2) State the Domain and Range of the given function : {(3,4),(1,2), (-1,0), (-3,-2)}
Domain:
Range:

The time-mean speed for the traffic stream that passes an observer standing at a point on a three-lane race track can be determined by collecting spot speed data for all vehicles that pass your observation point in one hour and calculating the average of all the spot speeds collected.

The time-mean speed is a statistical measure used in traffic engineering to quantify the typical speed of vehicles on a given roadway segment. It is defined as the average speed of all the vehicles passing a specific point on the road over a specified period of time. The time-mean speed is typically calculated by taking the average of all the spot speeds collected for a given time period (e.g., one hour).

In the given scenario, the observer is standing at a point on a three-lane race track, where vehicles in lane 1 are traveling at 40 mi/h, vehicles in lane 2 are traveling at 50 mi/h, and vehicles in lane 3 are traveling at 70 mi/h. The constant spacing between each vehicle is 0.5 miles. If the observer collects spot speed data for all the vehicles that pass their observation point in one hour, the time-mean speed for the traffic stream can be calculated by taking the average of all the spot speeds collected. This calculation can be done using the following formula: Time-mean speed = (total distance traveled by all vehicles passing the observer) / (total time taken by all vehicles passing the observer)Assuming that all the vehicles maintain their speeds and the spacing between them is constant, the total distance traveled by all vehicles in one hour can be calculated as follows: Total distance traveled = (40 mi/h x 0.5 mi) + (50 mi/h x 0.5 mi) + (70 mi/h x 0.5 mi) x (number of vehicles passing the observer in one hour)The total time taken by all vehicles passing the observer can be calculated as follows: Total time taken = (0.5 mi) / (40 mi/h) + (0.5 mi) / (50 mi/h) + (0.5 mi) / (70 mi/h) x (number of vehicles passing the observer in one hour)

To know more about observer visit:

https://brainly.com/question/25064184

#SPJ11

The population of blue whales in the southern hemisphere is approximately 404 in the year 2021 if the trend of decreasing population continues.

To find the population of blue whales in the year 2021 if the trend continues, we need to calculate N(41), where t = 41 corresponds to the year 2021.Substitute t = 41 in the given formula:

N(t) = \(4500e^-0.1345t= 4500e^-0.1345(41)≈ 404.5\)

Therefore, the population of blue whales in the southern hemisphere is approximately 404 in the year 2021 if the trend of decreasing population continues.

Learn more about population

brainly.com/question/27991860

#SPJ11

The relative atomic mass of Interactium is 290.14 amu.


We can calculate the relative atomic mass of Interactium using the following equation:

Ar = (Ab × Mb) + (Ac × Mc) + (Ad × Md) where Ar is the relative atomic mass, Ab is the abundance of Interactium-284, Mb is the mass of Interactium-284, Ac is the abundance of Interactium-289, Mc is the mass of Interactium-289, Ad is the abundance of Interactium-294, and Md is the mass of Interactium-294.  

Substituting the given values in the equation, we get:

Ar = (0.16 × 284) + (0.27 × 289) + (0.57 × 294)
Ar = 45.44 + 77.97 + 167.43
Ar = 290.14 amu

Therefore, the relative atomic mass of Interactium is 290.14 amu.

Learn more about atomic mass here:

https://brainly.com/question/29117302

#SPJ11

Answer:

Step-by-step explanation:

      The expanded value of n! is (n) * (n - 1) * (n - 2) until we reach one.

      Given:

4! - ((11-2)!) / 8!)

