Ask question

Ask question

All categories

2 years ago

8

Cassie is traveling 675 miles today to visit her brother and his family. So far, she has stopped for gas three times. At the fir

st stop, she put in 7.1 gallons of gas and paid $23.79. At her second stop, she put in 5.8 gallons of gas and paid $19.08. And, at the third stop, 6.6 gallons and paid $20.39.
If the gas station that Cassie stopped at first raises their price 8%, what will be their new price per gallon?

2 answers:

Paul [167]2 years ago

8 0

The answer is $3.62 per gallon

elena55 [62]2 years ago

6 0

Answer:

$3.62 per gallon

Step-by-step explanation:

You might be interested in

John, Sally, and Natalie would all like to save some money. John decides that it

brilliants [131]

Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2) $y=100x+300$

Part 3) $\$12,300$

Part 4) $\$2,700$

Part 5) Is a exponential growth function

Part 6) $A=6,000(1.07)^{t}$

Part 7) $\$11,802.91$

Part 8) $\$6,869.40$

Part 9) Is a exponential growth function

Part 10) $A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

Part 11) $\$13,591.41$

Part 12) $\$6,107.01$

Part 13) Natalie has the most money after 10 years

Part 14) Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

$m=\$100\ per\ month$

The y-intercept or initial value is

$b=\$300$

so

$y=100x+300$

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

so

$10\ years=10(12)=120 months$

For x=120 months

substitute in the linear equation

$y=100(120)+300=\$12,300$

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

so

$2\ years=2(12)=24\ months$

For x=24 months

substitute in the linear equation

$y=100(24)+300=\$2,700$

Part 5) What type of exponential model is Sally’s situation?

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$P=\$6,000\\ r=7\%=0.07\\n=1$

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}$

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{10}=\$11,802.91$

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute the value of t in the exponential growth function

$A=6,000(1.07)^{2}=\$6,869.40$

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$P=\$5,000\\r=10\%=0.10$

substitute in the formula above

$A=5,000(e)^{0.10t}$

Applying property of exponents

$A=5,000(1.1052)^{t}$

therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

$A=5,000(e)^{0.10t}$ or $A=5,000(1.1052)^{t}$

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

$A=5,000(e)^{0.10*10}=\$13,591.41$

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

$A=5,000(e)^{0.10*2}=\$6,107.01$

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

3 0

3 years ago

0.5, 3/16, 0.75, 5/48 least to greatest

jarptica [38.1K]

An easy way for me to do this is to either make all of the fractions into decimals or all the decimals into fractions, whatever you prefer. I prefer fractions, but for typing reasons I’m going to make them all decimals. Making 5/48 into a decimal you divide 5 by 48 and get 0.104... and divide 3 by 16 and get 0.1875. Then from there, look at whatever tenths place number is the least (the number after the decimal). Two of them have one, so moving onto the next number, 8>0, which means 0.104 is less then 0.1875. Then 5<7. So from least to greatest, 5/48 (0.104), 3/16 (0.1875), 0.5, 0.75.
Good Luck!

7 0

3 years ago

PLEASE HELP IM STUCK PLS

QveST [7]

Answer:

<u>The slope is -3.</u>

Step-by-step explanation:

The slope is the Rise/Run between the two points. The change in y for every change in x. Take the two points and calculate the:

RISE = (-6 - 3) = -9

RUN = (8 - 5) = 3

Rise/Run, or slope, is = -9/3 or -3

I graphed a line with slope of -3 and then added 18 to force the line to intersect the two given points.

3 0

2 years ago

What is 16% of 90 helpppp plssss

Lunna [17]

Answer:

first off, welcome to brainly, second, your answer is 14.4

Step-by-step explanation:

5 0

2 years ago

Does anyone know how to solve this problem?

marissa [1.9K]

7? Is seems that the 4 is being added with +2 when it got bigger so I’m thinking the 5 would be the same thing +2 equals 7..that’s what I’m thinking

8 0

2 years ago