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Monica [59]
3 years ago
15

Liola drives 17km up a hill that is at a grade of 14 degrees. What horizontal distance, to the nearest tenth of kilometer, has s

he covered?
Mathematics
1 answer:
nevsk [136]3 years ago
4 0

Answer:

16.5km

Step-by-step explanation:

Liola drives 17km up a hill that is at a grade of 14 degrees. What horizontal distance, to the nearest tenth of kilometer, has she covered?

We solve using Trigonometric function of Cosine

cos theta = Adjacent/Hypotenuse

Theta = 14°

Hypotenuse = Distance up the hill = 17km

Adjacent = Horizontal distance = x

Hence,

cos 14 = x/17

Cross Multiply

x = cos 14 × 17

x = 16.495027347km

Approximately = 16.5km

The horizontal distance = 16.5km

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3 years ago
When studying radioactive material, a nuclear engineer found that over 365 days,
Gnom [1K]

Answer:

a) The mean number of radioactive atoms that decay per day is 81.485.

b) 0% probability that on a given day, 50 radioactive atoms decayed.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\lambda is the mean in the given interval.

a. Find the mean number of radioactive atoms that decayed in a day.

29,742 atoms decayed during 365 days, which means that:

\lambda = \frac{29742}{365} = 81.485

The mean number of radioactive atoms that decay per day is 81.485.

b. Find the probability that on a given day, 50 radioactive atoms decayed.

This is P(X = 50). So

P(X = 50) = \frac{e^{-81.485}*(81.485)^{50}}{(50)!} = 0

0% probability that on a given day, 50 radioactive atoms decayed.

5 0
2 years ago
Some online banks offer "online bill pay."What does this mean?
sleet_krkn [62]
It means that you can pay your utility bill for example using internet banking.

5 0
3 years ago
Peter buys a camper van costing £35000 + 20% VAT. He pays a 50% deposit and then arranges to pay the remaining balance in 20 equ
shutvik [7]

The amount paid each month is 1050.

35,000 plus 20% is 42,000 because 20% of 35,000 is 7,000.

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3 0
3 years ago
High school students from grades 9–10 and 11–12 were asked to choose the kind of band to have play at a school dance: rap, rock,
yanalaym [24]
The correct two-way frequency table for the date will look like this:
                 
                               RAP      ROCK     COUNTRY     TOTAL
Grades 9-10           40           30            55                  125
Grades 11-12         60           25            35                  120
TOTAL                    100          55            90                  245

The sum of the row total is equal to the sum of the column total
125 + 120 = 100 + 55 + 90
245 = 245
8 0
3 years ago
Read 2 more answers
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