      Rewrite:

\(\displaystyle 4! - \frac{(11-2)!}{8!}\)

      Subtract:

\(\displaystyle 4! - \frac{9!}{8!}\)

      Expand:

\(\displaystyle 4*3*2*1 - \frac{9*8*7*6*5*4*3*2*1}{8*7*6*5*4*3*2*1}\)

      Cancel out values that equal one in the fraction:

\(\displaystyle 4*3*2*1 - \frac{9}{1}\)

      Multiply:

\(\displaystyle 24 - \frac{9}{1}\)

      Simplify:

24 - 9

      Subtract:

15

Answer:

1/7

Step-by-step explanation:

Answer:

The probability of flipping tails is 1/2

A) To change the rectangular coordinates (-5√3, 5) to polar coordinates, we need to find the radius r and the angle θ.

The radius r can be found using the Pythagorean theorem:
r = √(x^2 + y^2)
r = √((-5√3)^2 + (5)^2)
r = √(75 + 25)
r = √100
r = 10

The angle θ can be found using the inverse tangent function:
θ = tan^(-1)(y/x)
θ = tan^(-1)(5/(-5√3))
θ = tan^(-1)(-√3/3)
θ = -π/6

So, the polar coordinates are (10, -π/6).

B) Given a = (-5, 2) and b = <4, -7>, we need to find 3a - 4b.

3a = 3(-5, 2) = (-15, 6)
4b = 4(4, -7) = (16, -28)

3a - 4b = (-15, 6) - (16, -28) = (-15 - 16, 6 - (-28)) = (-31, 34)

So, the answer is (-31, 34).

Know more about polar coordinates here:

https://brainly.com/question/11657509

#SPJ11

The limit of the given expression as x approaches 4 is undefined.

To evaluate the limit, let's substitute the value x = 4 into the expression:

lim(x→4) [(x - 4) / (x²- 16)]

Substituting x = 4, we get:

[(4 - 4) / (4²- 16)]

[0 / 0]

Here, we encounter an indeterminate form, which means that we cannot determine the value of the expression simply by substituting the value x = 4. This indeterminate form occurs because both the numerator and the denominator become zero.To further analyze the expression and determine the limit, we can use algebraic manipulation. Factoring the denominator, we have:

[(4 - 4) / ((x - 4)(x + 4))]

Now, we can cancel out the common factor of (x - 4):

[1 / (x + 4)]

As x approaches 4, the denominator (x + 4) also approaches 8. Therefore, the limit of the expression is:

lim(x→4) 1/8

Thus, the main answer is that the limit of the given expression as x approaches 4 is 1/8.

Learn more about: Limit

brainly.com/question/12207539

#SPJ11

The type of association you are referring to is called a spurious correlation. In a spurious correlation, there is a relationship between two variables, but the relationship is actually caused by a third variable, also known as a confounding variable. This can lead to misleading conclusions if the third variable is not taken into account.

The type of association that occurs when there is a relationship between two variables, but the relationship is caused by a third variable is called a spurious association or a confounding variable. In this case, the relationship between the two variables is not a direct causal relationship, but is instead influenced by the third variable. It is important to identify and control for confounding variables in order to accurately interpret the relationship between the two variables of interest.

To learn more about spurious correlation, click here:

brainly.com/question/30309773

#SPJ11

Answer:

Option A

Step-by-step explanation:

The unit volume explains it all.

Volumes are measured in units of length cubed. This also is the volume occupied by unit cubes.

By unit cubes, I meant, view the photo above

The volume of an object's says, how many of these cubes will fill that object.

It may not necessarily by a whole number.

So, the answer is Option A

Step-by-step explanation:

HELP making brainliest if it's correct and explain NO explaintion=no brainliest

Answer:

20

Step-by-step explanation:

if you divide 50 from 2.5 you get 20

then take 20x2.5 and you get 50.

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

Read more on Functions here: https://brainly.com/question/29890699

#SPJ11

We know at centroid medians bisect each other in the ratio 2:1.

\(\\ \sf\longmapsto TY=2x\)

\(\\ \sf\longmapsto 2x=30\)

\(\\ \sf\longmapsto x=\dfrac{30}{2}\)

\(\\ \sf\longmapsto x=15\)

Answer:

A

Step-by-step explanation:

On the median TW the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint , then

YW = \(\frac{1}{2}\) × TY = \(\frac{1}{2}\) × 30 = 15

It is true that When the central bank raises the discount rate, commercial banks are likely to reduce their borrowing of reserves from the Fed.

