calls arrive at lynn ann fish's hotel switchboard at a rate of 2.0 per minute. the average time to handle each is 10 seconds. there is only one switchboard operator at the current time. the poisson and negative exponential distributions appear to be relevant in this situation. what is the probability, as a percent, that the operator is busy

Por descomposición factorial y el concepto de máximo común divisor, se tiene que cada trozo de cuerda debe medir 6 metros y que se debe preparar cinco trozos.

En este problema debemos determinar la cantidad de segmentos de cuerda de igual y máxima longitud, la cual puede ser hallado por descomposición factorial a los números asociados a las longitudes:

18 = 2 × 3²

12 = 2² × 3

La máxima longitud posible se obtiene mediante el máximo común divisor, es decir, se encuentra que la máxima longitud es 2 × 3 = 6 metros. Por último, la cantidad de trozos iguales es:

x = (18 m + 12 m)/6 m

x = 30 m/6 m

x = 5

Por descomposición factorial y el concepto de máximo común divisor, se tiene que cada trozo de cuerda debe medir 6 metros y que se debe preparar cinco trozos.

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By power properties the exponential expression [tex]\frac{8^{2\cdot m}}{8^{m^{2}}}[/tex] is only equivalent to [tex]8^{2\cdot m-m^{2}}[/tex]. (Correct choice: A)

In this question we must apply power properties to prove if a given expression have at least one equivalent. Now we proceed to show alternative forms:

[tex]\frac{8^{2\cdot m}}{8^{m^{2}}}[/tex]

[tex]8^{2\cdot m-m^{2}}[/tex]

By power properties the exponential expression [tex]\frac{8^{2\cdot m}}{8^{m^{2}}}[/tex] is only equivalent to [tex]8^{2\cdot m-m^{2}}[/tex]. (Correct choice: A)

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The two rational expressions will be; (x + 2)/(x² - 36) and 1/(x² + 6x)

We want to determine the two rational expressions whose difference completes the equation.

The two rational expressions will be;

(x + 2)/(x² - 36) and 1/(x² + 6x)

Now, this can be proved as follows;

Step 2 [(x + 2)/(x² - 36)] - [1/(x² + 6)]

= [(x + 2)/(x + 6)(x - 6)] - [1/(x(x + 6)]

Step 3; By subtracting, we have;

[x(x + 2) - (x - 6)]/[x(x + 6)(x - 6)]

Step 4; By further simplification of step 3, we have;

[x² + x + 6]/[x(x-6)(x + 6)]

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The number of hours it would take to make 450 wackiest widgets is 4 hours 30 minutes.

The first step is to determine how many minutes it would take to make 1 widget.

Minutes it would take to make 1 widget ; 90 / 120 = 3 / 4 minutes

Number of minutes it would take to make 450 widgets: 3/4 x 450 = 270 minutes

Now convert minutes to hours : 270 / 60 = 4 hours 30 minutes

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Answer:

`18. x=9

19. x=4

20. x=25,5

21. x=3

22. x=3,5

23. x=10

Step-by-step explanation:

Answer:

OA=4x²-19

Step-by-step explanation:

4(x²-5)+1

4x²-19

Answer: 450 rest 100

Step-by-step explanation:

So, we need to calculate this division 100.000/222 and get the rest.

Well, 222 enters in 1000 by 4 times.

222 times 4 is 888

So, 100.000/222 = 4

       888-

We subtract 888 from 1000.

That will be 112

100.000/222 = 4

888

  112

Now, get the next 0 down next to 112

100.000/222 = 4

888

 1120

222 get in 1120 by 5 times.

5 times 222 = 1110

divide 1120 by 1110

100.000/222 = 45

888

 1120

 1110

That will be 10

100.000/222 = 45

888

 1120

 ==10

Get the next zero down

100.000/222 = 45

888

 1120

 ==100

222 gets in 100 by 0 times.

100.000/222 = 450

888

 1120

 ==100

         0

100 subtracted by 0 is 100

100.000/222 = 450

888

 1120

 ==100

         0

     100

The rest is 100 and the result is 450

Now, you can do the verification:

222 time 450 is 99,900.

If you add the rest to 99,900 it will be 100.000. So the result is good

The solution of the equation is union of  x = a(π/2) where a = 1,2,3......∞ and x = n(π) where n = 1,3,5,7.......∞.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable.

sin²x = cosx + 1

1 - cos²x = cosx + 1

cos²x + cosx = 0

cosx(cosx + 1) = 0

When cosx = 0

x = a(π/2) where a = 1,2,3......∞

When cosx = -1

x = n(π) where n = 1,3,5,7.......∞

Hence the solution of the equation will be the union of x = a(π/2) where a = 1,2,3......∞ and x = n(π) where n = 1,3,5,7.......∞.

