Ulysses is spending his vacation in South Carolina. He rents a car and is offered two different payment options. He can either pay $25.00 each day plus $0.15 per mile (option A) or pay $10.00 each day plus $0.40 per mile (option B). Ulysses rents the car for one day.
Write an inequality representing the number of miles where option A will be the cheaper plan. (set up the inequality and then step by step how to solve)
How many miles will Ulysses have to drive for option A to be the cheaper option?
Please show step by step work

Answers

Answer 1
Hi there! First things first, we would set the inequality up like this: 25 + 0.15m < 10 + 0.40m. We set this up, because we are looking for A to be the better option and it’s only being rented for a day. Subtract 0.40m from both sides to get 25 - 0.25m < 10. This is because the number with the variable on the left side is now s negative. Now, subtract 25 to get -0.25m < -15. Now, divide each side by -0.25 to isolate the variable. When you do, you get m > 60. This is because you divided by a negative number, so you flip the symbol over to the opposite. Driving 60 miles will get you the same price, but Ulysses will have to drive 61 miles for option A to be cheaper.
Answer 2
The inequality that is set up and solved is as follows:

0.15x +25 < 0.40x +10     x represents the number of miles and the inequality is set up to make option a cheaper.

 0.15x +25 < 0.40x +10
 -0.15x         -0.15x                 Subtract 0.15x from both sides to get the variable on one side

 25> 0.40x + 10
-10             -10                    Subtract 10 from both sides to isolate the variable

    15> 0.40x
÷0.40   ÷0.40                        Divide both sides by 0.40 to isolate the variable          
60 < x

This shows that if the miles are greater than 60 miles then option A is cheaper. If the miles are less than 60, then option B is cheaper

Related Questions

hi I really need help with a and b. thank you

Answers

a) To solve this equation, you would need to fill in the blank with a substitute. Let x represent the unknown number. 
[tex] \frac{27}{45} [/tex] = [tex] \frac{x}{5} [/tex]

Next, you would cross multiply. 
135 = 45x

Now, the last step would be to isolate the x. To do this, you would divide both sides by 45. 
3 = x

[tex] \frac{27}{45} [/tex] = [tex] \frac{3}{5} [/tex]

b) To solve this equation, you would need to fill in the blank with a substitute. Let x represent the unknown number. 
[tex] \frac{2}{6} [/tex] = [tex] \frac{3}{x} [/tex]
Next, you would cross multiply. 
18 = 2x

Now, the last step would be to isolate the x. To do this, you would divide both sides by 2. 
9 = x

[tex] \frac{2}{6} [/tex] =[tex] \frac{3}{9} [/tex]

I hope this helps!

Robert's recipe has 5 onions and 9 tomatoes for the pizza. Jeff's recipe has 8 onions and 10 tomatoes for the pizza. Whose recipe has a lower ratio of onions to tomatoes

Answers

Robert- 5/9
Jeff-8/10
5 x 10
Robert-50/90
8 x 9
Jeff-72/90
Jeff has a lower ratio of onions to tomatoes

Please check over this!! 20 points! easy fractions
8 SIMPLE QUESTIONS
______________________________________
QUESTION 1
All of the following fractions are proper fractions, except

A-11/12
B-7/5
C-1/6
or D- 8/15
___________________________________________________________________
QUESTION 2
How could you model the fraction 3/8 with a circle?
A-Divide the circle into eight equal pieces, and shade three of them.
B-Draw three circles, and shade eight pieces.
C-Divide the circle into three equal pieces, and shade eight of them.
D-Divide the circle into eleven pieces, and shade one of them.
_________________________________________________________________
QUESTION 3
Kara has four boy cousins and three girl cousins. Write a fraction to represent the part of her cousins that are girls. Use / for the fraction line.

__________________________________________________________________
QUESTION 4
Josh has eight pairs of white socks, two pairs of black socks, and one pair of blue socks. Write a fraction to represent the part of his socks that are white. Use / for the fraction line.
__________________________________________________________________

Answers

1 is correct
2 is correct
3 is correct
4 is correct
5 is correct
6 is correct
7 is correct
8 is correct

Hoped I helped!








