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ycow [4]
1 year ago
8

Samantha and her children went into a grocery store and she bought $7 worth of bananas and peaches. Each banana costs $0.40 and

each peach costs $0.50. She bought a total of 15 bananas and peaches altogether. Determine the number of bananas and the number of peaches that Samantha bought.
Mathematics
1 answer:
fomenos1 year ago
5 0

Answer:

10 peaches and 5 bananas

Step-by-step explanation:

To solve the problem increase the cost by adding more peaches and less by adding more bananas

7 peaches = 3.50

8 bananas = 3.20 + 3.50 = 6.70

We need 30 more cents so add three more peaches

10 peaches = 5

5 x 0.4 = 2

2 + 5 = 7

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A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound o
Valentin [98]

Answer:

47.25 pounds

Step-by-step explanation:

\dfrac{dA}{dt}=R_{in}-R_{out}

<u>First, we determine the Rate In</u>

Rate In=(concentration of salt in inflow)(input rate of brine)

=(0.5\frac{lbs}{gal})( 6\frac{gal}{min})\\R_{in}=3\frac{lbs}{min}

Change In Volume of the tank, \frac{dV}{dt}=6\frac{gal}{min}-4\frac{gal}{min}=2\frac{gal}{min}

Therefore, after t minutes, the volume of fluid in the tank will be: 100+2t

<u>Rate Out</u>

Rate Out=(concentration of salt in outflow)(output rate of brine)

R_{out}=(\frac{A(t)}{100+2t})( 4\frac{gal}{min})\\\\R_{out}=\frac{4A(t)}{100+2t}

Therefore:

\dfrac{dA}{dt}=3-\dfrac{4A(t)}{100+2t}\\\\\dfrac{dA}{dt}=3-\dfrac{4A(t)}{2(50+t)}\\\\\dfrac{dA}{dt}=3-\dfrac{2A(t)}{50+t}\\\\\dfrac{dA}{dt}+\dfrac{2A(t)}{50+t}=3

This is a linear differential equation in standard form, therefore the integrating factor:

e^{\int \frac{2}{50+t}dt}=e^{2\ln|50+t|}=e^{\ln(50+t)^2}=(50+t)^2

Multiplying the DE by the integrating factor, we have:

(50+t)^2\dfrac{dA}{dt}+(50+t)^2\dfrac{2A(t)}{50+t}=3(50+t)^2\\\{(50+t)^2A(t)\}'=3(50+t)^2\\$Taking the integral of both sides\\\int \{(50+t)^2A(t)\}'= \int 3(50+t)^2\\(50+t)^2A(t)=(50+t)^3+C $ (C a constant of integration)\\Therefore:\\A(t)=(50+t)+C(50+t)^{-2}

Initially, 20 pounds of salt was dissolved in the tank, therefore: A(0)=20

20=(50+0)+C(50+0)^{-2}\\20-50=C(50)^{-2}\\C=-\dfrac{30}{(50)^{-2}} =-30X50^2=-75000

Therefore, the amount of salt in the tank at any time t is:

A(t)=(50+t)-75000(50+t)^{-2}

After 15 minutes, the amount of salt in the tank is:

A(15)=(50+15)-75000(50+15)^{-2}\\=47.25$ pounds

8 0
1 year ago
Nathan spins 2 different spinners at the same time. There are a total of 10 possible
kow [346]

Answer:

Since the spinners have been spun simultaneously, every side on each of the spinner carries equal probability of landing. In order for there to be only 10 possible outcomes, no more no less, the spinners cannot be identical. One of the spinner in two sided while the other spinner must then be a five sided spinner. Choosing this particular pair of spinners gives Nathan 10 possibilities of combinations.

Hope that answers the question, have a great day!

3 0
1 year ago
Read 2 more answers
Round the number 76.4491 to 1 decimal place
solniwko [45]

Answer:

Step-by-step explanation:

76.4

4 0
1 year ago
Sammy the turtle can walk 1/8 of a mile in an hour.How many hours will it take him to walk 1^1/4 miles?
Eduardwww [97]
It will take him 10 hours 

5 0
2 years ago
if the current batch of pills is the first of the day and your goal is to produce a total of 600 what percentage of your goal wi
Zanzabum

Answer:

<u>12.5% ≈ 13%</u>

Step-by-step explanation:

The rest of the question is: There are 75 pills in the batch.

The current batch of pills is the first of the day and our goal is to produce a total of 600.

If there are 75 pills in the batch so percentage of goal completed will be

[(number of pills in the batch)/(Total pills)] * 100

\frac{75}{600}*100 = 12.5 \%

≈ 13% to the nearest whole number

7 0
1 year ago
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