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The set is expressed using inequalities; [tex]0 < x\leq 3[/tex], option D is correct.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

A collection of inequalities for which we consider a common solution for all inequalities is called a system of inequalities.

The set be expressed using inequalities are;

[tex]0 < x\leq 3[/tex].

Thus, option D is correct.

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Answer:

74.8 cm^2

Step-by-step explanation:

The figure is a parallelogram with base of 11cm and height of 6.8cm . To find the area, we multiply the base by the height to get 11 × 6.8 = 74.8 cm^2

121.3 grams of caffeine is remaining in her blood

The given parameters are:

The amount of caffeine is calculated as:

A(t) = a(1 - r)^t

This gives

A(t) = 175 * (1 - 11.5%)^t

At 3 hours, we have:

A(3) = 175 * (1 - 11.5%)^3

Evaluate

A(3) = 121.3

Hence, 121.3 grams of caffeine is remaining in her blood

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Using translation concepts, it is found that the new function was reflected over the x-axis and vertically compressed by a factor of 3.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The functions are given as follows:

The translated function was multiplied by -1/3, hence it was reflected over the x-axis(multiplication by negative number) and vertically compressed by a factor of 3(fraction of 1/3).

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Answer:

d. The triangles are not similar because 6/13 ≠ 8/20.

Step-by-step explanation:

△ABC is similar to △DEF ,If the length of their corresponding sides are proportional.

ie : 6/13 = 8/20 = 10/25

Since , 6÷13 = 0.461538461538 ≠ 0.4 = 8÷20

Then

6/13 ≠ 8/20

Therefore , the triangles are not similar.

Answer:

[-7, + ∞)    is domain

Step-by-step explanation:

Domain    is all of the 'x' values a function has

  this one goes from   -7 to + inf

The choice which is equivalent to; √(4-x²)/√(2-x) is; √(2-x).

According to the task content, it follows that the expression whose equivalent is to be determined can be evaluated as follows;

√(4-x²)/√(2-x) = √(4-x²)/(2-x)

Hence, the numerator can be evaluated by difference of two squares where;

(4-x²) = (2-x)(2+x)

Hence; we have; √(2-x)(2+x)/(2-x) = √(2-x).

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Answer:

sqrt 2+x

Step-by-step explanation:

The quotient of [tex]x^{4} +5x^{3} -3x-15[/tex] and [tex]x^{3} -3[/tex] is (x+5).

Given expression  [tex]x^{4} +5x^{3} -3x-15[/tex] and [tex]x^{3}-3[/tex] and we have to find the quotient of the first expression.

Quotient is any quantity produced by dividing two numbers. It can be of simple numbers or expressions also. Remainder is a number or expression that is left after division.

To find the quotient of [tex]x^{4}+5x^{3} -3x-15[/tex], we have to divide the expression by [tex]x^{3}-3[/tex].

We know that,

Divident=Divisor*quotient+remainder

[tex]x^{4}+5x^{3}-3x-15[/tex]=([tex]x^{3}-3[/tex])*(x+5)+0

By equating from the given formula we can find that the value of quotient is  (x+5).

Hence the quotient of [tex]x^{2} +5x^{3} -3x-15[/tex] by dividing it by [tex]x^{3} -3[/tex] is (x+5).

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Question is incomplete as the expressions are incomplete. They should be like [tex]x^{4} +5x^{3} -3x-15[/tex] and [tex]x^{3} -3[/tex]

Answer: [tex]33.56^{\circ}[/tex]

Step-by-step explanation:

[tex]\sin \alpha=\frac{\sqrt{11}}{6}}\\\\\alpha=\sin^{-1} \left(\frac{\sqrt{11}}{6}} \right)\\\\\alpha \approx 33.56^{\circ}[/tex]

Answer:

33.56

Step-by-step explanation:

The distance apart of the two guy wire is 187.7 metres

The distance apart of the two wires can be found using trigonometric ratios.

