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3 years ago

Simplify Completely:

2 answers:

5 0

$5 \sqrt{162}-3 \sqrt{18}-4 \sqrt{98}= \\ 5\cdot 9 \sqrt{2}-3\cdot 3 \sqrt{2} -4\cdot 7\sqrt{2}=\\ 45 \sqrt{2}-9 \sqrt{2} -28\sqrt{2}=\\ 8 \sqrt{2}$

B) 8√2

MaRussiya [10]3 years ago

3 0

The correct answer is (B)

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What is the area of a semicircle with a diameter of 12?

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Answer:

So, area of the semicircle = 18π mm.

Step-by-step explanation:

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3 years ago

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Geologists estimate the time since the most recent cooling of a mineral by counting the number of uranium fission tracks on the

Oliga [24]

Answer:

(a) The value of P (X = 7) is 0.1388.

(b) The value of P (X ≥ 3) is 0.9380.

(d) $\mu_{X}=6$

(e) $\sigma_{X}=2.45$

Step-by-step explanation:

Let X = number of uranium fission tracks on per cm² surface area of the mineral.

The average number of track per cm² surface area is, λ = 6.

The random variable X follows a Poisson distribution with parameter λ = 6.

The probability mass function of a Poisson distribution is:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0, 1, 2, 3...$

(a)

Compute the value of P (X = 7) as follows:

$P(X=6)=\frac{e^{-6}(6)^{7}}{7!}=\frac{0.0025\times 279936}{5040}=0.1388$

Thus, the value of P (X = 7) is 0.1388.

(b)

Compute the value of P (X ≥ 3) as follows:

P (X ≥ 3) = 1 - P (X < 3)

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

$=1-\frac{e^{-6}(6)^{0}}{0!}-\frac{e^{-6}(6)^{1}}{1!}-\frac{e^{-6}(6)^{2}}{2!}\\=1-0.00248-0.01487-0.04462\\=0.93803\\\approx0.9380$

Thus, the value of P (X ≥ 3) is 0.9380.

(c)

Compute the value of P (2 < X < 7) as follows:

P (2 < X < 7) = P (X = 3) + P (X = 4) + P (X = 5) + P (X = 6)

$=\frac{e^{-6}(6)^{3}}{3!}+\frac{e^{-6}(6)^{4}}{4!}+\frac{e^{-6}(6)^{5}}{5!}+\frac{e^{-6}(6)^{6}}{6!}\\=0.08924+0.13385+0.16062+0.16062\\=0.54433\\\approx0.5443$

Thus, the value of P (2 < X < 7) is 0.5433.

(d)

The mean of the Poisson distribution is:

$\mu_{X}=\lambda=6$

(e)

The standard deviation of the Poisson distribution is:

$\sigma_{X}=\sqrt{\sigma^{2}_{X}}=\sqrt{\lambda}=\sqrt{6}=2.4495\approx2.45$

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3 years ago

C) does An altitude Intersects the opposite side?

lora16 [44]

Answer:

An altitude of any triangle is a line from a vertex that intersects the opposite side at the right-angled vertex.

Therefore yes it does intersect the opposite side.

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3 years ago

Express the confidence interval (0.036, 0.086) in the form of p-e< p

lina2011 [118]

Answer:

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

Step-by-step explanation:

Given;

Confidence interval CI = (a,b) = (0.036, 0.086)

Lower bound a = 0.036

Upper bound b = 0.086

To express in the form;

p-e< p < p+e

Where;

p = mean Proportion

and

e = margin of error

The mean p =( lower bound + higher bound)/2

p = (a+b)/2

Substituting the values;

p = (0.036+0.086)/2

Mean Proportion p = 0.061

The margin of error e = (b-a)/2

Substituting the given values;

e = (0.086-0.036)/2

e = 0.025

Re-writing in the stated form, with p = 0.061 and e = 0.025

p-e< p < p+e

(0.061 - 0.025) < 0.061 < (0.061 + 0.025)

0.036 < 0.061 < 0.086

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4 years ago

What is the surface area of the rectangular prism

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340 you were right

Step-by-step explanation:

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