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PIT_PIT [208]
2 years ago
5

Larry is starting his own lawn service company. He has initial startup costs totaling $300, plus ongoing operating expenses. The

function representing Larry's expenses and the function representing Larry's income for lawn services are shown in the graph below. Approximately how many lawns will Larry have to mow before he starts making a profit?
Mathematics
1 answer:
baherus [9]2 years ago
4 0

Answer:

Larry must mow approximately 25 lawns before he starts making a profit

Step-by-step explanation:

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A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain
MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}

(i) Set up an expression for the rate of change of salt concentration.

\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}

(ii) Integrate the expression

\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C

(iii) Find the constant of integration

\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)

(iv) Solve for A as a function of time.

\text{The integrated rate expression is}\\\ln A = -0.003t +  \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}

b.Calculate the concentration

A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is  

\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}

(c) Concentration at infinite time

\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0
3 years ago
A sales analyst listed the probabilities of profits and losses in dollars for a certain company. Find the mean for the probabili
kakasveta [241]

Answer: The mean for the probability distribution will be 69.25.

Explanation:

Since we given that

At\ x_1= -500 ,P(x) = 0.076\\

At\ x_2= -250,P(x)= 0.191\\

At\ x_3=0, P(x)= 0.265\\

At\ x_4=250 , P(x)= 0.316\\

At\ x_5=500 , P(x)= 0.152\\

As we know the formula for expectation of x i.e. known as mean for the probability distribution,

E(x)=x\sum_{1}^{5} P(x)

So, we  apply this formula in our case,

-500\times 0.076+(-250)\times 0.191+0\times 0.265+250\times 0.316+500\times 0.512=69.25

\mu = 69.25

Hence, the mean for the probability distribution will be 69.25.



4 0
3 years ago
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B. During two years of college, a student earned $12,000. The second year she earned $500
Nana76 [90]

Answer:

6000 dollars duhhhhhhhhhhhh

5 0
3 years ago
2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2=
Tomtit [17]

Answer:

48

Step-by-step explanation:

i counted 24 2's and 24 x 2 is 48 also i did the math

3 0
2 years ago
Read 2 more answers
Jorge ordered 22 bottles of juice. Each bottle holds 6.32 ounces of juice.
Umnica [9.8K]

Answer: On the first one its either A or D. (I think)

Step-by-step explanation:

So what I did was I multiplied 22 and 6.32 together and got 139.04 and the closest estimate to that would be 160 because 39 is closer to 60 than 20 (A) and since its not 150 the estimate would be lower than higher. (D)

4 0
3 years ago
Read 2 more answers
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