Therefore,

tan ∅ = opposite / adjacent

Therefore,

tan 13 = 27 / x

x = 27 / tan 13 = 27 / 0.23086819112 = 117.391304348

tan 21 = 27 / y

y = 27 / tan 21

y = 70.338144115

Therefore,

distance apart of the guy wire = 117.391304348 + 70.338144115 = 187.728144115 = 187.7 metres

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Q6: A, Árbol

Q7: D, nube

Q8: C, Viento

Q9: B,

Q10: D, Cielo

Q11: D, Hablarian

Answer:

The answer is x= -15

The statement and reason that complete the flowchart proof are:

1. ∠BDE ≅ ∠BAC

2. Corresponding angles postulate.

The corresponding angles postulate states that two angles that correspond to each other are congruent angles.

In the given flowchart proof, ∠BDE and ∠BAC are corresponding angles, So, they are congruent by the corresponding angles postulate.

Therefore, the missing statement and reason are:

1. ∠BDE ≅ ∠BAC

2. Corresponding angles postulate.

The remaining part of the question is

"In ΔABC shown below, BD over BA equals BE over BC:

Triangle ABC with segment DE intersecting sides AB and BC respectively.

Top path, by Given the ratio of line segments BD to BA is equal to the ratio of line segments BE to BC. By Side Angle Side.

Which reason can be used to fill in the numbered blank space?"

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Answer:

See below

Step-by-step explanation:

An invalid solution.

When you use the quadratic formula, for example, to  solve for 't', time, you will often find one of the values of 't' to be  NEGATIVE value for time.....this would be an extraneous solution.      

   Sometimes when working with LOG equations you may fin an answer which is negative.....you cannot have a LOG of a negative number...THAT solution would be EXTRANEOUS

 ETC

SO, always check your answers to see if they 'work' for your problem.

The constant of proportionality of the given graph is gotten as 4.

The constant of proportionality here is simply the slope of the graph.

Now, we will take two points and use their coordinates to find the slope from the formula;

m = (y2 - y1)/(x2 - x1)

Let us pick 2 points which are;

(1, 4) and (2, 8). Thus;

m = (8 - 4)/(2 - 1)

m = 4/1

m = 4

Thus, the constant of proportionality of the graph is gotten as 4.

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Answer: [tex]-3y^3 -4[/tex]

Step-by-step explanation:

[tex]\frac{27y^4 + 36y}{-9y}=-3y^3 -4[/tex]

Answer:

Hence, 3,40,000 can be expressed as [tex]$$3.4\times10^5$$[/tex]

Step-by-step explanation:

Step 1 of 1

Consider 3,40,000

3.4

So, 3.4 lies between 1 & 10

Now, Decimal has moved 5 places to left.

[tex]$3.4=10^{5}$[/tex]

So, 3,40,000=[tex]3.4 \times 10^{5}$[/tex]

The parabolas with respect to their positions are y = f(x + 3), y = f(x + 2), y = f(x - 1/2), y = f(x - 4) and f = (x - 7)

The parent function is given as:

f(x) = x^2

The parabolas are given as:

y = f(x - 4), y = f(x + 3), y = f(x - 7), y = f(x + 2) and f = (x - 1/2)

The transformation from the parent function to each of the parabola is a horizontal translation.

This means that the y coordinate of their vertices are the same.

Arrange the parabolas starting from the left translations

y = f(x + 3), y = f(x + 2), y = f(x - 1/2), y = f(x - 4) and f = (x - 7)

Hence, the parabolas with respect to their positions are y = f(x + 3), y = f(x + 2), y = f(x - 1/2), y = f(x - 4) and f = (x - 7)

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The critical z value which should be used in determining the confidence interval is z=1.29 and the confidence interval is (38.43355,66.82645).

Given sample mean of $52.63 and standard deviation of $22.01.

We have to construct  the confidence interval of 80% for the mean repair cost for the washers.

μ=52.63

σ=22.01

n=4

First we have to find the value of z for the confidence level of 80% from z table and which is 1.29.

Margin of error is the difference between the calculated values and real values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where μ is mean

σ is standard deviation

n is sample size

z is z value for the confidence level

Margin of error=1.29*22.01/[tex]\sqrt{4}[/tex]

=14.19645

Confidence interval =mean ±margin of error

Upper level=mean +margin of error

=52.33+14.19645

=66.82645

Lower level=mean-margin of error

=52.33-14.19645

=38.43355

Hence the confidence interval is (38.43355,66.82645) and the critical value used is z=1.29.

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Answer:

radius is 62.04

Step-by-step explanation:

use the formula V=

[tex] v= \frac{4}{3} \pi {r}^{3} [/tex]

The next step Nolan should take is to find the average of the distances from the mean.

A measure of variance in a data set is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.

The steps to find mean absolute deviation are:

Hence, The next step Nolan should take is to find the average of the distances from the mean.

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