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myrzilka [38]
3 years ago
9

1 kg = 2.2lb 6.3lb = ___kg show work

Mathematics
1 answer:
poizon [28]3 years ago
4 0
\dfrac{1kg}{xkg}=\dfrac{2.2lb}{6.3lb}\ \ \ \ |cross\ multiply\\\\2.2x=1\cdot6.3\\\\2.2x=6.3\ \ \ |divide\ both\ sides\ by\ 2.2\\\\x=\dfrac{6.3}{2.2}\\\\x=\dfrac{63}{22}\\\\\boxed{6.3lb=2\frac{19}{22}kg\approx2.86kg}
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Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than π/100 square
stepladder [879]

Answer: YES

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

  • Area of each stain=less than π/100 square feet  
  • Each one 3 feet from the nearest wall
  • Area of rug: 9π square feet
  • The centers of the stains are less than 4 feet apart.

First, we have to apply the formula AREA OF A CIRCLE(A)= π r², to obtain the radius of each stain:

π/100 = π r²  

π/100 (1/ π)= π r²  

1/100 = r²

√1/100 =r

r = 1/10 ⇒ radius of each stain

The centers of the stains are less than 4 feet apart, so:

Max diameter needed to cover is 4+ 1/10 + 1/10 = 21/5 = 4.2

Finally, we have to obtain the diameter of the rug to compare:

Area of rug: 9π

: 9π = π r2 ⇒ r= 3  

⇒ d (diameter)= 3 x2 = 6 ft

With statements (1) and (2), we know that the diameter of the rug (6ft) can completely cover both stains (max distance is 4 .2ft)

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Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will
Oksanka [162]

Answer:

Ella should add 32\dfrac{5}{6} lbs of water.

Total weight of syrup 33\dfrac{1}{3} lbs

Step-by-step explanation:

Weight:

Weight of sugar = 0.5 lbs.

Weight of water added = x lbs

Total weight = 0.5 + x lbs

Percentage:

0.5 + x  --  100%

0.5  --  1.5%

Write a proportion:

\dfrac{0.5+x}{0.5}=\dfrac{100}{1.5}

Cross multiply:

1.5(0.5+x)=0.5\cdot 100\\ \\0.75+1.5x=50\\ \\1.5x=50-0.75\\ \\1.5x=49.25\\ \\x=\dfrac{49.25}{1.5}=\dfrac{4,925}{150}=\dfrac{197}{6}=32 \dfrac{5}{6}\ lbs

Ella should add 32\dfrac{5}{6} lbs of water.

Total weight of syrup

32\dfrac{5}{6}+\dfrac{1}{2}=32\dfrac{5}{6}+\dfrac{3}{6}=33\dfrac{1}{3}\ lbs

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