Find the range of the function f(x) = 3x - 2, given the domain {-4, 0, 4}

Answer:

  about 11.856 time units

Step-by-step explanation:

We have to assume the equation has something to do with the path of the ball relative to the ground. Perhaps it represents height, with t representing time. The height (h) will be zero for the values of t that satisfy ...

  0 = -t^2 +10t +22

Using the quadratic formula, we can find the values of t that satisfy this equation:

  t = (-10 ±√(10² -4(-1)(22)))/(2(-1)) = (-10 ±√188)/-2 = 5±√47

The value of h is zero for t ≈ 11.856.

_____

About the quadratic formula

The quadratic formula tells you the solution to ...

  ax^2 +bx +c = 0

is given by ...

  x = (-b ±√(b^2 -4ac))/(2a)

Matching this form to the given equation, we see a=-1, b=10, c=22. The variable used in the given equation is t, instead of x.

Writing linear equations given two points can be a useful skill when graphing linear equations.

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It is often useful to find the constant term of a polynomial in order to find its roots.

Roots of polynomials are the solutions for any given polynomial for which we need to find the value of the unknown variable. If we know the roots, we can evaluate the value of polynomial to zero.

The polynomials are the expression written in the form of:

\($$a_n x^n+a_{n-1} x^{n-1}+\ldots . .+a_1 x+a_0$$\)

The formula for the root of linear polynomial such as ax+b is x=-b / a

The general form of a quadratic polynomial is\($a x^2+b x+c$\) and if we equate this expression to zero, we get a quadratic equation, i.e. \($a x^2+b x+c=0$\)

The formulas for higher degree polynomials are a bit complicated.

Hence, it is often useful to find the constant term of a polynomial in order to find its roots.

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The labor cost percentage for next Friday at Fawlty Towers would be approximately 0.63%, which is closest to the option a. 0.05%.

To calculate the labor cost percentage for next Friday at the Fawlty Towers, we need to consider the number of rooms, the time required to clean each room, the number of working hours, the labor rate, and the occupancy rate. Here are the steps to determine the labor cost percentage:

Calculate the number of rooms to be cleaned. If the hotel has 1000 rooms and the occupancy rate for next Friday is 80%, then the number of occupied rooms would be 1000 * 0.8 = 800 rooms.

Calculate the total time required to clean the rooms. Since each room attendant is allocated 30 minutes per room, the total time required would be 800 rooms * 30 minutes = 24,000 minutes.

Convert the total cleaning time to hours. Since there are 60 minutes in an hour, the total cleaning time would be 24,000 minutes / 60 = 400 hours.

Calculate the total labor cost. Each room attendant works 8 hours per day, so for 400 hours, the hotel would require 400 hours / 8 hours = 50 room attendants. Considering their hourly rate of $15, the total labor cost would be 50 room attendants * $15/hour = $750.

Calculate the total revenue. The Average Daily Rate (ADR) is expected to be $150, and with an occupancy rate of 80%, the total revenue would be 800 rooms * $150/room = $120,000.

Calculate the labor cost percentage. Divide the total labor cost ($750) by the total revenue ($120,000) and multiply by 100 to get the percentage: ($750 / $120,000) * 100 = 0.625%.

Therefore, the labor cost percentage for next Friday at Fawlty Towers would be approximately 0.63%, which is closest to the option 0.05%.

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The Fawlty Towers is a Nuxury 1000 room hotel catering to business executives. The occupancy for nad Friday is expected to be 80% Room attendants are allocated 30 minutes to clean each room Room attendants work 8 hours per day at a rate of $15/hour. ADR is expected to be $150 What would the labour cost percentage be for next Friday assuming everything stays the same?

a. 0.05%

b. 5.00%

c. 20.00%

d. 0.20%

Since it is a right triangle, we can apply the trigonometric function:

Sin a = opposite side / hypotenuse

Where:

a= angle = x

Opposite side = 5

Hypotenuse= 13

Replacing:

Sin x = 5/13

Solve for x

x = arc sin (5/13)

x= 22.6 = 23 ° (rounded)

Answer : A. 23°

2 I believe, there are 6 possibilities on a die, 1-2-3-4-5-6. 4 is one of those numbers. Any of the sides could be rolled so each has a probability of 1 out of 6. 1/6 is your answer.

Answer:

2 in

Step-by-step explanation:

Given data

Area= 7 in^2

Volume= 14 in^3

from

Volume= Area* height

substitute

14= 7*x

divide both sides by 7

x=14/7

x= 2 in

Hence the height is 2 in

The specific steps for using a travel time are determining your starting point and destination, choose the mode of transportation, set any relevant parameters, review the results, adjust your plans if necessary.

