3log2(x-1)+log2(4)=5

The accompanying data contains the depth (in kilometers) and magnitude, measured using the Richter Scale, of all earthquakes

Sunny_sXe [5.5K]

Answer:

Depth:

μ =20.2025 km

M = 15.625 km

Range = 47.15 km

σ ≈ 15.92 km

Q₁ = 5.7375 km

Q₃ = 34.6675 km

Magnitude:

μ = 2.08375

M = 1.465

Range, R = 5.17

σ = 1.801485 ≈ 1.8

Q₁ = 0.5625

Q₃ = 3.925

Step-by-step explanation:

The given data are;

Depth ${}$ Magnitude

0.76 ${}$ 0.84

4.93 ${}$ 0.47

8.16 ${}$ 0.35

33.58 ${}$ 1.32

21.2 ${}$ 1.61

35.03 ${}$ 4.57

10.05 ${}$ 5.52

47.91 ${}$ 1.99

For the Depth, we have;

The mean, μ = (0.76+4.93+8.16+33.58+21.2+35.03+10.05+47.91)/8 =20.2025 km

The median, M = The (n + 1)/2th term after arranging the term in increasing order as follows;

0.76, 4.93, 8.16, 10.05, 21.2, 33.58, 35.03, 47.91 , the median is therefore;

(8 + 1)/2th term or the 4.5th term which is 10.05 + (21.2 - 10.05)/2 = 15.625 km

The Range = The highest - The lowest value = 47.91 - 0.76 = 47.15 km

The Standard deviation of, σ, is given as follows;

$\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{N}}$

Where;

$x_i$ = The individual data point = (0.76, 4.93, 8.16, 10.05, 21.2, 33.58, 35.03, 47.91 )

N = The total number of data point = 8

Substituting, (using Microsoft Excel) we get;

$\sigma =\sqrt{\dfrac{\sum \left (x_i-20.2025 \right )^{2} }{8}} \approx 15.92 \ km$

Q₁ = The first quartile = The (n + 1)/4th = term arranged in increasing order

Q₁ = The (8 + 1)/4th term = The 2.25th term = 4.93 + (8.16 - 4.93)×0.25) = 5.7375 km

Q₃ = The first quartile = The 3×(n + 1)/4th = term arranged in increasing order

Q₃ = The 3×(8 + 1)/4th term = The 6.75th term = 33.58 + 3×(35.03 - 33.58)×0.25) = 34.6675 km

For the magnitude, we have, using the same formulas and procedures as above;

μ = 2.08375

M = 1.465

Range, R = 5.17

σ = 1.801485 ≈ 1.8

Q₁ = 0.5625

Q₃ = 3.925

4 0

4 years ago

A vehicle is purchased for $18,000, with a down payment of $6,098. The balance in financed for three years at an annual rate of

mestny [16]

The Present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt)/(r/t)
where: P is the monthly payment, r is the annual rate = 7% = 0.07, t is the number of periods in one year = 12 and n is the number of years = 3.

18,000 - 6,098 = P(1 - (1 + 0.07/12)^-(3 x 12)) / (0.07/12)
11,902 = P(1 - (1 + 0.07/12)^-36) / (0.07/12)
P = 0.07(11,902) / 12(1 - (1 + 0.07/12)^-36) = 367.50

Therefore, monthly payment = $367.50

7 0

3 years ago

There is a total of 1,500 people in the town of Markston.

FinnZ [79.3K]

Do 1,500x0.55 which equals
825 people

3 0

3 years ago

21. Angela until the same restaurant four times. Each time she ordered a salad and left at $ 5 tip. She spent a total of $ 54. W

Natalka [10]

So if Angela entered the same restaurant 4 times, we have 4 "instances" of her entering the restaurant.

Each instance, she ordered a salad. The price of this salad is unknown, so we'll say the price is "S".

Each instance, she payed a $5 tip.

So we have 4 instances of spending S, and 4 instances of spending 5.

We know this totals 54.

Knowing all of this information, we can write our equation like this:

4(S + 5) = 54

Divide

S + 5 = 13.50

Subtract

S = 8.50

The cost of salad is $8.50

3 0

3 years ago

Read 2 more answers

The price for a gallon of whole milk has increased from 2006 to 2008. from 2006 to 2007, the cost of whole milk increased by app

valkas [14]

You have the starting price of $1.99. To get the increased price, divide 1.99 by .56 (.56 is the decimal form of 56%). You would get $3.55. This is for the year 2007. So for 2008, divide 3.55 by .42. The answer is $8.45. You can check the answers by multiplying the answers you go the the percentage. Ex. 8.45* .42=3.55 (rounded)

3 0

3 years ago