at a checkout counter customers arrive at an average of 1.5 per minute. find the probabilities that (a) at most 4 will arrive in any given minute. (b) at least 3 will arrive during an interval of 2 minutes.

Answer:

28 is the ans of 252÷9here we go

252 divided by 9 equals 28.

To divide 252 by 9, you can use long division, which involves dividing the number in steps until there is no remainder left.

Here's the step-by-step process:

Write down the dividend (252) and the divisor (9), and set up the long division format:

9 | 252

Look at the leftmost digit of the dividend (2) and see if it's divisible by the divisor (9). Since 2 is less than 9, we bring down the next digit (5) to the right of 2, making it 25.

9 | 252

2

Divide the new number (25) by the divisor (9). The result is 2, which is the first digit of the quotient. Multiply this result by the divisor (2 x 9 = 18) and write it below the 25, then subtract it from 25:

9 | 252

25

18

--

7

Bring down the next digit (2) from the dividend to the right of the remainder (7), making it 72. Now, divide 72 by 9, which gives you 8. Multiply this result by the divisor (8 x 9 = 72) and write it below the 72, then subtract it from 72:

9 | 252

25

18

--

72

72

---

0

There is no remainder left, and the dividend has been completely divided. The quotient is the result of the division, which is 28.

Therefore, 252 divided by 9 equals 28.

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Answer:

volume=12930.79

Step-by-step explanation:

[tex]v=\pi r^{2} h\\v=\pi (14)^{2} (21)\\v=12930.79[/tex]

Answer: 50 uk pounds

Step-by-step explanation:

Step-by-step explanation:

See image below

(e): Approximately normal with mean 5.5 days and standard deviation 0.26 days.

What is standard deviation?

Standard deviation is a measure of the spread or dispersion of a set of data from its mean or average. It measures how far the values in a dataset are from the mean of the dataset.

The sample size needed for this approximation to hold depends on the shape of the population distribution, but a commonly used rule of thumb is that a sample size of at least 30 is sufficient for most cases.

In this case, the sample size is 100, which is larger than 30, so we can use the central limit theorem to approximate the sampling distribution of the sample mean.

The mean of the population distribution is 5.5 days, and the standard deviation is 2.6 days. The standard deviation of the sampling distribution of the sample mean can be approximated using the formula:

standard deviation of the sample mean = standard deviation of the population / square root of sample size

= 2.6 / sqrt(100)

= 0.26

Therefore, the best description of the sampling distribution of x is option (e): approximately normal with mean 5.5 days and standard deviation 0.26 days.

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the HCF of x, 2y, 3y, 4z, x², 3z, and 5, where x, y, z are

distinct prime numbers is 1.

To find the highest common factor (HCF) of the given numbers, we need to find the common factors of each pair of numbers and then find the highest common factor of all the resulting common factors.

First, let's find the prime factors of the given numbers:

x = a prime number (distinct from y and z)

2y = 2 × y

3y = 3 × y

4z = 2² × z

3z = 3 × z

x² = a prime number squared (distinct from y and z)

5 = a prime number

Next, we can pair up the numbers and find their common factors:

Common factors of x and 2y: 1, 2, y

Common factors of 3y and 4z: 1, 2, 3, y, z, 6

Common factors of x² and 3z: 1, 3, x, z, xz

Common factors of 5 and 2: 1

Finally, we find the highest common factor of all the resulting common factors:

The highest common factor of x, 2y, 3y, 4z, x², 3z, and 5 is 1, since it is the only factor that is common to all the pairs.

Therefore, the HCF of x, 2y, 3y, 4z, x², 3z, and 5 is 1.

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The probability that at least one surgery is successful, given that a new surgery is successful 80% of the time, is 99.20%.

Let X denote the number of successful surgeries out of n randomly selected surgeries. The random variable X follows a binomial distribution. The probability of X = x successful surgeries out of n randomly selected surgeries is given by:

P(X=x)=nCxp^x(1−p)^n−x

where p is the probability that a new surgery is successful, and (1-p) is the probability that a new surgery is unsuccessful. In this case, p = 0.80 and (1-p) = 0.20. Let n = 5. Then, we have:

P(X≥1)=1−P(X=0)=1−nC0p0(1−p)n−0

=1−(0.20)5

=0.9936 ≈ 99.20%

Therefore, the probability that at least one surgery is successful is 99.20%.

