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2 years ago

How many liters of wine can be held in a wine barrel whose capacity is 28.0 gal? 1 gal = 4 qt = 3.7854 l?

2 answers:

7 0

This is the concept of conversions;
given that:
1 gal=4 qt=3.7854 l
then:
28 gal will be equivalent to the following number of liters;
28/1*3.7854
=105.9912 l
thus the number of liters of wine that can be held in a wine barrel is 105.99 l

wel2 years ago

4 0

Answer:

105.9912 liters of wine can be held in a wine barrel whose capacity is 28.0 gal.

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

Let x be the liters of wine can be held in a wine barrel whose capacity is 28.0 gal.

Given that:

1 gal = 3.7854 l

then

by definition of proportions;

$\frac{1}{3.7854} =\frac{28}{x}$

By cross multiply we get;

$x = 28 \times 3.7854 = 105.9912$ liters

Therefore, 105.9912 liters of wine can be held in a wine barrel whose capacity is 28.0 gal.

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Is 16.45 greater than, less than or equal to 16.454

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2 years ago

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The first term of a finite geometric series is 6 and the last term is 4374. The sum of all the term os 6558. find the common rat

Oliga [24]

A geometric series is written as $ar^n$ , where $a$ is the first term of the series and $r$ is the common ratio.

In other words, to compute the next term in the series you have to multiply the previous one by $r$ .

Since we know that the first time is 6 (but we don't know the common ratio), the first terms are

$6, 6r, 6r^2, 6r^3, 6r^4, 6r^5, \ldots$ .

Let's use the other information, since the last term is $4374 > 6$ , we know that $r>1$ , otherwise the terms would be bigger and bigger.

The information about the sum tells us that

$\displaystyle \sum_{i=0}^n 6r^i = 6\sum_{i=0}^n r^i = 6558$

We have a formula to compute the sum of the powers of a certain variable, namely

$\displaystyle \sum_{i=0}^n r^i = \cfrac{r^{n+1}-1}{r-1}$

So, the equation becomes

$6\cfrac{r^{n+1}-1}{r-1} = 6558$

The only integer solution to this expression is $n=6, r=3$ .

If you want to check the result, we have

$6+6*3+6*3^2+6*3^3+6*3^4+6*3^5+6*3^6 = 6558$

and the last term is

$6*3^6 = 4374$

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1 year ago

Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula?

lbvjy [14]

Answer:

x = StartFraction negative

(negative 2) plus or minus StartRoot (negative 2) squared minus 4 (negative 3)(6) EndRoot Over 2(negative 3) EndFraction

Step-by-step explanation:

0 = – 3x2 – 2x + 6

It can still be written as

– 3x2 – 2x + 6 =0

Quadratic formula=

-b+or-√b^2-4ac/2a

Where

a=-3

b=-2

c=6

x= -(-2)+ or-√(-2)^2-4(-3)(6)/2(-3)

x = StartFraction negative

(negative 2) plus or minus StartRoot (negative 2) squared minus 4 (negative 3)(6) EndRoot Over 2(negative 3) EndFraction

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1 year ago

Rectangular arrays whose dimensions are whole numbers can be used to illustrate the factors of a number. What can be said about

natali 33 [55]

Answer:

Step-by-step explanation:

a) For a prime numbers we have array with 2 rectangulars R1: a=1 and b=prime number; R2: a=prime number and b=1. Both has the same are, that prime number.

b) For a composite number which are not square number we have rectanular array with even numbers of ractangulars. For example, number 6.

R1: a=1,b=6; R2: a=2,b=3; R3: a=3, b=2; R4: a=6,b=1. Each rectangular has the same area, 6.

c) The square number we alway have te odd number of rectanulars, because of the square a=x,b=x can not be simetric. For example 16.

R1: a=1,b=16; R2: a=2 , b=8; R3: a=4,b=4; R4: a=8, b=2; R5:a=16,b=1.Each rectangular has the same area, 16.

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1 year ago

To find the area of parallelogram RSTU, Juan starts by drawing a rectangle around it. Each vertex of parallelogram RSTU is on a

STatiana [176]

Answer:

The value that can be subtracted from the area of the rectangle to give the area of the parallelogram = 1/2 × 4.1245 × 0.1085

Step-by-step explanation:

The given parameters are;

The coordinates of parallelogram RSTU are;

R(-4, -3), S(-5, 1), T(4, 3), U(5, -1)

The lengths of the sides are (using an online length calculator);

RS = 4.1231

RT = 10

ST = 9.2195

SU = 10.198

TU = 4.1231

UR = 9.2195

Therefore, by definition of a parallelogram, we have;

RS║TU and ST║UR

The slope of RS = (1 - (-3))/(-5 - (-4)) = -4

The slope of ST = (3 - 1)/(4 - (-5)) = 2/9

The equation of the line perpendicular to ST is therefore;

y - 1 = -9/2×(x - (-5))

y = -9x/2 - 43/2

The equation of RS = y - (-3) = 1/4×(x - (-4)) = x/4 + 1

y = x/4 - 2

The point where the two lines meet is therefore;

-9x/2 - 43/2 = x/4 - 2

x = -78/19

y = -115/38

The length of the side of the rectangle = 4.1245

The excess width of the rectangle = 0.1085

The value that can be subtracted from the area of the rectangle to give the area of the parallelogram = 1/2 × 4.1245 × 0.1085.

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1 year ago