Nora was out at a restaurant for dinner when the bill came. Her dinner came to $19. After adding in a tip, before tax, she paid $24.70. Find the percent tip.

The population of each country will become double in 47 years.

Given that,

The population of the Dominican republic is, n = 10.7 million.

The growth rate of the Dominican republic is, p = 1.5 %.

The population of Paraguay is, n' = 6.0 million.

The growth rate of Paraguay is p' = 1.5 %.

The doubling time of population growth depends on the rate of population growth.

Here,

n is the final population and n0 is the initial population and doubling the value in the future, n= 2*n0.

Solving this, we get:

t= ln (2*n0/n0)/(1.5/100) = 47 years.

Thus, we can conclude the population of each country will become double in 47 years.

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The Surface area of the container that is in contact with the lip balm ≈ 30.4 cm³.

A hemisphere is half of a sphere. Thus, the volume of a hemisphere is given as: V = = (2/3)πr³, where r is the radius of the hemisphere.

Surface area of a hemisphere is given as, SA = 2πr²

Given the following:

Volume of hemisphere = 30 cm³

i. Radius (r) of the container = radius of the hemisphere

2πr² = 30

r² = 30/2π

r² = 4.8

r ≈ 2.2 cm

ii. Surface area of the container that is in contact with the lip balm = surface area of hemisphere = 2πr²

Surface area = 2(3.14)(2.2²)

Surface area of the container that is in contact with the lip balm ≈ 30.4 cm³.

In summary:

i. The radius of the container is 2.2 cm

ii. The surface area of the container that is in contact with the lip balm ≈ 30.4 cm³.

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Answer:

¿Qué quieres comer?

Step-by-step explanation:

By Using the Cumulative distributed Function(CDF)m we get:

a) P (x <= 3 ) = 0.36

b) P ( 2.5 <= x <= 3  ) = 0.11

c) P (x > 3.5 ) = 1 - 0.49 = 0.51

d) x = 3.5355

e) f(x) = x / 12.5

f) E(X) = 3.3333

g) Var (X) = 13.8891  , s.d (X) = 3.7268

h) E[h(X)] = 2500

Given:

The cdf is as follows:

F(x) = 0                    x < 0

F(x) = (x^2 / 25)     0 < x < 5

F(x) = 1                   x > 5

Now,

a) Evaluate the CDF given with the limits 0 < x < 3.

So, P (x <= 3 ) = (x^2 / 25) | 0 to 3

P (x <= 3 ) = (3^2 / 25)  - 0

P (x <= 3 ) = 0.36

b) Evaluate the CDF given with the limits 2.5 < x < 3.

So, P ( 2.5 <= x <= 3 ) = (x^2 / 25) | 2.5 to 3

P ( 2.5 <= x <= 3  ) = (3^2 / 25)  - (2.5^2 / 25)

P ( 2.5 <= x <= 3  ) = 0.36 - 0.25 = 0.11

c) Evaluate the CDF given with the limits x > 3.5

So, P (x > 3.5 ) = 1 - P (x <= 3.5 )

     P (x > 3.5 ) = 1 - (3.5^2 / 25)  - 0

    P (x > 3.5 ) = 1 - 0.49 = 0.51

d) The median checkout for the duration that is 50% of the probability:

   So, P( x < a ) = 0.5

         ⇒ (x² / 25) = 0.5

          ⇒ x² = 12.5

          ⇒ x = 3.5355

e) The probability density function can be evaluated by taking the derivative of the cdf as follows:

      pdf f(x) = d(F(x)) / dx = x / 12.5

f) The expected value of X can be evaluated by the following formula from limits - ∞ to +∞:

      E(X) = integral ( x . f(x)).dx          limits: - ∞ to +∞

       E(X) = integral ( x² / 12.5)    

        E(X) = x³ / 37.5                    limits: 0 to 5

        E(X) = 5³ / 37.5 = 3.3333

g) The variance of X can be evaluated by the following formula from limits - ∞ to +∞:

 Var(X) = integral ( x² . f(x)).dx - (E(X))^2          limits: - ∞ to +∞

 Var(X) = integral ( x³ / 12.5).dx - (E(X))^2    

 Var(X) = x⁴/ 50 | - (3.3333)^2                         limits: 0 to 5

 Var(X) = 5⁴/ 50 - (3.3333)^2 = 13.8891

Standard Deviation (s.d) (X) = sqrt (Var(X)) = sqrt (13.8891) = 3.7268

h) Find the expected charge E[h(X)] , where h(X) is given by:

      h(x) = (f(x))^2 = x^2 / 156.25

The expected value of h(X) can be evaluated by the following formula from limits - ∞ to +∞:

E(h(X))) = integral ( x . h(x) ).dx          limits: - ∞ to +∞

E(h(X))) = integral ( x^3 / 156.25)    

E(h(X))) = x^4 / 156.25                      limits: 0 to 25

E(h(X))) = 25^4 / 156.25 = 2500

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The mean of the data is 8.

