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user100 [1]
2 years ago
12

The area of the triangle below is 5.52 square feet. What is the length of the base?

Mathematics
1 answer:
pogonyaev2 years ago
8 0

Answer:

  4.6 ft

Step-by-step explanation:

The formula for the area of a triangle is ...

  A = 1/2bh

Fill in the given values and solve for the base.

  5.52 = 1/2b(2.4)

  5.52/1.2 = b = 4.6 . . . . divide by the coefficient of b

The base is 4.6 feet.

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Answer:

y+5=c

6y=g

Step-by-step explanation:

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3 years ago
A system of equations is shown below: n = 3m + 5 n − 2m = 3 What is the solution, in the form (m, n), to the system of equations
marshall27 [118]
n=3m+5 \\
n-2m=3 \\ \\
\hbox{substitute 3m+5 for n in the second equation:} \\
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3 years ago
Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article "Methodo
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Answer:

a) P(X \leq 4) = 0.6289

P(X < 4) = 0.4335

b) P(4 \leq X \leq 8) = 0.5452

c) P(X \geq 8) = 0.0511

d) 0.2605

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

It is important to know that the variance has the same value as the mean in a Poisson distribution. The standard deviation is the square root of the variance.

In this problem, we have that:

\mu = 4, \sigma = \sqrt{4} = 2.

To help our solution, i am going to find each of P(X = x) from x = 0 to 8[/tex]

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-4}*4^{0}}{(0)!} = 0.0183

P(X = 1) = \frac{e^{-4}*4^{1}}{(1)!} = 0.0733

P(X = 2) = \frac{e^{-4}*4^{2}}{(2)!} = 0.1465

P(X = 3) = \frac{e^{-4}*4^{3}}{(3)!} = 0.1954

P(X = 4) = \frac{e^{-4}*4^{4}}{(4)!} = 0.1954

P(X = 5) = \frac{e^{-4}*4^{5}}{(5)!} = 0.1563

P(X = 6) = \frac{e^{-4}*4^{6}}{(6)!} = 0.1042

P(X = 7) = \frac{e^{-4}*4^{7}}{(7)!} = 0.0595

P(X = 8) = \frac{e^{-4}*4^{8}}{(8)!} = 0.0298

(a) Compute both P(X ≤ 4) and P(X < 4)

P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0183 + 0.0733 + 0.1465 + 0.1954 + 0.1954 = 0.6289

---------

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0183 + 0.0733 + 0.1465 + 0.1954 = 0.4335

(b) Compute P(4 ≤ X ≤ 8).

P(4 \leq X \leq 8) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.1954 + 0.1563 + 0.1042 + 0.0595 + 0.0298 = 0.5452

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That is P(X \geq 8).

The sum of the probabilities must be 1 in decimal. Either X is greater or equal to 8, or X is lesser than 8.

So

P(X < 8) + P(X \geq 8) = 1

P(X \geq 8) = 1 - P(X < 8)

From what we have in a) and b)

P(X < 8) = P(X < 4) + P(4 \leq X < 8) = 0.4335 + 0.1954 + 0.1563 + 0.1042 + 0.0595 = 0.9489

So

P(X \geq 8) = 1 - P(X < 8) = 1 - 0.9489 = 0.0511

(d) What is the probability that the number of anomalies exceeds its mean value by no more than one standard deviation

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P(4 < X \leq 6) = P(X = 5) + P(X = 6) =  0.1563 + 0.1042 = 0.2605

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We know that triangle LMN is congruent to triangle HJL so that ==> angle H measures = angle L measures
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