The entrance of a tunnel can be modeled by y=−11/50(x−4)(x−24), where x and y are measured in feet. The x-axis represents the ground. Find the width of the tunnel at ground level

The equations 3x − y + 8 = 0 and 6x − ky = −16 represent coincident lines. So values of k is 2. The correct option is C.

Given the equation

3x − y + 8 = 0

6x − ky = −16 ⇔ 6x − ky + 16 = 0

Here, a₁ = 3, b₁ = -1, c₁ = 8

and    a₂ = 6, b₂ = -k, c₂ = 16

The equations will only represent coincident lines if the two equations have an infinite number of solutions, then [tex]\displaystyle \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex].

Therefore

[tex]\begin{aligned} \frac{a_1}{a_2} & = \frac{b_1}{b_2} \\ \frac{3}{6} & = \frac{-1}{-k} \\ \frac{1}{2}& = \frac{1}{k} \\ k & = 2\end{aligned}[/tex]

So the value of k is 2

Learn more about the two equations in two variables here:

brainly.com/question/19518995

#SPJ4

There are totally six ways to solve the train problems,

Clear and Precise definition

Informational

Brainstorming

Options analysis

Practice

Monitoring

Workplace issues can be resolved in a variety of ways, and the best strategy will depend on the issue's specifics and the situation it arises in. Among the tactics that may be successful are:

         So, by using this points you can solve train problems.

         Therefore ,this 6 points are important to solve train problems.

To know more about train problems at :

brainly.com/question/361996

#SPJ4

The relationship between the independent variable (x) and the dependent variable is depicted by a ratio known as a constant of variation (k) (y).

So long as the matrix is singular, we can use any value of k. Thus, k has an unlimited total value.

The ratio of achievable energy to charge-to-mass in a cyclotron is known as the K value, or bending limit, where is the particle's kinetic energy, is the atomic mass number, and is the charge-to-mass ratio.

A ratio called a constant of variation (k) shows how the independent variable (x) and the dependent variable are related to one another (y). If both of those variables have known values, you can find it by dividing y by x.

In order to obtain k given any position, we must divide the y-coordinate by the x-coordinate because k is constant (the same for every point).

To learn more about the value of K refer to:

https://brainly.com/question/9109365

#SPJ4

Answer: 4 apples 10 banana

Step-by-step explanation: 4 apples is 4 dollars + 1/2 of 10 which is 5 = 9

to figure this out I start out adding 1 apple and 1 banana to each side starting with 0 apples and 6 bananas until I got to 9 dollars worth of fruit

The system of linear inequalities that represents the situation are x + y ≤ 20, x ≤ 15 and y ≤ 10.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given that,

Let x represent the number of surfperch y represent the number of rockfish.

Gaming laws allow you to catch no more than 15 surfperch per day.

x ≤ 15

Gaming laws allow you to catch no more than 10 rockfish per day.

y ≤ 10

Gaming laws allow you to catch no more than 20 total bottomfish per day.

x + y ≤ 20

Hence the system of inequalities are  x + y ≤ 20, x ≤ 15 and y ≤ 10.

Learn more about Linear Inequalities here :

https://brainly.com/question/11897796

#SPJ1

There is a 6.7 percent probability that you are making a mistake by failing to reject the null hypothesis. Hence, option C is the correct answer to this question.

The p-value is a measure of the evidence against a null hypothesis. A smaller p-value means that there is stronger evidence against the null hypothesis. A common threshold for rejecting the null hypothesis is a p-value of less than 0.05, which corresponds to a confidence level of 95%. In this case, the p-value of 0.067 is greater than 0.05, meaning that there is not enough evidence to reject the null hypothesis and conclude that there is a statistically significant difference between the two experimental groups. Therefore, there is a 6.7% probability that you are making a mistake by failing to reject the null hypothesis, which means that the two experimental groups may be statistically identical.

