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Andre45 [30]
2 years ago
6

Eileen is taking a trip to Louisiana and expects to drive 850 miles round trip. If her car gets 23 miles per gallon, and the cos

t per gallon of gas is $2.79, how much will she spend on gasoline? Round to the nearest dollar. (Points : 2)
$98
$103
$41
$69
Mathematics
1 answer:
bazaltina [42]2 years ago
4 0
The answer is <span>$103.

To determine </span><span> how much Eileen will spend on gasoline, first we need to calculate how many gallons she needs.
If she drives 850 miles and </span><span>her car gets 23 miles per gallon, we can use the proportion:
850 miles : x gallons = 23 miles : 1 gallon
Crossing the products:
x = 850 miles </span>× 1 gallon ÷ 23 miles
x = 36.96 gallons

Thus, Eileen needs 36.96 gallons of gas. If the cost per gallon of gas is$2.79, using the proportion:
36.96 gallons : x = 1 gallon : <span>$2.79
x = 36.96 gallons </span>× $2.79 <span>÷ 1 gallon
x = </span>$103.12 
x ≈ $<span>103</span>
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<span>The<u> correct answer</u> is:

153/200.

Explanation<span>:

The amount for the first 6 months is 76500 and the amount for the last 6 months is 100000. This makes the ratio 76500/100000.

Both of these end with two 0's; this means they are both divisible by 100. 76500/100 = 765 and 100000/100 = 1000; this makes the ratio 765/1000.

Since these end with a 5 or a 0, they are divisible by 5; 765/5 = 153 and 1000/5 = 200; this makes the ratio 153/200.

153 is only divisible by 3 or 9; 153/3 = 51 and 153/9 = 17. None of these will divide evenly into 200, so we stop at 153/200.</span></span>
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2 years ago
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A brochure from the department of public safety in a northern state recommends that motorists should carry 12 items (flashlights
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Answer:

Mean = 6.07

Median = 7

Mode = 7

Step-by-step explanation:

Given

Data: 5\ 3\ 7\ 8\ 0\ 1\ 0\ 5\ 12\ 10\ 7\ 6\ 7\ 11\ 9

n = 15

Solving (a): The mean

Mean is calculated as:

Mean = \frac{\sum x}{n}

This gives:

Mean = \frac{5+ 3+ 7+ 8+ 0+ 1+ 0+ 5+ 12+ 10+ 7+ 6+ 7+ 11+ 9}{15}

Mean = \frac{91}{15}

Mean = 6.07

Solving (b): The median

Sort the data in ascending order:

Data: 5\ 3\ 7\ 8\ 0\ 1\ 0\ 5\ 12\ 10\ 7\ 6\ 7\ 11\ 9

Sorted: 0\ 0\ 1\ 3\ 5\ 5\  6\ 7\ 7\ 7\ 8\ 9\ 10\ 11\ 12

The median is:

Median = \frac{n + 1}{2}th

Median = \frac{15 + 1}{2}th

Median = \frac{16}{2}th

Median = 8th    

The 8th item on the sorted dataset is 7; So:

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Solving (c): The mode

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Because it has a frequency of 3 (more than any other element of the dataset).

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It looks like you're given

g(x)=\displaystyle\int_{6x}^{7x}\frac{u^2-1}{u^2+1}\,\mathrm du

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g(x)=\displaystyle\int_0^{7x}\frac{u^2-1}{u^2+1}\,\mathrm du-\int_0^{6x}\frac{u^2-1}{u^2+1}\,\mathrm du

(presumably this is what the hint suggests to use)

Then by the fundamental theorem of calculus, we have

\dfrac{\mathrm dg}{\mathrm dx}=7\dfrac{(7x)^2-1}{(7x)^2+1}-6\dfrac{(6x)^2-1}{(6x)^2+1}=\dfrac{1764x^4+169x^2-1}{1764x^4+85x^2+1}

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Answer:

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Answer:

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