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Your average waiting time will be approximately 1 minute.

As the first passenger, you will not have to wait for any other passengers to get in the taxi. However, the taxi will wait for 2 passengers to arrive or 3 minutes to pass since your boarding.

Since passengers arrive according to a Poisson process with an average of 60 passengers per hour, the arrival rate lambda can be calculated as:

lambda = average number of passengers per time unit = 60/60 = 1 passenger per minute

The time between two consecutive passenger arrivals follows an exponential distribution with parameter lambda. Thus, the probability of waiting less than t minutes for the second passenger to arrive can be calculated as:

P(wait < t) = 1 - e^(-lambda*t)

We need to find the average waiting time until the second passenger arrives. This can be calculated as the area under the probability distribution curve divided by the arrival rate lambda:

average waiting time = integral from 0 to infinity of t*(1 - e^(-lambda*t)) dt / lambda

Using integration by parts, we can solve this integral to get:

average waiting time = 1/lambda + (1 - e^(-lambda*t))/(lambda^2)

Plugging in the values, we get:

average waiting time = 1/1 + (1 - e^(-1*3))/(1^2) = 1 + (1 - 0.0498) = 1.9502 minutes

Therefore, as the first passenger, your average waiting time until the second passenger arrives is 1.9502 minutes.

To answer your question, let's consider the two possible scenarios:

1. Two passengers are collected: In this case, the first passenger (you) waits for the second passenger to arrive. Since the arrival rate is 60 passengers per hour, the average time between arrivals is 1 minute (60 minutes / 60 passengers).

2. Three minutes have expired: In this case, the taxi departs after 3 minutes even if only one passenger (you) is in the taxi.

On average, the waiting time for the first passenger (you) will be the minimum of these two scenarios. Thus, your average waiting time will be approximately 1 minute.

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The value of x in the quadrilateral is 20 degrees.

The sum of angles in a quadrilateral is 360 degrees. Therefore, a quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angle.

Hence, let's find the value of x in the quadrilateral.

x + x + 32 + 8x - 16 + 8x - 16  = 360

2x + 16x + 32 - 32 = 360

18x + 0 = 360

18x = 360

18x = 360

divide both sides by 18

x = 360 / 18

x = 20

Therefore,

x = 20 degrees

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The daily inpatient census for July 16 is 271.

To determine the daily inpatient census for July 16, we need to take into account the census at midnight on July 15, the number of discharges, admissions, and additional patients (content loaded) throughout the day on July 15 and July 16.

Starting with the census at midnight on July 15 of 239, we subtract the number of discharges (59) and add the number of admissions (67) and additional patients (24) to get the total number of patients in the hospital on July 16.

239 - 59 + 67 + 24 = 271

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Alma has to utilize 6/5 glasses of blue paint and 6/5 mugs of ruddy paint with the 2 mugs of white paint to create 2 glasses of her favorite shade of purple paint.

To form 5 mugs of purple paint, Alma makes use of 3 mugs of blue paint, 1frac{1}{2} glasses of ruddy paint, and frac{1}{2} a container of white paint.

So, to form 1 container of purple paint, she has to utilize:

3/5 glasses of blue paint

1frac{1}{2}/5 cups of ruddy paint

frac{1}{2}/5 mugs of white paint

Presently, Alma needs to form 2 glasses of purple paint utilizing 2 glasses of white paint.

Since she already has frac{1}{2} a container of white paint, she as it were needs another 1frac{1}{2} mugs of white paint.

To form 2 glasses of purple paint, Alma must twofold the sum of each color utilized to create 1 glass of purple paint.

In this way, she will require:

2 * 3/5 = 6/5 glasses of blue paint

2 * 1frac{1}{2}/5 = 3/5 + 3/5 = 6/5 glasses of ruddy paint

2 * frac{1}{2}/5 = 1/5 cups of white paint

Since she as of now has 2 glasses of white paint, she will as it were ought to utilize 1/5 glasses of the white paint that she as of now has.

