Potential customers arrive at a full-service, one-pump gas station at a Poisson rate of20 cars per hour. However, customers will only enter the station for gas if there are no more than two cars (including the one currently being attended to) at the pump. Suppose that the amount of time required to service a car is exponentially distributed with a mean of five minutes.

Required:
a. What fraction of the attendant’s time will be spent servicing cars?
b. What fraction of potential customers are lost?

Answer:

last step is (2x + 5)(2x + 1)

Step-by-step explanation:

4x^2 + 12x + 5

4x^2 + (10 + 2)x + 5

4x^2 + 10x + 2x + 5

2x(2x + 5) +1(2x + 5)

(2x + 5)(2x + 1)

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Answer:

  $163,002

Step-by-step explanation:

If you're working problems of this sort, you have been shown formulas and examples. Use the appropriate formula with the numbers of this problem.

For the formula below, you have d=3000, r=0.045, k=4, N=11

  P = (3000)(1 -(1 +0.045/4)^(-11·4))/(0.045/4) ≈ 163,002

The account needs to hold about $163,002 to make this possible.

Answer:

x = 82.1º

Step-by-step explanation:

tan = opp/adj

tan75 = x/22

multiply both sides by 22

22 * tan75 = x

use calculator

82.1051177665153 = x

Rounded

x = 82.1º

Answer:

someone else tell me to thank you

[tex]\Huge \bf \over \rightarrow\mid\mathcal {\underline{ \orange{12 \: : \: 00}}} \mid[/tex]

Answer:

I think 10:45 is the nearest quarter hour.

Answer:

3:7

Step-by-step explanation:

We know that there are 4 girls and 3 boys and 4+3=7.

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Answer:

  36 9/16 cubic feet

Step-by-step explanation:

Volume formula

  V = LWH

  V = (3 3/4 ft)(3 ft)(3 1/4 ft) = (15/4)(3)(13/4) ft³ = 585/16 ft³

  V = 36 9/16 ft³ . . . the volume of the shipping box

__

Packing cubes

Each cube measures 1/4 ft on a side. In terms of cubes, the dimensions of the box are ...

  3 3/4 ft = 15/4 ft = 15×(1/4 ft)   ⇒   15 cubes

  3 ft = 12/4 ft = 12×(1/4 ft)   ⇒   12 cubes

  3 1/4 ft = 13/4 ft = 13×(1/4 ft)   ⇒   13 cubes

This means 15 cubes can be lined up along the bottom front of the box. 12 such lines can make one layer of cubes covering the bottom of the box, and 13 such layers will fill the box.

The total number of cubes in the box is ...

  15 × 12× 13 = 2340 . . . . fish food cubes

Each cube has a volume of (1/4 ft)³ = 1/64 ft³, so the volume of the shipping box is ...

  (2340 cubes)×(1/64 ft³/cube) = 2340/64 ft³

  = 36 9/16 ft³ . . . shipping box volume

__

Using the volume formula, the volume is 36 9/16 ft³

Using the packing cubes method, the volume is 36 9/16 ft³

__

If you consider the math used in the packing cubes method, you see it looks like ...

  V = (15)(12)(13) × (1/64 ft³)

  = (15)(12)(13)×(1/4 ft)³ = (15×1/4 ft)(12×1/4 ft)(13×1/4 ft)

  = (3 3/4 ft)(3 ft)(3 1/4 ft)

  = LWH

That is, the "packing cubes method" is simply a rearrangement of the volume formula product using the commutative and associative properties of multiplication. The same numbers are used to compute the product, but in a different order. Hence the result must be the same.

Answer:

20

Step-by-step explanation:

15+(-2)+7=13+7=20

[tex]\longrightarrow{\blue{20}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]\:15 + ( - 2) + 7[/tex]

➺ [tex] \: 15 - 2 + 7[/tex]

➺ [tex] \: 22 - 2[/tex]

➺ [tex] \: 20[/tex]

[tex]\sf\pink{PEMDAS\: rule.}[/tex]

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

[tex] \frac{b}{3} \geq - 1 \\ = 3 \times \frac{b}{3} \geq \times ( -1 ) \\ = b \geq3 \times ( - 1) \\ = b \geq - 3 \times 1 \\ \\ = b \geq - 3[/tex]

Step By Step Explanation:

#CarryOnLearning

Answer:

40

Step-by-step explanation:

If you take 15, and divide it by the 3 out of the 3/8 left, you get 5. You then multiply 5 by 8 to get the full amount of candies she had before sharing, 40.

