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1 year ago

12) -6n – 20 = -2n +4(1 – 3n) What’s the first step

Mathematics

1 answer:

EastWind [94]1 year ago

4 0

Answer:

n = 3

Step-by-step explanation:

-6n - 20 = -2n + 4 (1-3n)

First distribute the 4 (1-3n)

-6n - 20 = -2n + 4 - 12n

Combine like terms on the right side

-6n - 20 = -14n + 4

Get 'n' on one side by adding -6n to both sides

-20 = -8n + 4

Subtract 4 to both sides

-24 = -8n

Divide -8 to both sides

3 = n

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In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that

attashe74 [19]

Answer:

(a) The probability of more than one death in a corps in a year is 0.1252.

(b) The probability of no deaths in a corps over 7 years is 0.0130.

Step-by-step explanation:

Let X = number of soldiers killed by horse kicks in 1 year.

The random variable $X\sim Poisson(\lambda = 0.62)$ .

The probability function of a Poisson distribution is:

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

(a)

Compute the probability of more than one death in a corps in a year as follows:

P (X > 1) = 1 - P (X ≤ 1)

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

$=1-\frac{e^{-0.62}(0.62)^{0}}{0!}-\frac{e^{-0.62}(0.62)^{1}}{1!}\\=1-0.54335-0.33144\\=0.12521\\\approx0.1252$

Thus, the probability of more than one death in a corps in a year is 0.1252.

(b)

The average deaths over 7 year period is: $\lambda=7\times0.62=4.34$

Compute the probability of no deaths in a corps over 7 years as follows:

$P(X=0)=\frac{e^{-4.34}(4.34)^{0}}{0!}=0.01304\approx0.0130$

Thus, the probability of no deaths in a corps over 7 years is 0.0130.

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1 year ago

Which expression is equivalent to 4√6/3√2

VLD [36.1K]

Given

$\frac{4\sqrt{6}}{3\sqrt{2}} = \frac{4\sqrt{2\times3}}{3\sqrt{2}} \\ \\ = \frac{4\sqrt{2}\sqrt{3}}{3\sqrt{2}} = \frac{4}{3} \sqrt{3}$

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1 year ago

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Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest ra

Oksana_A [137]

Answer:

The area of the pyramid is 360 unit²

Step-by-step explanation:

Given

Base Edge, a = 10

Height, h = 12

Required

Determine the surface area

The surface area of a regular pyramid is calculated as thus;

$A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}$

Substitute values for a and h

$A = 10^2 + 2 * 10 * \sqrt{\frac{10^2}{4} + 12^2}$

Evaluate all squares

$A = 100 + 2 * 10 * \sqrt{\frac{100}{4} + 144}$

$A = 100 + 2 * 10 * \sqrt{25 + 144}$

$A = 100 + 2 * 10 * \sqrt{169}$

Take positive square root of 169

$A = 100 + 2 * 10 * 13$

$A = 100 + 260$

$A = 360$

Hence, the area of the pyramid is 360 unit²

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1 year ago

1. which angle is congruent to Angle 1?

Inessa [10]

Part 1) which angle is congruent to Angle 1?

we know that

When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles

m∠5=m∠1 ----------> by corresponding angles postulate

therefore

the answer Part 1) is

Angle $5$

Part 2) Which can be used to directly prove that Angle 1 =~ Angle 8?

we know that

Alternate exterior angles are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.

in this problem

m∠1=m∠8 -------> by alternate exterior angles theorem

therefore

the answer part 2) is the option

Alternate Exterior Angles Theorem

Part 3) If m Angle 5 = 42 degrees, what is m Angle 4?

we know that

Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal

m∠4=m∠5 --------> by alternate interior angles theorem

m∠4= $42\ degrees$

therefore

the answer Part 3) is

$42\ degrees$

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73/12 or 6 1/12 hours more than before

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