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Naya [18.7K]
2 years ago
13

A water tank has a square base with each side of length 4 meters. water enters through a hose at a constant rate of 20 liters pe

r minute. at the same time a valve in the bottom is opening, so that after t minutes, water leaves at a rate of t liters per minute. if the tank starts out filled to a depth of 5 meters, after how many minutes will the tank be empty?
Mathematics
1 answer:
levacccp [35]2 years ago
8 0
43.66 minutes

4^2*5+20*x-x^2/2=0
Or
Initial volume of water plus rate of water in minus rate of water out
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To calculate this, the Hardy-Weinberg principle can be used:

p² + 2pq + q² = 1 and p + q = 1

where p and q are the frequencies of the alleles (p - dominant, q - recessive), and p², q² and 2pq are the frequencies of the genotypes.

a) Since 32 plants have rough seed (recessive genotype: q²) out of 100 plants in total, then 

q² = 32/100 = 0.32


b) q = √q² = √0.32 = 0.56


c) Since p + q = 1, then

p = 1 - q = 1 - 0.56 = 0.44


d) 19 plants with rough seeds (recessive genotype: q²) in a population of 100 means that q² = 19/100 = 0.19

We need to calculate p (the allele frequency for smooth seeds).
We can find q because we know q²:

q = √q² = √0.19 = 0.44

Since p + q = 1, then

p = 1 - q = 1 - 0.4 = 0.56

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2 years ago
There are two calculus classes at your school. Both classes have a class average of 75.5. The first class has a standard deviati
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Answer:

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Step-by-step explanation:

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When Gene and Kelly were planning their trip to Paris, one United States dollar was worth about $\frac{7}{10}$ of a euro. Before
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Answer:

$280 dollars

Step-by-step explanation:

When they were leaving

\$1 \approx \frac{7}{10}$ Euro\\Therefore:\\\$1000 \approx  \dfrac{7}{10}\times 1000 =700$ Euro

When they returned home, they brought 196 Euros.

If\:\:\$1 \approx \frac{7}{10}$ Euro\\Then: 1 Euro $=\$  \dfrac{10}{7}\\\\$Therefore:\\\\196 Euros = \$ 196 \times \dfrac{10}{7} =\$280

They brought back $280 dollars to the United States.

3 0
2 years ago
Read 2 more answers
containers a and b hold 11,875 L of water together. conatainer b holds 2,391L more than container B holds. How many Liters of wa
Licemer1 [7]
Step 1 : 11875=2x+2391 Step 2: 11875-2391=2x Step 3: 9484=2x Step 4: 9484/2=x Step 5: x=4742
4 0
2 years ago
Problem 5 (4+4+4=12) We roll two fair 6-sided dice. Each one of the 36 possible outcomes is assumed to be equally likely. 1) Fin
tekilochka [14]

Answer:

1

p(b) =  \frac{1}{6}

2

p(k) =  \frac{1}{3}

3

P(a) =  \frac{1}{3}

Step-by-step explanation:

Generally when two fair 6-sided dice is rolled the doubles are

(1 1) , ( 2 2) , (3 3) , (4 4) , ( 5 5 ), (6 6)

The total outcome of doubles is N = 6

The total outcome of the rolling the two fair 6-sided dice is

n = 36

Generally the probability that doubles (i.e., having an equal number on the two dice) were rolled is mathematically evaluated as

p(b) =  \frac{N}{n}

p(b) =  \frac{6}{36}

p(b) =  \frac{1}{6}

Generally when two fair 6-sided dice is rolled the outcome whose sum is 4 or less is

(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)

Looking at this outcome we see that there are two doubles present

So

The conditional probability that doubles were rolled is mathematically represented as

p(k) =  \frac{2}{6}

p(k) =  \frac{1}{3}

Generally when two fair 6-sided dice is rolled the number of outcomes that would land on different numbers is L = 30

And the number of outcomes that at least one die is a 1 is W = 10

So

The conditional probability that at least one die is a 1 is mathematically represented as

P(a) =  \frac{W}{L}

=> P(a) =  \frac{10}{30}

=> P(a) =  \frac{1}{3}

3 0
2 years ago
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