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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
Mathematics
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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b/a must = 1

so

a/b is equivalent to b/a as a/b=1 as well.

So the last answer choice.

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
1 year 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})

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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:

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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
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