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3 years ago

Solve each system of equations by adding.

Mathematics

1 answer:

Archy [21]3 years ago

8 0

Answer:

3. x+y = -1

x-y = 7

(x+x+y-y) 2x=6

x=3

4. 2x+2y = -2

3x-2y = 12

(2x+3x+2y-2y) 5x=-2+12

5x=10

x= 2

5. 6x+5y = 4

-6x+7y = 20

(6x-6x+5y+7y)= 4+20

12y=24

y=2

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A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.93. Assume indepen

noname [10]

Answer:

There is a 99.99998% probability that at least one valve opens.

Step-by-step explanation:

For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.

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 combinatios 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.

In this problem we have that:

$n = 5, p = 0.93$

Calculate P(at least one valve opens).

This is $P(X \geq 1)$

Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:

$P(X = 0) + P(X \geq 1) = 1$

$P(X \geq 1) = 1 - P(X = 0)$

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

$P(X = 0) = C_{5,0}.(0.93)^{0}.(0.07)^{5} = 0.0000016807$

Finally

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000016807 = 0.9999983193$

There is a 99.99998% probability that at least one valve opens.

5 0

3 years ago

Read 2 more answers

A vegetable garden with an area of 200 square feet is to be fertilized. If the length of the garden is 1 foot less than three ti

charle [14.2K]

Ok so I like to go in steps with these questions- first draw a picture and identify your variables.

W=width
L= 3w-1

Now we know that length times width gets us area so we plug in our variables into the area equation.

200 = w(3w-1)

When you foil that equation you end up with a quadratic : 3w^2-w-200 = 0

Either factor that or use the quadratic formula to get
w= 8.33 and w= -8

Since you can't have a negative dimension you need to use 8.33 and plug it back into your length equation.

Final answer:

w= 8.33ft
l= 23.99ft

*Now I simplified the decimals a little bit so you end up with 199.8ft^2 for the area so just add a few decimals on here and there*

5 0

3 years ago

Read 2 more answers

A pair of shoes has an original price of $65 but is on sale for a 20 percent discount. What number can you multiply by $65 to ge

Contact [7]

Answer:

0.8

Step-by-step explanation:

20 / 100 = 0.2

1 - 0.2 = 0.8

5 0

3 years ago