A cone a radio of 3 cm and volume of 94. 2 cm find. It’s height

The total cost of the cell phone, including sales tax, is $921.55.The total cost of the cell phone, including sales tax, is $921.55.

To calculate the total cost, we need to add the sales tax to the purchase price of the cell phone. The sales tax rate in New Jersey is 7.25% of the purchase price.

Step 1: Calculate the sales tax amount:

Sales tax amount = Purchase price * Sales tax rate

Sales tax amount = $857 * 0.0725

Sales tax amount = $62.18

Step 2: Calculate the total cost:

Total cost = Purchase price + Sales tax amount

Total cost = $857 + $62.18

Total cost = $919.18

Rounding to the nearest two decimals, the total cost of the cell phone is $921.55.

The total cost of the cell phone, including sales tax, is $921.55.

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Answer:

Step-by-step explanation:

the angle of measure 4x + 12 and the angle of measure 64 are Vertically opposite angles then they are equal in measure

therefore

4x + 12 = 64

⇔ 4x = 64 - 12

⇔ 4x = 52

⇔ x = 52/4

⇔ x = 13

Answer:

The answer is C.) y = 2x + 5

The momentum magnitude observed in frame s' is √(15m^2c^4).

In special relativity, the relationship between energy (E) and momentum (p) is given by the equation:

E^2 = (pc)^2 + (mc^2)^2

where m is the rest mass of the particle, c is the speed of light, and p is the momentum of the particle.

In frame of reference s, the energy of the electron is given as 4mc^2. Plugging this into the equation, we have:

(4mc^2)^2 = (pc)^2 + (mc^2)^2

Simplifying this equation, we get:

16m^2c^4 = p^2c^2 + m^2c^4

Canceling out the common terms, we have:

15m^2c^4 = p^2c^2

Taking the square root of both sides, we get:

pc = √(15m^2c^4)

The momentum magnitude observed in frame s', denoted as p', is related to the momentum in frame s (p) by the relativistic velocity addition formula:

p' = γ(p - βE/c)

where γ is the Lorentz factor and β is the velocity of frame s' relative to frame s. Since the electron is moving along the x-axis, the velocity β is zero, and the Lorentz factor γ is equal to 1.

Therefore, the momentum magnitude observed in frame s' is the same as the momentum magnitude in frame s:

p' = p

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Step-by-step explanation:

Aight, so the same intercept

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

m=½

\(y = \frac{1}{2} x + b = = = > \\ now \: let \: us \: replace \: the \: point \\ 1 = \frac{1}{2} ( - 3) + b = = = > \\ \frac{5}{2} = b\)

soooo

\(y = \frac{1}{2} x + \frac{5}{2} \)

3c² ·(g(b)-g(a)) = g'(c)(b³-a³) by the mean value theorem they are equal.

The Mean Value Theorem, if a function g(x) is continuous on the interval [a, b] and differentiable on the interval (a, b), then there exists a point c ∈ (a, b) such that:

g'(c) = (g(b) - g(a))/(b - a)

Now, we can rearrange the equation:

3c²·(g(b) - g(a)) = g'(c)(b³ - a³)

To prove the existence of c, we need to show that there exists a value c ∈ (a, b) that satisfies the above equation.

Let's define a new function h(x) = g(x) - [(g(b) - g(a))/(b - a)](x³ - a³).

We can see that h(x) is continuous on the interval [a, b] and differentiable on the interval (a, b).

Now, let's evaluate h(a) and h(b):

h(a) = g(a) - [(g(b) - g(a))/(b - a)](a³ - a³) = g(a) - 0 = g(a)

h(b) = g(b) - [(g(b) - g(a))/(b - a)](b³ - a³) = g(b) - (g(b) - g(a)) = g(a)

Since h(a) = g(a) and h(b) = g(b), we have h(a) = h(b).

By Rolle's Theorem, since h(x) is continuous on [a, b] and differentiable on (a, b), and h(a) = h(b), there exists a point c ∈ (a, b) such that h'(c) = 0.

Taking the derivative of h(x), we have:

h'(x) = g'(x) - 3[(g(b) - g(a))/(b - a)]x²

Setting h'(c) = 0, we get:

0 = g'(c) - 3[(g(b) - g(a))/(b - a)]c²

Rearranging this equation, we obtain:

3c²·(g(b) - g(a)) = g'(c)(b³ - a³)

Therefore, we have shown that there exists c ∈ (a, b) such that:

3c²·(g(b) - g(a)) = g'(c)(b³ - a³)

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Answer:

256

Step-by-step explanation:

According to the rule of exponents: 16 to the power of 2 can be written as 162.

