) a mathematical organization is producing a set of commemorative license plates. each plate contains a sequence of five characters chosen from the four letters in aime and the four digits 2007. no character may appear in a sequence more times than it appears among the four letters in aime or the four digits in 2007. a set of plates in which each possible sequence appears exactly once contains n license plates. find n

For the 0.5 mm thickness, the two principal stresses are 66.5 MPa (tension) and 0 MPa (compression), and the maximum shear stress is 33.25 MPa. For the 5 mm thickness, the two principal stresses are 3.5 MPa (tension) and 0 MPa (compression), and the maximum shear stress is 1.75 MPa.

To solve this problem, we can use the formula for the hoop stress in a thin-walled cylinder:
Hoop stress = (pressure x radius) / thickness

(i) For the 0.5 mm thickness:
Radius = (10 mm - 0.5 mm) / 2

= 4.75 mm

Hoop stress = (7 MPa x 4.75 mm) / 0.5 mm

= 66.5 MPa

To find the principal stresses, we can use the following formula:
Principal stress = \(\frac{(\text{hoop stress} + \text{axial stress}) }{2} \pm \sqrt{((\text{hoop stress} - \text{axial stress}) / 2)^2 + \text{shear stress}^2}\)

Since the tube is thin-walled, we can assume that the axial stress is negligible.

Therefore.
Principal stress = \(\frac{(66.5 \ MPa + 0 \ MPa) }{2} \pm \sqrt{((66.5 \ MPa - 0 \ MPa) / 2)^2 + 0^2 \ MPa}\)
Principal stress = 33.25 MPa ± 33.25 MPa
The two principal stresses are 66.5 MPa (tension) and 0 MPa (compression).

The maximum shear stress is equal to half the difference between the two principal stresses, i.e. 33.25 MPa.

(ii) For the 5 mm thickness:

Radius = (10 mm - 5 mm) / 2

= 2.5 mm

Hoop stress = (7 MPa x 2.5 mm) / 5 mm

= 3.5 MPa

Principal stress = \(\frac{(3.5 \ MPa + 0 \ MPa) }{2} \pm \sqrt{((3.5 \ MPa - 0 \ MPa) / 2)^2 + 0^2 \ MPa}\)
Principal stress = 1.75 MPa ± 1.75 MPa
The two principal stresses are 3.5 MPa (tension) and 0 MPa (compression).
The maximum shear stress is equal to half the difference between the two principal stresses, i.e. 1.75 MPa.

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Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

please mark brainiest

Answer:

7. 110

8. 250

9. 280

10. 230

During the winter season, a family sets up a hot chocolate stand near a local ice skating rink. They sell cups of hot chocolate for $1.50 each and typically sell 50 cups per day.

However, due to changes in weather conditions and customer preferences, the family decides to conduct a market experiment by varying the price of hot chocolate to assess the impact on sales volume. The experiment involves increasing the price to $2.00 per cup and monitoring the resulting sales.

By increasing the price of hot chocolate from $1.50 to $2.00 per cup, the family aims to observe how the change in price affects the demand for their product. The experiment helps them understand the price elasticity of demand, which measures the responsiveness of quantity demanded to changes in price. If the increase in price leads to a significant decrease in sales volume, it suggests that the demand for hot chocolate is elastic, meaning consumers are sensitive to price changes. Conversely, if sales remain relatively stable despite the price increase, it indicates that the demand is inelastic, indicating that consumers are less sensitive to price changes. The family can analyze the results of this experiment to make informed pricing decisions and optimize their profitability during the winter season.

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Answer:

4-3 = 1

Step-by-step explanation:

hopefully it will help you anyway

Answer:

180

Step-by-step explanation:

\( sa = 2( \frac{1}{2} )(6)(4) + 10(5 + 5 + 6)\)

\( = 24 + 10(16)\)

= \(24 + 160\)

\(180\)

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

hope it helps...

have a great day! ! !

