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10 days ago

The amount of water flowing into a tank doubles every minute. The tank if full in an hour. When is the tank half full.

1 answer:

7 0

Given that the water in the tank doubles every minute, it implies that when the tank was full, it was half full just one minute prior. If it reaches fullness after 60 minutes, it was indeed double what it was a minute earlier. Hence, the opposite of doubling is halving. A minute before the tank filled completely, it was at half capacity. Therefore, it confirms that it was half full after 59 minutes.

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The function g(x) is graphed. On a coordinate plane, a curved line enters the plane at point (negative 2.3, 5), crosses the x- a

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Step-by-step explanation:

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13 days ago

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g European roulette. The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A bal

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Answer:

The total expected value and standard deviation of your winnings are -$0.081 and $3, respectively.

Step-by-step explanation:

In European roulette, a wheel with 37 slots is spun: 18 are red, 18 are black, and 1 is green.

Bettors can wager on either red or black. Winning on their chosen color means they double their bet, while losing means they forfeit their stake.

Define the probability for the ball landing in a red slot = $\frac{18}{37}$

The probability of it landing in a black slot = $\frac{18}{37}$

The probability for landing in the green slot = $\frac{1}{37}$

Since bets are only placed on red or black,

The winning probability = $\frac{18}{37}$

and losing probability = $\frac{18}{37}+\frac{1}{37}$

= $\frac{19}{37}$

If a gambler wins, they receive $3, and if they lose, it amounts to -$3.

The expected value of the total winnings is hence;

E(X) = $\sum X \times P(X)$

= $\$3 \times \frac{18}{37} + (-\$3 \times \frac{19}{37})$

= $\$3 \times (-\frac{1}{37})$ = -$0.081

Furthermore, the standard deviation of the total winnings is given by;

S.D.(X) = $\sqrt{(\sum X^{2} \times P(X))-(\sum X \times P(X))^{2} }$

<pTherefore, $E(X^{2})=\sum X^{2} \times P(X)$

= $\$3^{2} \times \frac{18}{37} + (-\$3^{2} \times \frac{19}{37})$

= $\$9 \times (\frac{18}{37}+\frac{19}{37})$ = $9

Thus, S.D.(X) = $\sqrt{\$9-(-\$0.081)^{2} }$

= $\sqrt{8.993}$ = $2.99 ≈ $3

Consequently, the anticipated value and standard deviation of your total winnings are -$0.081 and $3, respectively.

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9 days ago

L'età media di Aldo, Bruno, Carlo e Davide è 16 anni. Se non si tiene conto di Davide, l'età media dei tre rimanenti sale a 18.

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Answer:

Davide is 10 years old.

L'età di Davide è 10.

Step-by-step explanation:

The average ages of Aldo, Bruno, Carlo, and Davide amount to 16 years.

Let’s denote:

x for Aldo's age.

y for Bruno's age.

z for Carlo's age.

w for Davide's age.

The average for all four is 16 years.

This gives us:

$16 = \frac{x + y + z + w}{4}$

$x + y + z + w = 64$

Excluding Davide, the average age of the other three is 18. Therefore:

$18 = \frac{x + y + z}{3}$

$x + y + z = 54$

Substituting into the original equation:

$x + y + z + w = 64$

$54 + w = 64$

$w = 10$

Hence, Davide’s age is indeed 10.

L'età di Davide è 10.

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4 days ago

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Answer: The hourly charge for the rototiller is $3.

Step-by-step explanation:

Let h denote the hourly rate for the rototiller rental.

The rental provider imposed a base fee of $43 in addition to a charge per hour. Assuming the rototiller was rented for x hours, the cost incurred would total

43 + hx.

If they paid $64 for 7 hours of rental, the equation representing this situation would be

43 + 7h = 64.

Resolving gives us 7h = 64 - 43 = 21.

Therefore, h = 21/7 = $3.

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