Read more about p-value:

brainly.com/question/13786078

#SPJ4

The complete question is -

As a statistician, you conducted an experiment and obtained a t-test value for the two experimental groups. At a confidence level of 5 percent, the corresponding statistical p-value of 0.067 would suggest that:

a. The inherent error of the experiment is calculated to be 6.7 percent.

b. There is probably a statistically significant difference between the two groups of interest.

c. There is a 6.7 percent probability that you are making a mistake by failing to reject the null hypothesis.

d. There is a 6.7 percent probability that you are making a mistake in accepting the experimental hypothesis.

e. The two experimental groups are statistically identical.

Prior to the Romans, who "Latinized" the entire nation and kept it united until the fifth century .

An example of a radical is the square root or nth root. Expressions with square roots are referred to as roots. There is a radical's radicand, which might be a number or word. Examples include the radicals 2y+1 and 7. The following terminology can be used to describe radicals: Radical equations are referred to as equations containing radicals. A "root expression" is the phrase that appears inside the square root. The radical representations of the numbers 2, 372, 2x+7, and 41p are shown. The expression found inside the square root is known as a "root expression." The digits 2, 372, 2x+7, and 41p serve as illustrations of radical representations.

given

Prior to the Romans, who "Latinized" the entire nation and kept it united until the fifth century,

the Etruscans in Tuscany and Umbria and the Greeks in the south.

Jews arrived in Italy during the Roman Republic and stayed there till the present.

To know more about radicals visit:

https://brainly.com/question/11707044

#SPJ1

Answer:Answer is 2,945,208

Step-by-step explanation:Hope it helps tara:)

7 Children were in attendance.

18 adults were in attendance.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Number of children at party = 25

Dinner cost of a child = $ 5

Dinner cost of an Adult = $ 22

Total cost of dinner = $ 431

let x be the number of children in party.

and, y be the number of adults in party.

According tot the Question,

x + y = 25 ....................(1)

5x + 22y = 431 ..................(2)

Solving the above equation we get

5 ( 25- y) + 22y = 431

125 - 5y + 22y= 431

17y = 306

y= 18

and, x = 25- 18 = 7

Hence, 18 adults and 7 children attended.

Learn more about algebra here:

https://brainly.com/question/24875240

#SPJ1

The sample space is 18. The probability of getting a 2 or a b is 8/18 = 4/9.

The sample space is the set of all possible outcomes of the experiment. In this case, the sample space is all the possible combinations of a die being tossed and a spinner being spun.

There are 6 possible outcomes for the die (1,2,3,4,5,6) and 3 possible outcomes for the spinner (a,b,c). Therefore, the sample space consists of 6x3=18 possible outcomes.

Now, to calculate the probability of getting a 2 or a b, we can count the number of outcomes in which this occurs. There are 4 outcomes that satisfy this condition (2a, 2b, 2c, b). Therefore, the probability of getting a 2 or a b is 4/18 = 8/18 = 4/9.

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ4

Answer:

C.

Step-by-step explanation:

The equation that can be used to predict the number of owners who own a driving game is d = (p*N)/100 where p is the percentage of the population that owns a driving game, and N is the population size and based on the sample, Jaime can predict that 102 video game owners own a driving game.

Sample proportion, p is

p = 24/ 80

A. The equation used to predict the number of owners who own a driving game is:

d = (p*n)/100

Where d is the number of owners who own a driving game, p is the percentage of the population that owns a driving game, and n is the sample size.

B. Based on the sample, Jaime can predict that:

d = (24/80) * 340 = 102

To know more on sample proportion

https://brainly.com/question/29912751

#SPJ4

The value of the rate of change =5 and the value of the initial fee =20

The rate of change (slope) [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]

For solving the given, we will pick any two points,

Let us take the points as:(2,30) and (3,35)

Now, finding the slope of the points:

We will get it as:

[tex]=\frac{35-30}{3-2}=\frac{5}{1}=5[/tex]

So, from above, we can conclude that the equation of the line passing through (2,30) has a slope of 5.

