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neonofarm [45]
3 years ago
8

The length of each side of a triangle is increased by 30%. By what percentage is the area increased?

Mathematics
1 answer:
patriot [66]3 years ago
5 0

Answer:

When sides are doubled, the area of new triangle will always be 4 times the original, the change in area will be 3 times. Hence the % change will always be 300% irrespective of the type of triangle.

Step-by-step explanation:


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A certain kind of sheet metal has, on average, 3 defects per 18 square feet. Assuming a Poisson distribution, find the probabili
Fofino [41]

Answer:

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

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.

In this problem, we have that:

3 defects per 18 square feet.

So for 31 square feet, we have to solve a rule of three

3 defects - 18 square feet

x defects - 31 square feet

18x = 3*31

x = \frac{31*3}{18}

x = 5.17

So \mu = 5.17

Assuming a Poisson distribution, find the probability that a 31 square foot metal sheet has at least 4 defects.

Either it has three or less defects, or it has at least 4 defects. The sum of the probabilities of these events is decimal 1.

So

P(X \leq 3) + P(X \geq 4) = 1

We want P(X \geq 4)

So

P(X \geq 4) = 1 - P(X \leq 3)

In which

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

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

P(X = 0) = \frac{e^{-5.17}*(5.17)^{0}}{(0)!} = 0.0057

P(X = 1) = \frac{e^{-5.17}*(5.17)^{1}}{(1)!} = 0.0294

P(X = 2) = \frac{e^{-5.17}*(5.17)^{2}}{(2)!} = 0.0760

P(X = 3) = \frac{e^{-5.17}*(5.17)^{3}}{(3)!} = 0.1309

So

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0057 + 0.0294 + 0.0760 + 0.1309 = 0.242

Finally

P(X \geq 4) = 1 - P(X \leq 3) = 1 - 0.242 = 0.758

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

8 0
3 years ago
Zara has forgotten her 4-digit PIN code. She knows the first digit is a prime number and the 4 digits make a number divisible by
vredina [299]

Answer:

2,500 different sets

Step-by-step explanation:

According to the scenario, calculation of the given data are as follows,

Let 4-digit PIN code be WXYZ

As first digit is a prime number

So, W = 1, 2, 3, 5, 7

n(W) = 5

X and Y are number from 0 - 9

So, n(X) = 10 & n(Y) = 10

Z makes the whole number divisible by 2.

So, Z must even number

So, Z = 0,2,4,6,8 or n(Z) = 5

We can calculate the number of different sets by using following formula,

n(W) × n(X) × n(Y) × n(Z)

By putting the value, we get

5 × 10 × 10 × 5 = 2,500

6 0
3 years ago
Suppose a simple random sample of size 50 is selected from a population with ? = 10. Find the value of the standard error of the
viktelen [127]

Answer:

The population size is N = 50,000

Step-by-step explanation:

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3 years ago
This diagram shows the flag of a local soccer club what is the area of the area of the red portion of the flag?
ella [17]
The answer is C A= 90 in^2. This is because the total area is represented by 10x18, which equals 180. The red occupies half of the flag, and 180 divided by 2 is 90.  
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3 years ago
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Let me guess, Shlurpy Victory?

Also here's some motivation king

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2 years ago
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