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?

Answer:

Perimeter = 24p + 18 cm

Step-by-step explanation:

Perimeter = 2[(8p+5)+(4p+4)]

simplify:

Perimeter = 16p + 10 + 8p +8

combine like terms:

Perimeter = 24p + 18

Answer:

Total hour Talia spend at math camp = 100 hour

Step-by-step explanation:

Given:

Number of days = 5 days

Per hour attended = 5/6 per hour

Find:

Total hour Talia spend at math camp

Computation:

Total number of hour per day = 24 hour

Total hour Talia spend at math camp = Number of days x Per hour attended x

Total number of hour per day

Total hour Talia spend at math camp = 5 x 5/6 x 24

Total hour Talia spend at math camp = 5 x 5 x 4

Total hour Talia spend at math camp = 25 x 4

Total hour Talia spend at math camp = 100 hour

Answer:

10.2 is the answer not sure

Answer:

Regular megagon

Step-by-step explanation:

Regular megagon is a shape called with 1000000000 sides.

Answer:

12² = 144

12 to the power of 2 us equal to 144

Answer:

6

Step-by-step explanation:

6

The best option regarding the solutions of the trigonometric equation presented in this problem is given as follows:

A. 60º + n360º, 300º + n360º.

The trigonometric equation for this problem is defined as follows:

[tex]\cos{x} - \sqrt{1 - 3\cos^2{x}} = 0[/tex]

Then, isolating the cosine, we have that:

[tex]\cos{x} = \sqrt{1 - 3\cos^2{x}}[/tex]

Applying the square for both sides, we have that:

cos²(x) = 1 - 3cos²(x).

4cos²(x) = 1.

cos²(x) = 1/4

cos²(x) = 0.25.

Applying the square root to both sides, we have that:

cos(x) = 0.5.

Meaning that the angle measures of x with the cosine of 0.5 are given as follows:

x = 60º, x = 300º.

(as the cosine is positive on the first and fourth quadrant).

One entire lap over the unit circle is equivalent to 360º, hence adding 360º n times to any of these solutions is also a solution to the trigonometric equation, meaning that option a is correct.

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Answer:

Step-by-step explanation:

The dimensions of a rectangular prism are length, width, and depth.

Volume = length * width * depth

Here, V = 3y3 + 16y2 + 5y. If you can factor that into three terms, those could be the dimensions of the prism.

How do you factor it? Do all three terms have something in common? Sure, they all have a y, so factor a y out of each term.

V = y(3y2 + 16y + 5)

Then, factor what's left.

V = y(3y + 1)(y + 5)

The dimensions of the prism are y, (3y + 1), and (y + 5).

Answer:

The dimensions of a rectangular prism are length, width, and depth.

Volume = length * width * depth

Here, V = 3y3 + 16y2 + 5y. If you can factor that into three terms, those could be the dimensions of the prism.

How do you factor it? Do all three terms have something in common? Sure, they all have a y, so factor a y out of each term.

V = y(3y2 + 16y + 5)

Then, factor what's left.

V = y(3y + 1)(y + 5)

The dimensions of the prism are y, (3y + 1), and (y + 5).

Step-by-step explanation:

it's this write ... comments plz have a nice day

Answer:

{-1, 5} (two real solutions).

Step-by-step explanation:

On the left side we want x^2, not x?

We need to rewrite x? = 4x - 5 in standard form, that is, as a quadratic with x terms in decreasing powers of x:

x^2 - 4x + 5 = 0

This factors easily to (x - 5)(x + 1) = 0.

We let each factor equal zero (0) separately and solve for x:  

{-1, 5} (two real solutions).

Answer:

5.1

Step-by-step explanation:

so the leaning ladder makes a right angled triangle so we can use pythagoras to calculate the the length (the hypotenuse):

5²+1²=x²

25+1=x²

√26=x

x=5.099...

and now we round to one d.p so it becomes 5.1 (1 d.p) as the hundreths digit is 9 and 9 is rounded up.

