Write an equation for the value of y in terms of x. Then solve the equation for x.

If 'n' passenger are there the probability that the last passenger will take the right seat is \(\frac{1}{2}\) .

We can use a much lesser number for the number of passengers boarding the plane to solve this issue.

Let's assume that there are just two passengers and that seat numbers A and B are assigned to the first and second passengers, respectively, when they board the aircraft.

The second passenger will choose seat B if the first passenger, who misplaced his ticket, chooses seat A. The second passenger is seated in the proper place in this instance. The second passenger will have to take seat A if the first passenger, who misplaced his ticket, chooses seat B. In this instance, the second passenger is seated incorrectly. We can see that if there are only two passengers, there is a\(\frac{1}{2}\) probability that the second person, who is the last, will take the right seat.

The allotted seats for the first passenger, the second passenger, and the third passenger are A, B, and C, respectively, for a plane with only three passengers.

Scenario 1:

If the first passenger, who misplaced his ticket, chooses seat A, the second and third passengers will choose seats B and C, respectively.

Scenario 2:

If the first passenger chooses seat B, the second passenger will either choose seat A or C. If he chooses seat A, the third passenger will occupy seat C, which is where he is supposed to be. However, if passenger number two chooses seat number C, then passenger number three will choose seat number A, which is the incorrect seat.

Scenario 3:

If the first passenger chooses seat C, the third passenger will be seated in the incorrect seat no matter which seat the second passenger chooses.

The probability that the third person, or the last person, will occupy the appropriate seat is \(\frac{1}{3}\) in Scenario 1,  \(\frac{1}{3}\times \frac{1}{2}\) = \(\frac{1}{6}\) in Scenario 2, and 0 in Scenario 3. The total likelihood is therefore \(\frac{1}{3}+ \frac{1}{6}+0=\frac{2}{6}+ \frac{1}{6}=\frac{3}{6} =\frac{1}{2}\) .

As we can see, the probability that the last passenger will take the right seat is \(\frac{1}{2}\) regardless of how many passengers board the aircraft.

Therefore, If 'n' passenger are there the probability that the last passenger will take the right seat is \(\frac{1}{2}\) .

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Answer:

(a) The function has a minimum value

(b) The minimum value is 2

Step-by-step explanation:

(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is

y = ax^2 + bx + c.  

We know that for our function a = 1.

Thus, y = x^2 + 4x + 6 must have a minimum value.

(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.

Step 1:  First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.  

Plugging in 4 for b and 1 for a, we get:

x-coordinate of minimum = -4 / 2(1)

x-coordinate of minimum = -4 / 2

x-coordinate of minimum = -2

Step 2:  Now we can plug in -2 for x in the quadratic function.  The result will be our minimum value:

f(-2) = (-2)^2 + 4(-2) + 6

f(-2) = 4 - 8 + 6

f(-2) = -4 + 6

f(-2) = 2

Thus, the minimum value of the quadratic function is 2.

Answer:

A=a2=142=196cm²

Answer: 196 cm²

hope this helps :)

Answer:

196cm²

Step-by-step explanation:

All of a square's sides are congruent which means if one side is 14cm then all the other sides have to be 14cm as well.

To find the area you multiply the length and the width (A=l*w)

l=14, w=14

14*14=196cm²

Answer:

0.167

Step-by-step explanation:

if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6

technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167

that should end up being your answer if i did the math right

Answer:

Step-by-step explanation:

5/12 * 6/15 =30/180

1/6=1/6

which is true, Right-hand side is equal to left-hand side

Answer:

A sample size of 2080 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

98% confidence level

So \(\alpha = 0.02\), z is the value of Z that has a pvalue of \(1 - \frac{0.02}{2} = 0.99\), so \(Z = 2.327\).

Based on previous evidence, you believe the population proportion is approximately 60%.

This means that \(\pi = 0.6\)

How large of a sample size is required?

We need a sample of n.

n is found when \(M = 0.025\). So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.025 = 2.327\sqrt{\frac{0.6*0.4}{n}}\)

\(0.025\sqrt{n} = 2.327\sqrt{0.6*0.4}\)

\(\sqrt{n} = \frac{2.327\sqrt{0.6*0.4}}{0.025}\)

\((\sqrt{n})^{2} = (\frac{2.327\sqrt{0.6*0.4}}{0.025})^{2}\)

\(n = 2079.3\)

Rounding up

A sample size of 2080 is needed.

Answer:

$3400

Step-by-step explanation:

800+(26x100)

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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Answer:

4/16

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

2000=1 ton so 4000=2tons

Answer:

D 4000 pounds=2 tons

Step-by-step explanation:

2 tons is equal to 2000 pounds so 2 tons equal to 4000 pounds.

Answer: I believe it’s C

Step-by-step explanation: I hope i’m right

Using proportions, it is found that one sandwich costs $4.25.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Considering x as the cost of a sandwich, the total cost is given as follows:

1.08(3x + 1.75) + 5 = 20.66.

The multiplication by 1.08 is because of the sales tax. We solve for x to find the cost of one sandwich, hence:

1.08(3x + 1.75) = 15.66

3x + 1.75 = 14.5

3x = 12.75

x = 12.75/3

x = 4.25.

Hence one sandwich costs $4.25.

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Answer:

5/14

Step-by-step explanation:

add 5 and 9 to get the denominator

Answer:

A

Step-by-step explanation:

I took the test so yeah hope this helps

Consequently, there are 5 elements in A B'.

Given the following definitions:

U = {1, 2, 3, 4, 5, 6, 7}A = {1, 2, 4, 5}B = {1, 3, 5, 7}

The complement of a set B is the set of all elements that belong to the universal set U but not to B.

A’ = {x | x ∈ U and x ∉ A} = {3, 6, 7}B’ = {x | x ∈ U and x ∉ B} = {2, 4, 6}

The union of sets A and B is the set of all elements that belong to set A or set B, or both.

A ∪ B = {x | x ∈ A or x ∈ B}

= {1, 2, 3, 4, 5, 7}A ∪ B'

= {x | x ∈ A or x ∈ B’}

= {1, 2, 4, 5, 6}

Therefore, the number of elements in A ∪ B' is 5.

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From the passage that Helen was blind thus she was unable to see water and could only know it via a sensation on her hands.

Hellen Keller was one of the educators in America. Her influence was of importance because she was both blind and deaf. Thus, her memoir chronicles the details of the challenges that one faces when trying to educate a physically challenged child.

As such, we can see from the passage that Helen was blind thus she was unable to see water and could only know it via a sensation on her hands.

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From the passage that Helen was blind thus she was unable to see water and could only know it via a sensation on her hands.

Who is Helen Keller?

Hellen Keller was one of the educators in America. Her influence was of importance because she was both blind and deaf. Thus, her memoir chronicles the details of the challenges that one faces when trying to educate a physically challenged child.

As such, we can see from the passage that Helen was blind thus she was unable to see water and could only know it via a sensation on her hands.

The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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Answer: 1/6

Step-by-step explanation: 2/3 / 4 is 1/6 or 0.1666666....

Answer:

Thus, the equation of line for point (-1, 2)  is y = x + 3.

Step-by-step explanation:

Answer:

The equation of the line is y = x + 3.

Step-by-step explanation:

A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.

y = mx + b

y = 1 * -1 + b

y = -1 + b

b = y + 1

b = 2 + 1

b = 3

The final price is $291.

We know that a 25% discount has been applied.

Then, if P is the original price, we can write the equality as:

The original retail price is $ 388.

Let's begin by identifying key information given to us:

Truck A = $50 per day + $0.70 per mile

Truck B = $20 per day + $0.80 per mile

Where x = number of days, y = number of miles

To find the number of miles in a day at which the rental of Trucks A & B are the same, we will have to equate both equations above. We get this:

This therefore, means that at 300 miles, the cost of renting Truck A is the same as renting Truck B

Answer:

Step-by-step explanation:

b·b·b= b³

Answer:

Length of the rectangular prism = 4 meters

But other possible values = (-5meters or - 9 meters)

Step-by-step explanation:

The volume of a rectangular prism = Length × Width × Height

From the question above,

Length = x meters

Width = x - 1 meters

Height = x + 11 meters

Volume of the Rectangular prism = 180 cubic meters

Hence,

(x) × (x - 1) × (x + 11) = 180

We expand the brackets

(x)(x - 1) (x + 11) = 180

x² - x(x + 11) = 180

x² (x + 11) - x(x + 11) = 180

x³ + 11x² - x² + 11x =180

x³ +10x² - 11x = 180

x³ + 10x² - 11x -180 = 0

The above is a polynomial

We solve this polynomial to find x

x³ + 10x² - 11x -180 = 0

(x - 4)(x + 5) (x + 9) = 0

x - 4 = 0

x = 4

x + 5 = 0

x = -5

x + 9 = 0

x = -9

We are asked to find the various values for the length hence,

From the above question, we are told that

Length = x meters

Therefore, the length of this rectangular prism = 4 meters or -5 meters or -9 meters.

Answer:

(1, 4)

Step-by-step explanation:

Answer:

a) Based on Franka's annual salary of $79,600, approximately 25% of her salary would be deducted for taxes. This means that the amount deducted from Franka's pay each year would be approximately $19,900 ($79,600 x 0.25).

b) After receiving a 3% increase in pay, Franka's new annual salary would be $82,068 ($79,600 + ($79,600 x 0.03)).

c) The amount deducted for taxes from Franka's new pay would be approximately $20,517 ($82,068 x 0.25).

Step-by-step explanation:

x + y = 200

x : y = 4 : 6

x + y = 200

y = 200 - x

x : y = 4 : 6

x : (200 - x) = 4 : 6

6.x = 4(200 - x)

6x = 800 - 4x

10x = 800

x = 800/10

x = 80

y = 200 - x

y = 200 - 80

y = 120

(x,y) = (80,120)

Answer:

B. (2, 2)

Step-by-step explanation:

(x, y)

3x = 8 - y

a) 3(3) = 8 - 1

9 = 8 - 1

9 = 7  False

b) 3(2) = 8 - 2

6 = 6  True

c) 3(8) = 8 - 0

24 = 8 False