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The survey ratings provide valuable feedback for drivers who are looking for quality tires for their vehicles. These ratings can give insight on steering responsiveness, how quickly a tire wears, and overall customer satisfaction. Drivers can also see how their tire of choice stacks up against other tires, making it easier to make an informed decision when shopping for tires.

The Tire Rack is America’s leading online distributor of tires and wheels. They conduct extensive testing to ensure that customers are provided with the most suitable tires for their vehicles, driving styles, and driving conditions. They also use an independent consumer survey to help drivers gain insight on long-term tire experiences.

The following data show survey ratings on a 1-10 scale, with 10 being the highest rating, of 18 maximum performance summer tires, as of February 3, 2009 (Tire Rack website). The variables are Steering (steering responsiveness), Tread Wear (quickness of wear), and Buy Again (overall tire satisfaction and desire to purchase the same tire again). The Yokohama Aegis LS4 has a Steering rating of 7.9, Tread Wear rating of 7, and Buy Again rating of 7.1. The Dunlop SP20 FE has a Steering rating of 5.7, Tread Wear rating of 5, and Buy Again rating of 3.3.

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The percentage of students passing the partial exam is:

Option c. 70%

To answer this question, we use the Z-table. We have:

Given, mean (μ) = 120 and standard deviation (σ) = 17
Passing Score = 111

To find out what percentage of students passed the midterm, we need to find the probability that a score picked at random from the distribution is greater than or equal to 111. We can convert this score into a standard score (Z-score) using the Z-table. We have:

Z-score = (111 - μ) / σ
       = (111 - 120) / 17
       = -0.53

Using the Z-table, we can find the area (probability) to the left of this Z-score as follows:

Area to the left of Z-score = 0.2981 (from Z-table)

The area to the right of this Z-score (i.e. the probability that a score picked at random from the distribution is greater than or equal to 111) is:

Area to the right of Z-score = 1 - 0.2981
                           = 0.7019
                           = 70.19%

Therefore, the percentage of students who passed the midterm is approximately 70% (Option C).

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Answer:

C. 70%

Step-by-step explanation:

A zero balance in Armando's account can be achieved by subtracting $250 from the account balance. This can be done through a combination of withdrawals and/or transfers out of the account.

Subtracting is a mathematical operation that involves taking one number away from another. It is the inverse of addition, and is represented by the minus sign (-). Subtracting is used to determine the difference between two numbers, or to reduce a number by a given amount. In algebraic terms, subtracting is represented by the equation: a - b = c, where a is the starting number, b is the number to be subtracted, and c is the resulting difference. Subtracting can also be used on fractions, decimals, and other forms of numbers.

For example, Armando could make a $250 withdrawal from the account or transfer $250 to another bank account.

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Answer:

a=1/3

Step-by-step explanation:

First, expand the brackets by doing multiplication:

2+6a+3=3a+6

Then, move the unknown to the left and the numbers to the right:

3a=6-5

3a=1

a=1/3

The solution to the given equation is -1.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is 2+3(2a+1)=3(a+2)

2+6a+3=3a+2

6a+5=3a+2

6a-3a=2-5

3a=-3

a=-1

Therefore, the solution to the given equation is -1.

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Answer:

Step-by-step explanation:

(a) The formula to calculate the amount of money in the account after t years with an initial deposit of P and an annual interest rate r compounded annually is:

A = P(1 + r)^t

In this case, P = $500, r = 0.015 (1.5% expressed as decimal), and the interest is compounded annually, so the equation is:

A = 500(1 + 0.015)^t

Simplifying this gives:

A = 500(1.015)^t

Therefore, the equation that represents the amount of money in the savings account as a function of time in years is A = 500(1.015)^t.

(b) To find the amount of time it takes for the account balance to reach $800, we can set the equation A = 500(1.015)^t equal to 800 and solve for t:

500(1.015)^t = 800

Dividing both sides by 500:

(1.015)^t = 1.6

Taking the natural logarithm of both sides:

ln(1.015)^t = ln(1.6)

Using the power rule of logarithms:

t ln(1.015) = ln(1.6)

Dividing both sides by ln(1.015):

t = ln(1.6) / ln(1.015)

Using a calculator:

t ≈ 24.7

Therefore, it takes approximately 24.7 years for the account balance to reach $800.

