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3 years ago

Solve for x with an explanation pls

Mathematics

2 answers:

m_a_m_a [10]3 years ago

7 0

X=9

A squared + b squared = c squared

C is the hypotenuse (the side opposite of the right angle)

X*2 + square root of 63 squared = 12*2
Squaring 63 would cancel out with the square root. You are left with x*2 + 63 = 144. 144-63= 81. X*2=81 ; square root both sides. You are now left with x=9

Tatiana [17]3 years ago

6 0

Answer: 9

Step-by-step explanation:

Use Pythagorean's Theorem for a right triangle.

$a^2+b^2=c^2$

$(\sqrt{63}) ^2+x^2=12^2\\63+x^2=144\\x^2=81\\x=9$

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Pollution of the rivers in the United States has been a problem for many years. Consider the following events: a: the river is p

vampirchik [111]

Answer:

The answer is below

Step-by-step explanation:

P(A') = 1 - P(A) = 1 - 0.3 = 0.7

P(B'/A) = 1 - P(B/A) = 1 - 0.75 - 0.25

P(B/A') = 0.2, P(B'/A') = 1 - 0.2 = 0/8

P(C|A∩B) = 0.20,

P(C|A'∩B) = 0.15,

P(C|A∩B') = 0.80, and

P(C|A'∩B') = 0.90.

A) From conditional probability;

P(B/A) = P(B ∩ A) / P(A)

P(B∩A) = P(B/A) × P(A) = 0.75 × 0.3 = 0.225

P(C/A∩B) = P(A∩B∩C)/P(A∩B)

P(A∩B∩C) = P(C/A∩B) × P(A∩B)

P(A∩B∩C) = 0.2 ×0.225 = 0.045

B) P(A∩B∩C) = P(A) × P(B/A) × P(C/A∩B)

P(B'∩C) = P(A∩(B'∩C)) + P((A'∩B')∩C)

P(B'∩C) = P(A) × P(B'/A) × P(C/A∩B') + P(A') × P(B'/A') × P(C/A'∩B')

P(B'∩C) = 0.3 × 0.25 × 0.8 + (0.7 × 0.8 × 0.9) = 0.06 + 0.504 = 0.564

C) P(C) = P(A∩B∩C) + P(A'∩B∩C) + P(A∩B'∩C) + P(A'∩B'∩C)

P(A'∩B∩C) = P(A') × P(B/A') × P(C/A'∩B) = 0.7 × 0.2 × 0.15 = 0.021

P(A∩B'∩C) = P(A) × P(B'/A) × P(C/A∩B') = 0.3 × 0.25 × 0.8 = 0.06

P(A'∩B'∩C) = P(A') × P(B'/A') × P(C/A'∩B') = 0.7 × 0.8 × 0.9 = 0.504

P(C) = P(A∩B∩C) + P(A'∩B∩C) + P(A∩B'∩C) + P(A'∩B'∩C) = 0.045 + 0.021 + 0.06 + 0.504 = 0.63

D) P(A/B'∩C) = P(A∩B'∩C)/P(B'∩C)

P(A/B'∩C) = 0.06 / 0.564 = 0.106

6 0

4 years ago

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egoroff_w [7]

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6 0

4 years ago

Find the distance between the points (5,-6), (-3,12)

grigory [225]

Answer:

$\displaystyle d = 2\sqrt{97}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

Step 1: Define

Point (5, -6)

Point (-3, 12)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formula]: $\displaystyle d = \sqrt{(-3-5)^2+(12+6)^2}$
[√Radical] (Parenthesis) Subtract/Add: $\displaystyle d = \sqrt{(-8)^2+(18)^2}$
[√Radical] Evaluate Exponents: $\displaystyle d = \sqrt{64+324}$
[√Radical] Add: $\displaystyle d = \sqrt{388}$
[√Radical] Simplify: $\displaystyle d = 2\sqrt{97}$