The discount rate is the interest rate at which commercial banks can borrow reserves from the central bank, such as the Federal Reserve in the United States. An increase in the discount rate makes borrowing from the Fed more expensive for commercial banks.

As a result, commercial banks may choose to call in loans to replace the reserves they would have otherwise borrowed from the central bank. Calling in loans refers to the process of demanding the repayment of outstanding loans from borrowers, which allows the bank to obtain funds to maintain their required reserve levels. By calling in loans, banks can avoid the higher cost of borrowing from the Fed due to the increased discount rate.

Overall, a higher discount rate can encourage commercial banks to reduce their borrowing of reserves from the central bank and instead call in loans to maintain their reserve requirements. This can lead to tighter credit conditions in the economy, as banks may be less willing to extend new loans to borrowers, potentially slowing down economic growth.

Know more about discount rate here;

https://brainly.com/question/31430480

#SPJ11

The series ∑ₖ₌₁ᵢₙfₖ does not converge as the limit of the ratio of its terms is infinite (∞).

What is converge series?

In mathematics, a convergent series is one in which, as the number of terms rises, the sum of the terms approaches a finite value. In other words, a convergent series "converges" to a particular value or limit when its terms are added together.

To determine whether the series converges or diverges, we can use the limit comparison test. The limit comparison test states that if the limit of the ratio of the terms of the given series and a known convergent series is a positive finite value, then both series have the same convergence behavior.

Let's consider the known convergent p-series ∑ₖ₌₁ᵢₙ₁/k²,q where p = 2. Now, we can apply the limit comparison test by calculating the limit of the ratio of the terms of the given series and the known convergent series:

limₖ→∞ [(k³ - 6)/(k⁴ + 7)] / (1/k²)

Simplifying the expression inside the limit:

limₖ→∞ [(k³ - 6)/(k⁴ + 7)] * (k²/1)

Taking the limit as k approaches infinity:

limₖ→∞ [(k³ - 6)/(k⁴ + 7)] * (k²/1) = limₖ→∞ [(k³ - 6)(k²)] / (k⁴ + 7)

By evaluating the limit, we find:

limₖ→∞ [(k³ - 6)(k²)] / (k⁴ + 7) = ∞

Since the limit is divergent (∞), the given series does not converge.

learn more about Converge series here:

https://brainly.com/question/30757955

#SPJ4

The values of x and y are 19 and 14 respectively.

Given the hypotenuse = 24

Opposite = x

Adjacent = y

Let's use the sine ratio to find the opposite side

sin of angle = opposite/hypotenuse

sin 54 = x/24

Cross multiplysin 54 × 24 ,= x

x = 19.42

x = 19

To find the adjacent side, we use cosine ratio

cos = adjacent/hypotenuse

cos 54 = y/25

Cross multiply

cos 54 × 24 = y

y = 14

Thus, the values of x and y are 19 and 14 respectively.

Learn more about trigonometric identities here:

https://brainly.com/question/20094605

#SPJ1`

The corollary states that for every positive real number ε, there exists a positive integer n such that

The corollary of the Archimedean principle states that for any positive real number ε, there exists a positive integer n such that ε is greater than the reciprocal of n, i.e., ε > 1/n. In other words, there exists a positive integer n such that the fraction 1/n is smaller than any given positive real number ε.

To prove this corollary, we can assume that ε is a positive real number. By the Archimedean principle, there exists a positive integer m such that m > ε. Now, consider the positive integer n = ⌈1/ε⌉ + 1, where ⌈x⌉ denotes the ceiling function, rounding up x to the nearest integer.

We have:

1/ε < 1/(⌈1/ε⌉ + 1) ≤ 1/(1/ε) = ε.