Answer:

jwjwi7svwisg, I have y2ywgeu

Answer: m= 2    n =7

Step-by-step explanation:

i think to find the answer you can make the sides equal each other so 7m+4 = 9m  2m=4m m =2

and for the other angle

2n-1 = n+6  n - 1 = 6 n = 7

Nicolas drinks 3/2 liters of water in total - 1/3 liters of water in the morning, 1/2 liter of water at lunch, and 2/3 liter of water during basketball practice.

Nicolas drinks to third liter of water in the morning, which is 1/3 liters of water. At lunchtime, he drinks 1/2 litre of water. During basketball practice, he drinks another 2/3 liter of water.

To find the total amount of water that Nicolas drinks, we need to add these quantities together:

Total amount of water = 1/3 + 1/2 + 2/3

To add these fractions, we need to find a common denominator, which is 6 in this case. We can convert each fraction to have a denominator of 6 as follows:

1/3 = 2/6

1/2 = 3/6

2/3 = 4/6

Now we can add the fractions with the same denominator:

Total amount of water = 2/6 + 3/6 + 4/6

Total amount of water = 9/6

We can simplify this fraction by dividing both the numerator and denominator by 3:

Total amount of water = 3/2

Therefore, Nicolas drinks 3/2 litres of water in total.

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All monuments cast a shadow when the sun is shining, as they block the sunlight and create a shadow on the ground or nearby surfaces. T

The size and shape of the shadow will depend on the position of the sun in the sky, the orientation of the monument, and its size and shape.

Some famous monuments that cast impressive shadows include the Pyramids of Giza, the Eiffel Tower, the Washington Monument, and the Stonehenge.

We can use proportions to solve the problem.

Let x be the length of Kyle's shadow.

We know that the length of the monument's shadow is 16 feet, and its height is  [tex]64 f[/tex] Feet. So the ratio of the length of the monument's shadow to its height is:

[tex]16/64 = 1/4[/tex]

This ratio is equal to the ratio of Kyle's shadow length to his height:

[tex]x/6.25 = 1/4[/tex]

To solve for x, we can cross-multiply:

[tex]x = 6.25/4 = 1.5625[/tex]

Therefore, the length of Kyle's shadow is approximately [tex]1.56[/tex] feet (or  [tex]18.72 inches)[/tex] .

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The percent change of 31 to 7 is found as  77.42% which is percent decrease of the number.

You can determine the amount of change that has occurred over this time period if you have data at two points in time. The outcome is known as the rate of change, sometimes known as the percentage change, and is given in percentage form (in absolute numbers, it really is merely a difference).

Using a percentage is one method of calculating a percent of change. Keep in mind that a percentage indicates "per 100." You can rephrase your problem as a % out of 100 by first describing the change as a fraction and measuring the amount of change to the original.

Original number = 31

Final number = 7

percent change = (7 - 31)/31 *100

percent change = - 24*100 / 31

percent change = - 77.42

Here negative sign shows the percent decrease of the number.

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Answer: 8

Step-by-step explanation:

The sum of the interior angles in a triangle in 180.

So we can add up all the values and set it equal to 180 to find x.

4x + (5x + 5) + 103 = 180

9x + 108 = 180

9x = 72

x = 8

Answer:

x=8

Step-by-step explanation:

4x+5x+5+103=180

9x+108=180

9x=180-108

9x=72

x=72÷9

x=8

The total number of pairwise comparisons for k is (k*(k-1))/2.