I hope this helped!

Thanks!

Your friend in answering,

~Steve

Answer:

40.

Step-by-step explanation:

If 15 candies are the rest of 3/8, then the total candies were 40.

Answer:

CosC

Step-by-step explanation:

EDG

Answer:

6x^3+x^2+3x-6

Step-by-step explanation:

f(x) = 4x² + 3x - 2

g(x) = 6x³ - 3x²-4

(f +g) (x)​ =4x² + 3x - 2+6x³ - 3x²-4

Combine like terms

             =6x^3+4x^2-3x^2+3x-2-4

             =6x^3+x^2+3x-6

Answer:

H0 : μ ≥ 350

H1 : μ < 350

Step-by-step explanation:

It is claimed that the mean is atleast 350 psi ;

10 such pipes were experimentally sampled ;

Here, the null hypothesis is the claim ; this means that the alternative hypothesis will be the opposite of the claim.

The hypothesis

H0 : μ ≥ 350

H1 : μ < 350

Answer:

y = 5x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 5, then

y = 5x + c ← is the partial equation

To find c substitute (2, 3) into the partial equation

3 = 10 + c ⇒ c = 3 - 10 = - 7

y = 5x - 7 ← equation of line

Answer:

294 in.²

Step-by-step explanation:

I believe this figure is a rectangular prism.

------------------------------------------------------------------------------------

Explain:

To find the surface area of a rectangular prism, use this formula:

[tex]SA=2lw+2lh+2wh[/tex]

              or

[tex]SA=2(lw+lh+wh)[/tex]

[tex]l-length[/tex]

[tex]w-width[/tex]

[tex]h-height[/tex]

A phrase I use to help remember this formula is:

LISA WILSON LOST HER WITCH HAT TWICE (2)

------------------------------------------------------------------------------------

Solve:

The length of this rectangular prism is 9 in.

This width is 10 in.

The height is 3 in.

Now, I will plug the numbers into the first formula.

[tex]SA=(2*9*10)+(2*9*3)+(2*10*3)=294 in.^2[/tex]

------------------------------------------------------------------------------------

Conclude:

I, therefore, believe the area of this rectangular prism is 294 in.²

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Answer:

Step-by-step explanation:

Add or subtract multiples of 360° to find coterminal angles.

Positive

  75° +360° = 435°

  75° +2×360° = 795°

Negative

  75° -360° = -285°

  75° -2×360° = -645°

Answer:

h = [tex]\frac{V}{\pi r^2}[/tex]

Step-by-step explanation:

Given

V = πr²h ( isolate h by dividing both sides by πr² )

[tex]\frac{V}{\pi r^2}[/tex] = h

Answer:

(-2, 3)

Step-by-step explanation:

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Answer:

  26 square units

Step-by-step explanation:

Counting grid squares on the graph, we see that segment AB is the hypotenuse of a right triangle with legs 2 and 3. Its length is ...

  AB = √(2²+3²) = √13

We can also see that the adjacent longer sides are twice this length, each being the hypotenuse of a triangle that is 6 wide and 4 high.

  AC = √(6² +4²) = √52 = 2√13

Then the area is ...

  A = LW

  A = (2√13)(√13) = 2·13 = 26 . . . square units

Answer:

x+3y =6

2x+8y=-12​

The solutions to your equations are:

x= 42 and y= -12

lets check this

42+-36 =6

84+-96=-12​

Hope This Helps!!!

Answer:

the awnser is 2,0

Step-by-step explanation:

Answer:

(1,-2) is the correct answer

Answer:

The median weight for shelter A is greater than that for shelter B.

The data for shelter B are a symmetric data set.

The interquartile range of shelter A is greater than the interquartile range of shelter B.

Step-by-step explanation:

The median weight for shelter A is greater than that for shelter B.

The median of A = 21 and the median of B = 18  true

The median weight for shelter B is greater than that for shelter A.

The median of A = 21 and the median of B = 18   false

The data for shelter A are a symmetric data set.

False, looking at the box it is not symmetric

The data for shelter B are a symmetric data set.

true, looking at the box it is  symmetric

The interquartile range of shelter A is greater than the interquartile range of shelter B.

IQR = 28 - 17 = 11 for A

IQR for B = 20 -16 = 4  True

Answer:

it's the first one where X is greater or equals to -1 and X is less or equals to positive 7

The compound inequality in x : -1 ≤ x ≤ 7

The correct graph is A .

