on average, a customer waits 8 minutes in a queue and the average interarrival time is 4 minutes. what is the average number of customers waiting according to the single-server queue model? (round to the nearest integer)

Answer:

1/2

Step-by-step explanation:

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Answer:

20% of the animals are giraffes

80% of the animals are zebras

=====================================

Explanation:

Let's say there are 5 animals. This would mean there's 1 giraffe and 4 zebras, since we have four zebras per giraffe.

The percentage of giraffes is 1/5 = 0.20 = 20%

and the percentage of zebras is 4/5 = 0.80 = 80%

The requried percentage of giraffes is 20% and the percentage of Zebras is 80%.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,

A zoo has the ratio to zebras (1 giraffe for every 4 zebras)
The total proportion of the zebras and giraffes = 5,
Percentage of giraffe = 1 / 5 × 100% = 20%
Percentage of zebras = 4 / 5 × 100% = 80%

Thus, the requried percentage of giraffes is 20% and the percentage of Zebras is 80%.

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The positive solution of the quadratic equation \(\rm 0=-x^2+2x+1\)  is x=2.41

It is given that the quadratic equation:

\(\rm 0=-x^2+2x+1\)

It is required to find the solution to the above quadratic equation.

A quadratic equation is a second-degree algebraic equation represented by the:

\(\rm ax^2+bx+c=0\)........(1)

Where a, b, and c are the constants and \(\rm a\neq 0\)

We know that:

\(\rm x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

We have:

\(\rm 0=-x^2+2x+1\\\rm or \\\rm -x^2+2x+1=0\) ..........(2)

After comparing (1) and (2) we get:

\(\rm a=-1, b=2, and \ c=1\)

Put these values in the above formula we get:

\(\rm x=\frac{-2\pm \sqrt{2^2-(4)(-1)(1)}}{(2)(-1)}\\\rm x=\frac{-2\pm \sqrt{8}}{-2}\\\rm x=\frac{-2\pm 2\sqrt{2 }}{-2}\\\rm x={1\pm \sqrt{2}}\)

\(\rm x=1+\sqrt{2} \ or \ x=1-\sqrt{2} \\\\\sqrt{2} = 1.41\\\rm so \ x= 1+1.41 \ or \ x= 1-1.41\\\rm x=2.41 or \ x=-0.41\)

Thus, the positive solution of the quadratic equation is x=2.41

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Answer:

x= 2.41

Step-by-step explanation:

Answer:

HJ/LN = HI/LM

Step-by-step explanation:

H corresponds to L

I corresponds to M

J corresponds to N

Answer:

B

Step-by-step explanation:

it's the only one with y^2, which is found by 7y^2-6y^2

Answer:

May I know your question neatly please? I didn't understand your question?

Answer:

False

Step-by-step explanation:

Samantha, this is the solution:

d. x-intercept 3, y-intercept - 5

In consequence the ordered pairs we have are:

(3, 0)

(0, -5)

Now we can find the equation in the form y = mx + b, as follows:

m = (- 5 - 0)/(0 - 3)

m = 5/3

Using the same form, we calculate b, this way:

-5 = 5/3 * 0 + b

-5 = 0 + b

b = -5

Finally, our equation is:

y = 5/3x - 5

On the number line, It is true to the claim that the solution to the expression 32 + (-17) is 17 units from 32 in the positive direction.

A number line is an illustration of a graded straight line that represents actual numbers. What we call a "number line" is really a horizontal line with regularly spaced number increments. The number line's response format is determined by the numbers it contains.

All possible numbers may be plotted along a line called a number line. Any real number may be represented by a single dot on a number line.

On the number line, we have the negative numbers on the -ve x-axis to the left and they are smaller than the positive numbers to the right, and this is immediately apparent when looking at a number line.

Given that:

= 32 + (-17)

= 32 - 17

= 17

We can therefore conclude that the given expression shows that we are 17 units far away from 32 in the positive x-axis on the number line.

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The delivery radius for a pizza restaurant in a town with a population density of 1200 people per square mile that wants to deliver to approximately 25,000 people is 2.6 miles.

To calculate the delivery radius, we can use the following formula:

Delivery radius = square root(population / density)

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In this case, the population is 25,000 and the density is 1200 people per square mile. So, the delivery radius is:

Delivery radius = square root(25,000 / 1200) = 2.6 miles

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This means that the pizza restaurant can deliver to approximately 25,000 people within a 2.6 mile radius of its location.

Here is another way to think about it. If we imagine a circle with a radius of 2.6 miles, then the area of that circle will be approximately 25,000 square miles. This means that the pizza restaurant can deliver to approximately 25,000 people within that circle.

It is important to note that this is just an estimate. The actual delivery radius may be slightly different depending on the terrain, traffic conditions, and other factors.

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We use the format (x, y) to write the coordinates in format XY. Coordinates XY is a coordinate that use in Cartesian coordinate.

What is Cartesian coordinate?

Cartesian coordinate is system to draw a specific location of an unique point in the numerical condition that oriented in the two constant line where the vertical line called ordinate or Y and the horizontal line called abscess or X. The Cartesian coordinate commonly use in architecture or  a design of a certain object that has a certain dilate with its original plan. This design later is use to control the construction process of the original object.

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Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

Step-by-step explanation:

arrange the data from ascending to descending order

2,5,6,10,13,16,26,26,26,27,30

Median=N+1/2      (N means no of data)

=11+1/2

=12/2

=6 th term

=16

rangle = highest value - lowest value

=30-2

=28

Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members’ shared attributes or characteristics, such as income or educational attainment. Stratified random sampling has numerous applications and benefits, such as studying population demographics and life expectancy.

