1) Alice decides to take a trip from the East Coast of the United States to the West Coast. While planning, she chooses to drive, fly, and ride a train. Her first leg of the trip is traveling by car, from Sacramento, California to Denver, Colorado. Along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. After driving for many hours, Alice finally makes it to Denver, Colorado spending $874.80 in gas.

a) Let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. Create an equation that models the situation.

b) If Alice purchases 87 gallons for regular unleaded gas, how many gallons of premium gas did she purchase? Show all work to receive full credit.

2) After spending a week in Denver, Alice decides to leave her car at a friend’s house in order fly from Denver, Colorado to Chicago, Illinois. Her plane ticket cost $475 and $35 per checked bag.
a) Write a function that models the number of checked bags, b, as it relates to the total cost, c(b).

b) Compete the table
Number of Bags (b) Total Cost c(b)
0
1
2
3
4
6
8

3) After spending time in Chicago, Alice decides to finish her trip by riding a train 700 miles to Washington D.C. The train travels at an average speed of 80mph. Answer the following questions using the graph.


a) Describe the y-intercept in this scenario.

b) Describe the x-intercept in this scenario

c) Finish the ordered pairs (2.5, ____ ) and (____,300).

d) What are the domain and range?
Domain: {h I ___ < h < ____}
Range: {f(h) I ___ < f(h) < ____}

We see Alice chose a journey to travel from the East coast United States to the West Coast. She had a starting place and ending place in mind and did not aimlessly find her way from Sacramento, California to Washington D.C. But rather, she made decisions along the way to accomplish her goal. One could also say your life is like a journey or race in which you are running. 1 Corinthians 9:24-25 (NIV version) says, “Do you not know that in a race all the runners run, but only one gets the prize? Run in such a way as to get the prize. Everyone who competes in the games goes into strict training. They do it to get a crown that will not last, but we do it to get a crown that will last forever.” How do you interpret this passage in the bible and what does it look like in your life?

2170 toys Jamal assemble altogether during his first 20 days.

What is the arithmetic sequence?

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

Here, we have

Given: Jamal got a job working on an assembly line in a toy factory. On the 20th day of work, he assembled 137 toys. He noticed that since he started, every day he assembled 3 more toys than the day before.

We have to find how many toys did Jamal assemble altogether during his first 20 days.

We apply the arithmetic sequence formula and we get

tₙ = t₁ + (n-1)d

137 = t₁ + (20-1)(3)

t₁ = 80

To calculate the total number of toys that Jamal assemble in his first 20 days,

S₂₀ = (20/2)(2×80 + (20-1)(3))

S₂₀ = 2170

Hence, 2170 toys Jamal assemble altogether during his first 20 days.

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The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached

The values of the constants in the sinusoidal function, h = a + b·(c·t) are;

a = 30

b = -20

c = π/1.5

A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.

The diameter of the Ferris wheel = 40 m

The location of the axle above the ground = 30 m

The time it takes to make a complete a rotation = 3 minutes

The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;

h = a + b·cos(c·t)

The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.

Therefore;

At t = 0, h = 30 - 40/2 = 10

h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b

a + b = 10

Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;

a = 30

a + b = 10, therefore;

b = 10 - a

b = 10 - 30 = -20

b = -20

At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50

50 = a + b·cos(1.5·c)

50 = 30 - 20 × cos(1.5·c)

20 × cos(1.5·c) = 30 - 50 = -20

cos(1.5·c) = -1

cos(π) = -1

Therefore; 1.5·c = π

c = π/1.5

The equation is therefore;

h = 30 - 20·cos((π/1.5)·t)

a = 30, b = -20, c = π/1.5

Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel

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A slope field for the given differential equation dy/dx = xy/2 at the 9 points indicated is shown below.

We know that a slope field represents the slope of a differential equation at certain vertical and horizontal intervals on the coordinate plane.

First we construct a table which contains the values of slope.

Consider given differential equation dy/dx = xy/2

where -1 ≤ x ≤ 1,

1 ≤ y ≤ 3

Let the slope be m

so, dy/dx = m

For x = -1, y = 1

m = (-1 × 1)/2

   = -1/2

For x = -1, y = 2

m = (-1 × 2)/2

   = -1

For x = -1, y = 3

m = (-1 × 3)/2

   = -3/2

For x = 0, y = 1

m = (0 × 1)/2

   = 0

For x = 0, y =2

m = (0 × 2)/2

   = 0

For x = 0, y = 3

m = (0 × 1)/2

   = 0

For x = 1, y = 1

m = (1 × 1)/2

   = 1/2

For x = 1, y = 2

m = (1 × 2)/2

   = 1

For x = 1, y = 3

m = (1 × 3)/2

   = 3/2

So, the table is:

x/y     1  2    3

-1     -1/2   -1      -3/2

0     0   0   0

1       1/2     1      3/2

Therefore, the slope field is as shown below.

