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sertanlavr [38]

3 years ago

9

A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would c

ost for this car to travel 2,727 typical miles?
A. $44.44
B. $109.08
C. $118.80
D. $408.04
E. $444.40

1 answer:

worty [1.4K]3 years ago

8 0

Answer:

Option D is correct.

$408.04 the gas would cost for this car to travel 2,727 typical miles

Step-by-step explanation:

Unit rate defined as the rates are expressed as a quantity 1 such as 3 miles per second or 4 kilometer per hour

As per the statement:

A car averages 27 miles per gallon.

⇒ $\text{Unit rate per gallon} = 27 miles$

Total distance of car travel typical miles = 2727 miles.

$\text{Number of gallons}=\frac{\text{Total distance}}{\text{Unit rate per gallon}}$

Substitute the given values we have;

$\text{Number of gallons} = \frac{2727}{27} = 101$

It is also given that if gas costs $4.04 per gallon.

then;

In 1 gallon of gas = $4.04

then;

in 101 gallons of gas = $101 \cdot 4.04 = \$408.04$

Therefore, $408.04 the gas would cost for this car to travel 2,727 typical miles

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Svetlanka [38]

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but a-b==0 so both are the same unknown number

b/a must = 1

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7 0

3 years ago

Expand<br> (2x - 3)4 <br><br> Can you help me expand this by using the binomial theorem?

saw5 [17]

The value of expanding (2x -3)^4 is 16x^4 + 96x^3 +216x^2 -216x + 81

<h3>How to expand the expression?</h3>

The expression is given as:

(2x -3)^4

Using the binomial expansion, we have:

$(2x -3)^4 = ^4C_0 * (2x)^4 * (-3)^0 +^4C_1 * (2x)^3 * (-3)^1 + ^4C_2 * (2x)^2 * (-3)^2 + ^4C_3 * (2x)^1 * (-3)^3 + ^4C_4 * (2x)^0 * (-3)^4$

Evaluate the combination factors.

So, we have:

$(2x -3)^4 = 1 * (2x)^4 * (-3)^0 + 4 * (2x)^3 * (-3)^1 + 6 * (2x)^2 * (-3)^2 + 4 * (2x)^1 * (-3)^3 + 1 * (2x)^0 * (-3)^4$

Evaluate the exponents and the products

$(2x -3)^4 = 16x^4 + 96x^3 +216x^2 -216x + 81$

Hence, the value of expanding (2x -3)^4 is 16x^4 + 96x^3 +216x^2 -216x + 81

Read more about binomial expansions at:

brainly.com/question/13602562

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8 0

2 years ago

d(t)=750t/(t+12) where t is the age in years and d is the dosage. what is an expression for the rate of change of a child's dosa

Maksim231197 [3]

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3 0

3 years ago

Mica bought a new smart phone for $258.13. That was the price after his 18.25% discount. What was the original price of the phon

julia-pushkina [17]

The original price of phone is $ 315.76

<em><u>Solution:</u></em>

Given that Mica bought a new smart phone for $ 258.13.

That was the price after his 18.25% discount

<em><u>To find: original price of phone</u></em>

From given question,

price after discount = $ 258.13

discount = 18.25 %

Let "x" be the original price of phone

price after discount = original price - discount

$258.13 = x - 18.25 \% \text{ of } x$

$258.13 = x - \frac{18.25}{100}x$

$258.13 = x(1 - \frac{18.25}{100})$

$258.13 = x(1 - 0.1825)\\\\258.13 = x( 0.8175)\\\\x = \frac{258.13}{0.8175}\\\\x = 315.76$

Thus original price of phone is $ 315.76

4 0

3 years ago

Find the linear approximation of the function g(x) = 3 1 + x at a = 0. g(x) ≈ Correct: Your answer is correct. Use it to approxi

EleoNora [17]

Answer:

$3.296x+3$

2.835

3.330

Step-by-step explanation:

$g(x) = 3^{1+x}$

Let the linear approximation be L(x) at a = 0. This is given by

$L(x) = g(a) + g'(a)(x-a)$

$g'(x)$ is the derivative of $g(x)$ . To find this, we use the form

If $f(x) = a^x$ , then $f'(x) =a^x\ln a$

By doing this and applying chain rule for the power (which is a function of x), we have

$g'(x) = 3^{1+x}\ln 3$

Then

$g'(0) = 3^{1+0}\ln 3 = 3.296$

Also $g(0) = 3^{1+0} = 3$

Hence $L(x) = 3+(x-0)\times3.296 = 3.296x + 3$

For $3^{0.95}$ , $1+x = 0.95$ and $x=-0.05$

Using this in $L(x)$ ,

$3^{0.95} = 3.296(-0.05) + 3 = 2.835$

For $3^{1.1}$ , $1+x = 1.1$ and $x=0.1$

Using this in $L(x)$ ,

$3^{1.1} = 3.296(0.1) + 3 = 3.330$

7 0

3 years ago