A family wants to rent a car to go on vacation. Company A charges 70.50​$ and 16cents . Company B charges ​30.50$ and 8 cents . How much more does Company A charge for x miles than Company B ​?

Answer:

9

Step-by-step explanation:

The damping ratio (ζ) is 1, indicating critical damping, and the natural frequency (ωn) is 7.

To illustrate the location of poles and zeros on the s-plane for the given transfer function G(s) = 49/(s+7)(s+7), we first need to factorize the denominator. The transfer function has two poles at s = -7 and s = -7, indicating a double pole at s = -7. The denominator (s+7)(s+7) represents a second-order system.

The poles represent the points on the s-plane where the transfer function becomes infinite, or the system becomes unstable. In this case, the poles are located at s = -7, indicating that the system is critically damped since there is a double pole at the same point.

To determine the damping ratio (ζ) and natural frequency (ωn), we can compare the given transfer function to the standard second-order transfer function form:

G(s) = ωn^2 / (s^2 + 2ζωn s + ωn^2)

By comparing the coefficients, we can see that ωn^2 = 49 and 2ζωn = 14 (since 2ζωn is the coefficient of s). Solving for ωn and ζ, we get:

ωn = sqrt(49) = 7 2ζωn = 14 => ζ = 1

Therefore, the damping ratio (ζ) is 1, indicating critical damping, and the natural frequency (ωn) is 7.

Learn more about damping ratio

https://brainly.com/question/28941371

#SPJ11

The value of the x and y in the given equations is 7 and 5 respectively.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given is a situation, the  value of x is 8 less than 3 times the value of y. The sum of x and y is 12, we need to make two equations that represent this situation and solve for x and y,

Establishing the equations,

3y-x = 8

3y = x+8

y = x+8 / 3....(i)

x+y = 12....(ii)

Put eq(i) in eq(ii)

x + x+8 / 3 = 12

Multiply the equation by 3,

3x + x+8 = 36

4x = 28

x = 7

Put x = 7 in eq(i)

y = 7+8 / 3

y = 5

Hence, the value of the x and y in the given equations is 7 and 5 respectively.

Learn more about equations, click;

https://brainly.com/question/29657988

#SPJ1

Answer:

faut-il faire les ponits avec le pallergrom de (−2 ; 3), (6 ; 2) (−1 ; 0) ?

Step-by-step explanation:

Given:

Total cost P(x) as a function of the number of tickets, x is

\(P(x)=x+8\)

To find:

The domain for visiting and riding rides at Paul’s Pumpkin Patch.

Solution:

Domain is the set of input values.

Here, domain is x and it represents the number of tickets.

We know that, number of tickets cannot be negative or decimal or fraction vales. So, x must be non-negative and integer value.

Domain = x ≥ 0, x is an integer

Therefore, the correct option is D.

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The values of x for which f(x) = 8 are :

Answer:

y=-2x+3

Step-by-step explanation:

y=mx+b

The acceleration of the sled and the normal force acting on it is

a = 1.3 m/s²; FN = 63.1 N.

The force produced when two surfaces collide and slide against one another is known as frictional force. The following variables impact the frictional force: Surface roughness and the amount of force pressing them together have the biggest an impact on these forces..

Given that,

8 kg is indicated as the sled[mass. ]'s

The fictional force is given as 2.4 N

A force of 20 N was exerted on the sled at angle of 50⁰.

The force is split into vertical and horizontal components,

\(F_{h} =F_{p}cos\)  And  \(F_{v}=F_{p} sin\)

Here  \(F_{h}\) is the horizontal component and \(F_{v}\)  is the vertical component.

\(F_{h} =20\) × \(cos50\) = 12.85575219 N

Similarly,  \(F_{v} =\) 20 × \(sin50=15.32088886 N\)

Since there is no motion in the vertical direction, the sum of the vertical components is 0.

Hence, \(F_{N}\)+\(F_{P}sin =mg\) where g is the acceleration due to gravity.

\(F_{N}=mg-F_{p}sin50\)⁰

\(F_{N}=8\) × \(9.8-15.32088886\)  [In this case, g is 9.8 m/s²]

= 63.1 N

The acceleration of the sled and the normal force acting on it is

a = 1.3 m/s²; FN = 63.1 N.

To know more about fictional forces, visit:

https://brainly.com/question/12152715

#SPJ4

The value of the investment of $2500 for 3 years will be $3703.86.

Compound interest is applicable when there will be a change in principle amount after the given time period.

For instance, if you give someone $500 at a 10% yearly rate, $500 is considered your primary sum. After a year, the interest will be $50, making the principle amount $550. Moving forward, the interest will be $550 rather than $500.

Given,

Principle amount (P) = $2500

Rate of interest (R) = 14%.

Time period (T) = 3 years.

Compound interest formula

A = P\([1 + R/100]^{T}\)

So,

A = 2500[1 + 14/100]³

A = $3703.86

Hence the investment of $2500 at a rate of 14% for 3 years will be $3703.86.

