All categories

2 years ago

Jersey constructed a small wooden jewelry box, shown below, for her mother.

Mathematics

1 answer:

Andrei [34K]2 years ago

3 0

Answer:

(D)117 Cubic Inches

Step-by-step explanation:

Dimensions of the box are:

Length $=7\frac{1}{2}\:inch$

Width $=4\frac{1}{3}\:inch$

Height $=3\frac{3}{5}\:inch$

Volume of the Box =Length X Width X Height

$=7\dfrac{1}{2}X4\dfrac{1}{3}X3\dfrac{3}{5}\\\\=\dfrac{15}{2}X\dfrac{13}{3}X\dfrac{18}{5}\\\\=\dfrac{15X13X18}{2X3X5}\\\\=\dfrac{3510}{30}$

=117 Cubic Inches

The volume of the box is 117 cubic inches.

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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.

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

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

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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:

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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.

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