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3 years ago

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For their birthdays phoebe and raoul each got a round 12 inch cake. Phoebe's mother cut her cake into twelfths; raoul's mother c

ut his cake into sixteenths. Phoebe ate three pieces of her cake. How many pieces of his cake will raoul need to eat to have eaten an equal amuont?

1 answer:

Elza [17]3 years ago

6 0

Raoul would have to eat four pieces of cake

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A ferry operator takes tourists to an island.

Oksanka [162]

The fare of $(20 - 2.5) = $17.5 will maximize the total fare.

<h3>What is Differentiation?</h3>

Differentiation means the rate of change of one quantity with respect to another. The speed is calculated as the rate of change of distance with respect to time.

Here, The operator for a round-trip fare of $20, carries an average of 500 people per day.

It is estimated that 20 fewer people will take the trip, for each $1 increase in fare.

for $x increase in fare, 20x less people will take the trip and at that time the total fare F is given by

f(x) =(20 + x)(500 - 20x)

f (x) = 10000 + 100x - 20x²

For f(x) to be maximum, the condition is dy/dx = 0

100 - 40x = 0

⇒ x = 2.5

Thus, the fare of $(20 - 2.5) = $17.5 will maximize the total fare.

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1 year ago

Kaylee and Olivia go to the movie theater and purchase refreshments for their friends.

KatRina [158]

The price of one bag of popcorn is $3.75

Step-by-step explanation:

Let,

x represent the cost of a bag of popcorn

y represent the cost of a drink.

According to given statement;

4x+12y=30 Eqn 1

x+6y=11.25 Eqn 2

Multplying Eqn 2 by 2

$2(x+6y=11.25)\\2x+12y=22.50\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 1

$(4x+12y)-(2x+12y)=30-22.50\\4x+12y-2x-12y=7.50\\2x=7.50$

Dividing both sides by 2

$\frac{2x}{2}=\frac{7.50}{2}\\x=3.75$

4x+12y=30 and x+6y=11.25 can be used to find the price of one bag of popcorn and the price of one drink.

The price of one bag of popcorn is $3.75

Keywords: linear equation, elimination method

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3 0

3 years ago

X+13/2=4 what x equal

Harlamova29_29 [7]

Step-by-step explanation:

x+13÷2×2=4×2

x+13=8

x+13-13=8-13

x=8-13

x=-5

7 0

3 years ago

Read 2 more answers

a fish tank is shaped like a rectangular prism. it has a length of 5 ft., a width of 2 ft., and a height of 3 ft. what is the vo

coldgirl [10]

Answer:

V (volume) = 30

Step-by-step explanation:

V=whl=2·3·5=30

4 0

2 years ago

write an equation in slope intercept form for the line that passes through the point, and is perpendicular to the line y=-1/3x+9

aleksklad [387]

Answer:

Step-by-step explanation:

y=-1/3x+9

This is written in the format y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

Perpendicular lines have a slope that is the negative inverse of the slope of the reference line, in this case -(1/3). The new slope is 3. equation is:

y = 3x + b

To find b, enter the given point, (-6,-2) and solve for b:

y = 3x + b

-2 = 3(-6) + b

-2 = -18 + b

b = 16

The full equation is y=3x + 18

8 0

2 years ago