1:B
2:A
3: 3/7 
4: 2/11 for black, 1/11 blue, and 8/11 is the white

If it takes 6 hr. for a 2,400 mi. flight from Philadelphia to Los Angeles, what is the average speed of the plane?

Answers

To find Average speed, you need to divide the overall time by the overall distance traveled. The equation used to solve this problem is 2,400 mi/ 6 hrs. The Average Speed would be 400 mi/ hr.

Which of the following is an equivalent form of the mixed number -12 3/4?
A) 45/5
B) -51/4
C) -45/4
D) -48/4

Answers

b is the most reasonable answer. -12 times 4 is -48 plus -3. That's a total of -51/4
B. 51/4 Since 12 multiplied by 4 is 48 and then you add the 3 from the 3/4 and then put the negative sign to make it negative. 

Use linear approximation to estimate 1/4.002

Answers

The estimation for 1/4.002 is approximately 0.2499.

Linear approximation involves using the equation of a line to estimate a value close to a given point. In this case, to estimate 1/4.002, we can use the fact that 1/4 is approximately 0.25 and find the equation of the line passing through 1/4 and 1/4.002.

To find the linear approximation, we first determine the slope between the two points, which is the derivative of the function at the known point. Then, we use the point-slope form of a line equation to find the approximation. Rounding to four decimal places, the estimate for 1/4.002 is approximately 0.2499

Andrea gets 3 7/8 yards of purple ribbon, 3.7 yards of pink ribbon and 3 4/5 yards of blue ribbon. List the numbers in order from least to greatest.

Answers

3.7
3 4/5 = 3.75
3 7/8 = 3.875

3.7 yards of pink, 3 4/5 yards of blue, 3 7/8 yards of purple is your answer


you can change all of them to fractions too, but i decided to change them all to decimals

hope this helps

Which expressions result in a product that has a best estimate of 80? Select all that apply.

A. 0.82 x 112
B. 42.3 x 21
C. 1.2 x 78
D. 0.19 x 37
E. 8 x 9.62

Answers

Answer:

Step-by-step explanation:

E and B are he answers

Answer:

Step-by-step explanation:

i took it and it was a, c and e

Please help!! I really don’t know what this is

Answers

-1/2x-7=-11
Add 7 on both sides.
Divide by -1/2 or multiply by -2.
Answer should be 8
The answer is 8. Hope this very helpful to you and i will love to answer questions again.



In a science experiment, two tomato seeds were planted and watered. After six weeks, the plant that was fertilized was 26 centimeters tall. The plant that was not fertilized was only 74% as tall. What was the height of the shorter plant?

Answers

19.76 cm is the answer

Answer:


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Use the Change of Base Formula to solve: 2^2x = 90. Round to the nearest tenth.

Answers

2x(2)=90
4x=90
x=22.5

A cell phone company charges a monthly fee plus $0.25 for each text message. The monthly fee is $30.00 and you owe $59.50. Write and solve an equation to find how many text messages x you had.

Answers

the equation is at the top, the steps are in between, and the answer is at the bottom
hope this helps

Answer:

An equation is 0.25x+30=59.5.

You had 118 text messages.

Step-by-step explanation:

Austin is going to the movie theater. It is 3 3/5 miles from his house. Austin takes his scooter, but it breaks down 2/3 of the way to the theater. How far is Austin from his house?

Answers

Final answer:

Austin's scooter breaks down 2/3 of the way to the movie theater, which is 3 3/5 miles away from his house. After covering 2/3 of the journey, he is therefore 1 1/5 miles from his house.

Explanation:

Austin is going to the movie theater which is 3 3/5 miles from his house. When his scooter breaks down 2/3 of the way there, we need to calculate how far he is from his house. To find this, we multiply the total distance to the movie theater by the fraction 2/3:

3 3/5 miles = 18/5 miles (since 3 3/5 = 15/5 + 3/5 = 18/5)(18/5) * (2/3) = 36/15 = 12/5 miles

This means Austin covered 12/5 miles when his scooter broke down, leaving him with the remainder of the journey to complete:

Total distance - distance covered = 18/5 miles - 12/5 miles = 6/5 milesTherefore, Austin is 6/5 miles or 1 1/5 miles from his house.

