= 185 - (9 + 180 + 18)

= 185 - 207

= -22

Since the result is negative, we know that the 185th digit must be the 3rd digit from the end of the 15th number, which is 1 5.

Therefore,

The 185th digit in the pattern is 5.

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Hello !

Answer:

\(\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Step-by-step explanation:

To find the volume of a cone with the radius of its base and its height, we will apply the following formula:

\( \sf V{cone} = \dfrac{\pi \times r^2 \times h}{3} \)

Where r is the radius of its base and h is its height.

Given:

Let's substitute our values into the formula:

\(\sf V{cone} = \dfrac{\pi (10)^2(23)}{3} = \dfrac{2300\pi}{3} \ \ \\\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Have a nice day ;)

The percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

We are given that:

Total moment of inertia of moving parts = I = 1 kgm²

Moment of inertia of air-screw = I = 18 kgm²

Outer diameter of hollow shaft = D₀ = 80 mm

Inner diameter of hollow shaft = Dᵢ = 35 mm

Length of hollow shaft = L = 0.30 m

Stiffness of the crank-throw = K = 2.5 × 10⁴ Nm/rad

Shear modulus of elasticity = G = 83000 N/mm²

We need to calculate the natural frequency of torsional vibration of the custen.

The formula for natural frequency of torsional vibration is: f = (1/2π) [(K/L) (J/GD)]^(1/2)

Where, J = Polar moment of inertia

J = (π/32) (D₀⁴ - Dᵢ⁴)

The formula for equivalent length of hollow shaft is given by:

q₁ = q₁₁ + q₁₂

Where, q₁₁ = (π/32) (D₀⁴ - Dᵢ⁴) / L₁q₁₂ = (π/64) (D₀⁴ - Dᵢ⁴) / L₂

L₁ = length of outer diameter

L₂ = length of inner diameter

For the given shaft, L₁ + L₂ = L

Let L₁ = L₀D₀ = D = 80 mm

Dᵢ = d = 35 mm

So, L₂ = L - L₁= 0.3 - L₀...(1)

For the given crank-throw, q₁ = (π/32) (D⁴ - d⁴) / L, where D = 80 mm and d = 80 mm

Hence, q₁ = (π/32) (80⁴ - 35⁴) / L

Therefore, q₁ = (π/32) (80⁴ - 35⁴) / L₀...(2)

From the formula for natural frequency of torsional vibration, f = (1/2π) [(K/L) (J/GD)]^(1/2)

Substituting the values of K, J, G, D and L from above, f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) ((π/32) (80⁴ - 35⁴) / (83000 N/mm² (80 mm)³))]^(1/2)f = (1/2π) [(2.5 × 10⁴ Nm/rad) / (L₀) (18.12)]^(1/2)f = 25.7 / L₀^(1/2)...(3)

Now, if we assume that the air-screw mass is infinite, then the moment of inertia of the air-screw is infinite.

Therefore, the formula for natural frequency of torsional vibration in this case is:

f = (1/2π) [(K/L) (J/GD)]^(1/2)Substituting I = ∞ in the above formula, we get:

f = (1/2π) [(K/L) (J/GD + J/∞)]^(1/2)f = (1/2π) [(K/L) (J/GD)]^(1/2)f = 25.7 / L₀^(1/2)

So, in this case also the frequency is the same.

Therefore, the percentage change in frequency is 0%.Hence, the natural frequency of torsional vibration of the custen is given by f = 25.7 / L₀^(1/2) and the percentage change in frequency is 0%.

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Answer:

x=10

Step-by-step explanation:

If we subtract 2 from 52 we get 50 and ten mutiplys into 50.

The statement " The random device method involves using an apparatus or a procedure to ensure that every member of the population has the same chance of being selected into the sample" is true

The random device method is defined as the method used to choose one member from the population. The random device method is also called the random sampling method. It is also allows the the randomization of sample selection from the population

The selection of member is fully random. So the chances of the being selected will be same for all the members in the population

Therefore, the given statement is true

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Diamonds are incorporated in solidified magma called kimberlite, which originates deep within the Earth.