Answer: total surface area would be 28.3310501 cm2 or 28.3 cm2 rounded to the nearest tenth

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Simplifying the expression, -(4x³+x²) + 2(x³ - 3x²), the simplest form would be: B. -2x³ - 7x².

To simplify the expression, -(4x³+x²) + 2(x³ - 3x²), do the following:

Apply the distributive property to eliminate the parentheses

-4x³ - x² + 2x³ - 6x²

Combine like terms together

-4x³ + 2x³ - 6x² - x²

-2x³ - 7x²

Thus, simplifying the expression, -(4x³+x²) + 2(x³ - 3x²), the simplest form would be: B. -2x³ - 7x².

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Answer:

3 + n = 2n - 5

Step-by-step explanation:

let 'n' equal 'a number'

'more than' implies 'addition', so 3 + n

'is' in math implies 'equals', so 3 + n =

'double the number' means to multiply it by 2

'less than' implies 'subtraction'

So final result is:

3 + n = 2n - 5

Answer:

4116

Step-by-step explanation:

2014

12000÷10=1200 (10%)

1200x3=3600

12000-3600=8400

2015

8400÷10=840

840x3=2520

8400-2520=5880

2016

5880÷10=588

588x3=1764

5880-1764=4116

Vertically compressing the exponential parent function f(x) = 2^x by a factor of 3 means multiplying every function value by 1/3, resulting in a steeper and narrower curve closer to the x-axis.

If we vertically compress the exponential parent function f(x) = 2^x by a factor of 3, it means that every point on the graph of the function will be compressed closer to the x-axis. In other words, the function values will be multiplied by 1/3.

Let's consider a point on the original exponential function, (x, f(x)). After the vertical compression, this point will have the coordinates (x, (1/3)f(x)). For example, if f(x) = 8 for some x, after compression, the corresponding point will be (x, (1/3)(8)) = (x, 8/3).

This vertical compression affects all points on the graph uniformly, resulting in a steeper and narrower curve compared to the original exponential function.

The y-values of the compressed function will be one-third of the y-values of the original function for each x-value. Therefore, the graph will be squeezed vertically, with the y-values closer to the x-axis.

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The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

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Mean of country A is $29600 and median $29000. Mean of country B is $49800 and median is $29000. Country B has greater income inequality. So option B is the correct answer.

Mean of incomes in country A = (9000+ 21000+ 29000 + 39000+ 50000)/5   =  $29600

Median income of country A = (5+1)/2 th term = 3rd term = $29000

Mean to median ratio = 29600/ 26000= 1.02

Mean income of country B = ( 9000+ 21000+ 29000+ 39000+ 151000)/5 = $ 49800

Median income = (n+1)/2 th term = (5+1)/2 = 3rd term = 29000

Mean to median ratio of country B = 49800/29000 = 1.71

Since mean and median are closer to each other, standard deviation is less. The mean to median ratio is greater for country B. So country B has greater income inequality.

If the income inequality has been increasing, then the mean-median ratio will increase, due to the extreme values, mean will increase. So option B is the correct answer.

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Answer:

200 per hour 800 in 4 hours

Step-by-step explanation:

Answer:25

Step-by-step explanation:

100 divided by 4 is 25                                             please mark brainliest.

Factor by grouping.

(2x + 3)(x − 6)

Answer:

(2x-3) (x+6)

Hope this helps :)

15 protrusions were counted by her.

Clearly, there are multiple ways to treat verruca. For this type of patient, we would try a prescription for Drysol to apply topically once daily. In many of these patients, the skin is too moist. In our practice, we write a prescription for physical therapy for ultrasound application to the verruca. There is no guarantee with any treatment for verruca. Vitamin A adjunct treatment is often instituted: approx 7500 IU /day for 3 weeks.

Let no. of protrusions be x

3 * x = -4 * (-x) - 15

3x-4x = -15

x = 15

Therefore 15 protrusions were counted by her.