Subsequently, Alma has to utilize 6/5 glasses of blue paint and 6/5 mugs of ruddy paint with the 2 mugs of white paint to create 2 glasses of her favorite shade of purple paint.

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The slope of perpendicular line is -1.

We have,

Equation: 3x - 3y = 63

Now, writing the given equation in slope intercept form

3y= 3x- 63

y= 3x/ 3 - 63/3

y= x - 21

So, the slope of given equation is 1.

Now, the slope of two perpendicular line have the product -1.

let the slope of perpendicular line be m.

So, m x 1 = -1

m = -1

Thus, the slope of perpendicular line is -1.

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Answer:

6log 2

Step-by-step explanation:

log 16 + log 4 = log 2⁴ + log 2² = 4log 2 + 2log 2 = 6log 2

Answer: -1/3-(-3/5)=4/15

Step-by-step explanation:

P.S i'm emo

False. The statement you described is not an equivalent form for a conditional statement. The process you mentioned, which is reversing and negating the antecedent and consequent, is known as forming the contrapositive of the statement.

A conditional statement has the form "If P, then Q," where P is the antecedent and Q is the consequent. The contrapositive is formed by negating both the antecedent and consequent, and reversing their order: "If not Q, then not P." The contrapositive is equivalent to the original conditional statement.

However, simply reversing the antecedent and consequent without negating them gives you the converse, which is "If Q, then P." The converse is not equivalent to the original conditional statement.

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Answer:

22.98133...

Step-by-step explanation:

30 x cos(40°)

then refine to a decimal form

The measure of the missing angle is38 degrees.

The figure in the image is a right triangle.

Missing angle θ = ?

Hypotenuse = 55

Opposite to angle θ = 34

To find the missing angle, we use the trigonometric ratio.

sine = opposite / hypotenuse

Plug in the given values and solve for the missing angle.

sinθ = 34/55

Take the sine inverse

θ = sin⁻¹( 34/55 )

θ = 38⁰

Therefore, the angle is 38 degrees.

Option A) 38⁰ is the correct answer.

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Writing 1/(1 + x) + 2/(1 + x) as a single fraction , we get 3​/(1 + x)

From the question, we have the following parameters that can be used in our computation:

1/1_x+2/1+x​

Express properly

So, we have

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

Take the LCM of the fractions

So, we have

(1 + 2)/(1 + x)

Evaluate the sum of like terms

3​/(1 + x)

HEnce, the solution si 3​/(1 + x)

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The zeros of the function are x = 0, x = 7, and x = 9.

The graph of f(x) is concave down near x = 7 and concave up near x = 9.

We have,

To find the zeros of the function f(x) = x^4 - 16x^3 + 63x^2,

We need to set f(x) equal to zero and solve for x:

x^4 - 16x^3 + 63x^2 = 0

Factor out x^2:

x^2(x^2 - 16x + 63) = 0

Factor the quadratic term:

x^2(x - 7)(x - 9) = 0

So the zeros of the function are x = 0, x = 7, and x = 9.

To describe the behavior of the graph at each zero, we can use the first and second derivative tests.

The first derivative of f(x) is:

f'(x) = 4x^3 - 48x^2 + 126x

The second derivative of f(x) is:

f''(x) = 12x^2 - 96x + 126

At x = 0, we have a double root, since x = 0 is a zero of multiplicity 2.

From the first derivative test, we see that f'(x) changes sign from negative to positive at x = 0, indicating that f(x) has a local minimum at x = 0.

From the second derivative test, we see that f''(0) = 126, which is positive. This means that the local minimum at x = 0 is a relative minimum, and the graph of f(x) is concave up near x = 0.

At x = 7 and x = 9, we have simple zeros.

From the first derivative test, we see that f'(x) changes sign from positive to negative at x = 7 and from negative to positive at x = 9, indicating that f(x) has local maximums at x = 7 and x = 9.