Suppose you randomly select a letter from BURGER AND STARBIRD. Imagine writing these letters on Ping-Pong balls – one letter per ball – then putting them all in a barrel and removing one. What is the probability of pulling out an R? What is the probability of pulling out a B? What is the probability of pulling out a letter that appears in the first half of the alphabet? What is the probability of pulling a vowel?

Answers

First, count the total number of letters in BURGER AND STARBIRD.
There are 17 letters.
Now count each type of letter you are interested in and divide by 17.

a) There are four R's, so the probability of pulling out an R is 4/17.

b) There are two B's, so the probability of pulling out an B is 2/17.

c) Letters A through M appear in the first half of the alphabet.
These letters are from the first half of the alphabet:
BGEADABID
There are 9 of them.
The probability of pulling out a letter that appears in the first half of the alphabet is 9/17.

d) These letters are vowels
UEAAI
There are five vowels.
The probability of pulling out a vowel is 5/17.

a person who is at least 65 years old is often considered a senior citizen. Write an inequality that represents this situation

Answers

your inequality is going to be

x greater than/equal to 65

Which expression is equivalent to 5.4−1.8 ? A. −1.8+5.4 B.−1.8−5.4 C. 1.8 + 5.4 D.1.8−5.4

Answers

The correct answer is A: -1.8 + 5.4. Adding a negative is the same as subtracting. 
The answer is A. -1.8 + 5.4

The expression 3.14 x 10^3 is scientific notation for which of the following values?

A. 314

B. 3,140

C. 31,400

D. 314,000

Answers

B.3140 (number after 3 represents the power of10,here power is 3so no after 3is 3i.e. 1,4,&0

The expression 3.14 x 10³ is scientific notation for B. 3,140.

What is meant by Scientific Notation?

Scientific notation is a way of writing a large number or small number with many digits in a simpler form using the power of 10.

For example, 30,000 can be written as 3 × 10⁴.

So the given number is 3.14 x 10³.

The power of 10 has the number 3.

Hence the decimal point has to moved 3 decimal places to the right.

When it is moved to 1 place, it becomes 31.4.

When it is moved to 2 decimal places, it becomes 314.

When it is moved to 3 decimal places, it becomes 3140.

Hence the given expression is equivalent to 3140.

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Which digit in 98.765 is in the thousandths place

Answers

The thousandths place is the third digit after the decimal point.
5 is in the thousandths place since it is the third digit after the decimal.

Have an awesome day! :)
5 would be in the thousandths place because 3 spaces away from the decimal point would be the thousandths place

which function is increasing? HELP

Answers

A because it is 5/1 so you go up 5 and over 1

Hiya :)

The answer is

f(x)=5^x

Hope this helped!!!!

Have a great day!!!!

:)))

Paloma used these steps to solve the equation 6x+5=3(2x+1)6x+5=3(2x+1). Which choice describes the meaning of her result, 2=02=0?

Answers

No values of x make the equation true. 

The given equation 6x + 5 = 3(2x + 1) has no possible solution.

What is a mathematical function, equation and expression?function : A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is the equation as follows -

6x + 5 = 3(2x + 1)

The given equation is -

6x + 5 = 3(2x + 1)

6x + 5 = 6x + 3

5 = 3

Therefore, the given equation 6x + 5 = 3(2x + 1) has no possible solution.

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write an equation, in slope-intercept form, to model each sitution. : the population of pine bluff is 6791 and is decreasing at the rate of 7 per year.

Answers

6791 of per year answer
y = -7x + 6791 

So since it's decreasing we know that it'll be a negative. It decreases by 7 pine bluffs per year. We can use that equation to model the situation. 
But let me show you an example to prove it. 

Lets say we want to know how many pine bluffs there would be in 3 years
y = -7(3) + 6791 
y = -21 + 6791 

The -21 is the total amount lost in those 3 years, but we have to subtract it from the original amount which was 6791 

y = -21 +6792 
y = 6770
In three years there would only be 6,770 pine bluffs.

if 2=27,what is the measure of the supplement of gbc

Answers

<GBC and <2 are vertical angles, so they are congruent.
m<GBC = m<2 = 27
Supplementary angles have measures that add to 180 deg.
The supplement of <GBC measures 180 - 27 = 153 deg.