Now further solving:

(y-y1)=m(x-x1)

(y-30)=5(x-2)

(y-30)=5x-10

y=5x+20

Now, comparing the above with the general equation of slope-intercept form:

As we know, in slope-intercept form, we can write it as: y = mx+c, where. m = slope of the line.

For more questions on Slope intercept form:

https://brainly.com/question/1884491

#SPJ4

The required table is attached below:

The long term rate is defined by r = 3/2.

Probability deals with the likelihood of an event or phenomena occurring and is quantified as a number between 0 and 1 inclusive, where 0 indicates an impossible chance of occurrence and 1 denotes the certain outcome of an event. Joint probability refers to a statistical measure that determines the probability of two events occurring together and at the same point in time. Joint probability is the probability of event Y occurring at the same time that event X occurs. Hence, joint probability is a measure of two events happening at the same time and can only be applied to situations where more than one observation can occur at the same time.

A random variable with probability density function is f(x) = 2x, 0 <x<1.

Let Xi denote the life-time of the ith component , then Sn = ∑Xi represents the time of the nth failure. The long-term rate failures occur, is defined by

[tex]r = \lim_{n \to \infty} \frac{n}{S_n}[/tex]

Let Xi denote the ith component and understand that X1, X2,.., is a sequence of independent and similarly distributed random variables, with finite mean.

[tex]Mean = E[Xi] = \int\limits^0_1 {xf(x)} \, dx = \int\limits^0_1 {2x^{2} } \, dx = \frac{2}{3}[/tex]

So,

[tex]r = \lim_{n \to \infty} \frac{n}{S_n} = \frac{1}{Mean} = \frac{3}{2}[/tex]

Thus, the long term rate is defined by r = 3/2.

To learn more about probability, visit brainly.com/question/30034780

#SPJ4

The long term rate is defined by r = 3/2.

Probability deals with the likelihood of an event or phenomena occurring and is quantified as a number between 0 and 1 inclusive, where 0 indicates an impossible chance of occurrence and 1 denotes the certain outcome of an event. Joint probability refers to a statistical measure that determines the probability of two events occurring together and at the same point in time. Joint probability is the probability of event Y occurring at the same time that event X occurs. Hence, joint probability is a measure of two events happening at the same time and can only be applied to situations where more than one observation can occur at the same time.

A random variable with probability density function is f(x) = 2x, 0 <x<1.

Let Xi denote the life-time of the ith component , then Sn = ∑Xi represents the time of the nth failure. The long-term rate failures occur, is defined by

[tex]r = \lim_{n \to \infty} \frac{n}{S_n}[/tex]

Let Xi denote the ith component and understand that X1, X2,.., is a sequence of independent and similarly distributed random variables, with finite mean.

[tex]Mean = E[X_i] = \int\limits^0_1 {x} f(x) \, dx =\int\limits^0_1 {2x^2} \, dx =\frac{2}{3}[/tex]

So,

[tex]r = \lim_{n \to \infty} \frac{a_n }{S_n} = \frac{1}{mean} = \frac{3}{2}[/tex]

To learn more about probability

brainly.com/question/30034780

#SPJ4

The equation 5(2x – 3) = 5  has one solution.

The solution of the equation is x = 2.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, let's solve the equation as follows:

5(2x – 3) = 5

open the brackets

5(2x – 3) = 5

10x - 15 = 5

add 15 to both sides of the equation

10x - 15 = 5

10x - 15 + 15 = 5 + 15

10x  = 20

divide both sides by 10

x = 20 / 10

x = 2

Hence, the solution of the equation is x = 2.

The equation has only one solution.

learn more on equations here:https://brainly.com/question/20014939

#SPJ1

         A + (100 +4.5A) = 1675

Now, According to the question:

The given data is:

The area of the playground section is 1,675 square feet.

It is 100 square feet more than 4. 5 times the area of the sandbox section.

To write an equation the area, A, of the sandbox section.

The area of the sandbox and playground together is 1675 square feet. Using A as the area of the sandbox section, the playground section is said to be (100 +4.5A).