For more information about compound interest

brainly.com/question/26457073

#SPJ1

Answer:

x = 0

Step-by-step explanation:

y = x + 4 and y = 2x + 4

Let's solve

x + 4 = 2x + 4

-x  + 4 = 4

-x = 0

x = 0

So, there is only one solution is x = 0

True. Probability of an uncertain outcome is a number between 0 and +1, exclusively.

The probability of an uncertain outcome is a measure of the likelihood that the outcome will occur, and it is always a number between 0 and 1, inclusive. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain. Probabilities between 0 and 1 indicate the degree of uncertainty about whether the event will occur or not.

Probabilities cannot be negative or greater than 1, as they represent a proportion of the total possible outcomes. If the probability of an event were negative or greater than 1, it would imply that the event is impossible or certain to occur, respectively, and violate the fundamental laws of probability theory.

Learn more about Probability here

https://brainly.com/question/13604758

#SPJ11

Answer: 112.5 km5.

-

Alexander was able to cover 25% of 150 km journey in the morning. What percent of journey is still left to be covered?

112.5km5

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

\(x-4\leq -3\\x\leq 1\)

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

Learn more about volume of cone here: brainly.com/question/16419032

#SPJ11

\( \large \mathfrak{Answer : }\)

The equation of the given circle is :

(x - 3) + (y - 5) = 8

where, r² = 8

therefore, value of radius (r) = \(2\sqrt{2}\) units

Answer:

38

Step-by-step explanation:

She makes 17 bags an hour. Multiply 17 bags by each hour. Additionally, multiply that by 5 for each day worked. The total number is 510.

Out of 510 bags made in that week, only 90% are perfect. 90% of 510 is 459.

If there are 459 bags, and each box can hold 12, how many boxes will be full?  Keep adding bags into boxes until you reach 0 bags. The equation you'll want is 459/12.

38 boxes will be full, with 3 remainder bags.

Answer:

42%

Step-by-step explanation:

K-Means uses Euclidean distance. The output includes average and maximum distances, separation, and convergence after iterations related to the number of starting seeds.

In the output of a K-Means cluster analysis, "Ave Distance" refers to the average distance between the data points and their assigned cluster centroids.

"Max Distance" represents the maximum distance between any data point and its assigned centroid. "Separation" indicates the distance between the centroids of different clusters, reflecting how well-separated the clusters are.

Convergence in K-Means clustering refers to the point when the algorithm reaches stability and the cluster assignments no longer change significantly.

When the video mentions convergence after 4 iterations, it means that after four rounds of updating cluster assignments and re-computing centroids, the algorithm has achieved a stable result.

The "Number of starting seeds" option determines how many initial random seeds are used for the algorithm, and it can affect the number of iterations needed for convergence. Increasing the number of starting seeds may result in faster convergence as it explores different initial configurations.

Learn more about Euclidean here:

https://brainly.com/question/31120908

#SPJ11

Answer:First suppose that the roots of the equation

x2−bx+c=0(1)

are real and positive. From the quadratic formula, we see that the roots of (1) are of the form

b±b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2.

For the root or roots to be real, we require that b2−4c≥0, that is, b2≥4c. In order for them to be positive, we require that

b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√>0.

This immediately tells us that b>0, but we can go further. We can rearrange this to get

b>b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√,

which (assuming that b>0) is true if and only if

b2>b2−4c,

since both sides of the inequality are positive so we may square. But then

4c>0.

That is, if the roots are real and positive then b>0 and b2≥4c>0.

Now suppose that b>0 and b2≥4c>0.

Then the roots of (1) are real since b2−4c≥0, and b>0 guarantees that the root b+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√ is positive.

So it remains to show that b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√>0. We have that

4c>0,

so that

b2>b2−4c,

then square rooting shows that

b>b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√,

so the roots of (1) are real and positive, as required.

Approach 2

the curve y equals x squared minus b x plus c showing two positive roots for y equals zero

This is intended to be a proof without words! We have from the diagram that:

If c, b and b2−4c are all positive, there are two real positive roots for x2−bx+c=0 (if b2=4c, we have two real positive equal roots).

If there are two real positive roots for x2−bx+c=0, then c and b are positive and b2−4c is non-negative.

(Why is the distance between the roots b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√?)

Approach 3

When solving problems about the roots of polynomials, it is often useful to find expressions those roots must satisfy and see if this tells us anything new. If α and β denote the roots of the equation, then

x2−bx+c=(x−α)(x−β)=x2−(α+β)x+αβ

and so α+β=b and αβ=c.

We also know that the roots of a quadratic equation are real if and only if the discriminant is non-negative, that is, if and only if b2−4c≥0.

Using these facts, if α and β are both real and positive, then b=α+β>0, c=αβ>0 and b2≥4c, as above.

Conversely, if b>0 and b2≥4c>0, then we know the discriminant is positive and hence both roots are real. We also have that

αβ>0(2)

and

α+β>0.(3)

As α and β are both real, by (2), we know that α and β are either both positive or both negative. However, if α and β were both negative, then (3) could not possibly hold. Hence α and β are both positive, as required.

We now sketch on a graph the region where b>0, c>0 and b2≥4c:

The curve b squared = 4 c as a quadratic with the c-axis vertical and the b-axis horizontal. The region below it is shaded.

