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Brrunno [24]
3 years ago
6

Isabella painted her bedroom. She used 2 gallons of paint and finished in 8 hours. At what rate did Isabella paint the room?

Mathematics
1 answer:
GrogVix [38]3 years ago
6 0

Answer:  " \frac{1}{4} gal /hr ;  or, write as:  " 0.25 gal/hr. " .

_______________

Step-by-step explanation:

_______________

This is a "unit rate" problem;

that is:  we want to solve for a particular quantity per [single] unit.

_______________

→ in this case, per single "hour" ;

_______________

So we convert:

_______________

" 2 gal per 8 hours" ; to the correct number of:

 _?_ gal per [single] hr.

_______________

{<u>Note</u>:  "gal" refers to:  "gallon(s)" ;

           "hr" refers to:  "hour(s)" .}.

_______________

→ " \frac{2 gal}{ 8 hr} = [\frac{2}{8}] gal / hr. " ;

_______________

→ " { \frac{2}{8} = [2÷2] / [8÷2] = 1/4 ;

_______________

So, the answer is:  

  → " \frac{1}{4} gal /hr " ;

_______________

 or: write as decimal:

  → " \frac{1}{4} = (1 ÷ 4) = 0.25 " ;

_______________

write the answer as:

_______________

  → " 0.25 gal/hr. "

_______________

Or, when we had:

 → "2/8" gal/hr ;

_______________

 Use calculator:

 → " \frac{2}{8} = "2 ÷ 8" ;

 =  " 0.25 gal/ hr.

_______________

So:  The correct answer is:

_______________

 " \frac{1}{4} gal /hr ;  or, write as:  " 0.25 gal/hr. " ;

_______________

Hope this is helpful to you!

Best wishes in your academic endeavors—

  and within the "Brainly" community!

_______________

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JulijaS [17]

Answer: 0.3125.

Step-by-step explanation:

  • The chance of having a boy is 0.5,
  • the chance of having a girl is also 0.5.

<u>Outcome 1: all boys</u>

boy  boy  boy  boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

<u>Outcome 2: first child is a girl, all others are boys</u>

girl   boy   boy   boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

<u>Outcome 3: second child is a girl, all others are boys</u>

boy   girl   boy   boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

<u>Outcome 4: third child is a girl, all others are boys</u>

boy   boy   girl   boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

<u>Outcome 5: fourth child is a girl, all others are boys</u>

boy   boy   boy   girl

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Therefore,

0.0625 + 0.0625 + 0.0625 + 0.0625 + 0.0625 = 0.0625 * 5 = 0.3125

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Step-by-step explanation:

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Which graph best represents y=-x2 + 6 x - 1?​
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I need help with number 7, and the second part of number 8. Thank you!
tangare [24]

Answer:

7. \dfrac{\pi }{3},\ \pi ,\ \dfrac{5\pi }{3}

8. b. 0,\ \dfrac{2\pi }{3},\ \pi,\ \dfrac{4\pi }{3}

Step-by-step explanation:

7. Solve the equation

\cos x+\cos 2x=0

First, note that

\cos 2x=2\cos^2x-1

Hence,

\cos x+2\cos ^2x-1=0

Use substitution

t=\cos x,

then

2t^2+t-1=0\\ \\D=1^2-4\cdot 2\cdot (-1)=1+8=9\\ \\\sqrt{D}=\sqrt{9}=3\\ \\t_{1,2}=\dfrac{-1\pm 3}{2\cdot 2}=-1,\ \dfrac{1}{2}

Now,

\cos x=-1\ \text{or}\ \cos x=\dfrac{1}{2}

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8. b. Solve the equation

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Rewrite it:

\sin x(1+2\cos x)=0

By zero product property,

\sin x=0\ \text{or}\ 1+2\cos x=0

Solve each equation separately.

\sin x=0\\ \\x=\pi k,\ k\in Z\\ \\\text{for}\ x\in [0,2\pi),\ \ \ \ x_1=0\ \ x_2=\pi

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