There are (k*(k-1))/2 pairwise comparisons in a completely randomized design with k treatments. For example, if there are 4 treatments, there will be 6 pairwise comparisons (4C2 = 6). Here's the explanation:In a completely randomized design, the treatments are randomly assigned to the experimental units. The main objective of such a design is to determine whether the treatment means are different from each other or not.To compare the treatment means, we use the mean square between treatments (MST) and mean square error (MSE). The test statistic used to compare the means is F = MST/MSE.The ANOVA table for a completely randomized design has the following format:Source of variationSum of SquaresDegrees of freedomMean SquareF-testtreatmentSS(k-1)k-1MST=MSTrMSEResidualSSTn-kMSEReference: https://www.stat.yale.edu/Courses/1997-98/101/anovar.htmNow, we need to compare each pair of treatments using a multiple comparisons procedure. A pairwise comparison involves comparing the means of two treatments only.The total number of pairwise comparisons is given by the combination formula:$$ \frac{k!}{2!(k-2)!} = \frac{k(k-1)}{2} $$Therefore, the total number of pairwise comparisons for k is (k*(k-1))/2.

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Answer:

Order is important: If allowed 11881376

Order is important:If rep. Is not allowed 7893600

Step-by-step explanation:

If the order isnt important and repetition is not allowed 65780

If order isn’t important and repetition is allowed 142506

Answer:

Step-by-step explanation:

-11 +23-46+ (-12) =

12 - 46 + (-12) =

-34 - 12 =

-46

In the following question, among the conditions given, For the page reference string provided, the number of page faults for the following page replacement algorithms are as follows: A. FIFO: 8-page faults, B. Optimal: 6-page faults, C. LRU: 7-page faults.

To learn about them in brief-
A. FIFO: 8-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 1, 2
Step 6: 0, 1, 2
Step 7: 0, 1, 2
Step 8: 0, 1, 3
Step 9: 2, 7, 1
Step 10: 2, 0, 3
Step 11: 2, 1, 0
Step 12: 2, 1, 3
Step 13: 2, 0, 3
Step 14: 1, 0, 3
Step 15: 1, 2, 0
B. Optimal: 6-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 2, 3
Step 6: 1, 2, 3
Step 7: 1, 0, 3
Step 8: 1, 2, 0
Step 9: 1, 0, 3
Step 10: 2, 0, 3
Step 11: 2, 1, 0
Step 12: 2, 1, 3
Step 13: 2, 0, 3
Step 14: 1, 0, 3
Step 15: 1, 2, 0
C. LRU: 7-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 1, 2
Step 6: 1, 0, 2
Step 7: 1, 0, 3
Step 8: 1, 2, 0
Step 9: 2, 0, 3
Step 10: 2, 1, 0
Step 11: 2, 1, 3
Step 12: 0, 1, 3
Step 13: 0, 2, 3
Step 14: 1, 2, 3
Step 15: 1, 0, 3

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The probability that the sample contains exactly 4 minorities is 0.0577

We know that 25% of the employees of a large company are minorities. So, from any set of N employees that we ranodmly select from that large company, we can estimate that the number of minorities there is:

0.25*N

Now, we want to find the probability that the sample contains exactly 4 minorities.

Then we need to compute:

[tex]P = 0.25^4*0.75^3[/tex]

We also need to count the permutations for that probability, then we need to add the factor:

[tex]P = 0.25^4*0.75^3*(\frac{7!}{4!*3!} )[/tex]

Solving that we will get:

[tex]P = 0.25^4*0.75^3*(\frac{7!}{4!*3!} )\\\\P = 0.25^4*0.75^3*(\frac{7*6*5}{3*2} )\\\\P = 0.0577[/tex]

That is the probability.

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the perimeter of the 3-on-3 court is 86 meters.

Why it is?

The lengths of the 3-on-3 court (perimeter only) are:

Length: 28 meters

Width: 15 meters

To calculate the length and width of the 3-on-3 court, we can use the dimensions provided by FIBA, the international basketball federation. According to FIBA, the official size of a 3-on-3 court is 15 meters in width and 28 meters in length.

The perimeter of the 3-on-3 court is the sum of all four sides, which can be calculated as follows:

Perimeter = 2 × Length + 2 × Width

Substituting the values of length and width from FIBA's dimensions, we get:

Perimeter = 2 × 28 meters + 2 × 15 meters = 56 meters + 30 meters = 86 meters

Therefore, the perimeter of the 3-on-3 court is 86 meters. It's important to note that the dimensions of the court may vary depending on the location and the level of play, so it's always a good idea to check the official regulations before setting up a court.

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Answer:

  (1, 3) ∪ (5, ∞)

Step-by-step explanation:

You want the solution to the inequality ((x -1)(x -5))/(x -3) > 0.