Kimberlite is a volcanic rock formed in the Earth's mantle and brought to the surface through volcanic eruptions. The high pressure and temperature conditions in the mantle allow for the formation of diamonds from carbon atoms. When kimberlite eruptions occur, they transport diamonds and other mantle-derived materials to the Earth's surface, where they eventually cool and solidify.

The discovery of diamonds in kimberlite pipes has played a significant role in the development of the diamond mining industry. These pipes serve as primary sources for diamond extraction and are found in various locations around the world, including South Africa, Russia, and Canada. The study of kimberlites also provides valuable information about the Earth's mantle composition and its geodynamic processes. Overall, the relationship between diamonds and kimberlite is an essential aspect of both the gemstone industry and the study of the Earth's interior.

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Answer:

The profit function P(x) is defined as the difference between the revenue function R(x) and the cost function C(x): P(x) = R(x) - C(x). Substituting the given functions for R(x) and C(x), we get:

P(x) = (-31.72x^2 + 2030x) - (-126.96x + 26391) = -31.72x^2 + 2156.96x - 26391

To find the maximum profit, we need to find the vertex of this quadratic function. The x-coordinate of the vertex is given by the formula x = -b/(2a), where a = -31.72 and b = 2156.96. Substituting these values into the formula, we get:

x = -2156.96/(2 * (-31.72)) ≈ 34

Substituting this value of x into the profit function, we find that the maximum profit is:

P(34) = -31.72(34)^2 + 2156.96(34) - 26391 ≈ $4,665

The selling price of the dog food is given by the revenue function divided by x: R(x)/x = (-31.72x^2 + 2030x)/x = -31.72x + 2030. Substituting x = 34 into this equation, we find that the selling price of the dog food should be set to:

-31.72(34) + 2030 ≈ $92

So, the maximum profit of $4,665 can be made when the selling price of the dog food is set to $92 per bag.

Answer:

the height of nick is 1.46

Step-by-step explanation:

because to change cm into m we need to divide it by 100so 18/100is 0.18

and total height of Peter is 1.64 so if we -the 0.18then we can get nick's height

Answer:

1.46

Step-by-step explanation:

1.64 to cm is 164

164-18 = 146

146 to meters is 1.46

This leads to a contradiction, proving that the equation has no solutions.

To prove that the equation\(x^4 + 4y = z^2\) has no solutions, let's consider the reduced case where x > 0, y > 0, z > 0, (x, y) = 1, and x is odd.

Assume there exists a solution to the equation. Since x is odd, we can write it as x = 2k + 1 for some integer k. Substituting this into the equation, we have\((2k + 1)^4 + 4y = z^2.\)

Expanding the left side, we get\(16k^4 + 32k^3 + 24k^2 + 8k + 1 + 4y = z^2.\)

Rearranging, we have\(4(4k^4 + 8k^3 + 6k^2 + 2k + y) = z^2 - 1.\)

Since\(z^2 - 1\) is odd, the left side must also be odd. However, \(4k^4 + 8k^3 + 6k^2 + 2k + y\) is even since it is divisible by 2. This leads to a contradiction, proving that the equation has no solutions.

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Answer: \(x=\Large\boxed{\frac{m}{y-z} }\)

Step-by-step explanation:

Given expression

\(z=y-\dfrac{m}{x}\)

Subtract [ y ] on both sides

\(z-y=y-\dfrac{m}{x} -y\)

\(z-y=-\dfrac{m}{x}\)

Multiply [ -x ] on both sides

\((-x)(z-y)=(-x)(-\dfrac{m}{x} )\)

\((x)(-1)(z-y)=m\)

\((x)(y-z)=m\)

Divide [ y - z ] on both sides

\((x)(y-z)\div(y-z)=m\div(y-z)\)

\(x=\Large\boxed{\frac{m}{y-z} }\)

Hope this helps!! :)

Please let me know if you have any questions

The property illustrated in Step 4 is the "associative property of addition". which is the correct answer would be an option (A).

The associative property of addition is a rule which states that when adding three or more numbers, we can arrange them in any configuration, and the resultant sum is unaffected by how they are arranged.

(a + b) + c = a + (b + c)

The property illustrated in Step 4 is the "associative property of addition". This property states that the order in which we add numbers does not affect the result of the addition.

In Step 4, we use the associative property to rearrange the terms in the expression so that we can more easily apply the distributive property in the next step.