Then the total area is :

A + (100 +4.5A) = 1675  

Subtract 100 on both sides, we get

5.5A = 1575

Now, The area of the sandbox section is:

A = 1575/5.5 = 286 4/11.

Hence, The area of the sandbox section is about 286.4 square feet.

Learn more about Area of the sandbox at:

https://brainly.com/question/16981910

#SPJ4

Based on the data provided in the attached picture the value of f(- 1) is 0.

The function f (x) on the second column assigns a value to the x.  As it can be seen in the given table that at the value of x equal to -1, the function f (x) yields 0.

It can be understood as the given function is f (x) and you need to determine f (-1). Simply it means that you have to put x equal to -1 and check the table for the resulting value. At f (-1), the result obtained is 0.

Therefore, it is concluded that f(- 1) results in 0.

You can learn more about function at

https://brainly.com/question/25638609

#SPJ4

Answer:

The friend

Step-by-step explanation:

18% of 15.85 is 2.85

20% of 14.30 is 2.86

The probability of all heads occurring at the end of the sequence is 1/2^100, or approximately 0.00000000079.

Probability is the branch of mathematics that deals with the likelihood or chance of an event occurring. It is a value between 0 and 1 (or 0% to 100%), where 0 represents an impossible event and 1 (or 100%) represents a certain event.

The probability of each outcome in the sequence is 1/2 (i.e. heads or tails). The total number of possible outcomes is 2^100. This means that the probability of all heads occurring at the end of the sequence is 1/2^100. This can be expressed as 1/2 * 1/2 * 1/2 * ... (100 times), which simplifies to 1/2^100, or approximately 0.00000000079.

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ4

The solution of the given system of equations is x = -2.25, y = 8.25 and z = 4.75. This was obtained by using Gauss Jordan method by solving the equations one by one.

The given system of equations is,

x + y + z = 9

x - 2y + 3z = 8

2x + y - z = 3

We will add the first equation to the third equation to get,

3x + 2y = 12

We will subtract the second equation from the first equation to get,

-y + 4z = 1

We will divide the second equation by 4 to get,

z = 0.25

We will substitute the value of z in the third equation to get,

2x + y = 3

We will divide the third equation by 2 to get,

x + 0.5y = 1.5

We will substitute the value of x and y from the third equation in the first equation to get,

1.5 + 0.5y + z = 9

We will substitute the value of z from the second equation to get,

1.5 + 0.5y + 0.25 = 9

We will solve the above equation for y to get,

y = 8.25

We will substitute the value of y in the third equation to get,

2x + 8.25 = 3

We will solve the above equation for x to get,

x = -2.25

We will substitute the value of x and y in the second equation to get,

-2.25 - 2(8.25) + 3z = 8

We will solve the above equation for z to get,

z = 4.75

Hence, the solution of the given system of equations is,

x = -2.25

y = 8.25

z = 4.75

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The airplane's unit rate of speed in miles per hour is 450.

What is the rate of speed?

"Rate of speed" refers to "acceleration," or the rate at which your speed is varying. Units of "speed" are distances per time (eg miles per hour). Units for "rate of speed" are distance per time.

Here, we have

Given: Kelly flies a distance of 2,100 miles. the trip takes 4 2/3 hours.

Kelly flies at a distance of 2,100 miles

The time taken for the trip is 4 2/3 hours

The rate of speed can be calculated as follows

= 2,100 ÷ 4 2/3

= 2,100 ÷ 14/3

= 2100 × 3/14

= 150 × 3

= 450 miles per hour

Hence, the airplane's unit rate of speed in miles per hour is 450.

To learn more about the rate of speed from the given link

https://brainly.com/question/29737488

#SPJ1

Answer:

-1g + -7

Step-by-step explanation:

(-5g+-6) + (4g+-1)

(-5g + 4g) + (-6+-1)

-1g + -7

(posible answer)

A ratio of two integers where the denominator is not 0 is a mathematical expression that compares the value of two integers, the numerator, and the denominator.

