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2 years ago

A 3-gallon bottle of vinegar costs $26.40.

Mathematics

1 answer:

antiseptic1488 [7]2 years ago

8 0

Answer:

0.55

Step-by-step explanation:

There are 16 cups total in 1 gallon.

Multiply both 16 and 1 by 3.

Your answer so far should be 48 cups and 3 gallons.

Divide $26.40 by 48.

Final answer, $0.55 per cup.

You might be interested in

What are the real or imaginary solutions of the polynomial equation? x^3-8=0

Flura [38]

here,

x³-8=0

x³=8

x³=2³

x=2

I hope this may help you

8 0

2 years ago

A researcher conducted an Internet survey of 500 students at a particular college to estimate the average amount of money studen

bonufazy [111]

Answer:

The margin of error is $ME = 2.2962$

Step-by-step explanation:

From the question we are told that

The number of student is $n = 500$

The highest amount is $A =$ $200

The lowest amount is $B =$ $75

The sample mean is $x =$ &140

The Standard deviation of this set is mathematically evaluated as

$s = \frac{A-B}{4}$

Substituting values

$s = \frac{200-75}{4}$

$s = 31.25$

The margin of error (ME) is mathematically evaluated as

$ME = t_{n-1}__{\alpha }} * \frac{s}{\sqrt{n} }$

Where $t_{n-1}__{\alpha }}$ is the critical value for $\alpha = 0.05$ i.e the significance level

From the critical value table this is $t_{n-1}__{\alpha }} = 1.649$

$ME = 1.649 * \frac{31.25}{\sqrt{500} }$

$ME = 2.2962$

6 0

3 years ago

Let divf = 6(5 − x) and 0 ≤ a, b, c ≤ 12. (a) find the flux of f out of the rectangular solid 0 ≤ x ≤ a, 0 ≤ y ≤ b, and 0 ≤ z ≤

dusya [7]

Continuing from the setup in the question linked above (and using the same symbols/variables), we have

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal R}(\nabla\cdot f)\,\mathrm dV$
$=\displaystyle6\int_{z=0}^{z=c}\int_{y=0}^{y=b}\int_{x=0}^{x=a}(5-x)\,\mathrm dx\,\mathrm dy\,\mathrm dz$
$=\displaystyle6bc\int_0^a(5-x)\,\mathrm dx$
$=6bc\left(5a-\dfrac{a^2}2\right)=3abc(10-a)$

The next part of the question asks to maximize this result - our target function which we'll call $g(a,b,c)=3abc(10-a)$ - subject to $0\le a,b,c\le12$ .

We can see that $g$ is quadratic in $a$ , so let's complete the square.

$g(a,b,c)=-3bc(a^2-10a+25-25)=3bc(25-(a-5)^2)$

Since $b,c$ are non-negative, it stands to reason that the total product will be maximized if $a-5$ vanishes because $25-(a-5)^2$ is a parabola with its vertex (a maximum) at (5, 25). Setting $a=5$ , it's clear that the maximum of $g$ will then be attained when $b,c$ are largest, so the largest flux will be attained at $(a,b,c)=(5,12,12)$ , which gives a flux of 10,800.