a) Students returning to a secondary school have to pass through a check point at the rate of 50 per though. The average time for checking is 35 seconds. The arrival rate and service rate follow a Poisson distribution. There is a delay and the principal is willing to include another check point to reduce the average time of checking to 28 seconds if the idle time is less than 10% and the average queue length is more than 10 students, check whether the introduction of an extra check point is justifiable

A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.

En este problema tenemos un sistema formado por dos triángulos similares, la semejanza entre los dos triángulos se debe a la colinealidad entre los segmentos de línea AP' (triángulo pequeño) y AP'' (triángulo grande), así como de los lados AM y AB, así como los lados AN y AC, así como los mismos ángulos en la misma distribución. (Semejanza Lado - Ángulo - Lado)

En consecuencia, obtenemos las siguientes proporciones:

AP'/AP'' = MN/BC = 1/2     (1)

Finalmente, la proporción entre el triángulo AMN y el cuadrilátero BMNC es:

[tex]\frac{AMN}{ABC - AMN} = \frac{\frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)}{\frac{1}{2}\cdot (2\cdot a) \cdot h - \frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)} = \frac{\frac{1}{4}\cdot a\cdot h }{a\cdot h - \frac{1}{4}\cdot a \cdot h }[/tex]

[tex]\frac{AMN}{ABC - AMN} = \frac{\frac{1}{4} }{\frac{3}{4} } = \frac{1}{3}[/tex]

A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.

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Answer:

Step-by-step explanation:

B=CD-A

Answer:

  46

Step-by-step explanation:

The geometry can be modeled by a right triangle. The diagonal measure is the hypotenuse, and the height is one leg. The width is the other leg, and can be found using the Pythagorean theorem.

__

The relation between the leg lengths (a, b) and the hypotenuse (c) is ...

  c² = a² +b²

Solving for b gives ...

  b = √(c² -a²)

In this problem, we have c=55 and a=30. Then the width of the TV is ...

  b = √(55² -30²) = √(3025 -900) = √2125

  b ≈ 46.098

The width of the TV is about 46.

Answer:

4

Step-by-step explanation:

4

The possible values of x are:

x = -1/2 + i/2

x = -1/2 - i/2

A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.

To find the possible values of x in equation 8x² + 4x = -1, we need to solve for x.

First, we can rearrange the equation to get:

8x² + 4x + 1 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).

In this case, a = 8, b = 4, and c = 1. Substituting these values into the quadratic formula, we get:

x = (-4 ± √(4² - 4(8)(1))) / 2(8)

x = (-4 ± √(16 - 32)) / 16

x = (-4 ± √(-16)) / 16

x = (-4 ± 4i) / 16

where i is the imaginary unit, which is defined as the square root of -1.

Therefore, the possible values of x are:

x = (-4 + 4i) / 16

x = (-4 - 4i) / 16

These values can also be simplified as:

x = -1/2 + i/2

x = -1/2 - i/2

So the possible values of x are complex numbers, specifically x = -1/2 ± i/2.

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Answer:

[tex]\boxed{\sf x = \dfrac{1}{21}}[/tex]

Explanation:

[tex]\rightarrow \sf 3x+7-6= \dfrac{8}{7} - 0[/tex]

simplify the following

[tex]\rightarrow \sf 3x+1= \dfrac{8}{7}[/tex]

subtract 1 from both sides

[tex]\rightarrow \sf 3x+ 1 -1= \dfrac{8}{7} - 1[/tex]

simplify the following

[tex]\rightarrow \sf 3x= \dfrac{1}{7}[/tex]

multiply both sides by 1/3

[tex]\rightarrow \sf 3x \cdot \dfrac{1}{3}= \dfrac{1}{7}\cdot \dfrac{1}{3}[/tex]

simplify the following

[tex]\rightarrow \sf x = \dfrac{1}{21}[/tex]

[tex]3x + 7 - 6 = \frac{8}{7} - 0 \\ \\ 3x + 1 = \frac{8}{7} \\ \\ 3x = \frac{8}{7} - 1 \\ \\ 3x = \frac{ 8 - 7}{7} \\ \\ 3x = \frac{1}{7} \\ \\ x = \frac{1}{7 \times 3} \\ \\ x = \frac{1}{21} .[/tex]

Answer:Yes, the point lies on the line.

