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motikmotik
4 years ago
8

Half the gas in the tank was used when

Mathematics
1 answer:
Anvisha [2.4K]4 years ago
5 0

Answer: She had 20 gallons to begin with.

Step-by-step explanation:

16 = 6 + 1/2x

x = the amount she had to start with

Subtract 6 from each side

10 = 1/2x

Divide each side by 1/2

20 = x

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Simplify 4a2(a3)/16b(b2)
timurjin [86]

4a²(a³)/16b ( b²)

4a⁶/16b³

= a⁶/4b³

4 0
4 years ago
Chec<br> Match each data relationship with a type of correlation.
AleksandrR [38]

I've attached an image showing the data relationship.

Answer:

1) y does not change based on changes in x: no-correlation

2) y tends to increase as x increases: positive correlation

3) y tends to decrease as x increases: negative correlation

Step-by-step explanation:

1) y does not change based on changes in x: This means that there is no correlation between y and x since change in x doesn't affect y.

2) y tends to increase as x increases: This implies positive correlation because the output increases with increase in input.

3) y tends to decrease as x increases: This implies negative correlation because the output decreases with increase in input values.

5 0
3 years ago
Read 2 more answers
Lim x-0 3x²/(1-cos5x)
mylen [45]

The limit is presented in the following undefined form:

\displaystyle \lim_{x\to 0}\dfrac{3x^2}{1-\cos(5x)} \to \dfrac{3\cdot 0^2}{1-\cos(5\cdot 0)} = \dfrac{0}{0}

In cases like this, we can use de l'Hospital rule, which states that this limit, if it exists, is the same as the limit of the derivatives of numerator and denominator.

So, we switch

\dfrac{f(x)}{g(x)}\to\dfrac{f'(x)}{g'(x)}

The derivative of the numerator is

\dfrac{d}{dx} 3x^2 = 6x

Whereas the derivative of the denominator is

\dfrac{d}{dx} (1-\cos(5x)) = 5\sin(5x)

So, the new limit is

\displaystyle \lim_{x\to 0}\dfrac{6x}{5\sin(5x)} \to \dfrac{6\cdot 0}{5\cdot 0} = \dfrac{0}{0}

So, it would seem that we didn't solve anything, but indeed we have! Recall the limit

\displaystyle \lim_{x\to 0} \dfrac{ax}{\sin(bx)} = \dfrac{a}{b}

to conclude that the limit converges to \dfrac{6}{25} [/tex]

4 0
4 years ago
Read 2 more answers
A manufacturer ships its product in boxes with edges of 4 inches. If 12 boxes are put in a carton and completely fill the carton
SOVA2 [1]
Volume of carton would be 768 inches
4 × 4 × 4 = 64
12 × 64 = 768
4 0
4 years ago
Read 2 more answers
After plotting the data where x represents the length of the side of a polygon, and f(x) represents the area of the polygon, Jac
Zigmanuir [339]

Answer:

See the attachment

Step-by-step explanation:

It is convenient to use a spreadsheet or graphing calculator for this.

3 0
3 years ago
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