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snow_lady [41]
3 years ago
14

Sam picked 1/2 gallon of blueberries. he poured the blueberries into one of his plastic containers and noticed that the berries

filled the container 2/3 full. how many gallons of blueberries does it take to fill sam’s container completely full?
Mathematics
1 answer:
earnstyle [38]3 years ago
3 0

Answer:

3/4 gallons of blueberries

Step-by-step explanation:

we know that

1/2 gallon of blueberries filled the container 2/3 full

so

using proportion

Find out how many gallons of blueberries does it take to fill Sam’s container completely full

Remember that

completely full (100% filled) is the same that the fraction 3/3 or 1

so

\frac{(1/2)}{(2/3)}=\frac{x}{1}\\\\x=\frac{1}{2}:\frac{2}{3}\\\\x= \frac{1*3}{2*2}\\\\x=\frac{3}{4}\ gal

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It takes 2/3 of an hour to paint 2/5 of a room. How long does it take to paint 2/5 of a room?
Lubov Fominskaja [6]

It will take 40 minutes.

To solve, divide 60 by 3. 60 is how many minutes there are in a minute. 3 is how long it takes to paint 2/5 of the room. We do not need to use the number 2/5 in this situation. Now back to 60 divided by 3. The answer is 20 minutes. Now multiply 20 by 2 to get 2/3 of an hour. Therefore, it takes 40 minutes to paint 2/5 of a room.

8 0
3 years ago
Which expression is equivalent to *picture attached*
DiKsa [7]

Answer:

The correct option is;

4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3  \left (\dfrac{50(51) }{2} \right )

Step-by-step explanation:

The given expression is presented as follows;

\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3  \right )

Which can be expanded into the following form;

\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3  \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left  n^2 + 3  \times\sum\limits _{n = 1}^{50}  n

From which we have;

\sum\limits _{k = 1}^{n} \left  k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}

\sum\limits _{k = 1}^{n} \left  k = \dfrac{n \times (n+1) }{2}

Therefore, substituting the value of n = 50 we have;

\sum\limits _{n = 1}^{50} \left  k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}

\sum\limits _{k = 1}^{50} \left  k = \dfrac{50 \times (50+1) }{2}

Which gives;

4 \times \sum\limits _{n = 1}^{50} \left  n^2 =  4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}

3  \times\sum\limits _{n = 1}^{50}  n = 3  \times \dfrac{n \times (n+1) }{2} = 3  \times \dfrac{50 \times (51) }{2}

\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3  \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3  \times \dfrac{50 \times (51) }{2}

Therefore, we have;

4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3  \left (\dfrac{50(51) }{2} \right ).

4 0
3 years ago
Plz help ASAP I will add branliest to the first answer, I need to solve for the letter
harkovskaia [24]

Answer:

6. r=2

8.x=3

Step-by-step explanation:

6. 4r-3=5

4r-3=5 add 3 to both sides

4r=8 divide 4 by both sides

r=2

8. 5x-6=9

5x-6=9 add 6 to both sides

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x=3

6 0
3 years ago
Read 2 more answers
Please help and explain! *Serious answers only* 30 points :)
topjm [15]
Ok so it's a proportion so this fraction is to this fraction. the smaller rectangle has sides 4 and 12. the larger one has 8 and x. so u set it up 4/12=8/x. the 4 and 8 r both the short sides so u want those on top and 12 and x r long sides so those on bottom. since that is not an answer option u can set it up as 8/4=x/12 because u still keep the variables of the same rectangle from being multipled with each other. so answer #2 is correct
4 0
3 years ago
Read 2 more answers
Let cos A = <img src="https://tex.z-dn.net/?f=1%2F%5Csqrt%7B10%7D" id="TexFormula1" title="1/\sqrt{10}" alt="1/\sqrt{10}" align=
Rzqust [24]
Umm i’m sorry but what is the question here .

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3 0
2 years ago
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