Step-by-step explanation:

Given coordinate of the locus = (1,2)

 Equation of the line  2x+4y = 10

Unknown:

Does the given coordinate lie on the line?

Solution:

The equation given is that of a straight line. To solve this problem, we simply plug the coordinates of the point back into the equation and check if solves it.

  x  = 1 and y = 2;

  2x+4y = 10

So;

   2(1) + 4(2) gives 2 + 8 = 10

Yes, the point lies on the line.

Answer:

-3/2, -1

Step-by-step explanation:

Each coordinate contains one [tex]x[/tex] value and one [tex]y[/tex] value, [tex](x,y)[/tex].

If we work out the midpoint of each of these individually, it makes it much easier to find the midpoint of the line.

Let's take the [tex]x[/tex] values first. Our first  [tex]x[/tex] value is -4 and our second [tex]x[/tex] value is 1. Imagine the integers between -4 and 1 laid out in a sequence:

[tex]-4, -3, -2, -1, 0, 1[/tex]

If you take the middle value of this sequence, you get the midpoint of the [tex]x[/tex] values.

In this case, the middle is between values -2 and -1, leaving us with a midpoint of -1.5. This as a fraction is [tex]-\frac{3}{2}[/tex].

Now let's look at the [tex]y[/tex] values. Our first [tex]y[/tex] value is 2 and our second [tex]y[/tex] value is -4. Again, let's imagine those numbers laid out in a sequence:

[tex]2, 1, 0, -1, -2, -3, -4[/tex]

Here, the middle of these values is -1, and this is the midpoint of the [tex]y[/tex] values.

So if we put these two values in a coordinate, we get the midpoint of the line.

In this case, we get [tex](-\frac{3}{2} ,-1)[/tex].

Answer:

  $188.06

Step-by-step explanation:

The total cost for the film will be the sum of film cost, applicable sales tax, and applicable shipping charges. The film cost will be the product of the number of rolls and the cost per roll.

__

  film cost = (18 rolls) × ($9.95 /roll) = $179.10

  sales tax = 0.05 × $179.10 = $8.96

There is no shipping charge associated with the camera shop purchase, so the total cost is ...

  camera shop cost = film cost + sales tax = $179.10 +8.96 = $188.06

__

  film cost = (18 rolls) × ($9.76 /roll) = $175.50

  shipping charge = $15.00

There is no sales tax associated with the mail order, so the total cost is ...

  mail order cost = film cost + shipping charge = $175.50 +$15.00 = $190.50

__

The price from the camera shop is the better of the two prices. The purchase there would cost you $188.06 for 18 rolls of film.

_____

Additional comment

The after-tax charge per roll of film at the camera shop is 9.95×1.05 = 10.4475. This is $0.6975 more than the basic charge per roll from the mail order company. In order to get the shipping charge of $15 to be less than $0.6975 per roll, the number of rolls ordered must be more than 15/0.6975 = 21.5.

An order of 22 rolls of film from the mail order company would cost less than from the camera shop. ($229.50 vs. $229.85)

Answer: 1

Step-by-step explanation:

[tex]a-bc=7-2(3)=7-6=\boxed{1}[/tex]

Answer:

[tex]g(x) = x^3+1\\f(x) = x^2[/tex]

Step-by-step explanation:

Answer:

f(x)=x^2 and g(x)=x^3+1

Step-by-step explanation:

to find y=f(g(x))

substitute g(x) into f(x)

y= (x^3+1)^2.

Answer:

[tex]\boxed {\frac{343}{360}}[/tex]

Step-by-step explanation:

Probability Rule :

[tex]\boxed {P(A\cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B \cap C)}[/tex]

Solving :

⇒ 3/5 = 3/8 + 5/15 + 4/9 - P (A ∩ B ∩ C)

⇒ P (A ∩ B ∩ C) = 3/8 + 1/3 + 4/9 - 1/5

⇒ P (A ∩ B ∩ C) = 135/360 + 120/360 + 160/360 - 72/360

⇒ P (A ∩ B ∩ C) = (135 + 120 + 160 - 72) / 360

⇒ P (A ∩ B ∩ C) = 343/360

The Maximax decision is that Susan should build a very large gas station due to the largest value of row maximums.