Stratified random sampling is also called proportional random sampling or quota random sampling.

The percentage of adult spiders that have carapace lengths exceeding a certain value is equal to the area under the standard normal curve that lies to the right of that value.

This is because the normal distribution is symmetric around its mean, and the area to the right of a certain value represents the proportion of data points that are greater than that value. Therefore, by calculating the area under the standard normal curve to the right of a certain value, we can determine the percentage of adult spiders with carapace lengths exceeding that value.

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Answer:

135/270+48/96=1/2+1/2=1

Step-by-step explanation:

Answer:

1/15

Step-by-step explanation:

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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Answer:

it means wh

Step-by-step explanation:

it means that what are the size in each side

Step-by-step explanation:

there are multiple concepts we can use.

I will focus on similar triangles. that would mean all angles in both triangles are the same, and the side length ratio of a corresponding side pair is the same for all side pairs.

ABC is similar to WYC.

the lengths of the legs in WYC are clearly half the lengths in ABC.

so, also the baseline of WYC must be half of the baseline of ABC.

therefore,

AB = 2×WY = 2×38 = 76

WYC is similar to XBY. in fact, as the ratio of the side lengths is 1 (because CY = YB), they are not only similar but congruent.

but in any case, with the same ratio of 1 it means that WC = XY = 24

therefore,

AC = 2×WC = 2×24 = 48

AXW is again similar to ABC (because again, the side ratios are the same : 1/2).

so, WX is half of CB

therefore,

WX = CB / 2 = 66/2 = 33

Answer:

22

Step-by-step explanation:

c²= a²+b²= (5.6)²+ (7,1)²=9

P=5.6+7.1+9=21,7=22

The 3-sigma upper control limit for the chart would be 12.73 defects per unit.

To calculate the 3-sigma upper control limit for a control chart, we need to use the formula:
UCL = Average + (3 x Standard Deviation)
First, we need to calculate the average number of defects per unit in the sample. We can do this by dividing the total number of defects by the number of units in the sample:
Average = 500/40 = 12.5 defects per unit
Next, we need to calculate the standard deviation. Since we don't have information on the individual unit defect rates, we'll need to estimate the standard deviation using a method called the "square root of p-bar" formula. This formula assumes that the defect rate is constant across all units and uses the proportion of defective units in the sample to estimate the standard deviation.

p-bar = Total Defective Units / Total Units
p-bar = 500/40 = 0.125
Standard Deviation = \(\sqrt{pbar \cdot (1 - pbar) / n}\)
Standard Deviation = \(\sqrt{0.125 \cdot 0.875 / 40}\) = 0.077
Now we can plug these values into the formula for the UCL:
UCL = Average + (3 x Standard Deviation)
UCL = 12.5 + (3 x 0.077)
UCL = 12.5 + 0.231
UCL = 12.73 defects per unit
Therefore, the 3-sigma upper control limit for the chart would be 12.73 defects per unit.

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Answer:

y = -(1/2)x - 3

Step-by-step explanation:

it is the function for the two points.

The function is  y = -x/2 -3 for the line that includes points of (4,-5) and (8,-7).

A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Here, we have two points  (4,-5) and (8,-7).

Then the equation of line is:

y +5 = (-7+5) / (8-4) x (x - 4)

y + 5 = -1/2 (x-4)

y = -x/2 -3

Therefore, the required function is y = -x/2 -3.

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Answer:

Step-by-step explanation:

Y=(X-3) 3+1

1. Flip the way the equation is facing

1+3 (3-x)=Y

2. Add or Subtract

4 (3-x)=Y

3. Do the parentheses

4(-3x)=Y

4. Solve for X ( Undo addition or Subtraction)

(4-4)=0

What ever you do to one side you have to do to the other!

Y-4

Your New Equation Looks Like

-3x= -4 + Y

5. Undo Multiplication

-3x/3= x

What ever you do to one side you have to do to the other!

-4/3 y/3

6. Divide Y

y/3= 3

7. New equation

X= -4/3 + 3

8. Plug in X to the Original Equation

Y=2(-4/3+3) -3 +(3+1)

9. Solve accordingly

Answer:

\(1\frac{1}{2}\) or, \(\frac{3}{2}\)

Step-by-step explanation:

1.5 = \(1\frac{1}{2}\)

Answer:

Simplest Form: 1 \(\frac{1}{2}\)

Other forms you can use:

1 \(\frac{2}{4}\)

1 \(\frac{3}{6}\)

1 \(\frac{4}{8}\)

1 \(\frac{5}{10}\)

Answer:

Step-by-step explanation:

9) 9xt

10) r-10

The value of the variable x is 23

Supplementary angles are simply described as pair of angles which sum up to 180 degrees.

Some properties of supplementary angles are;

From the information given, we have that;

x + 1 and 7x - 5 area supplementary

Then, we have the representation as;'

x + 1 + 7x - 5 = 180

collect like terms

8x = 180 + 4

8x = 184

make 'x' the subject of formula

x = 23

Hence, the value is 23

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Answer:

about 179 blue candies in a bag 0f 1,000 candies . .

. .

Step-by-step explanation:

. . .

Answer:

216

Step-by-step explanation:

21/135 are blue

This is a ratio problem so first we find how many 135s go into 1000 by doing 1000/135 = approx 8

So with this we would expect approximately 27 x 8 candies which is 216 :)