Hence, the correct answer would be option (A).

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Values of parameters n and p for the binomial distribution with mean 6 and variance 3.6 are n=15 and p=0.4, respectively.

In probability theory and statistics, the binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent and identical trials, where each trial can result in only two possible outcomes, often labeled as "success" and "failure".

The distribution depends on two parameters: the probability of success (p) and the number of trials (n). The probability of getting exactly k successes in n trials can be calculated using the binomial probability mass function.

The binomial distribution has applications in various fields, including quality control, genetics, and finance, among others.

We know that for a binomial distribution, the mean and variance are given by:

Mean = np

Variance = np(1-p)

Substituting the given values, we have:

Mean = 6

Variance = 3.6

Thus, we can write two equations:

6 = np

3.6 = np(1-p)

We can solve for n and p by substituting the first equation into the second equation:

3.6 = (6/p) * (1-p) * p

3.6 = 6 - 6p

6p = 6 - 3.6

p = 0.4

Substituting this value of p into the first equation, we get:

6 = n * 0.4

n = 6 / 0.4

n = 15

Therefore, the values of the parameters n and p are n = 15 and p = 0.4, respectively.

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Step-by-step explanation:

the patern (3n - 1) is incorrect,

the correct pattern should be

Tn = n² + 1

The expressions for (r-s) (x) and (r+s)(x) can be written as:

(r-s) (x) = x + 4

(r+s)(x) = 9x - 4

(r+s)(4) = 32

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Since r(x) = 5x and s(x) = 4x-4

The expressions for (r-s) (x) and (r+s)(x) can be written as follow:

(r-s) (x) = 5x - (4x-4) = x + 4

(r+s)(x) =  5x + (4x-4) = 9x - 4

(r+s) (4) can be evaluated by substituting x = 4 into (r+s)(x). That is:

(r+s)(x) = 9x - 4

(r+s)(4) = 9(4) - 4 = 32

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The Rational numbers ( Q ) include the Natural numbers ( N ):

A natural number is always a rational number.

:)

The probability of scoring a goal exactly 8 times by Jon is given by 0.0234. It is obtained using the prerequisite knowledge of binomial distribution and probability.

What is Binomial Distribution in Probability?

When each trial has a probability of occurring equally likely, then the number of trials or observations is outlined using the binomial distribution. The chance of observing a specific number of successful outcomes in a specific number of trials is determined by using the binomial distribution.

Calculation of the probability of the given event

Total no. of possible outcomes, n = 11

The probability that Jon will kick the ball in the net, p(x) = 0.4

The probability that Alex will kick the ball in the net, q(x) = 0.6

Using Binomial Distribution, we get,

P(x = r) = C(n,r) × (p)r × q(n - r)

where x is the score made by Joe

P(x = 8) = C(11,8) × (0.4)8 × (0.6)3

             = 0.0234

Hence, the probability that Jon will score exactly 8 times is 0.0234.

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Answer:

C. 20

Step-by-step explanation:

Use the Pythagorean theorem which is \(a^{2} +b^{2} =c^{2}\).

\(a^{2}\) and \(b^{2}\) are the sides of the triangle squared, AB and AC. \(c^{2}\) is the hypotenuse (the slanted side of the triangle) or BC.

So, \(12^{2} + 16^{2} =400^{2}\). Then you square root 400 to get your answer.

\(\sqrt{400}\) = 20.

20 is your answer.

For an acceleration function in (m/s²), a( t) = t + 4,

a) The velocity of particle at time t is \( v(t) = [ \frac{t²}{2} + 4 t + 5] \) m/s.

b) The distance traveled during the time interval, 0≤t≤10 is equals to 416.66 m.

