Ocala software systems operates a technical support center for its software customers. if customers have installation or use problems with ocala software products, they may telephone the technical support center and obtain free consultation. currently, ocala operates its support center with one consultant. if the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. the customer is then asked to hold and is told that a consultant will provide assistance as soon as possible. the customer calls follow a poisson probability distribution, with an arrival rate of seven calls per hour. on average, it takes 8.5 minutes for a consultant to answer a customer's questions. the service time follows an exponential probability distribution. to improve customer service, ocala software systems wants to investigate the effect of using a second consultant at its technical support center. what is the probability that a customer will have to wait for one of the consultants

Answer:

9 plus 11 plus 12 =

Step-by-step explanation:

x is 22

The total cost price of the basket is $22.

What is Discount ?

 The discount is determined by dividing the purchase price by the item's par value. The discount is a type of cost price reduction or deduction for a product. It is primarily employed in consumer interactions when discounts on various goods are offered to customers. A percentage represents the discount rate.

Here ,

Original cost price of the basket = $40

After 50% offer the cost price of the bag is,

=> 40- 50% of 40

=> 40 - 20

=> $20.

Now the sales tax is 10% then,

=> 20+ 10% of 20

=> 20+ 2

=>$22

Therefore the total cost is $22 after discount.

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The fourth step of the risk assessment process is to determine current level of preparedness/mitigation.

The correct option is C.

A risk assessment is a procedure for identifying potential dangers and analyzing what might happen if one happens. A business impact analysis (BIA) is a procedure that determines the probable consequences of interrupting time-sensitive or important business processes. There are various potential hazards to be mindful of.

The ultimate goal of risk assessments is to improve workplace safety and health. However, to order to accomplish this, your risk assessment process must identify occupational hazards and eliminate or reduce the risks they represent.

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The problem can be modeled as a linear programming problem. We need to minimize the total cost of shipping the boots, which can be represented as a linear combination of the shipment quantities.

Thus, the objective function to be minimized can be written as:

Minimize Z = 4x11 + 5x12 + 7x13 + 6

32 + y33 ≤ 40 (capacity limit at warehouse 3)

y41 + y42 + y43 ≤ 30 (capacity limit at warehouse 4)

y51 + y52 + y53 ≤ 45 (capacity limit at warehouse 5)

xij, yjk ≥ 0 (non-negativity constraint)

Thus, the complete linear programming problem can be formulated as:

Minimize Z = 4x11 + 5x12 + 7x13 + 6x21 + 4x22 + 5x23 + 4y11 + 3y12 + 6y13 + 5y21 + 5y22 + 4y23 + 6y31 + 7y32 + 5y33 + 4y41 + 6y42 + 5y43 + 5y51 + 4y52 + 6y53

Subject to:

x11 + x12 + x13 ≤ 60

x21 + x22 + x23 ≤ 90

x11 + x21 = y11 + y21 + y31 + y41 + y51

x12 + x22 = y12 + y22 + y32 + y42 + y52

x13 + x23 = y13 + y23 + y33 + y43 + y53

y11 + y12 + y13 ≤ 35

y21 + y22 + y23 ≤ 50

y31 + y32 + y33 ≤ 40

y41 + y42 + y43 ≤ 30

y51 + y52 + y53 ≤ 45

xij, yjk ≥ 0

Solving this linear programming problem using a suitable solver will provide us with the optimal values of xij and yjk, which will help us in determining the minimum cost required for shipping the boots while satisfying all the constraints.

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Answer:

7

Step-by-step explanation:

Given the following :

7 heart stickers and 14 star stickers :

The greatest number of pages that can be decorated using the stickers above without any left over ;

To get this we obtain the greatest common factor of 7 and 14

Factors of 14

14 : 1, 2, 7, 14

Factors of 7

7 : 1, 7

The greatest factor common in both numbers is 7

Hence, greatest number of pages that can be decorated without any leftover is 7

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?

Alicia have to pay $10,000 and her insurance will pay $10,500.

What is limit of coverage in insurance?

This limit is the most the insurer will pay for sums as damages because of bodily injury or property damage included within the products-completes operations hazard during the policy period.

Given that Alicia has a collision deduction of $500 and a bodily injury coverage limit of $50,000.

And there is a verdict to compensate the injured person for $40,000

Therefore Alicia have to pay

$50,000-$40,000 = $10,000

And her insurance will pay

$10,000 + $500 = $10,500

Hence Alicia have to pay $10,000 and her insurance will pay $10,500.

