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3 years ago

Dexter paid $74.94 for 201⁄5 gallons of gas. What is the price of gas where Dexter filled up his vehicle?

Mathematics

1 answer:

pentagon [3]3 years ago

8 0

Answer:

C. $3.71/gallon

Step-by-step explanation:

Take $74.94 divided by 20 1/5 (or 20.2), this equals the unrounded decimal 3.70990099.

Rounded to 2 decimal places, this equals 3.71

Therefore, C. $3.71/gallon is correct.

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riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

4. The constant of proportionality between the height of the water in a sink (h) in centimeters and the number of minutes it has

RUDIKE [14]

Answer:

i got 38

Step-by-step explanation:

6 0

3 years ago

Jeremy’s fruit stand sells peaches and watermelons. In the first hour the fruit stand is open, 12 bushels of peaches and 5 water

polet [3.4K]

We define the variables:
p: cost of bushel of peaches
w: cost of watermelon
We wrote the system of equations:
12p + 5w = 150
15p + 8w = 198
We can represent the system in matrix form as
Ax = b
Where,
A = [12 5; 15 8]
b = [150; 198]
x = [p; w]

3 0

3 years ago

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<img src="https://tex.z-dn.net/?f=%5Csf%20HELP%21" id="TexFormula1" title="\sf HELP!" alt="\sf HELP!" align="absmiddle" class="l

ehidna [41]

Answer:

x=13

Step-by-step explanation:

Switch sides:

2x−9=17

Add 9 to both sides:

2x−9+9=17+9

Simplify

2x=26

Divide both sides by 2:

2x/2 =26/2

Simplify to get the result.

x=13

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3 years ago

Plz help! Correct gets brainliest :) I think I know the answer I just want to double check

Gnom [1K]

9x - 24 + 4x = -24 + 14x - x

13x - 24 = 13x - 24

0 = 0

Answer is All real numbers

4 0

3 years ago

Read 2 more answers