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Aleonysh [2.5K]
3 years ago
8

The average of 100 measurements is 23 and the average of 50 additional measurements is 27.

Mathematics
1 answer:
Elden [556K]3 years ago
8 0
Total value of 100 measurements
100 * 23
2300

Total value of additional 50 measurements
50 * 27
1350

Total value of 150 measurements
2300 + 1350
3650

Average of 150 measurements
3650 / 150
24.3

25 > 24.3

Answer is B
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Suppose that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water
Setler79 [48]

Answer:

Step-by-step explanation:

Given that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 4 gal/min, and when the solution is well stirred, it is then pumped out at the same rate.

Let Q(t) be the quantity of salt at time t.

Q(0) = 70 pounds

Inflow of water = outflow = 4 gal/min

So resulting volume of tank at time t = 400 gallons

Rate of change of salt = inflow - outflow

= 0 - \frac{Q(t)}{400}

i.e. \frac{dQ}{dt} =\frac{-Q(t)}{400}

This is a variable separable equation

\frac{dQ}{Q}=-\frac{dt}{400} \\ln Q = {-\frac{t}{400}} +C\\Q = A e^{-\frac{t}{400}}

Use when t =0 Q = 70

A =70

So A(t) = Q(t) = 70 e^{-\frac{t}{400}} and

A(0) = Q(0) = 70 lbs.

7 0
2 years ago
Mercy marks up all goods she sells by 30%.What is the mark up of a hat that cost her $42?
Delvig [45]

Answer:

$12.60

Step-by-step explanation:

42/30%=42/0.3=$12.60

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(comment if spelling is wrong anywhere)

3 0
3 years ago
If y = kx, what is the value of k if y = 20 and x = 0.4?
True [87]
Set up an equation 20=k(0.4)....to find k divide 20 by 0.4
8 0
3 years ago
What steps do I take for this
Luden [163]
First, divide the shape into two figures ( a semicircle and a rectangle)
Then, find the are or the two shapes using the area formula for a semicircle (\frac{ \pi r^{2} }{2}) and the are formula for a rectangle (base x height)
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7 0
3 years ago
The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The resistance R is slowly increasin
hoa [83]

Answer:

\frac{dI}{dt}=-0.00016 A/s

Step-by-step explanation:

We are given that

By ohm's law

V=IR

R=389 ohm

I=0.03 A

\frac{dV}{dt}=-0.06V/s

\frac{dR}{dt}=0.07ohm/s

We have to find rate of change of current I means \frac{dI}{dt}

Differentiate the equation w.r.t t

\frac{dV}{dt}=\frac{dI}{dt}R+I\frac{dR}{dt}

Substitute the values then we get

-0.06=\frac{dI}{dt}\times 389+0.03\times 0.07

-0.06=389\frac{dI}{dt}+0.0021

-0.06-0.0021=389\frac{dI}{dt}

-0.0621=389\frac{dI}{dt}

\frac{dI}{dt}=\frac{-0.0621}{389}=-0.000160 A/s

Hence, the current I is changing at the rate=-0.00016A/s

4 0
3 years ago
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