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4 years ago

a triangle with a base of 9 meters has an altitude of 12 meters.which would give the area of the triangle

Mathematics

1 answer:

user100 [1]4 years ago

7 0

Answer:

54 $m^2$

Step-by-step explanation:

To find the area of a triangle use the formula a = 1/2bh

The altitude is the same as height so we can substitute 12 for h and 9 for b

Now the equation will become

a = 1/2 · 9 · 12

When you multiply it, it become 108/2 = a simplified to a = 54

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3 years ago

Read 2 more answers

You’ve bought a half-dozen (six) eggs from the store but you forgot to check them first! The probability that no eggs are broken

GREYUIT [131]

Answer:

$P(X = 0) = C_{6,0}.(0.1416)^{0}.(0.8584)^{6} = 0.4$

$P(X = 1) = C_{6,1}.(0.1416)^{1}.(8584)^{5} = 0.3960$

$P(X = 2) = C_{6,2}.(0.1416)^{2}.(8584)^{4} = 0.1633$

$P(X = 3) = C_{6,3}.(0.1416)^{3}.(8584)^{3} = 0.0359$

$P(X = 4) = C_{6,4}.(0.1416)^{4}.(8584)^{2} = 0.0044$

$P(X = 5) = C_{6,5}.(0.1416)^{5}.(8584)^{1} = 0.0003$

$P(X = 6) = C_{6,6}.(0.1416)^{6}.(8584)^{0} = 0.00001$

b) 56.77% probability that an even number of eggs is broken.

Expectation: 0.8496

Variance: 0.7293

Step-by-step explanation:

For each egg, there are only two possible outcomes. Either it is broken, or it is not. The probability of an egg being broken is independent from other eggs. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

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

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

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

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

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

There are 6 eggs

So $n = 6$

The probability that no eggs are broken is 0.4.

This means that $P(X = 0) = 0.4$ . So

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

$P(X = 0) = C_{6,0}.p^{0}.(1-p)^{6}$

$(1 - p)^{6} = 0.4$

Taking the sixth root from both sides of the equality

$(1 - p) = 0.8584$

p = 0.1416

Each egg has a 0.1416 probability of being broken

(a) Write out the pmf of X.

Probability of each value, from 0 to 6

$P(X = 0) = C_{6,0}.(0.1416)^{0}.(0.8584)^{6} = 0.4$

$P(X = 1) = C_{6,1}.(0.1416)^{1}.(8584)^{5} = 0.3960$

$P(X = 2) = C_{6,2}.(0.1416)^{2}.(8584)^{4} = 0.1633$

$P(X = 3) = C_{6,3}.(0.1416)^{3}.(8584)^{3} = 0.0359$

$P(X = 4) = C_{6,4}.(0.1416)^{4}.(8584)^{2} = 0.0044$

$P(X = 5) = C_{6,5}.(0.1416)^{5}.(8584)^{1} = 0.0003$

$P(X = 6) = C_{6,6}.(0.1416)^{6}.(8584)^{0} = 0.00001$

(b) Compute the probability that an even number of eggs is broken.

0, 2, 4 or 6

$P = P(X = 0) + P(X = 2) + P(X = 4) + P(X = 6) = 0.4 + 0.1633 + 0.0044 + 0.00001 = 0.5677$

56.77% probability that an even number of eggs is broken.

(c) Compute the expectation and variance of X.

Expectation:

$E(X) = np = 6*0.1416 = 0.8496$

Variance:

$V(X) = np(1-p) = 6*0.1416*0.8584 = 0.7293$

7 0

4 years ago