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4366 softballs will fit inside of a storage.

What is volume ?

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape. The calculation is unaffected by how you refer to the various dimensions; for instance, you can use "depth" instead of "height."

Diameter of softball = 8.3 in

Radius of softball = 4.15 in

                              = 0.345 ft

Volume of sphere = 4/3 π r³

                = 4/3 π (0.345)³

                = 4/3 * 0.1289

                = 0.1718

Volume of cuboid = l * b * h

                              = 15 * 10 * 5

                              = 750

Number of softballs that can fit inside the storage = 750 / 0.1718

                                                                      = 4366

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Answer:

The cost for 1 pizza is $8.99

Step-by-step explanation:

We know

Natalia paid a total of 38.95 for 3 pizzas and a salad

A salad = $11.98

We first find the total cost of 3 pizzas by

38.95 - 11.98 = $26.97

$26.97 is the cost for 3 pizzas; to find the cost of 1 pizza, we take

26.97 divided by 3 = $8.99

So, the cost for 1 pizza is $8.99

Answer:

The cost of 1 pizza is $8.99.

Step-by-step explanation:

Let

[tex]t[/tex] = total price

[tex]p[/tex] = pizzas

[tex]s[/tex] = salads

Natalia bought 3 pizzas and 1 salad

[tex]38.95=3p+1s[/tex]

We are given the price of the salad.

[tex]38.95=3p+11.98[/tex]

Now we can find the cost of 1 pizza.

Lets solve for [tex]p[/tex].

Subtract 11.98 from both sides of the equation.

[tex]26.97=3p[/tex]

Divide both sides of the equation by 3.

[tex]p=\frac{26.97}{3}\\p=8.99[/tex]

Answer:

E

Step-by-step explanation:

Let

A = # of slices Alice got

B = # of slices Bob got

C = # of slices Charles got

D = # of slices Darwin got

First, write equations based on given information:

A = 0

B = 2C

5C = D

D = C + 8

5C = D -> D = 5C

Now that we have two equations for D, we can set them equal to each other:

5C = C + 8

4C = 8

C = 2

Now just plug in the rest:

A = 0

B = 2(2) = 4

C = 2

D = 2 + 8 = 10

Add all solutions together to get (E) 16 slices

To know whether Elena is correct or not, you need to find out the height of each stack of file folder.

Assume that all 200 files have the same height.

Let the height of each file folder be m inches.

So, by unitary method the height of each file folder would be,

m = Total height of stack / Number of file folders

here, the total height of stack = 5.125 inches

And the number of file folders = 200

So, m = 5.125 / 200

m = 0.0256 inches

But Elena guesses that each file folder is 0. 035 inches thick.

This means, Elena is wrong as the answer Elena gave is too large than the actual answer.

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Answer:

37/56

Step-by-step explanation:

Answer: 3/5 = 0.6

Step-by-step explanation:

1. 2 2/5 x 1/4 = 12/20

2. 2 times 5 over 5 + 2/5 = 10 + 2 over 5 = 12/5

3. 12/5 times 1/4 = 12/20

4. 12/20=3/5

Answer:

Slope = -2  Y intercept is (0,4)

Step-by-step explanation:

The number of hours that the team trians per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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Answer:

a：20 km

b：384

Step-by-step explanation:

a：

[tex] \frac{2.5}{ 8} = \frac{1}{x} [/tex]

[tex]x = 20[/tex]

b：

[tex] \frac{2.5}{8} = \frac{120}{y} [/tex]

[tex]y = 384[/tex]

Answer:

B

Step-by-step explanation:

14.50 / 1.75 = 8.3

26.25 / 2.5 = 10.5

3/8 * 2 = 0.75 .... 5.5 * 2 = 11 (no need to continue)

Three true statements about the angles of the given figure are,

1. angle 1 and the 55 degree angle are adjacent.

5. angle 1 = 180 degree - 55 degree

6. angle 2 = 180 degree - 55 degree - 45 degree.

Complementary angles are two angles whose measures add up to 90 degrees. For example, an angle of 45 degrees and an angle of 45 degrees are complementary. When two angles are complementary, they form a right angle. The symbol for complementary angles is ∠A + ∠B = 90°.

