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1 year ago

Solve the system of linear equations by substitution.

Mathematics

1 answer:

yaroslaw [1]1 year ago

5 0

Answer:

x=5, y=2

Step-by-step explanation:

1) Subtract 2y from both sides of x+2y to get x=9-2y

2) Substitute x into the first equation to get 3(9-2y)-2y=11

3) Solve for y (y=2)

4) Plug y into either equation: x+2(2)=9 x=5

5) The answer is (5, 2)

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Write the standard form of the line that contains a slope of -1/2 and y-intercept of 1. Include your work in your final answer.

NemiM [27]

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2 years ago

How many calories are in 3oz of ground beef

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2 years ago

an oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil.

bazaltina [42]

Answer:

4.92% probability that the third strike comes on the seventh well drilled

Step-by-step explanation:

For each drill, there are only two possible outcomes. Either it is a strike, or it is not. Each drill is independent of other drills. So we use the binomial probability distribution to solve this question.

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 combinations 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.

20% chance of striking oil.

This means that $p = 0.2$

What is that probability that the third strike comes on the seventh well drilled

2 stikers during the first 6 drills(P(X = 2) when n = 6)[/tex]

Strike during the 7th drill, with 0.2 probability. So

$P = 0.2P(X = 2)$

In which

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

$P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458$

Then

$P = 0.2P(X = 2) = 0.2*0.2458 = 0.0492$

4.92% probability that the third strike comes on the seventh well drilled

3 0

2 years ago

The amount of water remaining in the pool is decreasing at a rate of

Gnom [1K]

The average rate of change has a relationship with slopes. In this way, we can write the slope of a line as follows:

$Slope=\frac{Change \ y}{Change \ x}$

As you can see in the graph, we have a straight line whose slope is negative. This slope as we have said is the Average Rate of Change we need to find. So, to find the slope of this line we must choose two points and compute the following formula:

$ARC=Slope=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}$