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Bogdan [553]
3 years ago
9

Sophia is saving money for a new bicycle. The bicycle will cost at least $623. Sophia makes $8.22 per hour.

Mathematics
2 answers:
valina [46]3 years ago
7 0

Answer:

C.8.22 h\geq$ 623

Step-by-step explanation:

We are given that Sophia is saving money for a new bicycle.

The bicycle will  cost atleast $623.

Sophia makes $8.22 per hour.

We have to find the inequality that could be used to find the number of hours Sophia needs to work to make enough money to buy a new bicycle.

Let Sophia works h hours to make enough money to buy a new bicycle.

Sophia makes money per hour =$8.22

Total money made by Sophia in h hours =8.22 h

According to question

8.22 h\geq$623

Hence, option C is true.

Luda [366]3 years ago
3 0
$8.22h greater than or equal to $623
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Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per g
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Answer:

The quantity of salt at time t is m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} }), where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

(0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}

Where:

c - The salt concentration in the tank, as well at the exit of the tank, measured in \frac{pd}{gal}.

\frac{dc}{dt} - Concentration rate of change in the tank, measured in \frac{pd}{min}.

V - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

V \cdot \frac{dc}{dt} + 6\cdot c = 3

60\cdot \frac{dc}{dt}  + 6\cdot c = 3

\frac{dc}{dt} + \frac{1}{10}\cdot c = 3

This equation is solved as follows:

e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }

\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }

e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt

e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C

c = 30 + C\cdot e^{-\frac{t}{10} }

The initial concentration in the tank is:

c_{o} = \frac{10\,pd}{60\,gal}

c_{o} = 0.167\,\frac{pd}{gal}

Now, the integration constant is:

0.167 = 30 + C

C = -29.833

The solution of the differential equation is:

c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }

Now, the quantity of salt at time t is:

m_{salt} = V_{tank}\cdot c(t)

m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })

Where t is measured in minutes.

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John made this model to show \frac{4}{7}\times\frac{13}{9} 7 4 ​ × 9 13 ​ Using John's model, what is \frac{4}{7}\times\frac{13}
harkovskaia [24]

Answer:

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Step-by-step explanation:

Given

See attachment for model

Required

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The model is represented by:

\frac{4}{7}\times\frac{13}{9} = \frac{4}{7}\times\frac{9}{9} + \frac{4}{7}\times\frac{4}{9}

To get: \frac{4}{7}\times\frac{9}{9}, we consider the first partition

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The total boxes shaded at the bottom is 36 ---- this represents the numerator

So, we have:

\frac{4}{7}\times\frac{9}{9} = \frac{36}{63}

To get: \frac{4}{7}\times\frac{9}{9}, we consider the first partition

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So, we have:

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\frac{4}{7}\times\frac{13}{9} = \frac{36+16}{63}

\frac{4}{7}\times\frac{13}{9} = \frac{52}{63}

5 0
3 years ago
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