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algol
1 day ago
7

1200 cm per hour= ? Km per week

Mathematics
2 answers:
PIT_PIT [3.9K]1 day ago
5 0

Answer: 2.016 km weekly

Detailed explanation:

Starting value: 1200 cm per hour

It is known that 1\text{ km}=100000\text{cm}\\\\\Rightarrow\ 1\text{ cm}=\dfrac{1}{100000}\text{ km}

Furthermore,

1\text{ day}=24\text{ hours} \\\\\Rightarrow\ \text{1 week}=7\times24\text{ hours}=168\text{hours}\\\\\Rightarrow\ \text{1 hour}=\dfrac{1}{68}\text{ week}

\text{ 1200 cm per hour}=\dfrac{1200}{100000}\times\dfrac{1}{\dfrac{1}{168}}\\\\=\dfrac{1200}{100000}\times168=2.016\text{ km per week}

PIT_PIT [3.9K]1 day ago
4 0

Answer:

0.012 km/hr

Step-by-step explanation:

(1200 cm)(1 m/100 cm)(1 km/1000 m) = 0.012 km/hr

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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
Leona [4166]

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.

6 0
9 days ago
Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month
AnnZ [3877]

Answer:

a) The first inequality is 100 + 55x > 150 + 51x;

b) The final inequality results in x > 12.5

c) Sal's mother will need to use the second phone for at least 13 months.

Step-by-step explanation:

a) Let x represent the number of months.

1. The first phone is priced at $100, with a monthly fee of $55 for unlimited use, leading to a total cost of $(100 + 55x) for x months.

2. The second phone costs $150 with a monthly fee of $51 for unlimited use, resulting in a total of $(150 + 51x) for x months.

3. For the second phone to be cheaper, we set up the inequality:

150 + 51x < 100 + 55x

which simplifies to

100 + 55x > 150 + 51x

b) Now solve this:

55x - 51x > 150 - 100

4x > 50

so x > 12.5

c) This means Sal's mother has to retain the second phone for at least 13 months (since x > 12.5).

8 0
12 days ago
Read 2 more answers
At the warm-up event for Oscar’s All Star Hot Dog Eating Contest, Al ate one hot dog. Bob then showed him up by eating three hot
Inessa [3907]

Answer: Zeno consumed 51 hot dogs.

The total number of hot dogs consumed was 676.

Step-by-step explanation:

Al started by eating one hot dog. Bob then outperformed him by devouring three hot dogs. Carl, not wanting to fall behind, ate five hot dogs. This pattern continued, with each participant consuming two hot dogs more than the previous one. This indicates that the quantity of hot dogs eaten by each contestant followed an arithmetic sequence.

The formula for finding the nth term in an arithmetic series is given by

Tn = a + (n - 1)d

Where

a denotes the first term in the sequence.

d signifies the common difference.

n stands for the total terms in the sequence.

<pBased on the details provided,

a = 1 hot dog

d = 3 - 1 = 2 hot dogs

We aim to find how many hot dogs the 26th contestant, T26, consumed. Thus,

T26 = 1 + (26 - 1)2 = 1 + 50

T26 = 51 hot dogs

The formula to calculate the sum of n terms in an arithmetic sequence is

Sn = n/2[2a + (n - 1)d]

Hence, to find the total number of hot dogs consumed by 26 contestants, S26 is calculated as

S26 = 26/2[2 × 1 + (26 - 1)2]

S26 = 13[2 + 50]

S26 = 13 × 52 = 676 hot dogs

5 0
9 days ago
"Our customer retention rate has decreased 10% from last quarter's goal of 250 consumers retained. We need to increase our curre
Zina [3914]

1. Calculate 10% of 250 (250 × 0.10 = 25)
2. Subtract that from 250 (250 - 25 = 225)
3. Then find 16% of 225 (225 × 0.16 = 36)
4. Add 225 and 36 to get 261
5. Therefore, the target number of consumers retained is 261
6 0
18 days ago
Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section 3.7). If the cup is 6 inche
tester [3916]

Response:

The height of the water when it reaches 4 inches is \frac{3}{8\times \pi} inch/s.

Detailed Explanation:

Flow rate of water from the cone = R=\frac{3}{2} inch^3/s

Height of the cup = h = 6 inches

Radius of the cup = r = 3 inches

\frac{r}{h}=\frac{3 inch}{6 inch}=\frac{1}{2}

r = h/2

Volume of the cone = V=\frac{1}{3}\pi r^2h

V=\frac{1}{3}\pi r^2h

\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi r^2h)}{dt}

\frac{dV}{dt}=\frac{d(\frac{1}{3}\pi (\frac{h}{2})^2h)}{dt}

\frac{dV}{dt}=\frac{1}{3\times 4}\pi \times \frac{d(h^3)}{dt}

\frac{dV}{dt}=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}

\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3h^2\times \frac{dh}{dt}

h = 4 inches

\frac{3}{2} inch^3/s=\frac{1\pi }{12}\times 3\times (4inches )^2\times \frac{dh}{dt}

\frac{3}{2} inch^3/s=\pi\times 4\times \frac{dh}{dt} inches^2

\frac{dh}{dt}=\frac{3}{8\times \pi} inch/s

The height of the water when it is 4 inches deep is \frac{3}{8\times \pi} inch/s.

6 0
11 days ago
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