Given, inequality: -4 ≤ 3x -1 and 2x + 4 ≤ 18 .

First inequality:

-4 ≤ 3x -1

Take -2 from RHS to LHS .

-4 + 1 ≤ 3x

-3 ≤ 3x

x ≥ -1

X will have values greater than equal to -1 .

Second inequality:

2x + 4 ≤ 18

take 4 from LHS to RHS.

2x ≤ 18 - 4

2x ≤ 14

x ≤ 7

x will have values less than equals to 7.

Combined result of both inequalities: -1 ≤ x ≤ 7 .Thus graph A is correct.

Know more about inequality,

https://brainly.com/question/28823603

#SPJ3

Answer:

2B+5C

Step-by-step explanation:

Multiply them out....

2B=2*(4i-j) = 8i-2j

5C=5*(2i+3j) = 10i+15j

2B+5C= 8i-2j+10i+15j =18i+13j = A

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Answer:

  a)  2B +5C

Step-by-step explanation:

It is probably easiest to simply try the answer choices. You find the first one works, which means it is the one you want.

  2B +5C = 2(4i -j) +5(2i +3j) . . . . choice (a)

  = 8i -2j +10i +15j

  = 18i +13j = A

__

In general, you can solve for the coefficients p and q that make ...

  pB +qC = A

  p(4i -j) +q(2i +3j) = 18i +13j

  (4p+2q)i +(-p +3q)j = 18i +13j

Equating the coefficients of i and j gives us 2 equations in p and q.

  4p +2q = 18

  -p +3q = 13

Adding 2 times the second equation to 1/2 the first, we get ...

  1/2(4p +2q) +2(-p +3q) = 1/2(18) +2(13)

 7q = 35

 q = 5

Using the second equation to find p, we get ...

  p = 3q -13 = 3(5) -13 = 2

These coefficients tell us ...

  A = 2B +5C . . . . . . . matches choice (a)

Answer:

90

Step-by-step explanation:

Let the whole number be x.

100% is to x as 70% is to 63

100/x = 70/63

10/x = 10/9

10x = 90 * 10

x = 90

Answer: 90

Step-by-step explanation:

0.7x = 63, x = 63/0.7 = 90

Answer:10,666,66 [tex]\pi[/tex]m^3

Step-by-step explanation:

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

[tex]\frac{4}{3} \pi 20^{3} \\ V=10,666.66 \pi[/tex]

Answer:

Step-by-step explanation:

Law of sines says that the length of sides are proportional to the sine of the opposing angle.

Using the sine rule,

sin(x)/2.5 = sin(28)/3

therefore

sin(x) = 2.5 * sin(28) / 3

or

here we have

x = asin (2.5*sin(28) / 3)

so

box 1 = 2.5

box 2 = 28°

box 3 = 3

Answer: See explanation

Step-by-step explanation:

From the information given, the following can be deduced:

Let rate of jet in still air be J

Let rate of wind be W

The formula for distance:

d = rt

Therefore, r = d/t

When, flying against the wind, then the Jet flies at a rate of J - W which will be:

= 1590mi/3hrs

= 530mph

When flying with the wind the jet will fly at a rate of J+W which will be:

= 8240mi/8hrs

= 1030 mph

Their average rate will be:

J = (530+1030)/2

= 1560/2

J = 780 mph

Since J - W = 530

Therefore, so

780 - W = 530

W = 780 - 530

W = 250 mph

The Jet in still air flies at a rate of 780 mph and the wind speed is 250 mph

Answer:

a) 0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.

b) 0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.

c) 0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 8.1 minutes and a standard deviation of 2.0 minutes.

This means that [tex]\mu = 8.1, \sigma = 2[/tex]

a. between 5 and 10 min

This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5.

X = 10

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10 - 8.1}{2}[/tex]

[tex]Z = 0.95[/tex]

[tex]Z = 0.95[/tex] has a p-value of 0.8289

X = 5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 8.1}{2}[/tex]

[tex]Z = -1.55[/tex]

[tex]Z = -1.55[/tex] has a p-value of  0.0606

0.8289 - 0.0606 = 0.7683

0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.

b. less than 5 min

p-value of Z when X = 5, which, found from item a, is of 0.0606

0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.

c. more than 10 min

1 subtracted by the p-value of Z when X = 10, which, from item a, is of 0.8289

1 - 0.8289 = 0.1711

0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.