We have a acceleration function of a moving particle is a( t)= t + 4 --(1)

Initial velocity of particle, v( 0) = 5 m/s². The particle is moving along a line.

a) As we know acceleration is defined as the rate of change of velocity of particle with respect to time, that is \(a = \frac{ dv}{dt}\)

To determine the velocity at time t, we have to use the integration with respect to time t. So, \(v(t) = \int a(t) dt \)

which is an indefinite integral. So, plug the value of acceleration in above formula, \(v(t) = \int ( t + 4) dt \)

\( = [ \frac{t²}{2} + 4 t] + c \)

Using initial velocity v(0) = 5

=> 5 = 0 + c

=> c = 5

So, velocity is \( v(t) = [ \frac{t²}{2} + 4 t + 5] \) m/s².

b) Now, as we know distance is always positive. Velocity is defined as the rate of change of distance with respect to time. So, to determine the position or distance at time t, we have to use the integration . Therefore, distance on interval 0≤t≤10 is

\(d = \int_{0}^{10} v(t)dt \)

\( = \int_{0}^{10} [ \frac{t²}{2} + 4 t + 5] dt \)

\( = [ \frac{t³}{6} + 4 \frac{ t²}{2} + 5t]_{0}^{10} \)

\( = [ \frac{10³}{6} + 4 \frac{ 10²}{2} + 5× 10] \)

= 200 + 50 + 166.66

= 416.66 m

Hence, required value is 416.66 m.

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See the attached picture

Answer:

45

Step-by-step explanation:

(i just highlighting the answer from the other person's paper)

The period of the given trigonometric function is: 20.

The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period.

Sine and cosine functions start repeating the same pattern of y-axis values after every 2(pi). The period is defined as just the distance on the x-axis before the pattern repeats.

Now, looking at the trigonometric graph, we see that the x-interval for which the graph repeats itself is 20

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The curve is y = sqrt{x}.

Replace x in the curve with 1 and then with 4 to find your point.

y = sqrt{1}

y = 1

First point (1, 1).

y = sqrt{4}

y = 2

Second point (4, 2).

Take it from here.

The simplified expression is 2(x-2)(x-1) / (x+1).

To simplify the expression (2x-4)(x-1)/(x-3)(x+1)(x-3), we can cancel out common factors and simplify further.

First, let's cancel out common factors between the numerator and the denominator:

(2x-4)(x-1) / (x-3)(x+1)(x-3)

The numerator (2x-4) can be factored out to 2(x-2), and the denominator (x-3)(x-3) can be written as (x-3)^2:

2(x-2)(x-1) / (x-3)^2(x+1)

Now, we can check for any additional common factors that can be canceled out. The (x-3) term appears in both the numerator and the denominator, so we can cancel it out:

2(x-2)(x-1) / (x-3)(x+1)

After canceling out the common factor (x-3), we are left with:

2(x-2)(x-1) / (x+1)

Therefore, the simplified expression is 2(x-2)(x-1) / (x+1).

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Option B- They are the same​ because, in this​ case, the means and medians are the same values is the correct answer.

It is specified that the means and medians are the same values. This suggests that the histograms of the two distributions have the same central tendency and are not impacted by the probabilities of the x-values. Hence, the means and medians will rise in this situation.

In statistics, the mean and median are measures of central tendency utilized to portray the normal or normal value of a dataset. Whereas they both give profitable data around the dataset, they can in some cases vary depending on the shape and distribution of the information.

Within the given situation, it is expressed that the means and medians are the same values. This suggests that the dataset incorporates a symmetric distribution with no skewness. When the distribution is symmetric, the mean and median will coincide, demonstrating that the information focuses are equally distributed around the centre.

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Answer:

x=15

Step-by-step explanation:

5x+17+36=128

5x+53=128

5x=75

x=15

Answer:

They will need to sell 16 T-shirts to reach their goal

Step-by-step explanation:

Let us solve the question

∵ The school store is selling notebooks for $1.50 and T-shirts for $10.00

∴ The price of each notebook = 1.50 dollars

∴ The price of each T-shirt = 10.00 dollars

∵ They have sold 60 notebooks

∴ The number of notebooks sold = 60

∵ They have a goal of raising $250

∴ The total money they want to earn = 250 dollars

Assume that they will sell x T-shirt to reach their goal

Multiply the no. of notebooks by the price of each and the no. of T-shirts by the price of each, then add the two products and equate the sum by 250

∵ 1.50 (60) + 10.00 (x) = 250

∴ 90 + 10x = 250

→ Subtract 90 from both sides

∵ 90 - 90 + 10x = 250 - 90

∴ 10x = 160

→ Divide both sides by 10 to find x

∴ x = 16

∴ The number of T-shirts = 16

∴ They will need to sell 16 T-shirts to reach their goal