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Answer:

Chris will take 0.75 seconds to return to his starting height of 10 feet.

Step-by-step explanation:

Let the height of Chris be represented by \(h(t) = -16\cdot t^{2}+12\cdot t +10\), where \(h(t)\) is the height in feet and \(t\), the time in seconds. First, we equalize the formula to a height of 10 feet and simplify the resulting expression, that is:

\(-16\cdot t^{2}+12\cdot t +10 = 10\)

\(-16\cdot t^{2}+12\cdot t = 0\)

Then, we simplify the expression by algebraic means:

\(-16\cdot t\cdot \left(t-\frac{3}{4} \right) = 0\)

Roots of the polynomial are, respectively:

\(t = 0\,s\,\lor \,t = 0.75\,s\)

First root represents the initial height of Chris, whereas the second one represents the instant when Christ returns to the same height above the surface of the water. Hence, Chris will take 0.75 seconds to return to his starting height of 10 feet.

The probability in a normal distribution is approximately 90% percent.

According to the statement

we have given that the

Probability of the more three standard deviations and we have to find the percentage  in a normal distribution.

We know that the

A normal distribution is a type of continuous probability distribution for a real-valued random variable.

So,  In the presence of a more than three standard deviations the normal distribution is about 95%.

Because in the normal distribution is 95% due to the empirical rule.

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.

So, The probability in a normal distribution is approximately 90% percent.

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Answer:

every option but the first one

Step-by-step explanation:

5 and 7 are verticals meaning they have the same angle degree

7 and 4 are supplementary angles meaning the sum of them = 180

1 and 7 are corresponding meaning they have the same angle degree

the overall speedup in percentage is approximately 22.47%. This means that the system's execution time is improved by approximately 22.47% after the disk upgrade is applied.

Amdahl's Law is used to calculate the overall speedup of a system when only a portion of the system's execution time is improved. The formula for Amdahl's Law is: Speedup = 1 / [(1 - P) + (P / S)], where P represents the proportion of the execution time that is improved and S represents the speedup achieved for that proportion.

In this case, the system spends 55% of its time on I/O, so P = 0.55. The disk upgrade provides for 50% greater throughput, which means S = 1 + 0.5 = 1.5.

Plugging these values into the Amdahl's Law formula, we have Speedup = 1 / [(1 - 0.55) + (0.55 / 1.5)].

Simplifying further, we get Speedup = 1 / [0.45 + 0.3667].

Calculating the expression in the denominator, we find Speedup = 1 / 0.8167 ≈ 1.2247.

Therefore, the overall speedup in percentage is approximately 22.47%. This means that the system's execution time is improved by approximately 22.47% after the disk upgrade is applied.

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Tables are created by substitute a set of input values into the function to create outputs. The required table is as shown below

x | y

0   -3

1   -2.5

2   -2

Tables are created by substitute a set of input values into the function to create outputs

Using x = 0, 1 and 2 as the input values

Given the function

y = 1/2x - 3

If x = 0

y = 1/2(0) - 3

y = -3

If x = 1

y = 1/2(1) - 3

y = -2.5

If x = 2

y = 1/2(2) - 3

y = -2

Hence the required table is as shown below

x | y

0   -3

1   -2.5

2   -2

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Each function out of the given 4 functions has a horizontal asymptote.

An asymptote is a straight line that continually approaches a given curve but does not meet it at any finite distance.

Mathematically, if y=k is a horizontal asymptote for a function x=f(y) the limiting value of the function is infinity as y→k.

Out of the given curves, for every curve limiting value of the function tends to infinity as y→0

So, each function out of the given 4 functions has a horizontal asymptote.

Therefore, each function out of the given 4 functions has a horizontal asymptote.

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Answer:

All of them

Step-by-step explanation:

Answer:

no,the pathway of the walker and cub don't intersect

Step-by-step explanation:

(4 - 3)^2 x (5 x 4)^0 =

(1)^2 × (20)^0 =

1 × 1 =

1

respusta 1

corazon  esterllsa  5

Based on the given information, Carl's car wash takes a constant time of 4.5 minutes in its automated car wash cycle. Autos arrive following a Poisson distribution at the rate of 10 per hour. Using this information, Carl can calculate the expected time it would take to wash a car.

The first step is to calculate the average time between car arrivals, which is equal to 60 minutes divided by the arrival rate of 10 cars per hour, giving an average time of 6 minutes per car. Since the wash cycle time is constant at 4.5 minutes, Carl can add these two values together to get an expected wash time of 10.5 minutes per car.