In a multiple regression model, the variance of the error term ε is assumed to be constant or homoscedastic. This means that the variance of the error term remains the same across all values of the independent variables.

The assumption of homoscedasticity is important because it ensures that the errors are not systematically biased towards certain values, which could lead to inaccurate predictions and statistical significance tests. Violations of homoscedasticity can occur when there are outliers, heterogeneity in the sample, or when the relationship between the dependent and independent variables changes across different values of the independent variables. In such cases, alternative regression models such as weighted least squares or robust regression may be used.

In a multiple regression model, the variance of the error term ε is assumed to be constant and equal across all observations. This assumption, known as homoskedasticity, ensures that the model's predictions are reliable and the standard errors of the regression coefficients are accurate. If the variance is not constant, it can lead to heteroskedasticity, which can negatively impact the efficiency of the regression estimates and result in biased standard errors, potentially leading to incorrect inferences about the relationships between variables. Therefore, maintaining the assumption of constant error variance is crucial for a valid multiple regression analysis.

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a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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Answer:

2%

Step-by-step explanation:

Interest = Principal x Rate x Time

200 = 5000(2)·r

200/10000 = r

r = 2/100 which is .02 or 2%

Answer:

$25 per dog

Step-by-step explanation:

$300/12 dogs=price per dog

Answer:

25

Step-by-step explanation:

The next time all three lights will flash at the same time will be in 210 seconds, or 3 minutes and 30 seconds.

To find the time at which all three lights will flash at the same time, we need to find the LCM (Least Common Multiple) of the given times.

Prime factorizing each time, we get:

6 = 2 x 3

15 = 3 x 5

21 = 3 x 7

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers:

2 x 3 x 5 x 7 = 210

Therefore, the next time all three lights will flash at the same time will be in 210 seconds, or 3 minutes and 30 seconds.

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Answer:

Step-by-step explanation:

Given

The length of the side:

Volume of the box:

The volume is between 108 in³ and 256 in³:

As above, the minimum length is 6 in and maximum length 8 in

The given statement: "the statement is not a​ tautology, since it is false for all combinations of truth values of the components" is not a tautology because it is false for all combinations of truth values of the components.

A tautology is a compound statement that is always true, no matter what the truth values of its individual components are. On the other hand, a contradiction is a compound statement that is always false, no matter what the truth values of its individual components are.

The statement "the statement is not a​ tautology, since it is false for all combinations of truth values of the components" does not qualify to be a tautology because it is false for all combinations of truth values of the components.

It is a contradiction. The negation of a contradiction is always a tautology. Therefore, the negation of the given statement will be a tautology. Therefore, the statement "the statement is a​ tautology, since it is true for all combinations of truth values of the components" is the tautology.

The statement "the statement is not a tautology, since there is at least one combination of truth values for its components where the statement is false" is a contradiction as well because it is false for all combinations of truth values of the components. Hence, the correct answer is option A.

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Answer:

The answer is: A

Step-by-step explanation:

Answer:

a) q<0

Step-by-step explanation:

\( \frac{q}{r} < 0 \\ = r \times \frac{q}{r} < 0 \times r \\ = q < 0\)

Answer: 16

Step-by-step explanation:

The given function shows imply that the graph g(x) is shifted two units right and three units up.

Option B is correct.

The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.

From the given information:

Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.

Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.

Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0.  We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.

Combining the two transformations, we have:

Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.

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Answer: 13.05

Step-by-step explanation:

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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The weighted average cost per unit under the perpetual inventory system is $55.76.

To calculate the weighted average cost flow method under the perpetual inventory system, follow these steps:

1. Calculate the total cost of inventory on hand at the beginning of the year: 10,000 units * $75.00 = $750,000.

2. Calculate the cost of goods sold for each sale:
- For the first sale on March 18, the cost of goods sold is 8,000 units * $75.00 = $600,000.
- For the second sale on August 9, the cost of goods sold is 15,000 units * $77.50 = $1,162,500.