Answer:

I don't understand your language

Step-by-step explanation:

The distance between the girl and her bike is 25.00 ft.

Distance is the measure of how far apart two objects, places, or points are. It can be measured in a variety of units, such as miles, kilometers, inches, centimeters, or other units.

The distance between the girl and her bike can be found using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.

In this case, the girl is 20 ft. east of the school and 21 ft. south of the school. Therefore, the two sides of the triangle are 20 ft. and 21 ft. and the hypotenuse is the distance between the girl and her bike.

Using the Pythagorean Theorem, the hypotenuse is equal to the square root of (20^2 + 21^2) = 25.00 ft.

Therefore, the distance between the girl and her bike is 25.00 ft.

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Here's link[tex]^{}[/tex] to the answer:

bit.[tex]^{}[/tex]ly/3gVQKw3

Answer:

42/6 = 7

7 - 4 = 3

Step-by-step explanation:

Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.

the idea that time was the fourth dimension and that space and time were therefore inseparably connected. According to his general theory of relativity (opens in new tab), the mass and momentum of adjacent matter influence how much space-time enlarges and compresses.

Here,

Given : The game starts at 18:30

Thus,

They play for eight minutes quarters and half time last for 30 minutes.

So,

To find the time to pick up by your parents:

=> 8*4 + 30

=> 32 + 30

=> 62

Thus time after 62 minutes is 7:32

Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.

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Triangle is always 180 degrees because the sum of all angles in a triangle is 180 degrees. This is known as the "Triangle Angle Sum Theorem." The theorem states that the sum of all angles in a triangle is equal to 180 degrees.

1. A triangle is a three-sided polygon with three angles.

2. The sum of the three angles in any triangle must be 180 degrees.

3. This is known as the Triangle Angle Sum Theorem.

4. The Triangle Angle Sum Theorem states that the sum of the angles in a triangle must equal 180 degrees.

5. It does not matter which angles the triangle has, the sum will always equal 180 degrees.

6. This theorem is based on the fact that the sum of the angles in any triangle is equal to two right angles or 180 degrees.

7. The Triangle Angle Sum Theorem can be proven by drawing a triangle, and then measuring and adding the three angles.

8. The sum of the three angles will always equal 180 degrees.

9. Therefore, triangle is always 180 degrees.

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The solution to the equations is

The value of first x = € 160

The value of second y = € 120

The value of third z = € 140

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 equation be represented as A

Now , the value of A is

Let the first , second and third be represented as x , y , and z

The total amount to be distributed = € 420

So , x + y + z = € 420   be equation (1)

Now , first has €40 more than the second

So , x = y + 40   be equation (2)

And , third has half of what they have between the first two

So , z = ( 1/2 ) ( x + y )   be equation (3)

Substituting the value of x in the equation (3) , we get

z = ( 1/2 ) ( 2y + 40 )

z = y + 20   be equation (4)

Substituting the value of z and x in equation (1) , we get

( y + 40 ) + y + ( y + 20 ) = 420

On simplifying the equation , we get

3y + 60 = 420

Subtracting 60 on both sides of the equation , we get

3y = 360

Divide by 3 on both sides of the equation , we get

y = € 120

Therefore , the value of x = € 160

The value of z = € 140

Hence , the solution to the equation is € 160 + € 120 + € 140 = € 420

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An expression which is equivalent to given [tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex] is 5 / (z + 5)

The correct answer is an option (B)

Consider given quotient.

[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex]

Consider expression 5z + 15

We can write this expression as 5(z + 3) by  taking out the common factor 5.

So given quotient would be,

[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5(z+3)} }[/tex]

As we know a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator.

For fraction [tex]\frac{z+3}{5(z+3)}[/tex] , the common term is z + 3.