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Answer:

45/2

Step-by-step explanation:

3x-y/2

3(7)-(-3)/2

21+3/2

42/2+3/2

45/2

Answer:

B 39$

Step-by-step explanation:

\( \large \mathfrak{Solution : }\)

Distance between the places is :

Time taken to cover that distance is :

Average speed of the cyclist will be :

Avg speed = 20 km / h

\(y=-\dfrac 14 x~~....(i)\\\\x+2y = 4~~...(ii)\\\\\text{Substitute}~~ y= -\dfrac 14 x ~~ \text{in equation (ii):}\\ \\ \\x+2\left(-\dfrac 14 x \right) = 4\\\\\implies 4x -2x = 16~~~~;\left[\text{Multiply both sides by 4} \right]\\\\\implies 2x = 16\\\\\implies x =\dfrac{16}2 \\ \\\implies x =8\\\\\text{Substitute x = 8 in equation (i);}\\\\y= -\dfrac 14 \cdot 8 = -2\\\\\text{Hence,}~ (x,y) = (8,-2)\)

Answer:

\(y = - \frac{1 }{4} x \\ \)

\(x + 2y = 4 \\ \)

\(x + 2( - \frac{1}{4} x) = 4 \\ \)

\(x + ( - \frac{2}{4} x) = 4 \\ \)

\(x - \frac{1}{2} x = 4 \\ \)

\( \frac{2x - 1x}{2} = 4 \\ \)

\(2x - x = 8\)

\(x = 8\)

\(x + 2y = 4 \\ \)

\(8 + 2y = 4\)

\(2y = 4 - 8\)

\(2y = - 4\)

\(y = - 2\)

Answer: 48 gallons in 4 hours

Step-by-step explanation:

3 gallons every .4 hours > 12 gallons every 1 hour > 48 gallons every 4 hours

Answer:

(x-2)(x-3)

x(x-3)-2(x-3)

x²-3x-2x+6

x²-5x+6

The product or quotient is: b. 0.91.

Quotient can be defined as what we arrived at or the answer we get  when we divide a numerator by a denominator.

Example of quotient is when we divide 10 which is a numerator by 2 which is the denominator which in turn gives us the answer 5.

Now let find or determine the quotient of 0.6734 divided by 0.74:

Hence,

Quotient=0.6734/0.74

Quotient=0.91

The correct option is B which is 0.91 because when 0.6734 is divided by 0.74 it will gives us 0.91.

Therefore the product or quotient is: b. 0.91.

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Answer:

A≈565.5in²

Step-by-step explanation:

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Answer:

The area of the cylinder is 108. 108 rounded to the nearest ten is 110. I dont understand the one decimal place thing but if 108 would be turned into a decimal the decimal would be 10.8

Step-by-step explanation:

The exponential equation is \(y=ab^x\). Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

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The exponential equation is y = \(ab^{x}\) . Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

The formula for exponential regression is y = \(ab^{x}\) . This refers to the process of arriving at the best exponential curve equation for your dataset. This regression is very similar to linear regression and tries to find the best (straight line) line equation for a data set.

Exponential regression refers to the process of obtaining the best exponential curve equation for a data set.

A model that explains the process of doubling growth.

The exponential equation is y = \(ab^{x}\)

Exponential functions are commonly used in life sciences and are used to represent the specific quantity that you want to model. B. Population size modeled over time. Plots of experimental data are usually plotted with time on the x-axis and quantity on the y-axis.

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Answer:

Slope: -2

Y-intercept: 3.5

Step-by-step explanation:

Let's start solving the expression using the product to sum formulae.

Here's the given expression,

\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]

Using the product-to-sum formula,

\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]

Applying the above formula in the first term,

\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]

Using the product-to-sum formula,

\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]

Applying the above formula in the second term,

\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]

Substituting these expressions back into the original expression,

we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]

Therefore, the given expression can be written in terms of a single trigonometric function as:

\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}

Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.

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Answer:

The answer is -1.5.

Step-by-step explanation:

-3.4 - (-1.9)

-3.4 + 1.9

-1.5