3. Calculate the total cost of purchases during the year:
- The purchase on May 2 is 18,000 units * $77.50 = $1,395,000.
- The purchase on October 20 is 7,000 units * $80.25 = $561,750.
- The total cost of purchases is $1,395,000 + $561,750 = $1,956,750.

4. Calculate the total number of units available for sale during the year: 10,000 units + 18,000 units + 7,000 units = 35,000 units.

5. Calculate the weighted average cost per unit: $1,956,750 ÷ 35,000 units = $55.76 per unit.

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Answer:

x = -3

Step-by-step explanation:

\(y\geq -\frac{2}{3} x-3\\ y\leq 3x+8\)

\(-\frac{2}{3} x-3=3x+8\)

Add 2/3 x to both sides:  \(-3=\frac{11}{3}x+8\)

Subtract 8 from both sides: \(-11=\frac{11}{3}x\)

Multiply both sides by 3:  \(-33=11x\)

Divide both sides by 11:  \(x=-3\)

Therefore, point of intersection between both lines is at point (-3, -1)

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.

The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.

The measured distance on the map between Beitbridge and Musina is 1.3 cm.

To find the actual distance, we can set up a proportion using the scale:

1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.

Simplifying the proportion, we have:

1 / 3,000,000 = 1.3 / x.

Cross-multiplying, we get:

x = (1.3 * 3,000,000) / 1.

x = 3,900,000 / 1.

x = 3,900,000 km.

The actual distance between Beitbridge and Musina is 3,900,000 kilometers.

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Answer:y=3x+6

Step-by-step explanation:

Because the slope intercept equation is y=mx+b

The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.

a) The differential equation expressing the quantity Q(t)  of warfarin in the body, at t hours later when a patient who is suffering from Warfarin  is given a pill containing 2.5 mg of Warfarin then,

dQ/dt = -kQ
here Q(0) = 2.5

b) The differential equation the expressing the quantity Q(t)  of warfarin in the body, at t hours later when a patient who is not suffering from Warfarin  is given a pill containing 0.5 mg/hr then,

dQ/dt = -kQ + r
where Q(0) = 0
Here
k = rate constant
r = rate of administration
The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.

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The rate at which Warfarin leaves the body should be proportional to the amount still in the body, not a constant rate of 2.5. So the correct differential equation for part (b) is:

Q' = 0.5 - kQ, where Q(0) = 0

Where k is the proportionality constant for the rate of elimination.

Explanation

(a) Let's denote the rate of elimination as k, where k > 0. Since the elimination rate is proportional to the amount of warfarin, we can write the differential equation as:

Q'(t) = -kQ(t)

Given that the initial condition is a 2.5 mg pill, the initial condition should be:

Q(0) = 2.5

So the differential equation for part (a) is:

Q'(t) = -kQ(t), Q(0) = 2.5

(b) In this case, the patient receives warfarin intravenously at a rate of 0.5 mg/hour. Thus, we should add the rate of administration to our equation:

Q'(t) = 0.5 - kQ(t)

The initial condition is still that the patient has no warfarin in her system:

Q(0) = 0

So the differential equation for part (b) is:

Q'(t) = 0.5 - kQ(t), Q(0) = 0

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We have the following:

solving for x:

The answer is:

Answer:

C

because it looks right

Answer:

1/36

Step-by-step explanation:

On the first cube, there is a 1/6 probability to roll a 1. On the second cube, theres is a 1/6 probability to roll a 6

Multiply the two fractions and it would equal 1/36

There would be a 1/36 probability.

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

Side length of a square game board is  

11.916

inches.

Explanation:

If the area is  

142

∈

2

, as area is square of side length of a square,

Side length is  

√

142

=

11.916

inches.

Step-by-step explanation:

Answer:

13.7 inches

Step-by-step explanation

Area = base*height

(since it's a square, the lengths of all four sides of the board are equal. therefore, we can write the equation above like the following)

Area of square = side length^2

(square root both sides of the equation, and you get the following)

\(\sqrt{Area\\}\) = side length

(now, substitute the info)

\(\sqrt{188\\}\) = x

(solve)

x = 13.7 inches

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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9514 1404 393

Answer:

  D.  3.70 and 3.75

Step-by-step explanation:

Your calculator tells you that √14 ≈ 3.742.

The upper ends of the ranges of choices A, B, and C are all below this value, so the only interval that is applicable is choice D:

  √14 lies between 3.70 and 3.75