Therefore, we can conclude that for any positive real number ε, there exists a positive integer n = ⌈1/ε⌉ + 1 such that ε > 1/n.

Learn more about corollary states

brainly.com/question/13485668

#SPJ11

Energy and mass are related by the formula, E = mc², where m is the mass of the object and c is the speed of light. The equation that finds m, given e and c, is:   m = E/c²

The equation, E = mc² was coined from Albert Einstein's theory of relativity, which shows the relationship between mass and energy. It shows that energy and mass can be interchanged into each other. The equation tells us that if we multiply the mass of a body (m) with the square of the speed of light (c²), we will get the total amount of energy (E) contained in that body, which can potentially be converted to other forms of energy.

However, if are given the energy contained in a body and the speed of light, then told to find the mass of the body, we will divide the equation by the coefficient of m. The coefficient of m in the equation is c², thus:

                          E = mc²

                          E/c² = mc²/c²

   c² divided by c² is 1, therefore, the new equation is:

                               m = E/c²

 Thus, the equation that finds m, given e and c is m = E/c².

Learn more about energy and mass here:

https://brainly.com/question/15219830

#SPJ4                    

Answer:

part 1: You start with an annual "simple interest rate," which is the percentage of the principal balance your money earns each year. ... Add the daily interest earned to the balance.

part 2: Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period.

part 3: a compound interest account and here's why. When it comes to investing, compound interest is better since it allows funds to grow at a faster rate than they would in an account with a simple interest rate

Step-by-step explanation:

Answer:

Total length of fabric pieces is 8400 mm.

Step-by-step explanation:

Eva buys a piece of red fabric of length = 5.6 meters

Since, 1 meter = 1000 mm

Therefor, 5.6 meter = 5.6 × 1000

                                 = 5600 mm

Similarly, length of yellow fabric piece = 2.8 meters

                                                                ≈ 2.8 × 1000 mm

                                                                ≈ 2800 mm

If these pieces are joined together, total length of the fabric pieces

= 5600 + 2800

= 8400 mm

Therefore, total length of fabric pieces is 8400 mm.

Answer:

above is right

Step-by-step explanation:

The correct response is c. 8√2 . The length of the diagonal if the side of the square is 8√2.

A polygon's opposed vertices (or corners) are connected by a line segment known as a diagonal. Or to put it another way, a diagonal is a line segment joining two polygonal vertices that are not neighbouring. With the exception of the figure's edges, it connects a polygon's vertices. For instance, a diagonal line or movement runs slopingly from one corner of a square to the other corner. a type of straight line called a diagonal. Straight up, down, or across are not possible on a diagonal line. It is a line that joins the corners of a form at two points. Instead of running straight up or across, a diagonal is formed by a straight line that is positioned at an angle.

Right isosceles triangles with both legs 8 feet long would make up each half.

The hypotenuse that both of those triangles would share is the diagonal.

We must determine the hypotenuse's length, d, in feet.

According to the Pythagorean theorem, the lengths of the legs' squares sum up to the length of the hypotenuse's square, so

\(8^{2} +8^{2} =8\sqrt{2}\)

To know more about diagonal here

https://brainly.com/question/25740584

#SPJ4

A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8ft? Leave your answer in simplest radical form.

a. 16√8

b. 2√8

c. 8√2

d. 4

 The greatest common factor is the biggest number that divides evenly into each one of the numbers without a remainder...the only thing that's different about our situation is that we have variables in addition to regular number (but the same logic applies...we need to find the biggest variable that goes into k^4 , k^3 , and k^2 ).

