Two friends board an airliner just before departure time. There are only 11 seats left, 4 of which are aisle seats. How many ways can the 2 people arrange themselves in available seats so that at least one of them sits on the aisle?

The 2 people can arrange themselves in blank ways?

Answers

Answer 1

Using the Fundamental Counting Theorem, it is found that:

The 2 people can arrange themselves in 40 ways.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

With one people in the aisle and one in the normal seats, the parameters are:

n1 = 4, n2 = 7

With both in the aisle, the parameters is:

n1 = 4, n2 = 3

Hence the number of ways is:

N = 4 x 7 + 4 x 3 = 28 + 12 = 40.

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Related Questions

At hollywood connection, edgar plays laser tag 6 minutes for every 8 minutes he plays arcade games. If edgar plays arcade games for 48 minutes. for now many minutes will he play laser tag

Answers

Answer:

Step-by-step explanation:

48/8 = 6. 6*6 = 36.

Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
14√2
14
45
14√2
14√3
45
7√2 7√3

Answers

The legs of the big triangle are 14 units and the legs of the small triangle are 7√2 units

How to determine the lengths of the missing segments

From the question, we have the following parameters that can be used in our computation:

The right triangles

The right triangles are special triangles with acute angles of 45 degrees

This means that the relationship between the legs and the hypotenuse of the triangles is

Hypotenuse = Leg√2

Leg = Hypotenuse/√2

Using the above as a guide, we have the following:

Leg = 14√2/√2

Leg = 14

i.e. the legs of the big triangle are 14 units

Leg = 14/√2

Leg = 7√2

i.e. the legs of the small triangle are 7√2 units

See attachment for the triangles

Answers

144.) The value of X if the two angles of the triangle are congruent would be = 4. That is option D.

145.) The equation that should be used to find the value of X would be = 13x -15 = 22x + 9. That is option H.

How to determine the value of X when two triangles are congruent?

For question 144.)

Two triangles are congruent means that the angles are equal to each other. That is;

2.3x +25 = 5.8x + 11

Bring like terms together;

5.8x-2.3x = 25-11

3.5x = 14

X = 14/3.5

= 4.

For question 145.)

When two parallel lines are being cut across by a diagonal line a relationship exists between the angles that are formed.

The two given angles are congruent;

That is;

13x -15 = 22x + 9

Therefore the expression that can be used to calculate X would be = 13x -15 = 22x + 9

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What is 2x2 + 1000 x 1000

Answers

Answer: 2x2 + 1000 x 1000 = 1000004

Step-by-step explanation: you add on 5 0's to the one and 2x2 = 4 so add on the 4 also

Answer:

1000004

Step-by-step explanation:

First we do can separate it into the parentheses: (2*2) + (1000*1000)

= 4 + 1000000

= 1000004

A field in the shape of a right triangle is bordered on one side
by a lake, on another side by a street, and on a third side by a
tree line.
What angle does this lake make with the street?
Round only your final answer to the nearest degree.
Put just the number in the blank.
Lake
32 ft
Tree Line
18 ft
Street

Answers

Cos = 20/27 = 0.7407

angle that stream makes with the road = 42.2

answer

42 (Round only your final answer to the nearest degree)

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

Answer:

A. All sides of a rhombus are congruent, so if DK = 8, then KL = 8.

B. The diagonals of a rhombus are perpendicular to each other, so if angle KAL = 2x - 8, then we have:

2x - 8 = 90

2x = 98, so x = 49.

C. All sides of a rhombus are congruent, so if DM = 5y + 2 and DK = 3y + 6, then we have:

5y + 2 = 3y + 6

2y = 4, so y = 2, and KL = 5(2) + 2 = 12.

John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?

Answers

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

John received $200 dollars for his birthday. He went to Greenbriar Mail and purchased a pair of tennis shoes for $75.00. Then he went to the Cookie Store and bought $10.00 worth of cookies. Going to the car, John looked down and found $20.00 on the ground. How much money does John has now?

Answers

John has $135

Explanation:

Subtract 200 and 75 to and you get 125.
Next, subtract 125 and 10 to get 115.
Then, add 115 and 20 to get $135.

Test Prep What fraction is represented by the point on the number line?

Answers

The fraction represented by the point between 1 and 2 on the number line is 5/3.

If the point is between 1 and 2 on the number line, we can determine the fraction it represents by considering the distance between the point and the two adjacent integers.

The point A lies between the numbers 1 and 2, which indicates that the whole number part of the fraction is 1.

Also note that the segment between 1 and 2 is divided into 3 equal parts. A lies on the 2nd part, which implies that the fractional part is 2/3.

Thus, the point A corresponds to the mixed fraction 1 -

2 5

1 - = (1*3)+2 / 3 = -

3 3

So, the fraction represented by the point between 1 and 2 on the number line is 5/3.

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

Answer:

3/8 = (3 + AD)/20

8(3 + AD) = 60

24 + 8AD = 60

8AD = 36

A = 4 1/2

B is the correct answer.

(2x^2-9x-5) \div(x-5)

Answers

Answer:2x+1

Step-by-step explanation:

Each day, Nicole earns a fixed wage plus extra money for every hour of overtime she works. The graph shows her total pay (in dollars) versus the amount of
overtime (in hours) that she works.
Total pay
(dollars)
I Don't Know
737
Mostly cloudy
Overtime (hours)
Subm
(a) What is Nicole's total pay with 0 hours of overtime?
(b) Choose the statement that best describes how the amount
of overtime and total pay are related. Then fill in the blank.
Search
As the amount of overtime increases, the total pay
decreases.
At what rate is the total pay decreasing?
$ per hour
As the amount of overtime increases, the total pay
increases.
At what rate is the total pay increasing?
$ per hour

Answers

(a) Nicole's total pay with 0 hours of overtime is $737.
(b) The correct statement is: "As the amount of overtime increases, the total pay increases." The rate at which the total pay is increasing is $10 per hour of overtime.

Part D
Now use GeoGebra to measure the lengths of segments AB and BC and calculate the area of rectangle ABCD. Do you get the same result that you obtained in part C? Take a screenshot with the lengths of the sides labeled and the area displayed, and paste it below.

Answers

Answer:

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Step-by-step explanation:

idsifui piuh vSeth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity: