For which of the following graphs is y a function of x

(a) The probability that at most 8 involve a single vehicle = 0.057

(b) The probability that exactly 8 involve a single vehicle = 0.035

(c) The probability that exactly 10 involve multiple vehicles = 0.117

(d) The probability that between 5 and 8, involve a single

vehicle = 0.056

(e) The probability that at least 5 involve a single vehicle = 1

(f) The probability exactly 8 involve a single vehicle and the other 12 involve multiple vehicles = 0.035

Probability is defined as the ratio of favorable outcomes to all other possible outcomes of an event. For an experiment with 'n' number of outcomes, the symbol x can be used to indicate the number of excellent outcomes. The probability formula is as follows:

x/n, where Probability is Favorable Outcomes/Total Results (Event).

Now, P = 0.6

n = 20

x ≅ Binomial (20; 0.6)

P(x) = (nx) Px q n-x

Now, at most 8 involve a single vehicle is:

P (x ≤ 8) = 0.057

Again, exactly 8 involve a single vehicle is:

P (x =8) = 0.035

Now exactly 10 involve multiple vehicles is:

P (x = 10) = 0.117

Similarly, between 5 and 8, involve a single vehicle is:

P (5 ≤ x ≤ 8) = 0.056

The probability of at least 5 involve a single vehicle is:

P (x ≥ 5) = 1

The probability that 8 involve a single vehicle and the other 12 in multiple vehicles is:

P (x = 8) = 0.035

To know more about probability, visit:

https://brainly.com/question/9793303

#SPJ1

The critical value for a confidence level of 98% with a sample size of 32 is given as follows:

t = 2.4528.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 32 - 1 = 31 df, is t = 2.4528.

(df is one less than the sample size).

More can be learned about the t-distribution at https://brainly.com/question/27701525

#SPJ1

\(0.1875\)

\(rounds \: off \: to \: \: 0.19\)

Step-by-step explanation:

\( \frac{3}{16} = \frac{30}{16 \times 10} = \boxed{.1875} \)

Answer:

.1875

Step-by-step explanation:

A 95% confidence interval for the difference of the meantime that the customers stayed for lunch and for dinner the correct option is option a (3.35, 16.65).

Given:

The number of random customers n1 = 25

The number of random customers n2 = 30

x1 = 45, x2 = 55

σx1 = 10, σx2 = 15

Zα12 = Z0.025 = 1.96

95% confidence interval,

= {(x2-x1) ± Zα12 [(σx1)^2/n1 + (σx2)^2/n2]^0.5}

= {(55-45)  ± 1.96 [\(10^{2}\)/25 + \(15^{2}\)/30]^0.5}

= {10 ± 1.96(4 + 7.5)^0.5}

= {10 ± 1.96(11.5^0.5)}

= {10 ± 1.96(3.3911)}

= {10 ± 6.6466}

=> (10-6.6466, 10 + 6.6466)

=> (3.35, 16.65)

So, the correct option is a (3.35, 16.65) for the difference of the meantime.

To learn more about the confidence interval visit: https://brainly.com/question/24131141

#SPJ4

Answer:

9^1 has a power of 1.  it evaluates to 9

Step-by-step explanation:

Answer:

98% probability that at least one of Harold and Maude will make it to the cruise

Step-by-step explanation:

Independent probabilities:

When two events are independent, the probability of the two events happening simultaneously is the multiplication of each probability.

Probability that none makes it to the cruise:

Harold's flight has an 80% chance of making it, so 100 - 80 = 20% probability of missing.

Maude's flight has a 90% chance of making it on time, so 100 - 90 = 10% probability of missing.

Both missing: 0.2*0.1 = 0.02.

2% probability of both missing.

Probability that at least one makes it to the cruise:

Either both miss, or at least one makes it. The sum of the probabilities of these events is 100%. So

2 + p = 100

p = 98%

98% probability that at least one of Harold and Maude will make it to the cruise

Answer: 13

Step-by-step explanation:

4x+3y=-5 solve x :    

4x = -3y + -5           | -3y

1x = -0.75y + -1.25  | : 4

-3x + 7y = 13 solve x :

-3x + 7y = 13              | -7y

-3x = -7y = 13             | : (-3)

Equalization Method Solution: -0.75y+-1.25=2.333y+-4.333

-0, 75y - 1,25 = 2,333y - 4, 333 solve y:

-0, 75y - 1,25 = 2,333y -4, 333    | -2,333y

-3, 083y - 1,25 = -4,333               | + 1, 25

-3. 083y = -3,088                         | : (-3, 083)

y = 1

Plug y = 1 into the equation 4x + 3y = -5 :

4x + 3 · 1           | Multiply 3 with 1

4x + 3 = -5        | -3

4x = -8              | : 4

x = -2

So the solution is:

y = 1, x = -2

ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:

https://brainly.com/question/20333461  

may be the answer is :4g-2=8 ^-^

but donot depend in this answer it's not sure okay

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

Answer:

Step-by-step explanation:

Suppose F represents the value that a room is unlocked.

Then, we can assume that the probability of unlocked homes is:

P(unlocked homes) = P(U)

P(unlocked homes) = 40%

P(unlocked homes) = 0.40

Also, let us represent the value of the locked room with G.

P(locked homes) = P(G)

P(locked homes) = (1 - 0.40)

P(locked homes) = 0.60

Let the probability of selecting a correct key be P(S)

It implies that for the agent to use 3 keys, we have a combination of \(^8C_3\) possible ways for the set of keys.

Now; since only one will open the house, then:

P(select correct key) = P(S)

\(P(S) = \dfrac{ (^1_1) (^7_2) }{ ^8_3 }\)

\(P(S) = \dfrac{21}{56}\)

P(S) = 0.375

Finally, for the real estate agent to have access to specific homes supposing the agent select three master keys at random prior to the time he left his office, Then:

P(F ∪ (G∩S) = P(F) + P(G∩S)

P(F ∪ (G∩S) = P(F) + P(G) × P(S)

P(F ∪ (G∩S) = 0.40 + (0.60×0.375)

P(F ∪ (G∩S) = 0.40 + 0.225

P(F ∪ (G∩S) =0.625

The function with the steepest slope is \(y = 7x - 3\).

The correct answer is C.

The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.

Let's compare the coefficients of x in each of the given functions:

\(y = -8x + 5\)

Slope: -8

\(y - 9 = -2(x + 1)\)

Simplifying, we get \(y - 9 = -2x - 2\)

Rearranging, we have \(y = -2x + 7\)

Slope: -2

\(y = 7x - 3\)

Slope: 7

\(y + 2 = 6(x + 10)\)

Simplifying, we get \(y + 2 = 6x + 60\)

Rearranging, we have \(y = 6x + 58\)

Slope: 6

Therefore, the steepest slope is the \(y = 7x - 3\).

For such more questions on steepest slope

https://brainly.com/question/10726891

#SPJ8

The worker's utility function can be represented as a combination of consumption and leisure. Let x be the number of hours worked per day, and c be the amount of consumption. Then, the worker's utility can be represented as:

U(c, 24-x) = f(c) + g(24-x)

where f(c) represents the utility from consumption, and g(24-x) represents the utility from leisure. The worker faces a budget constraint that states the amount of income they earn from work must equal their spending on consumption:

wx = pc

This constraint can be used to solve for the optimal combination of leisure and consumption that maximizes the worker's utility. By combining the utility function and the budget constraint, the worker's problem can be formulated as a maximization problem:

Maximize U(c, 24-x) subject to wx = pc

This problem can be solved using techniques such as Lagrangian optimization or constraint optimization to find the optimal values of c and x that maximize the worker's utility. The solution will depend on the specific forms of the functions f and g, as well as the values of w and p.

To know more about Combination

https://brainly.com/question/28065038

#SPJ4

The solution for the given expression is 16.

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

First, you apply the Power Rules - Power for  \((\frac{2^2x^2y}{xy^3} )^2}\). For this rule, you should repeat the base and multiply the exponents. Thus, the result will be:\(\frac{16x^4y^2}{x^2y^6}\).

After that, you should apply the  Power Rules - Division . For this rule, you should repeat the base and  subctract the exponents. Thus, the result will be:\(\frac{16x^2}{y^4}\).

Now, you should replace the variable x by 4 and the variable y by 2. Thus, the result will be:\(\frac{16*4^2}{2^4}=\frac{16*16}{16} =16*1=16\)

Read more about power rules here:

brainly.com/question/12140519

#SPJ1

A. The margin of error for a 99% confidence interval is $$2,320.75.

B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75

PART A.

The margin of error (ME) is determined using the formula:

ME= z ∗ σ/√n

where:

z is the z-score for the desired confidence level

σ is the population standard deviation

n is the sample size

For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.

Substituting these values into the formula, we have:

ME =  2.576 ∗ 10272/√130

ME = $2,320.75

PART B

The confidence interval (CI) is determined using the formula:

CI = \(\bar{x}\) ± ME

where:

\(\bar{x}\) is the sample mean

ME is the margin of error

The sample mean is $44,783, and the margin of error is $2,320.75.

Substituting the values into the formula, we get:

CI= 44783 ± 2320.75

CI = $42,462.25 to $47,103.75

Learn more about margin of error on:

https://brainly.com/question/31876031

#SPJ1

Answer:

f(4) is the correct answer which gives the number 27.

Answer:

k ≥ 24

Step-by-step explanation:

ᵏ⁄₄ ≥ 6

Multiply each side by 4

ᵏ⁄₄ *4 ≥ 6*4

k ≥ 24

Answer:

k≥24

Step-by-step explanation:

k/4≥6

Use the multiplication property of equality by multiplying both sides by 4 to get

k≥24

If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem

Thank you

Answer:

Step-by-step explanation:

2 now help me :(

Based on the description provided, the section of the chart that represents the point where a bill is first debated in subcommittees is: C and D

In the given chart, the parallel lines represent the progression of a bill through various stages in the legislative process. The boxes on the top line represent one set of actions or steps, while the boxes on the bottom line represent another set of actions or steps.

Moving from left to right on the chart, the boxes A and B are paired, representing a particular stage in the process. Similarly, the boxes C and D are paired, indicating another stage in the process.

In the context of the question, the stage where a bill is first debated in subcommittees is represented by the boxes C and D.

Learn more about chart on

https://brainly.com/question/25032284

#SPJ1

let's try to understand this.

a fruit company delivers its fruit in two types of boxes: large and small.

DeA group of fruit companies delivers its fruit in two types of boxes: large and small.

You can set x = weight of the large box and y = weight of the small box. Since they tell you 3 large boxes and 5 small boxes have a total weight of 77 kg you can create an equation of 3x+5y = 77. They also tell you that 6 large boxes and 2 small boxes have a total weight of 104 kg so you can write 6x+2y = 104.

Now you have two equations and two unknowns so you can solve using systems of equations.

3x+5y=77

6x+2y=104

You can see that you can easily multiply the first equation by 2 to get a 6x and leave the second equation as is since it also has a 6x so you can subtract the two equations to eventually only have one variable.

6x+10y = 154

-(6x+2y=104)

___________

8y = 50

y = 50/8  = 25/4 kg

Now you solved for the smaller box's weight and you can plug it into any of the two equations above to solve for x.

6x+2(25/4) = 104

6x+25/2=104

6x+25/2 = 208/2

6x = 183/2

x = 183/12 = 61/4 kg (the larger box's weight)

You can check your answer by plugging in these values of x and y into both equations to make sure they still hold.

therefore: x = 183/12 = 61/4 kg (the larger box's weight)

Answer:

1/10  5    2

20    1     1/20

1/2    1/5  10

Step-by-step explanation:

Answer: 0.091125

Step-by-step explanation:

Given : P(dog) = 0.45

If 3 households are selected randomly and with replacement and the ownership is mutually exclusive.

Then , probability that all three randomly selected households own a dog = \((0.45)^3=0.091125\)

Hence, required probability = 0.091125

The probability that all three randomly selected households own a dog  is

0.091125.

Given that,

Based on the above information, the calculation is as follows:

\(= 0.45^3\)

= 0.091125

Learn more: brainly.com/question/17429689

Answer:

16 cups of water

The 9th term of the given sequence is 78732.

The given sequence is 12, 36, 108... is a geometric sequence with a common ratio of 3.To find the 9th term of the given sequence, we will use the formula for the nth term of a geometric sequence, which is given by:

aₙ = a₁rⁿ⁻¹

Here, a₁ = 12 and r = 3.

Therefore, the formula for the nth term becomes:

aₙ = 12(3)ⁿ⁻¹

Now, we need to find the 9th term of the sequence. Hence, n = 9. Substituting the values of a₁ and r, and n in the formula, we get:

a₉ = 12(3)⁹⁻¹= 12(3)⁸= 12(6561)= 78732

For more question  sequence

https://brainly.com/question/29017364?source=archive

#SPJ8

Answer: 516 out of 100 would be 516%

The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

To know more about measurement visit:

brainly.com/question/4804936

#SPJ1

Answer:

\(7+3^{2} - 2\) × \(5 < (\frac{3}{4} + \frac{1}{8} )\) ÷ \(\frac{1}{8}\)

Step-by-step explanation:

so <

hope this helps!

Step-by-step explanation:

\(5x - 4 {x}^{2} + 3\)

\(5(1) - 4 {(1)}^{2} + 3 \\ 5 - 4 + 3 = 4\)

Step-by-step explanation:

Given polynomial

5x - 4x² + 3

put x = 1

→ 5(1) - 4(1)² + 3

→ 5 - 4(1) + 3

→ 5 - 4 + 3

→ 8 - 4

→ 4.

A graph that shows a function must pass the vertical line test

The true statement is (b) No; the graph fails the vertical line test.

For a graph to show a function, the graph must pass the vertical line test

The given graph do not pass the vertical line test;

This is so because, a line drawn from the x-axis would touch the graph at at least two different points

Hence, the true statement is (b) No; the graph fails the vertical line test.

Read more about the vertical line tests at:

https://brainly.com/question/1821791

The value of 'n' is 18 in the given equation 8n - 5 = 139.

We have to find the value of 'n'.

To do so, we need to solve the given equation.

Let us see how we can solve the given equation.8n - 5 = 139

We need to find the value of 'n'.

Let us bring the constant term to the right side by adding 5 to both the sides of the equation.8n - 5 + 5 = 139 + 5On simplifying, we get8n = 144Now, we need to isolate 'n' to find its value.

To do so, we divide both the sides by 8.8n/8 = 144/8On simplifying, we get n = 18

Therefore, the value of 'n' is 18.

Hence, the value of 'n' is 18 in the given equation 8n - 5 = 139.

For more questions on equation

https://brainly.com/question/17145398

#SPJ8