A decision table can be defined as a type of table that is used for the graphical representation of the actions to perform, especially based on given conditions and business level rules.

The decision table for Susan’s problem is shown below:

Size            Good market   Fair market   Poor market    Row maximum

Small              50,000           20,000            -10,000           50,000

Medium          80,000           30,000            -20,000          80,000

Large              100,000          30,000            -40,000          100,000

Very large      300,000         25,000            -160,000         300,000

Thus, the Maximax decision is for Susan to build a very large gas station due to the largest value of row maximums.

For the Maximin decision, we have:

Size            Good market   Fair market   Poor market    Row minimum

Small              50,000           20,000            -10,000           -10,000

Medium          80,000           30,000            -20,000          -20,000

Large              100,000          30,000            -40,000          -40,000

Very large      300,000         25,000            -160,000         -160,000

Therefore, the Maximin decision is that Susan should build a small gas station due to the largest value of row minimums.

For the equally likely decision, we would find the row average:

Row 1 = (50,000 + 20,000 - 10,000)/3 = 20,000.

Row 2 = (80,000 + 30,000 - 20,000)/3 = 30,000.

Row 3 = (100,000 + 30,000 - 40,000)/3 = 30,000.

Row 4 = (300,000 + 25,000 - 160,000)/3 = 55,000.

Hence, the equally likely decision is that Susan should build a very large gas station due to the largest value of row average.

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Complete Question:

Even though independent gasoline stations have been having a difficult time, Susan has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline.  After a careful analysis, Susan developed the following table:

a. Develop a decision table for this problem

b. What is the maximax decision?

c. What is the maximin decision?

d. What is the equally likely decision?

The cash flow in year 1 is $15.

A growing perpetuity increases continuously and indefinitely.

Cash flow = present value x (rate of return - growth rate)

214 x (10% - 3%)

214 x 0.07 = $15

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The best buy is a 9 oz box of rice $1.25. (option d)

In order to determine the best buy, the unit cost of each option has to be determined. The best buy is the option with the lowest unit cost. The unit cost can be determined by dividing the total cost by the total quantity.

Unit cost = total cost / total oz

$0.90 / 6 = $0.15

$1.93 / 12 = $0.16

$2.42 / 16 = 0.151

$1.25 / 9 = 0.14

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Answer:

uhm where is x1 and y1?

Step-by-step explanation:

Y – y1 = m (x – x1)

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

Write the equation of the line in P.S. form given the information below.

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

We cannot write an equation in Point-Slope Form, without knowing the Point-Slope Equation. [tex]\bf{y-y1=m(x-x1)}[/tex].

Now, all that we need to do is plug in the information given, that is

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{y-(-3)=-\dfrac{1}{5}(x-0)}[/tex]

[tex]\triangledown[/tex]

[tex]\bf y+3=-\dfrac{1}{5}(x-0)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{y+3=-\dfrac{1}{5}(x-0).\;Hope\;the\;rest\;of\;your\;day\;is\;going\;to\;be\;fun!}[/tex]

[tex]\rule{300}{1.7}[/tex]

~[tex]\boxed{\bf{aesthetic \not101}}[/tex]~

Tioga Company manufactures sophisticated lenses and mirrors used in large optical telescopes, the values are mathematically given as

Generally, the equation for Material-handling cost for one lens mathematically given as

MH1=Total projected costs for material handling /{Total number of direct labor hours x Direct labor hours per unit)

MH1={$50,000/10.000)x 200

MH1=$1,000

2)

Material-handling cost for one mirror

MH2=Total budgeted material handling cost/ Total number of direct labor hours x direct labor hours per unit

MH2={$50,000/10.000)x 200

MH2=$1,000

3) Material-handling cost per lens

[tex]MH3=\frac{Total projected costs for material handling}{\frac{Number of material moves per lens + Number of material moves per mirror}{(Total number of lenses)}}* Material moves per lens[/tex]

[tex]MH3=\frac{50,000}{\frac{5+15}{25}}*5[/tex]

MH3=$1500

4)

[tex]MH4=\frac{Total projected costs for material handling}{\frac{Number of material moves per mirror + Number of material moves per lens}{(Total number of mirror)}}* Material moves per mirror[/tex]

[tex]MH4=\frac{50,000}{\frac{5+15}{25}}*5[/tex]

MH4=$1500

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Answer:

Step-by-step explanation:-49 - + 65= ?, 65-49 = 16 , so we take 65-49 as normal which is = 16 but it's -16,cuz we were given negative45

Answer:

how many times does 4.2 go into 14.7

1. 4.2

2. 8.4

3. 12.6

14.7-12.6=2.1 or one half of 4.2

3.5

Hope This Helps!!!

