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mojhsa [17]
3 years ago
10

The weight of a box varies directly as the volume of the box. If a 138-pound box has a volume of 23 gallons, what is the weight

of a box that has a volume of 25 gallons?
A. 29 pounds B. 138 pounds C. 31 pounds D. 150 pounds
Mathematics
1 answer:
kolezko [41]3 years ago
5 0

Answer:

D. 150 pounds

Step-by-step explanation:

For be directly proportional, it has to be that as one value increases the other does it equally, so

If  138 pound box has a volume of 23 gallons for 25 gallons ?. For being directly proportional tha value must be higest

138  →  23                       x=\frac{25*138}{23} = 150

x      →  25

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Find the greatest common factor of 30 and 75.
yarga [219]

Answer:

15

Step-by-step explanation:

prime factorization of 30 is 2*3*5

prime factorization of 75 is 3*5*5

3*5 is common

8 0
3 years ago
Find the approximate area between the curve f(x) = -4x² + 32x and on the x-axis on the interval [0,8] using 4 rectangles. Use th
Doss [256]

Split up the interval [0, 8] into 4 equally spaced subintervals:

[0, 2], [2, 4], [4, 6], [6, 8]

Take the right endpoints, which form the arithmetic sequence

r_i=2+\dfrac{8-0}4(i-1)=2i

where 1 ≤ <em>i</em> ≤ 4.

Find the values of the function at these endpoints:

f(r_i)=-4{r_i}^2+32r_i=-16i^2+64i

The area is given approximately by the Riemann sum,

\displaystyle\int_0^8f(x)\,\mathrm dx\approx\sum_{i=1}^4f(r_i)\Delta x_i

where \Delta x_i=\frac{8-0}4=2; so the area is approximately

\displaystyle2\sum_{i=1}^4(-16i^2+64i)=-32\sum_{i=1}^4i^2+128\sum_{i=1}^4i=-32\cdot\frac{4\cdot5\cdot9}6+128\cdot\frac{4\cdot5}2=\boxed{320}

where we use the formulas,

\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2

\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6

6 0
3 years ago
NEED HELP ASAP
lozanna [386]

Multiply dollars / unit * units.  It is actually a useful thing to know.  Many thing are done using the tools this question requires.

\dfrac{0.58 dollars}{unit} * 532 units

Steve takes home 308.56 dollars. The answer is B.

5 0
3 years ago
3 feet = _______ inches<br><br> help plzz :(
Romashka [77]

Answer:

36 inches

Step-by-step explanation:

We know that 1 ft = 12 inches

2 ft = 2 * 12 = 24 inches

3 ft = 3*12 = 36 inches

3 0
3 years ago
Read 2 more answers
A boat traveled 252 miles downstream and back. The trip downstream took 12 hours. The trip back took 84 hours. Find the speed of
Leokris [45]

Answer: the speed of the boat in still water is 12 mph and the speed of the current is 9 mph.

Step-by-step explanation:

Let x represent the speed of the boat in still water.

Let y represent the speed of the current.

The boat travelled 252 miles downstream and the same distance upstream.

The trip downstream took 12 hours. Assuming the boat travelled with the wind when going downstream, the total speed would be (x + y) mph.

Distance = speed × time

The expression for distance travelled downstream is

252 = 12(x + y)

Dividing through by 12, it becomes

21 = x + y- - - - - - - - - - 1

The trip back took 84 hours. Assuming the boat travelled against the wind when going back(upstream), the total speed would be (x - y) mph.

The expression for distance travelled upstream is

252 = 84(x - y)

Dividing through by 84, it becomes

3 = x - y- - - - - - - - - - 2

Adding equation 1 to equation 2, it becomes

24 = 2x

x = 24/2

x = 12 mph

Substituting x = 12 into equation 1, it becomes

21 = 12 + y

y = 21 - 12

y = 9 mph

7 0
3 years ago
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