Determine your starting point and destination: Enter the starting point and destination of your trip, typically using either the addresses or the names of the locations.

Choose the mode of transportation: Select the mode of transportation you plan to use for your trip, such as driving, walking, biking, or using public transit.

Set any relevant parameters: Depending on the travel time calculator you are using, there may be additional parameters you can set, such as the time of day you plan to travel or any stops you plan to make along the way.

Review the results: After entering the necessary information, the travel time calculator should provide you with an estimate of the travel time for your trip, as well as any additional information such as the distance traveled, estimated fuel cost, or suggested routes.

Adjust your plans if necessary: If the estimated travel time is longer than you expected or if there are any unexpected delays or road closures, you may need to adjust your plans accordingly.

Overall, a travel time calculator can be a useful tool for estimating travel times and planning your trip.

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Step-by-step explanation

2 + 12 = 14

Answer:

70

Step-by-step explanation:

180-120=60

180-(60+50)=70

Answer:

m∠U = 70°

Step-by-step explanation:

find the missing inside angle, V:

180° - 120°

60°

so now the total interior angle of triangle is 180°

m∠U + 60° + 50° = 180°

m∠U = 180° - 110°

m∠U = 70°

Answer:

4

100

=

0.04

Step-by-step explanation:

The solution to the given differential equation, subject to the initial conditions, is y(x) = (x^2/10 + 1)ex/5.

To solve the differential equation by variation of parameters, we follow these steps:

1. Find the complementary solution (y_c) by solving the homogeneous equation (25y'' - y = 0). The characteristic equation is r^2 - (1/25) = 0, which gives us the solutions r = ±1/5. Therefore, the complementary solution is y_c = c1e^x/5 + c2e^(-x/5).

2. Next, we need to find the particular solution (y_p) by assuming a solution of the form y_p = u1(x)e^x/5. We substitute this into the original equation and solve for u1(x). Differentiating y_p twice, we find y_p'' = (2/25)u1 + (2/25)xu1' + xu1''.

Substituting these expressions into the original equation and simplifying, we get (2/25)u1(x) = xex/5. Solving for u1(x), we find u1(x) = (x^2/10) + 1.

3. The general solution is given by y(x) = y_c + y_p. Substituting the values of y_c and y_p, we have y(x) = c1e^x/5 + c2e^(-x/5) + [(x^2/10) + 1]ex/5.

4. Finally, we use the initial conditions y(0) = 1 and y'(0) = 0 to determine the values of c1 and c2. Plugging in these initial conditions and solving the resulting equations, we find c1 = 1 and c2 = -1.

Thus, the solution to the given differential equation, subject to the initial conditions, is y(x) = (x^2/10 + 1)ex/5.

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Answer:  x > -8

Step-by-step explanation:

3x - 17 < 4x -  9   subtract 3x from both sides, and add 9 to both sides

-3x + 9 < -3x + 9

0  - 8   <  x  +  0      Rewrite and reverse the sign to simplify

     x > -8

Answer:

Questions aren't listed

Step-by-step explanation:

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

From the question, we have the following parameters that can be used in our computation:

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Answer:

56

Step-by-step explanation:

if she eats 2 hay flakes a meal and 2 meals a day that means she eats 4 hay flakes per day 7 days in a week times two is 14 days so thats 4 times 14 which is 56    

The number of hats Sara bought is 7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Sarah went shopping at a store and bought some hats that cost $6 each and 2 necklaces that cost $12 each.

The number of hats will be calculated as,

12N + 2H = 66

12 x 2 + 2 H = 66

2H = 66 - 24

2H = 42

H = 42 / 2

H = 21

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A rhombus with MK = 24 m, JL = 20, ∠MJL = 50°. So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

We need the information about the measurements or a description of the missing measures in the rhombus. We can make it MK = 24 m, JL = 20, ∠MJL = 50° for example. Since it's a rhombus, all sides are equal in length. Therefore, NK = MK = 24 m, JM = JL = 20 m, and ML = NL.

To find ML (or NL), we can use the Law of Cosines on the triangle MJL. In this case,

ML² = JM² + JL² - 2(JM)(JL)cos(∠MJL):

ML² = 20² + 20² - 2(20)(20)cos(50°)

ML² = 400 + 400 - 800cos(50°)

ML² ≈ 617.4

Taking the square root of both sides, we get ML ≈ √617.4 ≈ 24.8 m.

So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

The complete question is The quadrilateral below is a rhombus. Given MK = 24 m, JL = 20, ∠MJL = 50°. Find NK, NL, ML, and JM. Any decimal answers should be rounded to the nearest tenth.