Acute angles are angles whose measure is less than 90 degrees. They are sharp angles that are less than a right angle. On the other hand, obtuse angles are angles whose measure is greater than 90 degrees. They are angles that are greater than a right angle and less than 180 degrees. In other words, obtuse angles are angles that are wider than a right angle but less than a straight angle.

Analysing all the statements given in the question,the corrrect options are

Option 1, since angle 1 and 55 degree share the same vertex.

Option 5, since the sum of angle 1 and 55 degree is 180 degrees being supplementary angles.

Option 6, since the sum of all the interior angles of a triangle is 180 degrees.

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Answer:

1.Given points are:-

(1,2)=(x1/,y1)

(3,4)=(x2,y2)

Now,from two point formula,

y-y1=(y2-y1)/(X2-X1)×(X-X1)

or,y-2=(4-2)/(3-1)×(X-1)

or,y-2=2/2×(X-1)

or,y-2=1(X-1)

or,y-2=X-1

or, X -1-y+2=0

or,X-y+1=0 is the req. eqn in standard form

2.Given points are:-

(2,5)=(x1, y1)

(3,7)=(x2,y2)

Now, from two point formula,

y-5=(7-5)/(3-2)×(X-2)

or,y-5=2/1×(X-2)

or,y-5=2(X-2)

or,y-5=2X-4

or,2X-y-4+5=0

or,2x-y+1=0 is the req. eqn in standard form.

c.do similarly

and*mark me brainliest

Answer:

see explanation

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

First obtain the equations in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

(1)

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 2 ) and (x₂, y₂ ) = (3, 4 )

m = [tex]\frac{4-2}{3-1}[/tex] = [tex]\frac{2}{2}[/tex] = 1 , then

y = x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 4 ) , then

4 = 3 + c ⇒ c = 4 - 3 = 1

y = x + 1 ( subtract y from both sides )

0 = x - y + 1 ( subtract 1 from both sides

- 1 = x - y , that is

x - y = - 1 ← in standard form

Use the same procedure for the next 2 questions

(2)

(x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (3, 7 )

m = [tex]\frac{7-5}{3-2}[/tex] = [tex]\frac{2}{1}[/tex] = 2 , then

y = 2x + c ← is the partial equation

using the point (2, 5 ) to find c

5 = 2(2) + c = 4 + c ( subtract 4 from both sides )

1 = c

y = 2x + 1 ( subtract y from both sides )

0 = 2x - y + 1 ( subtract 1 from both sides )

- 1 = 2x - y , that is

2x - y = - 1 ← in standard form

(3)

(x₁, y₁ ) = (5, 2 ) and (x₂, y₂ ) = (3, 12 )

m = [tex]\frac{12-2}{3-5}[/tex] = [tex]\frac{10}{-2}[/tex] = - 5 , then

y = - 5x + c

using the point (5, 2 ) to find c

2 = - 5(5) + c = - 25 + c ( add 25 to both sides )

27 = c

y = - 5x + 27 ( add 5x to both sides )

5x + y = 27 ← in standard form

Answer:

  -4/17

Step-by-step explanation:

You want the slope of the line described by the equation 20x +85y = 120.

Putting the equation in slope-intercept form by solving for y gives ...

  20x +85y = 120

  85y = -20x +120

  y = -20/85x +120/85

  y = -4/17x +24/17

The slope is the coefficient of x: -4/17.

The rate of change is -4/17.

Answer:

240

Step-by-step explanation:

The total overall profit of all the weekdays is 1200. The question asks for the average. 1200 divided by 5 is 240. the average is 240 dollars per weekday

Answer:

278

Step-by-step explanation:

average = sum/count

count = 7 (7 days)

monday = 150

tuesday = 250

wednesday = 200

thursday = 250

friday = 350

saturday = 450

sunday = 300

sum = 150 + 250 + 200 + 250 + 350 + 450 + 300 = 1950

mean = 1950/7 = 278.571428571 ≈ 278

A random selection of one of the families is made, and a computer is discovered there. P(computer AND TV) = 5/6.

We surveyed 400 households. 60% of people had computers, while 90% of them had TVs.

These were something that every family owned at least one of.

A random selection of one of the families is made, and a computer is discovered there.