From the second derivative test, we see that f''(7) = -42 and f''(9) = 54, so the local maximum at x = 7 is a relative maximum, and the local maximum at x = 9 is a relative minimum.

Thus,

The zeros of the function are x = 0, x = 7, and x = 9.

The graph of f(x) is concave down near x = 7 and concave up near x = 9.

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The zeros of the graph are 0, 7, and 9.

To find the zeros of the function, we can set it equal to zero and factor:

[tex]x^4 - 16x^3 + 63x^2 \\= x^2(x^2 - 16x + 63) \\= x^2(x - 7)(x - 9)[/tex]

So the zeros are x = 0, x = 7, and x = 9.

We may look at the function's sign on either side of each zero to understand how the graph behaves there. The function's factored form may be used to our advantage here:

Examining the leading coefficient (which is positive) and the degree of the polynomial will also reveal the graph's general behavior (which is even). This indicates that if x increases or decreases, the graph will be upward-facing and will go closer to infinity in both directions.

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The valid values for probability are: a) P(A) = 0.4, d) P(A) = 4/5, f) P(B) = 20% and h) P(A) = 0

From the question, we have the following parameters that can be used in our computation:

List of options

The valid values for probability are any value between 0 and 1 (inclusive)

This means that numbers less than 0 or greater than 1 are invalid

using the above as a guide, we have the following:

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The number that is two more than the quotient of a number and is equal to 4 is 16. Let's break down the sentence into a numerical condition:

"Two more than the remainder of a number and 8" can be spoken to as (x/8) + 2, where x is the number we are attempting to discover.

The sentence moreover states that this expression is "equal to 4", so we are able to type in

(x/8) + 2 = 4

To fathom for x, we will confine the variable on one side of the condition. We will start by subtracting 2 from both sides:

(x/8) = 4 - 2

Streamlining the right-hand side gives:

(x/8) = 2

At long last, we are able to illuminate for x by increasing both sides by 8:

x = 2 x 8

x = 16

thus, the number we are seeking out is 16.

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complete question: What is the number which is two more than the quotient of a number and 8 is equal to 4?

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The possible observed values of a discrete random variable can be listed in a countable collection. A random variable is a measurement to be taken in a probability experiment.

An observed value of a random variable is the measurement that has been taken. A discrete random variable is a random variable in which there is a countable collection of possible observed values. That is, the discrete random variable can only take on specific values within a given range, and the probability associated with each value can be calculated. This countable collection of possible observed values is finite or countably infinite, and the probabilities sum up to 1.

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In summary, statement 1+2 is correct as it provides information about both c and a, while statement 1 alone and statement 2 alone are not sufficient to determine the value of a.

Statement 1+2: The first statement states that the value of c is not equal to zero, and for these values of c, a is always 1. The second statement states that h is equal to b*c, and since h is not equal to zero, neither b nor c can be zero. This means that statement 1+2 is correct, as it provides information about both c and a.

Statement 1: This statement provides information about the value of c, but it doesn't say anything about a. It states that h is equal to b*c and that h is not equal to zero, which means that neither b nor c can be zero. However, this information alone is not sufficient to determine the value of a.

Statement 2: This statement provides information about the relationship between a, c, and f. It states that c is equal to f, and a*c is equal to f. This expression can hold if c=f=0, but a can have any value. Additionally, if c and f are any non-zero value, a is always 1. This means that statement 2 alone is not sufficient to determine the value of a.

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Answer:     3 million

Step-by-step explanation:

180 divided by 60 equals 3 so that would be 3 million because there are only 60 thousand and that would be a million because it would not be a billion.

There are 36 cards in the box.  In this scenario, we are given that the probability of choosing a red card from a box is one-third. We also know that there are 24 blue cards in the box. Our goal is to find the total number of cards in the box.