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Answer:

a

Step-by-step explanation:

8

Using the standard deviation value of these interarrival times, the coefficient of variation is 0.012.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

The standard deviation to mean ratio, or coefficient of variation (CV), illustrates the degree of variability in proportion to the population mean. The dispersion increases with increasing CV.

Formula is given by:

\(CV = \frac {\sigma}{\mu}\)

\(\sigma = 0.02\)

Mean for the time of 0.02 sec is = 79 * 0.02

=1.58

CV= 0.02/1.58

=0.012

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Answer:

544

Step-by-step explanation:

34 * 2 = 68

68 *2 = 136

136 * 2 = 272

272 * 2 = 544 (month 12 = 1 year)

Answer:

140

Step-by-step explanation:

triangles equal to 180

64+76+x=180

x=40

180-40=140

Answer:

140°

Step-by-step explanation:

We know that,

  the exterior angle of a triangle is equal to the sum of the interior opposite angles of a triangle.

Accordingly,

k = 64 + 76

k = 140°

Answer:

\(\huge\boxed{x=65}\)

Step-by-step explanation:

Look at the picture.

\(m\angle VUP=180^o-2\cdot60^o=180^o-120^o=\boxed{60^o}\\\\m\angle UPQ=360^o-2\cdot60^o=360^o-120^o=\boxed{240^o}\\\\m\angle QRM=180^o-2\cdot60^o=180^o-120^o=60^o\\\\m\angle RMQ=180^o-135^o=45^o\\\\in\ \triangle QRM:\ m\angle MQR=180^o-(60^o+45^o)=180^o-105^o=75^o\\\\m\angle PQW=360^o-(2\cdot60^o+75^o+80^o)=360^o-(120^o+155^o)\\\\=360^o-275^o=\boxed{85^o}\\\\m\angle UVW=\boxed{90^o}\)

VWQPU is the pentagon. The sum of interior angles in a pentagon is equal 540°. Therefore:

\(x^o=540^o-(90^o+60^o+240^o+85^o)=540^o-475^o=65^o\)

Answer:

1st question: e. SSS

2nd question: b. SAS

3rd question: b. Δ JLK

4th question: e. SAS

Step-by-step explanation:

Note: Following condition should need to be fulfilled to be congruent triangle:

\(\hrulefill\)

For 1st Question:

In Δ PQR and ΔSTU
PQ=ST side

PR=SU side

QR=TU side

Therefore, Δ PQR ≅ ΔSTU By SSS axiom.

So, the answer is e. SSS

\(\hrulefill\)

For 2nd question:

In  ΔSTR and Δ PQR

TR=PR side

m ∡ SRT = m ∡ PRQ Vertically opposite angle
SR=QR side

Therefore, Δ STR ≅ ΔPQR By SAS axiom.

So, the answer is b. SAS

\(\hrulefill\)

For 3rd Question:

In Δ QPR and Δ JLK

PR=LK side

m ∡ PRQ = m ∡ JKL Given Angle

QR=JK side

Therefore, Δ QPR ≅ Δ JLK By SAS axiom.

We can named the name of triangle by comparing congruent side and angle of the triangle

So, the answer is b. Δ JLK

\(\hrulefill\)

For 4th Question:

In Δ QPR and Δ JLK

PR=LK side

m ∡ PRQ = m ∡ JKL Given Angle

QR=JK side

Therefore, Δ QPR ≅ Δ JLK By SAS axiom.

So, the answer is e. SAS

\(|\Omega|=12^2=144\\|A|=5^2=25\\\\P(A)=\dfrac{25}{144}\approx17.4\%\)

Ｉ ｔｈｉｎｋ ｔｈｅ ａｎｓｗｅｒ ｉｓ ａ!

The mass of the second box is 4.00 kg.

We can use conservation of momentum to solve this problem. The total momentum before the collision is:

P_before = m₁ × v₁ + m₂ × v₂

where m₁ and v₁ are the mass and velocity of the first box, and m₂ and v₂ are the mass and velocity of the second box. Since the first box is moving west and the second box is moving east, we need to use opposite signs for their velocities:

P_before = 3.00 kg × (-2.00 m/s) + m₂ × 1.50 m/s

Simplify this equation, we get:

P_before = -6.00 kg m/s + 1.50 m/s × m₂

After the collision, both boxes come to a stop, so their final velocities are zero. The total momentum after the collision is therefore:

P_after = 0

By conservation of momentum, the total momentum before the collision must equal the total momentum after the collision:

P_before = P_after

-6.00 kg m/s + 1.50 m/s × m₂ = 0

Solving for m₂, we get:

m₂ = 4.00 kg

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