The region of the b-c plane for which b>0, c>0 and b2≥4c

Sketch the region of the b-c plane in which the roots of the equation are real and less than 1 in magnitude.

We know that in order for the roots to be real we need b2≥4c as in the first part. We now need to find the region where

−1<b±b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2<1.(4)

We have b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2≤b+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2 so we only need to consider the values for which both

−1<b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2andb+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2<1.

Firstly, we will consider the values for which

b+b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√<2.

Rearranging gives

b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√<2−b.

So b<2, as the square root is non-negative, and we can square both sides to get

b2−4c<4−4b+b2,

which we may rearrange to find c>b−1.

We will now consider the values for which

−2<b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√.

Similarly, we can rearrange to get

b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√<b+2.

So b>−2, and we can, as before, square to get

b2−4c<b2+4b+4,

and hence c>−b−1.

To sketch the graph, we start by considering the boundary curves b2=4c, c=b−1 and c=−b−1, and the points at which they intersect. We can see that the two lines only intersect when b=0 and c=−1, and the lines intersect the curve when

b2=4b−4andb2=−4b−4

which rearrange to

(b−2)2=0and(b+2)2=0.

This tells us that each line intersects with the curve in only one place and so these lines must be tangent.

Is there a way we could have deduced this directly from (4)?

What do the lines being tangent signify in terms of our equation x2−bx+c=0?

Is this a representation of a well-known property of these equations?

Sketching the graph then yields the following picture:

The graph with the previous curve and the lines 4 c = 4 b minus 4 and 4 c = minus 4 b - 4. Each line touches the curve once and the two lines intersect at (0, minus 1). The region between the three lines/curves is shaded.

The shaded region is where b2≥4c, c>b−1, c>−b−1 and −2<b<2

We might notice that when we derived the inequalities c>b−1 and c>−b−1, a lot of the work we did was very similar.

We might also notice that the graph above is symmetric about the c axis. Why is this?

Does the graph give us any ideas about how we might deduce one inequality from the other?

Step-by-step explanation:

One of the primary goals when constructing a frequency distribution for quantitative data is to summarize the data in a manner that: accurately depicts the data as a whole.

Hence, option (a) is correct.

One of the primary goals of constructing a frequency distribution for quantitative data is to summarize the data by organizing it into classes or intervals and showing how many data points fall into each class.This allows for a quick visual representation of the data and can reveal patterns, trends, and insights that might not be apparent when looking at the raw data. The frequency distribution can also be used to calculate various descriptive statistics such as measures of central tendency (e.g., mean, median) and measures of dispersion (e.g., range, standard deviation) that further summarize the data and provide a more complete understanding of its characteristics.

for such more question on frequency

https://brainly.com/question/26177128

#SPJ4

The complete question may be:

One of the primary goals when constructing a frequency distribution for quantitative data is to summarize the data in a manner that:_____________

(a) accurately depicts the data as a whole.

(b) accurately add the data as a whole.

(c) Make a frequency distribution of data

(d) None of the above

Answer:

5+2=7-7+4=4 =4 the answer is 4

Step-by-step explanation:

do not cheat 1st grader

Answer:

4

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

I think -2 is the ans

Let the short piece = x

Th longer piece would be 2x ( twice as long)

Now you have x + 2x = 84 inches

Simplify:

3x = 84

Divide both sides by 3:

X = 28

The shorter piece is 28 inches.

Answer: 84/2=42, 42-12=28   42+12= 56      56+28=84

Step-by-step explanation:

The number 459 in the citation 319 N.W. 2d 459 represents the page number where the case or legal opinion can be found in the North Western Reporter, Second Series. The North Western Reporter is a series of case reporters that includes court decisions from various states in the northwestern region of the United States.

In legal citations, the number before the "N.W." indicates the volume number of the reporter. So in this case, "319" refers to the specific volume where the case is located. The abbreviation "N.W." stands for North Western Reporter, which is the name of the reporter series. The number "2d" after "N.W." indicates that this is the second series of the North Western Reporter.

To locate the case within the volume, the number "459" refers to the page number where the case begins. This allows readers, such as lawyers, judges, or researchers, to easily find and reference the specific case within the reporter.

In summary, the number "459" in the citation 319 N.W. 2d 459 represents the page number where the case can be found in the North Western Reporter, Second Series.

know more about northwestern region, state.

https://brainly.com/question/749299

#SPJ11

Answer:

3

Step-by-step explanation:

30 ×10%/100%=3

percentage is always out of 100 that's why 10%over 100%

hope this will help mate

The answer is 'The indicator variable and square footage would be combined to get the interaction term'

In an equation or formula, a variable is a symbol or letter that stands in for an unknowable or varying quantity or value.

To create an interaction term in this regression model, we would multiply the indicator variable (1 if the house is within 3 miles of campus, 0 if not) by the square footage. This would allow us to examine whether the effect of square footage on house price is different for houses that are within 3 miles of campus compared to those that are not.

So, the answer is: The indicator variable and square footage would be combined to get the interaction term.

To know more about variables, visit:

https://brainly.com/question/112703

#SPJ1