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3 years ago

Consider triangle ABC. The legs have a length of 5 units each. What is the length of the hypotenuse of the triangle?

Mathematics

2 answers:

Korvikt [17]3 years ago

6 0

Answer:

$5\sqrt{2}$ units.

Step-by-step explanation:

We have been given that two legs of triangle ABC measures 5 units each. We are asked to find the length of the hypotenuse.

We will use Pythagoras theorem to solve for the hypotenuse of triangle ABC.

$\text{Hypotenuse}^2=\text{Leg}^2+\text{Leg}^2$

Substituting our given values in above equation we will get,

$\text{Hypotenuse}^2=5^2+5^2$

$\text{Hypotenuse}^2=25+25$

$\text{Hypotenuse}^2=50$

Upon taking square root of both sides of our equation we will get,

$\text{Hypotenuse}=\sqrt{50}$

$\text{Hypotenuse}=\sqrt{25*2}$

$\text{Hypotenuse}=5\sqrt{2}$

Therefore, the length of hypotenuse of triangle ABC is $5\sqrt{2}$ units.

kolezko [41]3 years ago

3 0

Here's what you were looking for.

Ur welcome :)

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Answer:

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b) There is a 1.93% probability that six or more owners would say preparing for long hours and hard work is the most important advice.

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Step-by-step explanation:

Questions a), b), c) are all solved as binomial distribution problems.

Question d) is a simple calculation.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

For these problems

12 business owners were contacted, so $n = 12$ .

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20% of all small-business owners say the most important advice for starting a business is to prepare for long hours and hard work, so $\pi = 0.2$ .

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There is a 6.88% probability that none of the owners would say preparing for long hours and hard work is the most important advice.

b. What is the probability that six or more owners would say preparing for long hours and hard work is the most important advice?

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This is:

$P = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

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$P(X = 7) = C_{12,7}.(0.2)^{7}.(0.8)^{5} = 0.0033$

$P(X = 8) = C_{12,8}.(0.2)^{8}.(0.8)^{4} = 0.0005$

$P(X = 9) = C_{12,9}.(0.2)^{9}.(0.8)^{3} = 0.00006$

$P(X = 10) = C_{12,10}.(0.2)^{10}.(0.8)^{2} = 0.000004$

$P(X = 11) = C_{12,11}.(0.2)^{11}.(0.8)^{1} = 0.0000002$

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Twenty-five percent say the most important advice is to have good financing ready, so $\pi = 0.25$

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There is a 10.32% probability that exactly five owners would say having good financing ready is the most important advice.

d. What is the expected number of owners who would say having a good plan is the most important advice?

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The expected number of owners who would say having a good plan is the most important advice is 2.28

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3 years ago

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Answer:

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General Formulas and Concepts:

Pre-Algebra

Distributive Property

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Step-by-step explanation:

Step 1: Define

2(2 + g)

Step 2: Expand

Distribute 2: 2(2) + 2(g)
Multiply: 4 + 2g

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