My car gets 27 miles per gallon of gas. If I drive 513 miles, how many gallons of gas will I use?

larisa86 [58]

Part A
To estimate this, we should first look at our fractions and see if they can be combined to form a whole number. In this case, $\frac{3}{5}$ and $\frac{2}{3}$ equal approximately 1. We can add this "1" to the other to full gallons to estimate that the painter needs about 3 gallons.

Part B
To find the exact amount, we should first change the mixed numbers to improper fractions. We do this by multiplying the denominator by the whole number, adding the numerator, and placing that value over the denominator.

$1 \frac{3}{5} \\ \\ (5*1)+3 =8 \\ \\ \frac{8}{5} \\ \\ \\ \\ 1 \frac{2}{3} \\ \\ (3*1)+2=5 \\ \\ \frac{5}{3} 
$

Now, we need to find the least common denominator. This is the lowest value that both denominators will divide evenly into. In this case, that number is 15.

Next, we should multiply both fractions so that the denominator is that number. Remember that we must also multiply the numerator for the fraction to remain equivalent to its original value.

$\frac{8}{5} *3 = \frac{24}{15} \\ \\ \frac{5}{3} *5 = \frac{25}{15}$

Now, we can simply add our numerators.

$25+24=49$

We know that he needs $\frac{49}{15}$ gallons of paint, but this is not in the most simplified format. To simplify, we need to turn our improper fraction back to a mixed number. To do this, we need to divide our numerator by the denominator to create our whole number, and the remainder becomes our new numerator.

$\frac{49}{15} \\ \\ 49 / 15 = 3(Remainder: 4) \\ \\ 3\frac{4}{15}$

Using that logic, we can see that the painter needs exactly $3 \frac{4}{15}$ gallons of paint.

4 0

3 years ago

Lynn is a single mother with two children's . She qualifies to file as head of household her total income was $27267 last year h

storchak [24]

Answer:

$3,078.04

Step-by-step explanation:

-Given her income is $27,267, she falls under the 10% and 12% brackets with the following boundaries as attached.

-Her tax is then calculated as;

#10% bracket;

$Tax=Taxable \ Income \times Tax \ Rate\\\\=9700\times 10\%\\\\\\=\$970.00$

#12% Tax bracket:

$Tax=Taxable \ Income \times Tax \ Rate\\\\=(27267-9700)\times 12\%\\\\\\=\$2108.04$

The total tax=970+2108.04=$3,078.04

Hence, Lynn owes $3,078.04 in taxes.

7 0

3 years ago

Use only an associative property to rewrite the following expression. (pk)•r=

Gennadij [26K]

Answer:

Step-by-step explanation:

(pk) * r = p * (kr)

5 0

3 years ago

There are 12 pieces of pie that are going to be split between 5 people. How many slices of pie does each person get?

Phantasy [73]

Answer:

2.4 slices of pie per person

Step-by-step explanation:

Assuming each person is receiving an equal amount of pie, the answer is 2.4 slices per person.

12 ÷ 5 = 2.4

8 0

3 years ago

Read 2 more answers

If an object is dropped from a tower, then the velocity, V (in feet per second), of the object after t seconds can be obtained b

Amiraneli [1.4K]

Answer:

259.6 ft/sec

Step-by-step explanation:

it is a universal standard that acceleration due to gravity is 32ft/sec^2.

Now it can be verified by equation,

V(f) = V(i)+at (1st equation of motion derived by Newton's three laws of motion)

where,

V(f) is final velocity

V(i) is initial velocity

a is acceleration which is constant and have value 32ft/sec^2

t is time which is given as 7.8 seconds

In the given case, initial velocity that is V(i) will be 0ft/sec. Because, on dropping, object will start to move under the influence of gravity from zero speed.

So,

V(f) = 0 +(32) (7.8)

V(f) = 249.6 ft/sec

Now the condition is given that you have to add a constant 10 to the answer.

so, V(f) = 249.6 + 10

V(f) = 259.6 ft/sec

5 0

3 years ago