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pishuonlain [190]
1 year ago
15

Harvey the wonder hamster can run 3 1/6 km in 1/4 hour. Harvey runs at a constant rate. Find his average speed in kilometers per

hour.
Mathematics
2 answers:
ASHA 777 [7]1 year ago
7 0

Answer:

12\frac{2}{3}

Step-by-step explanation:

there are 4 quarters to 1 hour

3 1/6 x 4 =  

19/6 * 4 = 76/6 = 12 4/6, reduces to 12 2/3 km per hour

zhenek [66]1 year ago
7 0

Answer:

12 2/3  km  per hour

Step-by-step explanation:

What is Harveys speed?

Take the distance and divide by the time

3 1/6 km

--------------

1/4 hour

Change the mixed number to an improper fraction

3 1/6 = (6*3+1)/6 = 19/6

19/6 km

--------------

1/4 hour

Copy dot flip

19/6 * 4/1 = 76/6 = 38/3  km/hr

3 goes into 38 12 times  (12*3 = 36)  with 2 left over

12 2/3  km  per hour

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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
The function A(b) relates the area of a trapezoid with a given height of 10 and
Natali5045456 [20]

The function of the trapezoid area is:

A(x)=(B+b)*h/2

Where B and b are the bases and h is the height.

With the given data: h=10 B and b =7 and x (it may vary which one is bigger)

-----------

So that function becomes:

A(x)=(7+x)*10/2

A(x)=(7+x)*5

----------

So if you want the inverse function, you have to operate to find x:

A(x)/5=7+x

A(x)/5-7=x

----------

So the new function is:

x(A)=A/5-7

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2 years ago
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. find the prob
navik [9.2K]
Before I answer the question i am going to start with the blue Marble you would have a 1/8 chance of drawing the blue marble from the box and after that you would have a 3/7 of drawing a white marble because you did not replace the blue marble and I hope this help.
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1 year ago
If Line segment C B. bisects ∠ACD, what additional information could be used to prove ΔABC ≅ ΔDBC using SAS? Select three option
meriva

Answer:

Option (1)

Step-by-step explanation:

In the figure attached,

BC is the angle bisector of angle ACD.

To prove ΔABC and ΔDBC congruent by SAS property we require two sides and the angle between these sides to be congruent.

Since BC ≅ BC [Reflexive property]

∠ABC ≅ ∠CBD ≅ 125°

And sides AB ≅ BD

Both the triangles will be congruent.

Therefore, additional information required to prove ΔABC ≅ ΔDBC have been given in option (1).

Therefore, Option (1) will be the answer.

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1 year ago
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When putting data into a class for this case, 0.350 - 0.359, they should be within the class boundaries. The class boundaries are 0.3495 and 0.3595. So, the data that will go into that class are 0.356 and 0.358. The record 0.349 is not included since it is below 0.3495. Therefore, there are only two values in the class.


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!


4 0
1 year ago
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