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3 years ago

Determine the length of the hypotenuse in a right triangle with legs 5 inches and 12 inches

Mathematics

1 answer:

Alborosie3 years ago

7 0

In a right angled triangle we can use Pythagoras theorem to determine third side in case two sides are given.

The formula of Pythagoras theorem is given by:

$x^{2} +y^{2} =z^{2}$

Where x , y and z are sides of triangle , z is hypotenuse.

Now we use this formula to find hypotenuse.

Plugging other two sides which are 5 in. and 12 in.

$5^{2} +12^{2} =z^{2}$

$25 +144 =z^{2}$

$169 =z^{2}$

Taking square root on both sides

square root of 169 is 13

so we have z=13

Hypotenuse is 13 inches.

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Consider a binomial experiment with n = 10 and p = 0.10. (a) Compute f(0). If required, round your answer to four decimal places

ss7ja [257]

Answer:

(a) The value of f (0) is 0.3487.

(b) The value of f (2) is 0.1937.

(d) The value of P (X ≥ 1) is 0.6513.

(e) The value of E (X) is 1.

(f) The value of V (X) is 0.9 and σ is 0.9487.

Step-by-step explanation:

The random variable X follows a Binomial distribution with parameter n = 10 and p = 0.10.

The probability mass function of X is:

$P(X=x)={10\choose x}0.10^{x}(1-0.10)^{10-x};\ x=0,1,2,3...$

(a)

Compute the value of f (0) as follows:

f (0) = P (X = 0)

$={10\choose 0}0.10^{0}(1-0.10)^{10-0}\\=1\times 1\times 0.348678\\=0.348678\\\approx0.3487$

Thus, the value of f (0) is 0.3487.

(b)

Compute the value of f (2) as follows:

f (2) = P (X = 2)

$={10\choose 2}0.10^{2}(1-0.10)^{10-2}\\=45\times 0.01\times 0.43047\\=0.1937115\\\approx0.1937$

Thus, the value of f (2) is 0.1937.

(c)

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

P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)

$=\sum\limits^{0}_{2} {{10\choose x}0.10^{x}(1-0.10)^{10-x}}\\=0.3487+0.3874+0.1937\\=0.9298$

Thus, the value of P (X ≤ 2) is 0.9298.

(d)

Compute the value of P (X ≥ 1) as follows:

P (X ≥ 1) = 1 - P (X < 1)

= 1 - P (X = 0)

= 1 - 0.3487

= 0.6513

Thus, the value of P (X ≥ 1) is 0.6513.

(e)

Compute the expected value of X as follows:

$E(X)=n\times p$

$=10\times 0.10\\=1$

Thus, the value of E (X) is 1.

(f)

Compute the variance of X as follows:

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

$=10\times 0.10\times (1-0.10)\\=0.90$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{V(X)}$

$=\sqrt{0.90}\\=0.94868\\\approx0.9487$

Thus, the value of V (X) is 0.9 and σ is 0.9487.

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The correct answer is C. Angles 2 and 5.

Angles 2 and 5 are adjacent because they are right next to each other; they have a common side and a common vertex.

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3 years ago

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3 years ago

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mina [271]

Answer:

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here's your solution

=>. when any number. get multiplied with

same number then it bwcome square

=>. so, same thing will happen to X also

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