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2 years ago

12

Mr. Lobo is building a fence rectangular around his rectangular yard. It is 16 feet long and 14 feet wide. How much feet of feet

fencing will he need?

1 answer:

lawyer [7]2 years ago

4 0

Answer:

30

Step-by-step explanation:

14+16 1. Break it down 14 is equal to 10+4 16 is equal to 10+6 2. Add the biggest numbers together first 10+10 = 20 3. Add the smaller numbers together 6+4 = 10 4. Add all of the numbers together 20+10 = 30

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At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water t

grandymaker [24]

Answer:

(a1) The probability that temperature increase will be less than 20°C is 0.667.

(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.

(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c) The expected value of the temperature increase is 17.5°C.

Step-by-step explanation:

Let <em>X</em> = temperature increase.

The random variable <em>X</em> follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].

The probability density function of <em>X</em> is:

$f(X)=\left \{ {{\frac{1}{25-10}=\frac{1}{15};\ x\in [10, 25]} \atop {0;\ otherwise}} \right.$

(a1)

Compute the probability that temperature increase will be less than 20°C as follows:

$P(X$

Thus, the probability that temperature increase will be less than 20°C is 0.667.

(a2)

Compute the probability that temperature increase will be between 20°C and 22°C as follows:

$P(20$

Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.

(b)

Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:

$P(X>18)=\int\limits^{25}_{18}{\frac{1}{15}}\, dx\\=\frac{1}{15}\int\limits^{25}_{18}{dx}\,\\=\frac{1}{15}[x]^{25}_{18}=\frac{1}{15}[25-18]=\frac{7}{15}\\=0.467$

Thus, the probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c)

Compute the expected value of the uniform random variable <em>X</em> as follows:

$E(X)=\frac{1}{2}[10+25]=\frac{35}{2}=17.5$

Thus, the expected value of the temperature increase is 17.5°C.

7 0

2 years ago

The number of defective components produced by a certain process in one day has a Poisson distribution with a mean of 20. Each d

Kruka [31]

Answer:

The probability that exactly 15 defective components are produced in a particular day is 0.0516

Step-by-step explanation:

Probability function : $P(X=x)=e^{-\lambda} \frac{\lambda^x}{x!}$

We are given that The number of defective components produced by a certain process in one day has a Poisson distribution with a mean of 20.

So, $\lambda = 20$

we are supposed to find the probability that exactly 15 defective components are produced in a particular day

So,x = 15

Substitute the values in the formula :

$P(X=15)=e^{-20} \frac{20^{15}}{15!}$

$P(X=15)=e^{-20} \frac{20^{15}}{15!}$

$P(X=15)=0.0516$

Hence the probability that exactly 15 defective components are produced in a particular day is 0.0516

8 0

2 years ago

Trapezoid E F G H is reflected across line of reflection k to form trapezoid E prime F prime G prime H prime. Trapezoid E prime

Aleks [24]

Answer:

Its A

Step-by-step explanation:

i just took the quiz and got it right

8 0

2 years ago

Read 2 more answers

Select all the pairs that could be reasonable approximations for the diameter and circumference of a cirlce 5 meters and 22 mete

bazaltina [42]

Answer:

Option a) circle 5 meters and 22 meters

Step-by-step explanation:

We are given the following information in the question:

A pair of diameter and the circumference is given. We have to find a correct approximations for the diameter and circumference.

a) circle 5 meters and 22 meters

$\text{Diameter} = 5\text{ meters}\\\text{Circumference} = \pi d = 3.14\times 5 = 15.7\text{ meters}$

b) 19 inches and 50 inches

$\text{Diameter} = 19\text{ inches}\\\text{Circumference} = \pi d = 3.14\times 19 = 59.66\text{ inches}$

c) 33 centimeters and 80 centimeters

$\text{Diameter} = 33\text{ centimeters}\\\text{Circumference} = \pi d = 3.14\times 33 =103.62\text{ centimeters}$

Thus, no pair gives a reasonable approximation. Only the circle with diameter 5 and circumference 22 meters have closest approximation.

6 0

2 years ago

What is the final amount if 784 is decreased by 1% followed by a 4% increase?

Iteru [2.4K]

Answer:

The final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.

Step-by-step explanation:

General Formula

<em>A way to solve this problem is as follows</em>:

The general formula for this is taking into account that:

$\\ percent\;change = \frac{change}{starting\;point}$

The <em>starting point</em> is number 784.

The most important key is the solution for this answer is that:

$\\ change = starting\;point - x$

Where <em>x</em> is a number that we need to find. Then

$\\ percent\;change = \frac{starting\;point - x}{starting\;point}$ [1]

Is 784 increased or decreased after all?

We also need to evaluate the following: if a quantity decreases a percentage, and then increases in another percentage, what is the final percentage? In this case, we have first that 784 decreases by 1% and then increases by 4%. As a result 784 will +4% - 1% = +3%, that is, 784 will increase in 3%.

Finding the result

If 784 increases by 3%, we have:

$\\ 3\% = \frac{784 - x}{784}$

Which is equal to

$\\ 0.03 = \frac{784 - x}{784}$

Solving for <em>x</em>, we first multiply by 784 to both sides of the previous formula:

$\\ 0.03 * 784 = \frac{784 - x}{784}*784$

$\\ 0.03 * 784 = (784 - x)*\frac{784}{784}$

$\\ 0.03 * 784 = (784 - x)*1$

$\\ 0.03 * 784 = (784 - x)$

Remember that if we add, subtract, multiply, divide... to both sides of the equation, we do not "alter" this equation.

Subtracting 784 to both sides:

$\\ (0.03 * 784) - 784 = (784 - 784 - x)$

$\\ (0.03 * 784) - 784 = (0 - x)$

$\\ (0.03 * 784) - 784 = - x$

$\\ 23.52 - 784 = - x$

$\\ -760.48 = - x$

Multiplying by -1 to both sides:

$\\ -1 * (-760.48) = -1 * (-x)$

We have to remember that:

$\\ +*+ = +; - * - = +; - * + = -; + * - = -$

$\\ 760.48 = x$

Then

$\\ x = 760.48$

Therefore, using formula [1], an increase of 3% is

$\\ 3\% = \frac{784 - 760.48}{784}$

$\\ change = 784 - 760.48$

$\\ change = 23.52$

Since an increase of 3% is 23.52, we have to add this to the starting point 784, and finally the amount is 784 + 23.52 = 807.52.

As a result, the final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.

In a more <em>terse way</em> of solving this problem, we can say that:

Increase of 4% = 784 * 0.04 = 31.36.

Decrease of 1% = 784 * 0.01 = 7.84.

Difference = 31.36 - 7.84 = 23.52.

Then, we need to add this value to 784, and 784 + 23.52 = 807.52 (the same result).

5 0

1 year ago