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3 years ago

Find the speedExample: 396 miles in 6 hours

1 answer:

8 0

To find the speed with given distance and time you just have to divide the distance by time. In this situation it's 396 miles in 6 hours, so it's 396 / 6 = 66 miles in 1 hour. So the speed is 66 mph.

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Initially, 50 pounds of salt are dissolved in a large tank holding 300 gallons of water. A brine solution with a concentration o

kirill [66]

Answer:

dA / dt = 6 - A (t) / 100

600

Step-by-step explanation:

We have to:

dA / dt = In - Out

Input = input salt concentration * input rate of brine

replacing

Inlet = 2 lb / gal * 3 gal / min = 6 lb / min

there is no build up because the inlet flow equals the outlet, so there are 300 gallons in the tank at the start

Output: salt concentration at the output * output rate of brine

replacing

Output: A (t) / 300 * 3 gal / min = A (t) / 100

Thus:

dA / dt = 6 - A (t) / 100

this would be the differential equation.

now, when time tends to infinity, we would be left with:

100 * dA / dt = 600 - A (t)

When t tends to infinity, A (t) tends to 0, therefore, the amount of salt would be 600.

4 0

3 years ago

A basket contains 4 green marbles and 8 blue marbles. a marble is drawn without replacement. then another marble is drawn. what

irina1246 [14]

4/12 reduces to 1/3 and 1/3 * 3/11 = 1/11

3 0

3 years ago

George drove 168 miles in 4 hours. If this rate continues, how many miles can he drive in 7 hours?

Nataly [62]

Find the unit rate. He drove 168 miles in 4 hours.

168/4= 42

He drives 42 Mph.

Multiply that by 7.

42*7= 294

He drives 294 in 7 hours.

I hope this helps!
~kaikers

6 0

3 years ago

Read 2 more answers

In an exam, there is a problem that 60% of students know the correct answer. However, thereis 15% chance that a student picked t

SpyIntel [72]

Answer:

0.231

Step-by-step explanation:

Let the Probability of students that knew the correct answer be: P(A)

P(A) = 60% = 0.6

Let the Probability that the student picked the wrong answer even if he/she knows the right answer be: P(B)

P(B) = 15% =0.15

Let the Probability of the student that do not knew the correct answer Be P(C)

P(C) = 1 - P(A)

P(C) = 1 - 0.6

P(C) = 0.4

Let the Probability that the student does not know the right answer but guessed it correctly be: P(D)

P(D) = 25% = 0.25

Let the Probability that the student picked the right answer even if he/she knows the right answer be: P(E)

P(E) = 1 - P(B)

P(E) = 1 - 0.15

P(E) = 0.85

Probability that the student got the answer wrong = (0.60 X 0.15) + (0.40 X 0.75) = 0.39

P( Student knew answer given he answered wrong) = $\frac{P(Student knew answer) X P(Student answered wrong given he knew the answer}{0.39}$

= $\frac{0.6*0.15}{0.39}$

= $\frac{0.09}{0.39}$

= 0.23076923077

= 0.231

6 0

3 years ago

Of the students attending a school party, 60% of the students are girls, and 40% of the students like to dance. After these stud

elena-s [515]

Answer:

252 students at the party like to dance

Step-by-step explanation:

Given:

60% of the students are girls

40% of the students like to dance

20 more boy students

Percentage of the girls in the party = 58%

To Find:

How many students now at the party like to dance=?

Solution:

Let the number of girls be g.

Let the number of total people originally be t.

We know that

$\frac{g}{t}=\frac{60}{100}$

$\frac{g}{t}=\frac{3}{5}$ ----------------------------------(1)

We also know that

$\frac{g}{t+20}=\frac{58}{100}$

$\frac{g}{t+20}=\frac{29}{50}$ -----------------------------(2)

We now have a system of equation from (1) and (2)

3t=5g

$g = \frac{3t}{5}$ ------------------------(3)

50g=29t+580------------------------(4)

Substituting 3 in 4, we get

$50(\frac{3t}{5})=29t+580$

$(\frac{150t}{5})=29t+580$

$30t =29t+580$

$30t -29t = 580$

t =589

So originally there was 580 students

In this 580 students 40% liked to dance

Then the number of students liked to dance =

=> $40\% \text{of} 580$

=> $\frac{40}{100} \times 580$

=> $0.4 \times 580$

=> 232

We also know that with these people, 20 boys joined, all of whom like to dance.

Now the number of students like to dance = 232+20 = 252 students

7 0

2 years ago