However, it's important to note that this is just an expected time, and there may be variations due to factors such as queue length, equipment malfunctions, or other unforeseen circumstances. Therefore, Carl should regularly monitor his car wash operation and make adjustments as necessary to ensure efficient and consistent service.

In summary, Carl's car wash takes a constant time of 4.5 minutes in its automated car wash cycle, and with autos arriving at a rate of 10 per hour, the expected time it would take to wash a car is 10.5 minutes.

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(a) gcd(18675, 20112340) = 15.

(b) prime factors for 18675 are 3, 5, and 11 and for 20112340, prime factors are 2, 5, 17, 37, and 1129.

(c) the lcm of 18675 and 20112340 is: 2² * 3¹ * 5² * 11² * 17¹ * 37¹ * 1129¹

(a) To find the greatest common divisor (gcd) of 18675 and 20112340, we can use the Euclidean algorithm. We start by dividing the larger number, 20112340, by the smaller number, 18675.

The remainder of this division is obtained by subtracting the product of the quotient and the smaller number from the larger number. We repeat this process by dividing the previous divisor (18675) by the remainder until we reach a remainder of 0. The last non-zero remainder is the gcd.

Using the Euclidean algorithm:

20112340 = 18675 * 1076 + 240

18675 = 240 * 77 + 165

240 = 165 * 1 + 75

165 = 75 * 2 + 15

75 = 15 * 5 + 0

The last non-zero remainder is 15, so gcd(18675, 20112340) = 15.

(b) To factor the numbers 18675 and 20112340, we can find their prime factors. Prime factorization involves decomposing the numbers into a product of prime numbers.

For 18675, we can start by dividing it by the smallest prime number, 2, repeatedly until we can no longer divide evenly. The resulting prime factors are 3, 5, and 11, and their exponents are determined by the number of times each prime divides the number.

18675 = 3¹ * 5² * 11²

For 20112340, we can follow a similar process to find its prime factors. The resulting prime factors are 2, 5, 17, 37, and 1129.

20112340 = 2² * 5¹ * 17¹ * 37¹* 1129¹

(c) The least common multiple (lcm) of two numbers can be found by taking the product of their prime factors with the highest exponent for each prime factor that appears in either number.

To find the lcm of 18675 and 20112340, we consider their prime factorizations:

18675 = 3¹ * 5² * 11²

20112340 = 2² * 5¹* 17¹ * 37¹ * 1129¹

The lcm is obtained by taking the highest exponent for each prime factor:

Therefore, the lcm of 18675 and 20112340 is :

2² * 3¹ * 5² * 11² * 17¹ * 37¹ * 1129¹

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Answer:

diameter=radius divided by 2

The value of f(2) as calculated by the given function is 14.

Given function:-

\(f(x)=2x^3-2\)

We have to find the value of f(2).

Putting x = 2 in the given function, we get:-

\(f(2)=2(2)^3-2\)

We know that the cube of 2 is 8. Hence, we can write,

f(2) = 2*8 -2 = 16 - 2 = 14.

Function

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

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a. Two populations.

b. Qualitative (categorical) data.

c. Proportion stats.

d. Null hypothesis: p1 = p2 (The proportion of seniors who bring a bag lunch is equal to the proportion of sophomores who bring a bag lunch). Alternative hypothesis: p1 > p2 (The proportion of seniors who bring a bag lunch is greater than the proportion of sophomores who bring a bag lunch).

e. Z-test for two proportions.

f. P-value.

g. A small P-value provides convincing evidence to support Phoebe's hunch that older students are more likely to bring a bag lunch than younger students.

h. 95% confidence interval to estimate the difference in proportions.

What is hypothesis?

A hypothesis is a proposed explanation or assumption that is tested through research and data analysis. It is a statement that suggests a relationship or difference between variables or phenomena and serves as a basis for scientific investigation.

a. There are two populations in this problem: the population of seniors and the population of sophomores.

b. This is a problem about qualitative (categorical) data since we are examining whether students bring a bag lunch or not.

c. We will use the proportion stats option in StatCrunch to complete this problem.

d. Null hypothesis (H0): The proportion of seniors who bring a bag lunch is equal to the proportion of sophomores who bring a bag lunch.