Let's use the concept of probability to solve this problem. The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the probability of choosing a red card is given as 1/3, and the favorable outcome is selecting a red card. Let R be the number of red cards, and T be the total number of cards in the box. The probability formula can be represented as:

Probability of choosing a red card = R / T

We are given that the probability of choosing a red card is 1/3:

1/3 = R / T

Since there are 24 blue cards in the box, we can represent the total number of cards as the sum of red and blue cards:

T = R + 24

Now, we can solve the system of equations to find the values of R and T:

1. 1/3 = R / T
2. T = R + 24

From equation 1, we can express R as:

R = (1/3) * T

Substitute this expression for R in equation 2:

T = (1/3) * T + 24

Multiplying both sides by 3 to eliminate the fraction, we get:

3T = T + 72

Subtracting T from both sides:

2T = 72

Now, divide by 2 to find the total number of cards, T:

T = 36

So, there are 36 cards in the box.

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The car loan has a monthly payment of around $971.56. Based on the loan amount, annual percentage rate, down payment, and loan term, this is determined using the present value of an annuity formula.

Christina has put down the following amount:

10% down payment times $43,599 equals $4,359.90.

She must borrow the upcoming amount:

Loan amount = $43,599 - $4,359.90 = $39,239.10

We must apply the of an annuity formula to determine the monthly payment:

Present value of annuity

=  PV = A×((1 – (1 / (1 + r)⁻ⁿ)) / r)

If A is the monthly payment, then r denotes the annual interest rate, n the frequency at which interest is compounded annually, and t the number of years.

Due to the loan's three-year term and monthly compounding of interest, we have:

n = 12 and t = 3

The annual interest rate is 1.99%, but we need to convert it to a monthly interest rate by dividing it by 12:

r = 1.99% / 12 = 0.1667%

Substituting the given values, we get:

Present value of annuity = A × [1 - (1 + 0.01667)⁻¹²ˣ³] / (0.01667)

≈ $35,056.33

Therefore, the monthly payment is:

Monthly payment = $35,056.33 / (12 × 3) ≈ $971.56

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There are 200.96 square inches that make up half of the cookie cake.

We have to given that;

The diameter of a circular cookie cake is 16 inches.

Now, We know that;

Area of circle = πr²

Here, Diameter = 16 inches

Hence, Radius = 16 / 2

                       = 8 in

Thus, Area of circular cookie cake is,

⇒ A = πr²

⇒ A = 3.14 × 8²

⇒ A = 200.96 inches²

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The probability that the drawn bead will be blue is 1/3.

Given that,

A cloth sack contains 25 red beads, 75 green beads, and 50 blue beads.

Total number of beads in the sack = 25 + 75 + 50 = 150

Number of blue beads = 50

Probability of drawing a blue bead = Number of blue beads / Total number of beads

= 50/150

= 1/3

Hence the required probability of drawing blue bead is 1/3.

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Answer:

16 tiles

Step-by-step explanation:

The theoretical probability of flipping heads and rolling a 1 or 2 is 1/6.

Now, We have;

The sample space for flipping a coin and rolling a number cube are:

Flipping a coin: {H, T}

There are 2 possible outcomes, since the coin is fair.

Rolling a number cube: {1, 2, 3, 4, 5, 6}

Since, There are 6 possible outcomes, since the number cube is standard

So, the total number of outcomes for the combined experiment is,

2 x 6 = 12.

The events of flipping heads and rolling a 1 or a 2 are independent,

Hence, The probability of flipping heads is,

⇒ 1/2,

And, The probability of rolling a 1 or 2 is,

⇒ 2/6,

So, the probability of flipping heads and rolling a 1 or 2 is;

= (1/2) x (2/6)

= 1/6

Therefore, the theoretical probability of flipping heads and rolling a 1 or 2 is 1/6.

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Increase in taxes is one of the reasons why the change in Mr. Henderson's net income

It is possible that Mr. Henderson's net income has decreased this month despite having received the same gross income as last month. Let us examine some of the plausible rationales behind it:

An increase in taxes: If Mr. Henderson worked more hours or obtained a raise, his gross income would be higher. However, if he now belongs to a higher tax bracket, he will owe more money in taxes and therefore have lower net income.