So, [tex]\frac{z+3}{5(z+3)} = \frac{1}{5}[/tex]

We know that for fractions a/b and c/d where b ≠ 0, d ≠ 0, if we take quotient of these fraction then that would be,

(a/b) / (c/d) = (a/b) × (d/c)

So, given quotient would be,

[tex]\frac{\frac{1}{z+5} }{\frac{1}{5} }\\\\\\=\frac{1}{z+5} \times \frac{5}{1} \\\\\\=\frac{1\times 5}{(z + 5)\times 1}[/tex]

= 5 / (z + 5)

Therefore, an equivalent expression is: 5 / (z + 5)

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Answer: 3.25 miles

Step-by-step explanation:

Given

Mike Jogged 6 laps around a 0.25-mile track on Tuesday

7 laps on Thursday

Miles jogged on Tuesday is [tex]6\times 0.25=1.5\ \text{mile}[/tex]

Miles jogged on Thursday is [tex]7\times 0.25=1.75\ \text{miles}[/tex]

Total miles Jogged is [tex]1.75+1.5=3.25\ \text{miles}[/tex]

The tasks that Keith can delegate to the assistant are List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet, Add the Debit and Credit columns of the trial balance and Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet.

List the account balances from the general ledger in the Trial Balance columns of the end-of-period spreadsheet: Keith should delegate this task to his assistant. This is a relatively straightforward task that does not require a deep understanding of accounting principles. The assistant can be provided with clear instructions on how to pull the account balances from the general ledger and list them in the trial balance columns of the spreadsheet.

Add the Debit and Credit columns of the trial balance: Keith should delegate this task to his assistant. This is a simple arithmetic task that the assistant can perform with clear instructions.

Make the adjusting entries on the spreadsheet: Keith should retain this task. Adjusting entries involve more complex accounting knowledge and require a deeper understanding of accounting principles. It would be difficult for the assistant to complete this task without proper training.

Complete the spreadsheet: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.

Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the spreadsheet: Keith should delegate this task to his assistant. The assistant can be provided with clear instructions on how to organize the data from the spreadsheet into formal financial statements. It does not require a deep understanding of accounting principles.

Journalize and post the adjusting entries: Keith should retain this task. This task requires a deep understanding of accounting principles and an understanding of how the various accounts and transactions relate to each other. It would be difficult for the assistant to complete this task without proper training.

--The question is incomplete, answering to the question below--

"Keith Martin is the controller for Daniels Printing Service. Keith has been putting in a lot of overtime; therefore, Mr. Daniels has allowed Keith to hire an assistant. Keith's assistant is a bright, high school graduate, but he has never taken an accounting class. Keith is trying to decide which accounting activities could be delegated to his assistant. Keith is willing to give the assistant a few simple instructions on how to complete each task, but he doesn't have the time to teach the assistant to be an accountant.

For each task listed, state whether Keith should continue to do the work or delegate the task to his assistant. Explain each answer.

1. List the account balances from the general ledger in the Trial Balance columns of the work sheet.

2. Add the Debit and Credit columns of the trial balance.

3. Make the adjusting entries on the work sheet.

4. Complete the work sheet.

5. Type the formal financial statements using the data from the Income Statement and Balance Sheet columns of the work sheet.

6. Journalize and post the adjusting entries."

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Answer:

140

Step-by-step explanation:

60+80=?......All you need to do is just add 60 and 80 and get the product

I hope that helped.

Answer: 1660

Step-by-step explanation: 70 + 1590 = QUICK MATHS

Answer:1660

Step-by-step explanation:

Answer:

1155

Step-by-step explanation:

let the ratio be 4x:11x

4x=420

x=105

11x=11*105

=1155

Answer:

x (blue circle thing) = 46

y (dna) = -63

z (molecules) = 52

Step-by-step explanation:

The coefficient is -1

From the universal set; N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}

Probability of drawing an even or prime number will be 15/17.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. The probability of all the events in a sample space adds up to 1.

N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}

Prime = {1,2,5,7,11,13,17}

Even = {2,4,6,8,10,12,14,16}

Pr(Prime) = 7/17

Pr(Even) = 8/17

Pr(Prime or even) = 7/17 + 8/17

Pr(Prime or even) = 15/17

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