Given data are,

                    \(8,7,5,9,6,13\)

Mean is computed as divide the sum of all data by total number of data.

Sum of all the data\(=8+7+5+9+6+13=48\)

Number of data\(=6\)

             \(Mean=\frac{48}{6}=8\)

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\((343a)^{3}\) - \((1000b)^{3}\) can be factorised as (343a - 1000b)(343\(a^{2}\) + 1000ab + 1000\(b^{2}\)).

Expression is a mathematical combination of symbol such as number and operators which produce the mathematical result and expression.

(343a - 1000b)(343\(a^{2}\) + 1000ab + 1000\(b^{2}\))

This expression can be factorised as the product of two binomials. The first binomial is (343a - 1000b). This can be seen by subtracting 1000\(b^{3}\) from 343\(a^{3}\), leaving us with 343\(a^{3}\) - 1000\(b^{3}\), which can be written as (343a - 1000b).

The second binomial is (343\(a^{2}\) + 1000ab + 1000\(b^{2}\)). This can be seen by expanding the cube of (343a - 1000b), leaving us with (343\(a^{2}\) - 1000\(b^{2}\) + 2000ab). Rearranging this expression gives us (343\(a^{2}\) + 1000ab + 1000\(b^{2}\))

Therefore, 343\(a^{3}\) - 1000\(b^{3}\) can be factorised as (343a - 1000b)(343\(a^{2}\) + 1000ab + 1000\(b^{2}\)).

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Answer:

Step-by-step explanation:

Answer:false

Step-by-step explanation:

Answer:-1 and -3

Step-by-step explanation: the first numbers of this are always going to be the point slope line.

Las viñetas o numerales en un juego de patio se utilizan para marcar el progreso de un juego o actividad.

Por ejemplo, en un juego de rayuela, cada viñeta representa un paso hacia el objetivo final y los jugadores avanzan saltando sobre las viñetas en un orden determinado.

En otros juegos, las viñetas o numerales se utilizan para llevar un registro de la puntuación de los jugadores o para determinar el orden en que deben realizarse las acciones.

En resumen, las viñetas o numerales son un elemento importante en muchos juegos de patio y pueden ser utilizadas de diversas maneras para marcar el progreso, la puntuación o el orden de las acciones en un juego.

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Answer:

The 6-day SMA for the ten consecutive trading day

= $2.63,  $2.63,  $2.62,  $2.59,  $2.54

Step-by-step explanation:

Determining the 6-day SMA for the given values

using the addition and subtraction methodology

First we will determine the Average closing prices for 1 - 6 days

=  \(\frac{2.65 + 2.63 + 2.70 + 2.63 + 2.5 + 2.65}{6}\)  =  15.76 / 6 =  $2.626 ≈ $2.63

next we have to determine the SMA for days 2 - 7

= 2.63 - \(\frac{2.65}{6} + \frac{2.66}{6}\)  =  \(\frac{15.77}{6}\)  ≈ $2.63

SMA for days 3 - 8

= 2.63 -  \(\frac{2.63}{6} +\frac{2.56}{6} = \frac{15.70}{6}\) ≈  $2.62

SMA for days 4 - 9

= 2.62 - \(\frac{2.70}{6} + \frac{2.52}{6} = \frac{15.52}{6}\)  ≈  $2.59

SMA for days 5 - 10

= 2.59 - \(\frac{2.63}{6} + \frac{2.37}{6} = \frac{15.26}{6}\)  ≈  $2.54

Hence the 6-day SMA for the ten consecutive trading day

= $2.63, $2.63, $2.62, $2.59, $2.54

Answer:

It costs $1.60 for 1lb of potatoes. It costs $11.70 for 7lb of potatoes.

