Omar wants to purchase a new bicycle for $134.45 and helmet for $22.55.
If the sales tax rate is 8%, what will be the total amount of sales tax?

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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The Steady-state gain can be found using the formula Kp = lim s->0 G(s).

A. (a) The inverse Laplace transform of the function 8 /s² (s+2) is given by f(t) = 8(t - e^(-2t)).

B. (a) To find the inverse Laplace transform of 8 /s² (s+2), we can use partial fraction decomposition and inverse Laplace transform tables.

First, we express the function in partial fraction form as follows: 8 /s² (s+2) = A/s + B/s² + C/(s+2).

To find the values of A, B, and C, we can equate the coefficients of corresponding powers of s in the numerator and denominator. This leads to the equations A + 2B + 2C = 0, A = 8, and B = -8.

Substituting the values of A and B into the equation A + 2B + 2C = 0, we find C = 4.

Now, we have the partial fraction decomposition as: 8 /s² (s+2) = 8/s - 8/s² + 4/(s+2).

Using inverse Laplace transform tables, we find the inverse Laplace transforms of each term: L⁻¹{8/s} = 8, L⁻¹{8/s²} = 8t, and L⁻¹{4/(s+2)} = 4e^(-2t).

Finally, we combine the inverse Laplace transforms of each term to obtain the inverse Laplace transform of the original function: f(t) = 8(t - e^(-2t)).

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The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer:

m1.m2 = -1

Step-by-step explanation:

In the case of the parallel line, the slope of the two lines is parallel to each other.

\(-3s\textless11s+1\\\\\\\\-3s-11s < 1\\\\\\-14s < 1\\\\\\-s < \frac{1}{14} \\\\s > -\frac{1}{14}\)

===========================

\(\textcopyright ELIZA\)

Therefore, the value of z needed to construct a 90% confidence interval on the population proportion is approximately 1.645 (rounded to two decimal places).

To construct a 90% confidence interval on the population proportion, we need to determine the corresponding z-value for a 90% confidence level.

For a 90% confidence level, we want to find the z-value that leaves 5% in each tail of the standard normal distribution. Since the distribution is symmetric, we need to find the z-value that corresponds to the upper 5% tail.

Looking up the z-value in a standard normal distribution table or using a statistical software, the z-value that corresponds to a 5% upper tail probability is approximately 1.645.

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Answer: 50 miles per hour

Step-by-step explanation:

The average speed of the car will be gotten by using the formula:

= Distance/Time

where,

Distance = 65 miles

Time = 14:48 - 13:30 = 1:18 hours = 1 hour 18 minutes = 1 18/60 = 1.3 hours

Speed = Distance / Time

= 65 miles / 1.3 hours

= 50 miles per hour

An arithmetic sequence is a list of numbers with a definite pattern.

If we take any number and subtract the previous number, the result is the same constant.(common difference)

-4, -40, -400, -4000,

-40-(4)= -40+4 = -36

-400-(-40)= -400+40 = -360

Not arithmetic

-11,-8,-5,-2

-8-(-11) = -8+11 = 3

-5-(-8)= -5+8 = 3

-2-(-5)=-2+5 = 3

Arithmetic

Common difference: d= 3

23, 17, 11, 5,

17-23 = -6

11-17= -6

5-11 = -6

Arithmetic

Common difference: d =-6

The evaluation of obtuse angle ∠AOC is 124°.

Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement: A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.

3x + 94 + x + 30 + 2x - 4 = 180

Sum of angle in a triangle

6x + 120° = 180°

6x = 180° - 120°

6x = 60°

x = 10°

Now, ∠AOC = 3x + 94

3 × 10 + 94

30 + 94

124°

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The length of one side of the garden is 6 meters is the length of fencing around a square garden is 24 m.

A square has four sides of equal length, so to find the length of one side of the garden, we can divide the total length of the fencing by 4.

Given that the length of fencing around the square garden is 24 m, we have:

Length of one side = Total length of fencing / Number of sides

Length of one side = 24 m / 4

Length of one side = 6 m

Therefore, the length of one side of the garden is 6 meters.

The complete question is:-

The length of fencing around a square garden is 24 m . what is the length of one side of the garden?

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The required equation of the line parallel to y = -2 that goes through the point (0,5) is y = 5.

The given line is y = -2, which is a horizontal line passing through y = -2. Any line parallel to this line will also be horizontal and have the same y-coordinate at any point.