Alternative hypothesis (Ha): The proportion of seniors who bring a bag lunch is greater than the proportion of sophomores who bring a bag lunch.

e. The test statistic is the z-test for two proportions.

f. The P-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

g. The strength of the P-value determines the level of evidence against the null hypothesis. If the P-value is small (below the significance level), it provides strong evidence against the null hypothesis. In this case, a P-value less than 0.05 (assuming significance level α = 0.05) would suggest convincing evidence to support Phoebe's hunch.

h. To construct a 95% confidence interval to estimate the difference in proportions, we use the formula:

Confidence interval = (p1 - p2) ± z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and z is the critical value corresponding to the desired confidence level (in this case, z value for a 95% confidence level).

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From the given information provided, the number of people having brown eyes in town is 180.

If the probability that a person in the town has brown eyes is 2/5, then we can expect that 2 out of every 5 people have brown eyes.

To find the number of people in the survey who would be expected to have brown eyes, we can use the following proportion:

(2/5) = (x/450)

where x is the number of people expected to have brown eyes.

Solving for x, we can cross-multiply:

5x = 2 × 450

5x = 900

x = 180

Therefore, the expected number of people in the survey who would have brown eyes is 180.

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For this case, the first thing we must do is define variables.

We have then:

n: number of cans that each student must bring

We know that:

The teacher will bring 5 cans

There are 20 students in the class

At least 105 cans must be brought, but no more than 205 cans

Therefore the inequation of the problem is given by:

Answer:

105 < 20n + 5 < 205

the possible numbers n of cans that each student should bring in is:

105 < 20n + 5 < 205

Hi! I will help you with a smile!

First of all, we have the slope of the line and a point that it passes through.

Let’s write the line’s equation in Point-Slope Form:

y-y1=m(x-x1)

Where

y1 is the y-coordinate of the point, m is the slope of the line, and x1 is the x-coordinate.

In this case, y1=-4, m=-6, and x1=3

Solve:

y-(-4)=-6(x-3)

y+4=-6x+18

y=-6x+18-4

y=-6x+14 (Answer)

Hope it helps.

Do comment if you have any query regarding my answer.

Answered by

PeacefulNature :-)

Answer:

y = -6x+14

Step-by-step explanation:

m = -6 ,given as x an y (3,-4)

solution y-y1 = m(x-x1)

y-(-4) = -6(x-3)

y+4 = -6x+18

then y = -6x+18-4

y = -6x+14

Yes, the conditions for inference are met. The teacher conducts 50 trials, which is large enough to meet the large counts condition (np ≥ 10 and n(1-p) ≥ 10).

The teacher's attempt to make the number cube unfair by inserting lead weights raises the question of whether the proportion of rolls that will land on a 1 has changed. To determine if she was successful, the teacher rolls the cube 50 times and keeps track of the number of times she rolls a 1. The data shows that she rolled a 1 15 times.

To determine if the data provides convincing evidence that the proportion of rolls that will land on a 1 is greater than one-sixth, we need to check if the conditions for inference are met.

The 10% condition requires that the sample size is less than 10% of the population size. Since we do not know the population size, we cannot determine if this condition is met.

The large counts condition requires that both the number of successes (15) and the number of failures (35) are greater than or equal to 10. This condition is met.

The randomness condition requires that the sample is random. Since the teacher rolled the cube, it is assumed that the rolls were random.

Therefore, the conditions for inference are met. We can use a hypothesis test to determine if the data provides convincing evidence that the proportion of rolls that will land on a 1 is greater than one-sixth.

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Answer:

14

Step-by-step explanation:

164 = 8x + 52

Subtract 52 from both sides

112 = 8x

Divide both sides by 8

14 = x

Answer: 5

Step-by-step explanation:

Using the law of similar triangles,

x/x-2 = x+(x+5)/x+1+x-2

x/x-2 = 2x+5/2x-1

x(2x-1) = x-2(2x+5)

2x²-x = 2x²+x-10

2x²-2x² + x +x -10 = 0

2x-10 = 0

2x = 10

x = 5

Hope this helps! :)

Complementary means something is hard

Answer:

According to an advertisement for Colgate toothpaste, 4 out of 20 Dentist prefer Colgate. There are 150 Dentist in a certain city.

Let the number of dentists prefer Colgate in the city be x

\( \frac{4}{20} = \frac{x}{150} \\ x = \frac{4 \times 150}{20} \\ \boxed{x = 30}\)

The inequality which represents is 2x + 3y ≤ 12 where x is the number of daisies and y is the number of tulips.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

Suppose the cost of one daisy is x while the cost of one tulip is y.

2x + 3y will be totally spent and it can be almost $12.

2x + 3y ≤ 12

Hence "The inequality which represents is 2x + 3y ≤ 12 where x is the number of daisies and y is the number of tulips.".

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