The ratio expresses the relative size of the numerator to the denominator. The numerator and denominator can be any integers, as long as the denominator is not equal to zero.

For example, the ratio of 3 to 4 is written as 3:4 and it means that for every 4 units, there are 3 units of the numerator. Another example is the ratio of 5 to 2, which is written as 5:2 and it means that for every 2 units, there are 5 units of the numerator.

To learn more about ratios at

https://brainly.com/question/13419413?referrer=searchResults

#SPJ4

The mean and standard deviation of the sampling distribution of the sample mean for samples of size 4 is 35.2435.24 and 9.549.54 respectively.

The mean and standard deviation of the sampling distribution of the sample mean for a sample size of 4 is calculated by first taking the population mean, which is 35.2, and dividing it by the square root of the sample size, which is 4. This gives us a mean of 35.2435.24. The standard deviation of the sampling distribution of the sample mean is calculated by taking the population standard deviation, which is 9.5, and dividing it by the square root of the sample size, which is 4. This gives us a standard deviation of 9.549.54. The formula for calculating the mean and standard deviation of the sampling distribution of the sample mean is:

Mean = Population Mean/ √n

Standard Deviation = Population Standard Deviation/ √n

Therefore, the mean and standard deviation of the sampling distribution of the sample mean for samples of size 4 is 35.2435.24 and 9.549.54 respectively.

Learn more about mean and standard deviation here:

https://brainly.com/question/28108712

#SPJ4

The distributive property when rewritten would be : [-18]a + [-17]b

According to the distributive property, it is mandatory to multiply each of the two numbers by the factor before adding them together when a factor is multiplied by the sum or addition of two terms. A (B+ C) = AB + AC is one way to represent this property symbolically.

Sometimes referred to as the distributive law of multiplication and division, the distributive property has two parts.

When we solve out [-18]a + [17]b, we would get the first part of the question which is

-(18a - 17b)

Read more on distributive property here: https://brainly.com/question/4077386

#SPJ1

The volume of sphere is 1437.33 if the given radius is 7 .

What is Surface area of sphere ?

Surface area of sphere can be defined as the product of four , pi and square of radius. And here the value of pi could be 3.14 or 22/7 .

Given ,

Volume of a sphere = 4/3πr³

π = 22/7

r = 7

Volume of a sphere = 4/3πr³

= 4/3 * 22/7 * 7³

= 4/3 * 22/7 * 7 * 7 * 7

= (4 * 22 * 7 * 7 * 7) / (3 * 7)

= 30,184/21

= 1437.3333333333

Volume of a sphere = 1,437.33

Therefore, the volume of sphere is 1437.33 if the given radius is 7 .

To learn more about Surface area of sphere from the given link.

https://brainly.com/question/14692728

#SPJ1

The probability of drawing a card that is more than 6 is given as 1 / 2.

The term probability can be defined as the concept in mathematics that has to do with the likelihood that an event is going to have to occur.

In the picture we have values that are numbered from 1 to 12 in the face of all of the cards.

The cards that are greater than 6 here are: [7, 8, 8, 10, 11, 12] = 6

The total numbers in the card are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] = 12

Hence the probability of card that is more than 6 = 6 / 12

= 1/2

Read more on probability here: https://brainly.com/question/24756209

#SPJ1

There are three basic methods of graphing linear functions. The first is by plotting points and then drawing a line through the points. The second is by using the y-intercept and slope. The third is applying transformations to the identity function f(x)=x f ( x ) = x .

Now, According to the question :

What is linear function ?

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.

Hence, There are three basic methods of graphing linear functions. The first is by plotting points and then drawing a line through the points. The second is by using the y-intercept and slope. The third is applying transformations to the identity function f(x)=x f ( x ) = x .

Learn more about Linear Function at:

https://brainly.com/question/21107621

#SPJ4

Answer:

0.270833333333333333333333333333333333333