The product of variables in inverse proportion is constant, so the equation is [tex]\boxed{xy=-3}[/tex]

Answer:

Step-by-step explanation:

Comment

The rule that governs this situation is the average of arc d and 94 = the angle where the chords cross.

Givens

Arc 1 = 94

Arc2 = d

interior angle = 75

Formula

(d + 94)/2 = interior angle/1

Solution

(d + 94)/2 = interior angle/1               Cross Multiply

1*(d + 94) = 75 *2                           Combine

d + 94 = 150                                        Subtract 94 from both sides

d + 94 - 94 = 150 - 94                         Combine

d = 56

Answer: d = 56

Answer:

A

Step-by-step explanation:

[tex]s=\frac{a+b+c}{2}[/tex]

multiply both sides by 2

[tex]2s = a + b +c[/tex]

substract b and c from both sides to get a by itself

[tex]a = 2s - (b + c)\\a = 2s - b - c[/tex]

so the answer is A.

Answer: -6

Step-by-step explanation:

[tex]\frac{-10-2}{2}=\boxed{-6}[/tex]

The Median of the density is -6.

An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).

It is clearly visible from the uniform density curve given in the question that the median of the population density is  -6.
Because the area to the left and right of the density curve is the same.

Hence, the Median of density is -6.

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Answer:

5/6

Step-by-step explanation:

4/3-1/2

1) make the denominators the same on both fractions

8/6-3/6=?

2) subtract numerators

5/6

3) simplify

cannot simplify

Answer:

5/6

Step-by-step explanation:

4/3  -1/2

The first step is to get a common denominator of 6

4/3 *2/2 = 8/6

1/2 * 3/3 = 3/6

8/6  -3/6

5/6

Answer:

Step-by-step explanation:

Step-by-step explanation:

since there is no other information, we have to assume that the prices for student passes and teacher passes are the same.

therefore, the pass price per person is

$737.38 / (44 + 2) = $737.38 / 46 = $16.03

and the lunch costs per student are

$393.36 / 44 = $8.94

altogether,

$16.03 + $8.94 = $24.97

was spent for each student.

a. 17 x 10 = 170

b. 24 x 100 = 2400

c. 6 x 1000 = 6000

[tex]\displaystyle\\|\Omega|=\binom{15}{3}=\dfrac{15!}{3!12!}=\dfrac{13\cdot14\cdot15}{2\cdot3}=455[/tex]

a)

[tex]\displaystyle\\|A|=\binom{10}{3}=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=120\\\\P(A)=\dfrac{120}{455}=\dfrac{24}{91}\approx26.4\%[/tex]

b)

[tex]\displaystyle\\|A|=\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdot5}{2}=10\\\\P(A)=\dfrac{10}{455}=\dfrac{2}{91}\approx2.2\%[/tex]

c)

[tex]\displaystyle\\|A|=\binom{10}{2}\cdot5=\dfrac{10!}{2!8!}\cdot5=\dfrac{9\cdot10}{2}\cdot5=225\\\\P(A)=\dfrac{225}{455}=\dfrac{45}{91}\approx49.5\%[/tex]

d)

[tex]A[/tex] - at least one is spoilt

[tex]A'[/tex] - none is spoilt

[tex]P(A)=1-P(A')[/tex]

We calculated [tex]P(A')[/tex] in a).

Therefore

[tex]P(A)=1-\dfrac{24}{91}=\dfrac{67}{91}\approx73.6\%[/tex]

Answer:

C. Lines with congruent alternate interior angles are parallel.

Answer:

A. 5 feet

Step-by-step explanation:

Answer: The best estimate of the number of miles that Alexia run is 4 miles.

Step-by-step explanation:

Since we have given that

Length of lap is given by

Number of laps around her neighborhood = 3

So, Total number of miles that Alexia ran is given by

Hence, the best estimate of the number of miles that Alexia run is 4 miles