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3 years ago

Partc

Mathematics

1 answer:

Lilit [14]3 years ago

8 0

Answer:

πr2

Step-by-step explanation:

area of a parallelogram = base × height

= 0.5 × circumference × radius

= 0.5(2πr)(r)

= πr2

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According to the article "Characterizing the Severity and Risk of Drought in the Poudre River, Colorado" (J. of Water Res. Plann

mihalych1998 [28]

Answer:

(a) P (Y = 3) = 0.0844, P (Y ≤ 3) = 0.8780

(b) The probability that the length of a drought exceeds its mean value by at least one standard deviation is 0.2064.

Step-by-step explanation:

The random variable Y is defined as the number of consecutive time intervals in which the water supply remains below a critical value y₀.

The random variable Y follows a Geometric distribution with parameter p = 0.409.

The probability mass function of a Geometric distribution is:

$P(Y=y)=(1-p)^{y}p;\ y=0,12...$

(a)

Compute the probability that a drought lasts exactly 3 intervals as follows:

$P(Y=3)=(1-0.409)^{3}\times 0.409=0.0844279\approx0.0844$

Thus, the probability that a drought lasts exactly 3 intervals is 0.0844.

Compute the probability that a drought lasts at most 3 intervals as follows:

P (Y ≤ 3) = P (Y = 0) + P (Y = 1) + P (Y = 2) + P (Y = 3)

$=(1-0.409)^{0}\times 0.409+(1-0.409)^{1}\times 0.409+(1-0.409)^{2}\times 0.409\\+(1-0.409)^{3}\times 0.409\\=0.409+0.2417+0.1429+0.0844\\=0.8780$

Thus, the probability that a drought lasts at most 3 intervals is 0.8780.

(b)

Compute the mean of the random variable Y as follows:

$\mu=\frac{1-p}{p}=\frac{1-0.409}{0.409}=1.445$

Compute the standard deviation of the random variable Y as follows:

$\sigma=\sqrt{\frac{1-p}{p^{2}}}=\sqrt{\frac{1-0.409}{(0.409)^{2}}}=1.88$

The probability that the length of a drought exceeds its mean value by at least one standard deviation is:

P (Y ≥ μ + σ) = P (Y ≥ 1.445 + 1.88)

= P (Y ≥ 3.325)

= P (Y ≥ 3)

= 1 - P (Y < 3)

= 1 - P (X = 0) - P (X = 1) - P (X = 2)

$=1-[(1-0.409)^{0}\times 0.409+(1-0.409)^{1}\times 0.409\\+(1-0.409)^{2}\times 0.409]\\=1-[0.409+0.2417+0.1429]\\=0.2064$

Thus, the probability that the length of a drought exceeds its mean value by at least one standard deviation is 0.2064.

6 0

3 years ago

Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 3 units long. Point C is on the line x = −1.

Shkiper50 [21]

C:8 is the answer my guy welcome

7 0

3 years ago

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Nate has 6 3/5 of fabric. He uses 3 1/2 yards of fabric to make a pillow. How much fabric dose he left

NNADVOKAT [17]

Answer:

3 and 1/2 minus 2/3 minus 1/3 =

7/2 minus 2/3 minus 1/3 =

21/6 minus 4/6 minus 2/6 =

17/6 - 2/6 =

15/6 = 5/2 = 2 and 1/2

Optionally, you can think of it this way:

He used 2/3 yards for the pillow and 1/3 yard for the scarf.

So he used 1 yard

3 and 1/2 minus 1 = 2 and 1/2 = 5/2

Step-by-step explanation:

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3 years ago

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the bottom of a 22-foot ladder must be placed 7 feet from a wall. to the nearest tenth of a foot, how far above the ground does

Kitty [74]

The ladder, the wall and the floor form together a triangle rectangle, where the ladder is the hypotenuse of the triangle and the floor and wall are the cathetus. We know from Pythagoreas theorem that the square of the hypotenuse is equal to the sum of the two cathetus squared added, so we can write an equation with the data we have:
hyp^2 = cath1^2 + cath2^2
hyp^2 = wall^2 + floor^2
so we have the hypotenuse value, the floor value and the unknown is the wall height:
(22)^2 = wall^2 + (7)^2
484 = wall^2 + 49
wall^2 = 484 - 49 = 435
wall = √435
wall = 20.9
therefore the ladder touches the wall 20.9 feet above the ground

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3 years ago

How do you solve 6=1/12v

Veronika [31]

Answer:

Step-by-step explanation:

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3 years ago

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