A change in deductions: It is likely that Mr. Henderson's employer may have modified his paycheck deductions which can lead to more taxes being held back from his earnings - an eventuality that could cause his net income to decrease.

Alterations in benefits: Changes in Mr. Henderson's approved employee benefits plan- insurance premiums increasing or retirement savings contributions stalling, for instance- could also explain why his net income reduced this month.

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Two possible ways to write 9/10 as a sum of fractions are 1/2 + 4/5 and 3/5 + 3/10.

To write9/10 as a sum of  fragments, we need to find two  fragments with a common denominator that add up to9/10. One way to do this is to express9/10 as the sum of two  fragments with denominators that are multiples of 10.   One possible way to do this is   = 1/24/5   Both  fragments on the right- hand side have denominators that are multiples of 10, and when we add them together, we get9/10.

9 = 2x + y

We can then solve for x and y by trying different values until we find a solution that works. One possible solution is x=3 and y=3:

9/10 = 3/5 + 3/10

3/5 + 3/10 = 6/10 + 3/10 = 9/10

Since 9/10 is equal to 9/10, we have shown that 9/10 can be written as a sum of fractions.

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The probability of either the system or the backup working properly is 1 - 0.02 = 0.98. Which is 0.02 x 0.02 = 0.0004 or 0.04%. Therefore, the probability that neither the system nor its backup is working properly at the end of the 30 days is very low, only 0.04%.

To find the probability that neither the primary computer system nor the backup system is working properly at the end of the 30-day period, we'll need to use the given probability of each system working properly (98%) and the fact that the systems work or fail independently.

Step 1: Find the probability of each system failing
Since each system has a 98% chance of working properly, the probability of it failing is 100% - 98% = 2%.

Step 2: Calculate the probability that both systems fail
Since the systems work or fail independently, we can multiply the probabilities of each system failing together:
2% (primary failing) x 2% (backup failing) = 0.02 x 0.02 = 0.0004

Step 3: Convert the probability to a percentage
0.0004 x 100% = 0.04%

Therefore, the probability that neither the primary computer system nor its backup are working properly at the end of the 30-day period is 0.04%.

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The pooled standard deviatio is 5.746. We can say with 95% confidence that the true difference between the population means falls between -4.019 and 0.719.

First, we need to calculate the pooled standard deviation:

s_p = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2)/(n1+n2-2))

s_p = sqrt(((6-1)*5.9^2 + (7-1)*5.6^2)/(6+7-2))

s_p = 5.746

Next, we can calculate the t-statistic:

t = ((x1 - x2) - 0) / (s_p * sqrt(1/n1 + 1/n2))

t = ((72.9 - 75.1) - 0) / (5.746 * sqrt(1/6 + 1/7))

t = -0.956

Using a t-distribution table with conservative degrees of freedom (df = min(n1-1, n2-1) = 5), we find that the critical value for a one-tailed test with α=0.05 is -1.833. Since our calculated t-statistic is greater than the critical value, we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is sufficient evidence to support the claim that the first population mean is less than the second population mean.

As for the confidence interval, we can use the formula:

(x1 - x2) ± t_(α/2, df) * s_p * sqrt(1/n1 + 1/n2)

Plugging in the values:

(72.9 - 75.1) ± t_(0.025, 5) * 5.746 * sqrt(1/6 + 1/7)

-4.019 < μ1 - μ2 < 0.719

Therefore, we can say with 95% confidence that the true difference between the population means falls between -4.019 and 0.719.

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The solution of the formula for the variable, m as required to be determined is; m = Fr² / GM.

It follows from the task content that the complete question indicates a formula;

F = GMm / r²

Hence, to solve for the variable m; multiply both sides by r² so that we have;

Fr² = GMm

Finally divide both sides by GM so that we have;

m = Fr² / GM

Ultimately, the formula with m as the subject is; m = Fr² / GM.

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