The sign of the function changes at values of x that make the factors zero, at x = 1, 3, 5. The function is positive for x > 5, so will also be positive for 1 < x < 3

The solution is ...

  1 < x < 3  or  5 < x

__

Additional comment

If any linear factor has an even degree (even multiplicity), there will not be a sign change. The numerator factors correspond to function zeros. The denominator factors correspond to function vertical asymptotes.

The attached graph shows zeros at x=1 and x=5, and a vertical asymptote with a sign change at x=3.

The probability of selecting a diamond or 9 is 1/13.

Step by step explanation: There are 4 suits (diamonds, clubs, hearts, and spades) and 13 ranks (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace). The probability of selecting a card from a standard deck of 52 cards is 1/52.

To calculate the probability of selecting a diamond or a 9, you must first calculate the total number of diamonds and nines in the deck, which is 8 (4 diamonds and 4 nines). The probability of selecting a diamond or 9 is 8/52, which reduces to 1/13.

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Answer:

The appropriate set of hypotheses for Fay's significance test is:

Null Hypothesis: p = 0.26 (the proportion of people in Fay's city who can speak more than one language is the same as the national average)

Alternative Hypothesis: p > 0.26 (the proportion of people in Fay's city who can speak more than one language is higher than the national average)

In other words, Fay is testing if the proportion of people in her city who speak more than one language is significantly different from the national average of 26%. The null hypothesis assumes that the proportion is the same as the national average, while the alternative hypothesis assumes that it is higher.

To conduct her significance test, Fay would need to collect a random sample of people from her city and determine how many of them speak more than one language. Based on this sample proportion, she can calculate a test statistic and determine if it is significantly different from what would be expected under the null hypothesis. If the test statistic is sufficiently large, she can reject the null hypothesis and conclude that the proportion of people in her city who speak more than one language is higher than the national average.

Step-by-step explanation:

Answer:4

Step-by-step explanation:

4

The linear function rule is   y = (1/5)x - 5 .

What is a linear equation, exactly?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                             Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. There are numerous instances of linear equations, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.

The graph of a linear function is a straight line.  

f(0) = -5 means that (0,-5) is a point on the line.  Similarly, (-5,-6) is also a point on the line.  

Slope of line = m = [-6-(-5)]/[-5-0] = -1/(-5) = 1/5

Using the point-slope form, an equation of the line is:

y - (-5) = (1/5)(x - 0)

So, y = (1/5)x - 5

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The complete question is -

Write a rule for a linear function y=f (x), given that f (0) =-5 and f (-5) =-6. Write answers using fractions or integers.

The function rule is f(x) =

The cost of playing Ratio Rage is provided by the equation "Cost(s) of 1 expression Game: 5.5-3 RATIO RAGE!", but we don't know the value of the game's ratio.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

The equation "Cost (s) of 1 Game: 12.70 - n +9" gives the cost of playing Decimal Decisions, but we don't know the number of n, thus we can't determine the overall cost for a group of n persons.

Similarly, the cost of playing Ratio Rage is provided by the equation "Cost(s) of 1 Game: 5.5-3 RATIO RAGE!", but we don't know the value of the game's ratio.

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To find the length of side b in triangle ABC, we can use the Law of Sines. The length of side b is approximately 20.058 inches.

To find the length of side b in triangle ABC, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

Using the Law of Sines, we have:

sin(A)/a = sin(B)/b

We are given the measure of angle B as 78 degrees and side a as 16 inches. We can substitute these values into the equation:

sin(A)/16 = sin(78)/b

To find sin(A), we can use the fact that the sum of the angles in a triangle is 180 degrees:

A + B + C = 180

A + 78 + 52 = 180

A = 180 - 78 - 52

A = 50 degrees

Now we can substitute the values into the equation again:

sin(50)/16 = sin(78)/b

To solve for b, we can cross-multiply and isolate b:

b = (16 * sin(78))/sin(50)

We can calculate the length of side b by evaluating this expression using a calculator. The measurement will be roughly 20.058 inches.

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Answer:

m<1=74

m<2=106

m<3=74

Step-by-step explanation:

m<1:

=180-106

=74

m<2:

=106

m<3;

if m<1 is 74, m<s will also be 74