Which values are solutions to the inequality –3x – 4 < 2? Check all of the boxes that apply.

-4

-2

0

3

Answers

it is c and d (edge)



Final answer:

To solve the inequality –3x – 4 < 2, subtract 4 from both sides and then divide by -3, we get x > -2. The values that satisfy this inequality are -4, 0, and 3.

Explanation:

To solve the inequality –3x – 4 < 2, we need to isolate the variable x. First, we subtract 4 from both sides of the inequality: –3x < 6. Next, we divide both sides of the inequality by –3, but since we are dividing by a negative number, we need to flip the inequality sign: x > -2. Therefore, the values that are solutions to the inequality are greater than -2. Among the options provided, the values that are greater than -2 are -4, 0, and 3. Therefore, you should check the boxes next to -4, 0, and 3.

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What is 45−−√ in simplest radical form?

Answers

6.708203932499369 is the answer

Consuela wrote the expression 2 × (31 + 47). She states that the expression is a product and that the expression (31 + 47) is a factor. Marcus states that the expression (31 + 47) is a sum of two terms. Who is correct? Explain.

Answers

They are both correct.

A product is anything multiplied together, and what you multiply to get that product is a factor of the product. with 2 x (31 + 47), you're multiplying two factors, 2 and (31 + 47), to get the product 2 x (31 + 47).

A sum is anything added together, so 31 + 47 is a sum.

Answer: They are both correct, A sum is anything added together, so 31 + 47 is a sum.

the line plot below shows how many points fewer trevor scored in 20 games. In how many games did trevor score 18 points fewer?

Answers

It should be 00.0076

jill has $9.96 in nickles,pennies, and dollar bills. she has 12 more pennies than nickles and fove fewer dollar bills than nickles. how many of each does she have?

Answers

Jill has 14 nickels, 26 pennies, and 9 dollar bills.

To solve Jill's problem involving money in nickels, pennies, and dollar bills, we can use algebra. Let's define the variables as follows:

n for number of nickels

p for number of pennies

d for number of dollar bills

We know that:

p = n + 12

d = n - 5

A nickel is worth 5 pennies, so 5n represents the value of nickels in pennies.

Each dollar bill is worth 100 pennies.

In total, Jill has $9.96, which is the same as 996 pennies.

The total amount in pennies can be written as:

5n (nickels) + p (pennies) + 100d (dollar bills) = 996

Substitute the first two equations into the total:

5n + (n + 12) + 100(n - 5) = 996

Simplify and solve for n:

106n - 500 = 996

106n = 996 + 500

106n = 1496

n = 1496 / 106

n = 14

Using the values we just found for n, we can find p and d:

p = n + 12 = 14 + 12 = 26

d = n - 5 = 14 - 5 = 9

So, Jill has 14 nickels, 26 pennies, and 9 dollar bills.

Two quantities, x and y, are directly proportional. If you take a third of x, what happens to y?

A: It is tripled.
B: It is cubed.
C: It depends on the starting value of x.
D: It is multiplied by 1/3.

Answers

D. if something is directly proportional then if something happens to X the exact same thing needs to happen to Y

One-third of x will also give one-third of y. The correct option is D.

What is an expression?

The mathematical expression is the combination of 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 two quantities, x and y, are directly proportional. If x is directly proportional to y it means that x varies directly with y.

x ∝ y

If multiply the value of x by ( 1 / 3 ) the value of y will also be multiplied by ( 1 / 3 ).

Therefore, one-third of x will also give one-third of y. The correct option is D.

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Aa a member of a music club you can order CDs for $14.99 each the music Club also charges 4.99 for each shipment the expression 14.99n + 4.99 represents the cost of n CDs find total cost for ordering 3 CDs

Answers

the total cost would be 59.94

n =3

equation 14.99n +4.99 =

14.99*3 + 4.99 = 44.97 + 4.99 = $49.96

Which expression shows the sum 9 + 21 rewritten as a product of the GCF and a sum?

A- 9(1 + 21)
B- 3(3 + 7)
C- 3(3 + 21)
D- 9(1 + 3)

Answers

B. 
9 = 3 x 3
21 = 3 x 7
GCF = 3
3 x 3 + 3 x 7 = 9 + 21 = 30
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