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katrin2010 [14]
2 years ago
14

In general, after a group makes a reservation at a restaurant, they do not show up 20% of the time. If a restaurant has 8 reserv

ations for the evening, what is the probability that exactly two do not show up?
Mathematics
1 answer:
sashaice [31]2 years ago
5 0

Answer:

P(more than 2 don't show up)=0.2031

Step-by-step explanation:

Multiplication rule for independent events:

If two events A and B are independent then the multiplication rule state that:

P(A and B)= P(A) x P(B)

Find the probability that more than two do not show up:

The probability that the reservations at the restaurant do not show up is 0.20 (=20%) and there were 8 reservations.

P(more than 2 don't show up)= 1- P(less than or equal to 2 don't show up)

= 1-( P(none show up) +P(one don't show up)+P(two don't show up)

=1- ((0.8⁸) +₈ C₁ (0.2¹)x(0.8⁷)  +₈ C₂ (0.2²)x(0.8⁶)

=1- (0.1678 +0.3355+0.2936)= 1-0.7969

P(more than 2 don't show up)=0.2031

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While driving home for the holidays, you can’t seem to get Little’s Law out of your mind. You note that your average speed of tr
suter [353]

Answer:

1,200 cars per hour

Step-by-step explanation:

Let's suppose the car flow is constant and based on the observations stated in the problem.

If we set and imaginary car counter where your car is, then there are 25 cars in ¼ of a mile (including yours) going at your same speed.

Now compute how long it will take to travel ¼ mile. As your speed is constant 60 mph, we can cross multiply  

60 miles -----------> 1 hour

¼ of a mile --------> x hours

and

60/ (¼) = 1/x ---------> x = 1/240 hours.

This means that in 1/240 hours the 25 cars will be passing the counter.

Now compute how many cars will pass through our counter in 1 hour. Again, cross multiplying

1/240 hours -------> 25 cars

1 hour --------------> x cars

and

1/240 = 25/x -------> x = 25*240 = 1,200 cars.

So, the flow rate of the highway (going in your direction) in cars per hour is 1,200 cars per hour.

7 0
2 years ago
A circle has diameter of 11cm
dlinn [17]

Since length of diagonal (  Diagonal= 9.9cm ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without touching the edge of the circle.

<u>Step-by-step explanation:</u>

Here we have , A circle has diameter of 11 cm  A square has side length of 7 cm . Use Pythagoras’ Theorem to show that the square will fit inside the circle without touching the edge of the circle . Let's find out:

We know the concept that for any square to fit inside the circle without touching the edge of circle  , diagonal of square must be less than diameter of circle  . Let's find out length of diagonal by using Pythagoras Theorem :

Hypotenuse ^2 = Perpendicular^2+Base^2

For a square , Perpendicular = base = side

⇒ Diagonal^2 = 2(side)^2

⇒ Diagonal= \sqrt{2}(side)

⇒ Diagonal= \sqrt{2}(7)

⇒ Diagonal= 9.9cm

Since length of diagonal (  Diagonal= 9.9cm ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without ruching the edge of the circle.

5 0
2 years ago
Andre ran 2 kilometers in 15 minutes, and Jada ran 3 kilometers in 20 minutes. Both ran at a constant speed. Did they run at the
Goshia [24]

Answer:

speed of Jada = 6km per hour which is not equal to

speed of Andre = 8km per hour

They did not run at same speed

Step-by-step explanation:

formula of speed = distance covered/ time taken

For Andre

Distance = 2 KM

time = 15 mins

60 mins = 1 hour

15 mins = 1/60 * 15 hour = 0.25 hours

thus,

speed = 2km/0.25 hour = 8 km per hour

Similarly for Jada

Distance = 3 KM

time = 20 mins

60 mins = 1 hour

20 mins = 1/60 * 20 hour = 1/3 hours

thus,

speed = 2km/(1/3)hour = 6  km per hour

Now we have

speed of Jada = 6km per hour which is not equal to

speed of Andre = 8km per hour

6 0
2 years ago
Milly wrote the quadratic equation 0 = –x2 + 4x – 7 in standard form. What is the value of c in her equation?
zysi [14]

Answer:

c = - 7

Step-by-step explanation:

the standard form of a quadratic equation is

ax² + bx + c = 0 : a ≠ 0

x² + 4x - 7 = 0 is in standard form

By comparison of the coefficients of the terms, c = - 7


6 0
2 years ago
What is the following product? (StartRoot 12 EndRoot + StartRoot 6 EndRoot) (StartRoot 6 EndRoot minus StartRoot 10 EndRoot)
Crank

Answer:

The product results in: 6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}, which agrees with answer A of the given choices.

Step-by-step explanation:

We need to apply distributive property for the product of two expressions each consisting of two terms, and also use the properties of products of radicals of the same root:

(\sqrt{12} +\sqrt{6} )(\sqrt{6} -\sqrt{10} )=\\=\sqrt{12*6} -\sqrt{12*10} +\sqrt{6*6} -\sqrt{6*10} =\\=\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60}

and now, we extract as many factors we can from the roots to reduce them:

\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60} =\\=6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}

5 0
2 years ago
Read 2 more answers
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