Step-by-step explanation:

price per pound = 12.8 / 8 = $1.60 per pound

1.6 * 7 = cost for 7 pounds

1.6 * 7 = $11.20 for 7 pounds

The probability that a fair coin will show tails exactly 3 times in 7 tosses is approximately 0.273.

The probability of getting tails in a single coin toss is 1/2, and the probability of getting heads is also 1/2 since the coin is fair.

Using the binomial probability formula, the probability of getting exactly 3 tails in 7 tosses can be calculated as:

P(3 tails) = (7 choose 3) * (1/2)^3 * (1/2)^(7-3)

P(3 tails) = (7! / (3! * (7-3)!)) * (1/2)^7

Simplifying the expression, we get:

P(3 tails) = 35 * (1/2)^7

P(3 tails) ≈ 0.273

Therefore, the probability that a fair coin will show tails exactly 3 times in 7 tosses is approximately 0.273, rounded to three significant digits.

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Answer:

Prices of the two stocks A and B become​ same in 42 hours

Step-by-step explanation:

Let t denotes number of hours in which the prices of the two stocks A and B become​ same.

Price of stock A = $15.59

Increase in price per hour = $0.12 t

Price of stock B = $16.34

Decrease in price per hour = $0.11 (t - 3)

(since price of stock A starts increasing per hour after 9 A.M. and price of stock B starts decreasing per hour after 12 noon that is 3 hours after 9 A.M.)

To find number of hours in which the prices of the two stocks A and B become​ same, solve \(15.59+0.12t=16.34+0.11(t-3)\)

\(15.59+0.12t=16.34+0.11(t-3)\\15.59+0.12t=16.34+0.11t-0.33\\0.12t-0.11t=16.34-0.33-15.59\\0.01t=0.42\\t=42\)

So, prices of the two stocks A and B become​ same in 42 hours

The alternative term that can be used to describe asymmetric cryptographic algorithms is "public key cryptography," option b.

Asymmetric cryptography is a cryptographic approach that utilizes a pair of distinct keys, namely a public key and a private key.

The public key is openly shared, allowing anyone to encrypt messages intended for the owner of the corresponding private key.

Conversely, the private key remains secret and is used for decrypting the encrypted messages.

Public key cryptography is named as such because the public key can be freely distributed among users, enabling secure communication without the need for a shared secret key.

So the correct option is B.

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When the doubling time is three, the growth rate is approximately 25.9%.

To find the growth rate when the doubling time is three, we can use the formula for exponential growth. The formula is:

Final Amount = Initial Amount * (1 + Growth Rate) to the power Time

In this case, we want to double the initial amount, so the final amount will be 2 times the initial amount. The doubling time is given as three units of time. We can represent this in the formula as:

2 * Initial Amount = Initial Amount * (1 + Growth Rate)³

Now, we can solve for the growth rate:

2 = (1 + Growth Rate)³

Taking the cube root of both sides:

Cube root of 2 = 1 + Growth Rate

Subtracting 1 from both sides:

Growth Rate = Cube root of 2 - 1

Calculating the cube root of 2:

Growth Rate ≈ 1.259 - 1

Growth Rate ≈ 0.259, or approximately 25.9%

So, when the doubling time is three, the growth rate is approximately 25.9%.

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Answer:

A 2kg body is moving a long a horizontal circular path of radius 2m with constant speed of 6m/s . please help

For the required value of the given complex numbers z₁z₂ = 32(cos 255° + isin 255°).

Complex numbers are those that expand on the idea of real numbers by incorporating an illogical element.

The formula for a complex number is "a + bi," where "a" and "b" are real numbers and "i" is the imaginary unit, which is equal to the square root of -1.

"A" stands for the complex number's real component, and "b" stands for the imaginary component.

We multiply the magnitudes of two complex numbers and add their arguments to determine their product.

Let's compute z₁z₂ with the supplied values.

Given:

z₁ = 8(cos 45° + isin 45°)

z₂ = 4(cos 210° + isin 210°)

We add the arguments and multiply the magnitudes to find z₁z₂:

Magnitude of z₁ = 8

Magnitude of z₂ = 4

Argument of z₁ = 45°

Argument of z₂ = 210°

Now, let's calculate z₁z₂:

Magnitude of z₁z₂ = (Magnitude of z₁) × (Magnitude of z₂) = 8 × 4 = 32

Argument of z₁z₂ = (Argument of z₁) + (Argument of z₂) = 45° + 210° = 255°

Therefore, z₁z₂ = 32(cos 255° + isin 255°).

