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serg [7]
3 years ago
11

one days discharge at its mouth, 3 trillion gallons, could supply all of country A’s household for 5 months. how much water an a

verage household uses each month. assume there are 200 million households
Mathematics
1 answer:
serious [3.7K]3 years ago
5 0

let's use engineering notation for the sake of brevity.

1 trillion is 1,000,000,000,000, or just 1E12, twelve zeros.

1 million is then 1E6, six zeros.

we know the discharge for one day is 3E12 gallons, and that'd do just fine for country A for 5 months.  How many gallons in 1 month only?

\bf \begin{array}{ccll} gallons&months\\ \cline{1-2} 3E12&5\\ x&1 \end{array}\implies \cfrac{3E12}{x}=\cfrac{5}{1}\implies 3E12=5x \\\\\\ \cfrac{3E12}{5}=x\implies 6E11=x\implies 600000000000=x

if there are 200million inhabitants in A, namely 200E6 or 2E8 inhabitants, how many gallons per inhabitant from all those 6E11 gallons?

\bf \begin{array}{ccll} gallons&households\\ \cline{1-2} 6E11&2E8\\ x&1 \end{array}\implies \cfrac{6E11}{x}=\cfrac{2E8}{1}\implies 6E11=2E8x \\\\\\ \cfrac{6E11}{2E8}=x\implies \cfrac{600000000000}{200000000}=x\implies 3000=x

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Consider a sequence defined by the recursive rule f(1) = 15; f(n)=f(n - 1) - 6 for n 2. Choose True or
Shkiper50 [21]

Answer:

The second term of the sequence is 8  False ⇒ B

The third term of the sequence is 3  True ⇒ A

The fourth term of the sequence is -3  True ⇒ A

Step-by-step explanation:

The form of the recursive rule is:

f(1) = first term; f(n) = f(n - 1) + d, where

  • f(1) is the first term
  • f(n) is the nth term
  • f(n - 1) is the term before the nth term
  • d is the common difference

∵ f(1) = 15, f(n) = f(n - 1) - 6 for n ≥ 2

∴ The first term = 15

∴ d = -6

let us find the 2nd, 3rd, and 4th terms

∵ n = 2

∴ f(2) = f(1) - 6

∵ f(1) = 15

∴ f(2) = 15 - 6 = 9

∴ The second term is 9

∴ The second term of the sequence is 8  False

∵ n = 3

∴ f(3) = f(2) - 6

∵ f(2) = 9

∴ f(3) = 9 - 6 = 3

∴ The third term is 3

∴ The third term of the sequence is 3 True

∵ n = 4

∴ f(4) = f(3) - 6

∵ f(3) = 3

∴ f(4) = 3 - 6 = -3

∴ The fourth term is -3

∴ The fourth term of the sequence is -3 True

5 0
3 years ago
Pleasee help mee<br><br>12sin(x)-5cos(x)=6,5​
abruzzese [7]

We turn -5,12 into polar coordinates.  It's a Pythagorean Triple so

r = 13   Ф=arctan(-12/5) + 180°   ( in the second quadrant )

so -5 = 13 cos Ф, 12 = 13 sin Ф

12 sin x - 5 cos x = 6.5

13 sinФ sin x + 13 cos Ф cos x = 6.5  

13 cos(x - Ф) = 6.5

cos(x - Ф) = 1/2

cos(x - Ф) = cos 60°

x - Ф = ± 60° + 360° k     integer k

x = Ф ± 60° + 360° k  

x = 180° + arctan(-12/5) ± 60° + 360° k  

That's the exact answer;

x ≈  180° - 67.38° ± 60° + 360° k  

x ≈  122.62° ± 60° + 360° k  

x ≈  { 62.62°, 182.62°} + 360° k,  integer k

3 0
2 years ago
Jane is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a number
sleet_krkn [62]

Answer:

The expected value of playing the game is $0.75.

Step-by-step explanation:

The expected value of a random variable is the weighted average of the random variable.

The formula to compute the expected value of a random variable <em>X</em> is:

E(X)=\sum x\cdot P(X=x)

The random variable <em>X</em> in this case can be defined as the amount won in playing the game.

The probability distribution of <em>X</em> is as follows:

Number on spinner:   1           2           3          4           5              6

Amount earned (<em>X</em>):   $1        $4         $7        $10     -$8.75     -$8.75

Probability:                 1/6       1/6         1/6        1/6         1/6           1/6

Compute the expected value of <em>X</em> as follows:

E(X)=\sum x\cdot P(X=x)

         =(1\times \frac{1}{6})+(4\times \frac{1}{6})+(7\times \frac{1}{6})+(10\times \frac{1}{6})+(-8.75\times \frac{1}{6})+(-8.75\times \frac{1}{6})

         =\frac{1}{6}+\frac{4}{6}+\frac{7}{6}+\frac{10}{6}-\frac{8.75}{6}-\frac{8.75}{6}

         =\frac{1+4+7+10-8.75-8.75}{6}

         =0.75

Thus, the expected value of playing the game is $0.75.

5 0
3 years ago
3/7 g=9 how do you do it?​
Lera25 [3.4K]

The answer is g = 21

just multiply the fraction.

3 × 7 is 21.

6 0
3 years ago
Devon needs 8 yards of fabric to make a blanket. He has a total of 332 yards of fabric. How many blankets can Devon make? A 4040
eimsori [14]
332/8= 41.5 but you cant make half of a blanket so itll be 41!
6 0
2 years ago
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