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Maksim231197 [3]

3 years ago

11

Maria needs to make 6 gallons of lemonade. She only has a 1 quart pitcher to use for measuring. How many times will she need to

fill the pitcher to make 6 gallons?

2 answers:

Len [333]3 years ago

6 0

Okay so we need more evidence to support your question. Maybe add more

UkoKoshka [18]3 years ago

3 0

Answer:

She will need to refill it 24 times

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A study on how circus ticket pricing influences ticket sales shows that there is an average increase of 4 people for every $3 de

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Let the price of a ticket be originally T dollars, and the number of clients be N.

let the price decrease by x 3-dollars.

"there is an average increase of 4 people for every $3 decrease on the price of the ticket."

means:

if the price is decreased by 1-3$:
then N become N+4, and T becomes T-3

if the price is decreased by 2-3$:
then N become N+4+4=N+2*4, and T becomes T-3-3=T-2*3

So if the price is decrease by x-3 dollars:

N becomes N+4x, and T becomes T-3x

"A circus owner sells an average of 340 tickets when the price of a ticket is $75."

In this case N=340, and T=75$

If the owner does not change the price ticket, x=0, the revenue is 340*75,

If the owner decreases the price of the tickets by x-3$, then the revenue will be
(N+4x)(T-3x)=(340+4x)(75-3x) dollars,

If R is the function of the revenue depending on x, then

R(x)=(340+4x)(75-3x) dollars

Answer: R(x)=(340+4x)(75-3x) dollars

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Karen has 3 pieces of ribbon that are each 2 3/4 yd long. She also has a piece of lace that is 3 1/5 yd long. Karen needs to cut

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3 years ago

Read 2 more answers

[Sin A + Sin 3A + Sin 5A + Sin 7A]÷<br><br>[Cos A + Cos 3A + Cos 5A + Cos 7A]<br>=Tan 4A<br>

Ainat [17]

Do the following rewrites:

sin(<em>x</em>) = sin(4<em>x</em> - 3<em>x</em>) = sin(4<em>x</em>) cos(3<em>x</em>) - cos(4<em>x</em>) sin(3<em>x</em>)

sin(7<em>x</em>) = sin(4<em>x</em> + 3<em>x</em>) = sin(4<em>x</em>) cos(3<em>x</em>) + cos(4<em>x</em>) sin(3<em>x</em>)

sin(3<em>x</em>) = sin(4<em>x</em> - <em>x</em>) = sin(4<em>x</em>) cos(<em>x</em>) - cos(4<em>x</em>) sin(<em>x</em>)

sin(5<em>x</em>) = sin(4<em>x</em> + <em>x</em>) = sin(4<em>x</em>) cos(<em>x</em>) + cos(4<em>x</em>) sin(<em>x</em>)

cos(<em>x</em>) = cos(4<em>x</em> - 3<em>x</em>) = cos(4<em>x</em>) cos(3<em>x</em>) + sin(4<em>x</em>) sin(3<em>x</em>)

cos(7<em>x</em>) = cos(4<em>x</em> + 3<em>x</em>) = cos(4<em>x</em>) cos(3<em>x</em>) - sin(4<em>x</em>) sin(3<em>x</em>)

cos(3<em>x</em>) = cos(4<em>x</em> - <em>x</em>) = cos(4<em>x</em>) cos(<em>x</em>) + sin(4<em>x</em>) sin(<em>x</em>)

cos(5<em>x</em>) = cos(4<em>x</em> + <em>x</em>) = cos(4<em>x</em>) cos(<em>x</em>) - sin(4<em>x</em>) sin(<em>x</em>)

So in the numerator, we have

sin(<em>x</em>) + sin(3<em>x</em>) + sin(5<em>x</em>) + sin(7<em>x</em>)

= 2 sin(4<em>x</em>) cos(3<em>x</em>) + 2 sin(4<em>x</em>) cos(<em>x</em>)

= 2 sin(4<em>x</em>) (cos(3<em>x</em>) + cos(<em>x</em>))

In the denominator,

cos(<em>x</em>) + cos(3<em>x</em>) + cos(5<em>x</em>) + cos(7<em>x</em>)

= 2 cos(4<em>x</em>) cos(3<em>x</em>) + 2 cos(4<em>x</em>) cos(<em>x</em>)

= 2 cos(4<em>x</em>) (cos(3<em>x</em>) + cos(<em>x</em>))

So we have

(sin(<em>x</em>) + sin(3<em>x</em>) + sin(5<em>x</em>) + sin(7<em>x</em>)) / (cos(<em>x</em>) + cos(3<em>x</em>) + cos(5<em>x</em>) + cos(7<em>x</em>))

= (2 sin(4<em>x</em>) (cos(3<em>x</em>) + cos(<em>x</em>))) / (2 cos(4<em>x</em>) (cos(3<em>x</em>) + cos(<em>x</em>)))

= sin(4<em>x</em>) / cos(4<em>x</em>)

= tan(4<em>x</em>)

QED

6 0

3 years ago