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The correct question =

Given z₁ = 8(cos 45° + isin 45°) and z₂ = 4(cos 210° + isin 210°), what is z₁z₂?

Answer:

The answ is 20 7/8

Step-by-step explanation:

Answer:

44 7/8

Step-by-step explanation:

Hope this helps!

And just to make sure do you mean twelve and seven eighths?

Number of Americans that had plans to travel to the United States Midwest = 16.18 millions

Total number of Americans that had plans to travel during the 2019 holiday season = 115.6 millions

Percentage of Americans that had plans to travel to the United States Midwest = 14%

Number of Americans that had plans to travel to the United States Midwest = (14/100) x 115.6 millions

Number of Americans that had plans to travel to the United States Midwest = 0.14 x 115.6 millions

Number of Americans that had plans to travel to the United States Midwest = 16.18 millions

Answer:

350x⁶+1360x⁵-1337x⁴-7618x³-5517x²+1620x+1836

The critical value c for a 90% confidence interval with a sample size of 77 is approximately 1.645. This value is obtained from the standard normal distribution, approximating the t-distribution due to the large sample size.

To determine the critical value c for a 90% confidence interval based on a random sample of 77 individuals, we need to consult the t-distribution table or use statistical software.

Since the sample size is relatively large (n > 30), we can approximate the t-distribution with a standard normal distribution.

For a 90% confidence level, we need to find the critical value that leaves 5% of the area in the tails (2.5% in each tail) under the standard normal curve.

Using a standard normal distribution table or a calculator, we can find that the critical value for a 90% confidence level is approximately 1.645.

Therefore, the critical value c for a 90% confidence interval with a sample size of 77 is approximately 1.645.

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a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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9514 1404 393

Answer:

  D.  81/m^7

Step-by-step explanation:

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

  a^-b = 1/a^b

__

Using these, your expression simplifies to ...

  \((3m^{-4})^3(3m^5)=(3^3)(3)(m^{-4\cdot3+5})=81m^{-7}=\boxed{\dfrac{81}{m^7}}\)

Answer:

For addition 7 1/4. For subtraction 1 3/4. For multiplication 12 2/8. For division 1 7/11.  

Step-by-step explanation:

There are 96 ways for four people to sit in six chairs so that the leftmost chair is occupied and the rightmost is empty.

There are 4 guests and the leftmost seat is to be occupied, so there are 4  such ways to choose the occupant of that seat.

Then, for each of those 4 ways, there are 4 ways to decide the occupant for the second seat -- the remaining three people plus the possibility of that seat being empty, that makes a total of 16 ways to decide the configuration of the first two seats.

Then, for each of those 16 ways, there are 3 ways to choose the occupant for the third seat (either 3 remaining guests if the second seat was left empty, or the two remaining guests plus the possibility of leaving the 3rd seat empty). Hence, 16 times 3 is 48. For each of those ways, there are two choices for the next seat, i.e. 48 times 2 = 96, and finally one choice for the fifth seat. So in all, there are 96 ways.

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The price-earnings ratio of the stock is 16.6. P/E ratios can vary widely across industries, so it's important to compare a stock's P/E ratio to other companies in the same industry.

The price-earnings ratio (P/E ratio) is calculated by dividing the stock price by the earnings per share (EPS). In this case, the EPS is $2.50 and the stock price is $41.50. So, the P/E ratio is:
P/E ratio = Stock price / EPS
P/E ratio = $41.50 / $2.50
P/E ratio = 16.6
Therefore, the price-earnings ratio of the stock is 16.6.

The price-earnings ratio is an important metric used by investors to evaluate the value of a stock. It reflects the amount that investors are willing to pay for each dollar of earnings generated by the company. A high P/E ratio may indicate that investors have high expectations for the company's future earnings growth, while a low P/E ratio may indicate that investors have lower expectations. In the case of National Advertising, the company had earnings of $2.50 per share last year and its stock price was $41.50 as of yesterday's close. By dividing the stock price by the EPS, we can calculate the P/E ratio, which is 16.6. This means that investors are willing to pay $16.60 for every dollar of earnings generated by the company. It's important to note that the P/E ratio should not be used in isolation when evaluating a stock. Other factors, such as the company's growth prospects, financial health, and industry trends, should also be taken into account.

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