Since the line we're looking for passes through the point (0,5), its equation must be of the form y = c, where c is the y-coordinate of the point. Therefore, the equation of the line parallel to y = -2 that goes through the point (0,5) is:

y = 5

Alternatively, we can also see that since the line we're looking for is parallel to y = -2, it will have the same slope as this line, which is 0. Therefore, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line. Substituting m = 0, x1 = 0, and y1 = 5, we get:

y - 5 = 0(x - 0)

Simplifying, we get:

y = 5

So the equation of the line parallel to y = -2 that goes through the point (0,5) is y = 5.

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All you have to do is take $32.10 and then subtract 1.80. So it should look like 32.10 - $1.80. The answer should be 30.30

Karan swam and biked for a total of 1 hour and 45 minutes.

let's say 60=100 for a total of 100 equaling 1 hour.

Therefore, 100+45= 145

Answer:

10/9

Step-by-step explanation:

average rate of change in 0≤x≤9

=(3-(-7))/(9-0)=10/9

Answer:

The solution is 10/9

Step-by-step explanation:

Step 1: identify the right approach:

Given a function g(x) over a period of time, to find the average rate of change of g(x) over this period of time, we divide the change in g(x) by the change in x.

Step 2: Perform the calculation:

As shown in picture,

x = 0 => g(x) = -7

x = 9 => g(x) = 3

=> The change of x over interval [0, 9] is:

x_change = 9 - 0 = 9

=> The change of g(x) over interval [0, 9] is:

g(x)_change = 3 - (-7) = 10

=> The average rate (r) of change of g(x) over interval [0, 9] is:

r = g(x)_change/x_change = 10/9

Hop this helps!

:)

Using a 35-bag sample with a mean of 406.0 grams, a known standard deviation of 25.0 grams, and a level of significance of 0.05, you can perform a one-tailed Z-test to determine whether to reject or fail to reject the null hypothesis.

To test if the potato chip manufacturer's bag filling machine is working correctly at the 411.0-gram setting, we will state the hypotheses using the given terms.

Null Hypothesis (H0): The machine fills bags correctly, with a mean weight of 411.0 grams (µ = 411.0 grams)
Alternative Hypothesis (H1): The machine is underfilling bags, with a mean weight less than 411.0 grams (µ < 411.0 grams)

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Answer:

60.2 is the average

Step-by-step explanation:

add all numbers together to get: 301

divide 301 by 5 because there are 5 numbers total to get: 60.2

Alicia want that 50 % of all people who visited one of the three coffee shops should visit her every week.

Total visitors to the other two coffee shops during one week = 840+1,220 i.e. 2,060

Total visits to Cool Beans should be 50 % of total visits i.e. equal to visits of the other two cafes combined

Visits to Cool Beans should be 2,060

Current Visits =548

Additional visits =2,060-548 i.e. 1,512 visits

Note for better understanding:

same or the demand of coffee will remain same, then the Additional people will be calculated as:

Total number of visits = 584+840+1,220  i.e. 2,608

Target number of visits =50 % of total visits i.e. 1,304 visit

Additional visits = 1,304-548 = 756 visits

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Answer:

If we are assuming that plan A produces a whole gallon then you would need 15 parts white and 6 parts red

Step-by-step explanation:

Answer:

Algebra is the part of mathematics in which letters and other general symbols represent numbers and quantities in formulae and equations. A system of algebra is based on given axioms.

Step-by-step explanation:

For example α+α+α=3α  but α×α×α=α³

or

t=2+1α

when α= 1,2,3

1st term= 3

2nd term=4

3rd term=5

Q. What would be the value of the 5th term?

A. 4th term =6

so 5th term = 7

I hope this is useful and that you give brainliest to me pls

Answer:

Yes

Step-by-step explanation:

1 yard is 3 feet. so 12 yards is 36 by 12*3

Answer:

x = 65

Step-by-step explanation:

Complete question is:

Which is the correct solution?

x = 1.8

x = 2.6

x = 45

x = 65

SOLUTION:

The given equation is : \(\frac{x}{5}-2=11\)

Substituting all the values of 'x' one by one

-> For  x = 1.8  : \(\frac{1.8}{5}-2=11\)

-1.64≠11

-> For x = 2.6 : \(\frac{2.6}{5}-2=11\)

-1.48≠11

-> For x = 45 : \(\frac{45}{5}-2=11\)

7≠11

-> For x = 65 : \(\frac{65}{5}-2=11\)

11=11

Therefore, by substituting x in every equation, x = 65

Answer:

Substitute 7 for a.

Simplify the equation after substituting the value for a.

Verify that a = 7 is correct when the result is a true statement.