The biggest number that goes into 15, 35 and 20 is the number 5. The biggest variable that goes into k^4 , k^3 , and k^2 is k^2

Combining the number and the variable, we get that the greatest common monomial factor is 5k^2

Since area is length x width, and we just figured out that width is 5k2 , all we have to do to find length is divide 15k4+35k3+20k2 by 5k2 , and we get that the length is 3k^2+7k+4

So the width is 5k^2 and the length is 3k2+7k+4

:))

-Eli

Answer:

atammy initially had $10 pay

Answer:

B. Tammy will type for 10 minutes each day.

C. Tammy initially had $4 pay.

D. Tammy will type for 4 minutes each day.

Step-by-step explanation:

I swear it is right. I got it wrong and so it told me the correct answer.

Answer:

dhdt≃0.283ft3s

Step-by-step explanation:

dhdt≃0.283ft3s

The draining from the tank when the water depth is 8 ft will be negative 1/π feet per minute.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

An inverted conical water tank with a height of 12 ft and a radius of 3 ft is drained through a hole in the vertex. If the water level drops at a rate of 1 ft/min.

\(\rm \dfrac{dV}{dt} = -1 \ ft/min\)

The volume of the cone is given as,

V = (1/3) πr²h

The relation between r and h is given as,

r / h = 3 / 12

r = h / 4

Then the volume is written as,

V = (1/3) π (h/4)² × h

V = (π / 48) h³

Differentiate the volume with respect to time. Then we have

(dV)/(dt) = (π/48) x 3h² x (dh / dt)

- 1 = (π/48) x 3(4)²  (dh / dt)

- 1/π = dh / dt

The draining from the tank when the water depth is 8 ft will be negative 1/π feet per minute.

More about the differentiation link is given below.

https://brainly.com/question/24062595

#SPJ5

Answer:

-2

Step-by-step explanation:

4y - 7 = - 15

4y = -15 + 7

4y = -8

y = - 8 / 4

y = - 2

The sampling technique used in each study is as follows: (a) convenience sampling, (b) systematic sampling, and (c) stratified random sampling.

(a) In the first study, where a journalist goes to a campground to ask people about their feelings regarding air pollution, the sampling technique used is convenience sampling. This is evident because the journalist approaches individuals who are readily available and easily accessible at the campground. However, convenience sampling may introduce bias as it does not ensure a representative sample of the population.

(b) In the second study, where every tenth machine part is selected from an assembly line for measurement, the sampling technique used is systematic sampling. Systematic sampling involves selecting every nth element from a population after establishing a sampling interval. In this case, every tenth machine part is selected to ensure a systematic and unbiased approach to quality assurance.

(c) In the third study, where attitudes about smoking are studied at a college and students are divided by class and then randomly sampled from each class for interviews, the sampling technique used is stratified random sampling. Stratified random sampling involves dividing the population into homogeneous subgroups (strata) and then randomly selecting samples from each subgroup. By dividing the students into different class strata and randomly selecting samples from each class, this study aims to ensure representation from each class in the final sample.

Learn more about sampling technique here:

https://brainly.com/question/31697553

#SPJ11

Answer:

  \(\displaystyle\textsf{a) }\binom{8}{4}\\\\\textsf{b) }\binom{-8}{4}\)

Step-by-step explanation:

Given a translation vector ...

  \(\displaystyle \binom{g}{h}\)

moves g to the right and h up, you want the vectors for 8 right, 4 up, and for 8 left, 4 up.

When we have g = units to the right, and we want 8 units to the right, we know that g = 8. Similarly, h = units up, and we want 4 units up, so h = 4.

Putting these values in the vector form, we have ...

a)   8 right, 4 up matches vector ...

  \(\displaystyle \boxed{\binom{8}{4}}\)

b)  Left is the opposite of right, so 8 units left will be represented by ...

  g = -8

As before, 4 units up means h = 4.

  \(\displaystyle \boxed{\binom{-8}{4}}\)

<95141404393>

Answer:

b = 7

Step-by-step explanation:

- 4(2 - 5b) = 132

- 4 × 2 - 4 × (- 5b) = 132

-8 + 20b = 132

20b = 132 + 8

20b = 140

b = 140/20

b = 7

Thus, The value of b is 7

-TheUnknownScientist