Check to see if there is a TV there as well.

union: # with computer, # with TV, - # with both, # with both

400 = 360 + 240 - # with both # with both = 200 / 400 = 0.9 * 400 + 0.6 * 400

P(computer AND TV) = 200/400 = 1/2 ——-

P(TV | computer) + P(TV and computer) / P(computer) = 0.5/0.6 = 5/6

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Yes , you can join Wikipedia as a creator who can help maintain the platform and update the content from time to time. There are also different types of job roles which you can find for Wikipedia .

You can also simply just create an account and start contributing as a member of Wikipedia.

For this the first step would be to select an appropriate username, which will be unique , as this will be used to identify and differentiate you from others. Then you can start contributing to Wikipedia and other Wikimedia projects.

Communicate with other editors via your own talk page. You can also opt in to exchanging emails with other users and thus increase your community.

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Step-by-step explanation:

one side : 2x - 1

so, 5 sides (the perimeter is the sum of all sides) :

5 × (2x - 1) = 10x - 5

The number of bottles of mustard they went through is given by the equation A = 1/6 of the bottle

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of bottles of mustard be represented as A

Now , the equation will be

The amount of ketchup used by Camille's Snack Shack = ( 1/4 ) of the bottle

Now , the amount of bottle of mustard used = ( 2/3 ) of the bottle of ketchup

Substituting the values in the equation , we get

The number of bottles of mustard used A = ( 2/3 ) of ( 1/4 ) of the bottle

On simplifying the equation , we get

The number of bottles of mustard used A = ( 2/3 ) x ( 1/4 )

The number of bottles of mustard used A = ( 1/6 ) of the bottle

Therefore , the value of A is 1/6

Hence , the number of bottles is 1/6

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A) The model that expresses the revenue R as a function of x is R(X) = -1/7x + 200

B) The domain of R is (-∞, +∞)

C) If 200 units are sold, then the revenue is $228.57

D) The quantity that maximizes revenue is 200 and the maximum revenue is $228.57

E) The price should the company charge to maximize revenue $228.57

Here we have given the function that can be model  that expresses the revenue R as a function of x is written as,

=> R(X) = -1/7x + 200

Here the domain value of R has take the value from negative infinity to positive infinity.

When we take the value of x as 200, then the revenues of the sold goods is calculated as,

=> R(200) = -1/7 (200) + 200

When we simplify this one then we get the value of R as

=> R = 28.57 + 200

=> R = 228.57

As per the given function the maximum number of units sold is written as 200, and the maximum revenue is written as 228.57

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Answer:

not sure if I understand but I believe you are talking about writing it down

In any version of Microsoft Word, type m2, then highlight the 2. Now press and hold Ctrl and Shift, then press the + key and it will be changed to superscript and will look like this: m2

Across the y-axis, translated 2 units to the right and four units to the left, the new function is now h(x) = -(x + 2)3 - 4

Step (i): The type of transformation change of the function

a) The translated left "c" units are x - c;

b) The translated right "c" units are x + c

Step (ii) The given function is translated "2" units right side, then the new function is

followed by the translated "4" units left sides and reflected across the y-axis.

Now the new function is h(x).

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The place with the highest temperature is Oslo.

The difference between the temperature in Ottawa and Oslo is 5.2 degrees Celsius .

The new temperature in Moscow is 11 degrees Celsius .

When temperatures are in the negatives, the higher temperature would be the smaller number. Oslo therefore has the highest temperature at - 4.3 °C.

The difference between the temperature in Ottawa and Oslo can be found by subtracting the temperatures:

= - 4 . 3 - ( - 9 . 5 )

= - 4.3 + 9 .5

= 5. 2 degrees Celsius

The new temperature in Moscow is:

= - 7.9 - 3.1

= 11 degrees Celsius

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Answer:

The Hypotenuse

Step-by-step explanation:

The Hypotenuse is the longest side of a Triangle.

The area of the circular base of the fountain is 179 square feet.

A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.

A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.

Combined area of the walkway and fountain: (3.14)112=379.94 ft2.

Fountain area: (3.14)8*2=200.96 feet

Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.

The area of the circular base of the fountain is 179 square feet.

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Answer:

[tex]21x \: - \frac{1}{3} \\ 3[/tex]

Answer:

x = 2

Step-by-step explanation:

4x + 3 = 11

(4x + 3) - 3 = 11 - 3

4x = 8

4x/4 = 8/4

x = 2

As you can see, to isolate x, we must do the opposite operations to both sides.

Answer:

6n-5

Step-by-step explanation:

let 'n' equal 'a number'

the equation above means you are multiplying 6 and that number, then reducing it by 5