Step-by-step explanation:

Here, the given equation is,,

And, after solving it the result is,

a = 7

We can check whether a result is the solution of an equation by substituting the result in the given equation.

If we get a true statement, then the result is the solution of the equation.

Thus, for verifying the solution, steps are as follow,

Step 1 : Substitute 7 ,

-9(7-5) = -18

Step 2 : Simplify the equation after substituting the value of a  

-9(2) = -18    

Step 3 : Verify that a = 7 is correct when the result is a true statement.

-18 = -18      

Answer:

y = 0

Step-by-step explanation:

The output of the following code snippet will be 1, 2, 3, and 4.

The reason is that the while loop runs infinitely until the break statement is executed. The break statement terminates the loop if the value of x is divisible by 5. However, the value of x is incremented at each iteration of the loop before checking the condition. Here is the step-by-step explanation of how this code works:

Step 1: Assign 1 to x.x = 1

Step 2: Start an infinite loop using the while True statement.

Step 3: Check if the value of x is divisible by 5 using the if x % 5 == 0 statement.

Step 4: If the value of x is divisible by 5, terminate the loop using the break statement.

Step 5: Print the value of x to the console using the print(x) statement.

Step 6: Increment the value of x by 1 using the x += 1 statement.

Step 7: Repeat steps 3-6 until the break statement is executed.

Therefore, the output of the code will be: 1 2 3 4.

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Peyton needs to buy at least 45 sets for the restaurant to have enough forks.

Let the number of sets of forks be represented by 'x'. according to the question there are 10 forks in each set.

Since there are currently 287 forks available in the restaurant, and the restaurant needs at least 732 forks.

The inequality used to represent the given scenario is given by:

10x + 287 ≥ 732

10x ≥ 445

x ≥ 44.5

As Peyton cannot buy 44.5 sets of forks so we round it off to 45.

Therefore, he requires 45 sets in total.

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a. After the 1-for-10 reverse split, the number of outstanding shares would be 3,560,880. This is because the reverse split reduces the number of outstanding shares by a factor of 10.

b. To determine the post-split price per share, we first need to calculate the total market capitalization of the corporation after the split. The total market capitalization is the product of the number of outstanding shares and the price per share.

Before the split, the market capitalization was:

35,608,800 shares * $0.41 per share = $14,597,008

After the split, the market capitalization is:

3,560,880 shares * x per share, where x is the post-split price per share.

Since this is a monetary non-event (as shown in part c below), the market capitalization after the split should be the same as the market capitalization before the split:

$14,597,008 = 3,560,880 shares * x per share

Solving for x, we get:

x = $4.10 per share

Therefore, the post-split price per share is $4.10.

c. This split was a monetary non-event for the corporation because it did not change the total market capitalization of the corporation. The market capitalization before the split was $14,597,008, and after the split, the market capitalization was still $14,597,008. This means that the split did not change the value of the corporation. Instead, it simply consolidated the number of outstanding shares and increased the price per share by a factor of 10.  The overall value of the company remained the same.

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a. After the 1-for-10 reverse split, the number of outstanding shares would be 3,560,880.

b. the post-split price per share is $4.10.

c. This split was a monetary non-event for the corporation because it did not change the total market capitalization of the corporation.

How to find splits?

a. After the 1-for-10 reverse split, the number of outstanding shares would be 3,560,880. This is because the reverse split reduces the number of outstanding shares by a factor of 10.

b. To determine the post-split price per share, we first need to calculate the total market capitalization of the corporation after the split. The total market capitalization is the product of the number of outstanding shares and the price per share.

Before the split, the market capitalization was:

35,608,800 shares * $0.41 per share = $14,597,008

After the split, the market capitalization is:

3,560,880 shares * x per share, where x is the post-split price per share.

Since this is a monetary non-event (as shown in part c below), the market capitalization after the split should be the same as the market capitalization before the split:

$14,597,008 = 3,560,880 shares * x per share

Solving for x, we get:

x = $4.10 per share

Therefore, the post-split price per share is $4.10.

c. This split was a monetary non-event for the corporation because it did not change the total market capitalization of the corporation. The market capitalization before the split was $14,597,008, and after the split, the market capitalization was still $14,597,008. This means that the split did not change the value of the corporation. Instead, it simply consolidated the number of outstanding shares and increased the price per share by a factor of 10.  The overall value of the company remained the same.

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Answer:

18 inches cubed

Step-by-step explanation:

to get the volume for something you must multiply it. length × width × hight

so in this case it would be 3×2×3=18 inches cubed

The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432